%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "1.41",
%%% date = "06 February 2018",
%%% time = "08:16:05 MST",
%%% filename = "borwein-jonathan-m.bib",
%%% address = "University of Utah
%%% Department of Mathematics, 110 LCB
%%% 155 S 1400 E RM 233
%%% Salt Lake City, UT 84112-0090
%%% USA",
%%% telephone = "+1 801 581 5254",
%%% FAX = "+1 801 581 4148",
%%% URL = "http://www.math.utah.edu/~beebe",
%%% checksum = "49849 42725 184843 1898353",
%%% email = "beebe at math.utah.edu, beebe at acm.org,
%%% beebe at computer.org (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "arithmetic--geometric mean (AGM); Atlantic
%%% Association for Research in the Mathematical
%%% Sciences (AARMS); BBP
%%% (Bailey--Borwein--Plouffe) algorithm;
%%% bibliography; BibTeX; Borwein--Preiss smooth
%%% variational principle in optimization theory;
%%% Centre for Computer-assisted Research
%%% Mathematics and its Applications (CARMA);
%%% classical analysis; cubic theta function;
%%% Douglas--Rachford algorithm; experimental
%%% mathematics; financial mathematics; functional
%%% analysis; high performance computing (HPC);
%%% International Mathematical Union (IMU)
%%% Executive's Committee on Electronic
%%% Information and Communication (CEIC); Jonathan
%%% Michael Borwein; mathematics by experiment;
%%% number theory; Online Encyclopedia of Integer
%%% Sequences (OEIS); operations research;
%%% optimization theory and practice; $\pi$; PSLQ
%%% algorithm; theory of computation",
%%% license = "public domain",
%%% supported = "yes",
%%% docstring = "This is a COMPLETE bibliography of works by,
%%% and about, the late distinguished
%%% Canadian/British mathematician Jonathan
%%% Michael Borwein (20 May 1951--2 August 2016).
%%%
%%% This bibliography is divided into four parts:
%%%
%%% 1: Academic works by Jonathan M. Borwein
%%% 2: Blog publications by Jonathan M. Borwein
%%% 3: Invited talks by Jonathan M. Borwein
%%% 4: Publications about Jonathan M. Borwein and his works
%%%
%%% Jon Borwein was born in Scotland to a
%%% mathematical family: his father David and his
%%% younger brother Peter are themselves
%%% distinguished mathematicians. His mother is
%%% a physician and retired medical-school dean.
%%%
%%% Jon grew up in Canada, taking a B.A. (Honours
%%% Mathematics) at the University of Western
%%% Ontario (later branded Western University),
%%% London, ON in 1972 (and the city in which he
%%% died in 2016 while holding the post of
%%% Distinguished Scholar in Residence), and an
%%% M.Sc. in 1974 and a D.Phil. in 1974 from
%%% Oxford University, where he was a Rhodes
%%% Scholar at Jesus College.
%%%
%%% Jon Borwein later worked at Dalhousie
%%% University, Halifax, NS, Canada (1974--1980,
%%% 1982--1991, 2004--), Carnegie--Mellon
%%% University, Pittsburgh, PA, USA (1980--1982),
%%% the University of Waterloo, Waterloo, ON,
%%% Canada (1991--1993), Simon Fraser University,
%%% Burnaby, BC, Canada (1993--2003), the
%%% University of Newcastle, Newcastle, NSW,
%%% Australia (2009--2016), King Abdulaziz
%%% University, Jeddah, Saudi Arabia
%%% (2011--2013), and Chiang Mia University,
%%% Thailand (2013--2016).
%%%
%%% Jon Borwein was President of the Canadian
%%% Mathematical Society (2000--2002), Governer
%%% at Large of the American Mathematical Society
%%% (2004--2007), co-winner of the Chauvenet
%%% Prize of the Mathematical Association of
%%% America (1993) --- see entry Borwein:1989:RME
%%% and the Web site
%%%
%%% http://www.maa.org/programs/maa-awards/writing-awards/chauvenet-prizes
%%%
%%% co-winner of the AMS 2017 Levi L. Conant
%%% Prize --- see entries Bailey:2016:BBM and
%%% Breen:2016:DBJ and the Web site
%%%
%%% http://www.ams.org/news?news_id=3232
%%%
%%% and a fellow of the Royal Society of Canada
%%% (1994), the American Association for the
%%% Advancement of Science (2002), the Bulgarian
%%% Academy of Sciences (2003), the Australian
%%% Academy of Science (2010), the American
%%% Mathematical Society (2014), and the Royal
%%% Society of New South Wales (2015).
%%%
%%% Jon Borwein travelled, spoke, and wrote,
%%% widely, and collaborated with many other
%%% mathematicians, including his father David
%%% and brother Peter, and David H. Bailey, with
%%% whom he co-authored more than 80 papers and
%%% five books, and co-wrote a blog on
%%% mathematical and scientific issues before the
%%% public, many of them reprinted in the
%%% Huffington Post and in The Conversation.
%%%
%%% There is an encyclopedia article about him at
%%%
%%% https://en.wikipedia.org/wiki/Jonathan_Borwein
%%%
%%% plus personal Web sites at
%%%
%%% http://carma.newcastle.edu.au/jon/
%%% http://carma.newcastle.edu.au/jon/CV/CV.html
%%% http://jonathanmborwein.com/
%%% http://jonborwein.com/
%%%
%%% a mathematical genealogy at
%%%
%%% https://genealogy.math.ndsu.nodak.edu/id.php?id=23187
%%%
%%% and obituaries at
%%%
%%% http://blogs.ams.org/beyondreviews/2016/08/03/jonathan-borwein/
%%% http://jonborwein.org/2016/08/he-left-this-world-a-better-place/
%%% https://cms.math.ca/MediaReleases/2016/borweinobituary
%%% https://www.science.org.au/fellowship/fellows/professor-jonathan-borwein
%%%
%%% The increasingly-famous BBP formula (entry
%%% Bailey:1997:RCV) is named after its authors:
%%% David Bailey, Jon's brother Peter Borwein,
%%% and Simon Plouffe. That astonishing formula
%%% allows computation of digits of pi in any
%%% number base that is an integral power of two,
%%% the power being greater than zero, starting
%%% from any prescribed digit, without knowing
%%% any previous digits! BBP-like formulas have
%%% since been found for several other
%%% transcendental contants. David Bailey and
%%% Jon Borwein have written and spoken
%%% extensively about the importance of, and use
%%% of, the BBP formula.
%%%
%%% Jon Borwein updated his curriculum vitae just
%%% five hours before he died, so we have some
%%% confidence that coverage of his works in this
%%% bibliography is complete as far as he
%%% recorded them. However, additional
%%% publications are to be expected, and are
%%% included here, such as from reprints,
%%% articles in accepted and in press, or
%%% submitted, and ones that he simply forgot, or
%%% chose not, to record.
%%%
%%% At version 1.41, the COMPLETE year coverage
%%% looked like this:
%%%
%%% 1972 ( 1) 1988 ( 31) 2004 ( 51)
%%% 1973 ( 0) 1989 ( 25) 2005 ( 80)
%%% 1974 ( 1) 1990 ( 52) 2006 ( 60)
%%% 1975 ( 0) 1991 ( 36) 2007 ( 57)
%%% 1976 ( 4) 1992 ( 27) 2008 ( 46)
%%% 1977 ( 5) 1993 ( 40) 2009 ( 56)
%%% 1978 ( 4) 1994 ( 37) 2010 ( 61)
%%% 1979 ( 10) 1995 ( 47) 2011 ( 78)
%%% 1980 ( 7) 1996 ( 31) 2012 ( 100)
%%% 1981 ( 9) 1997 ( 63) 2013 ( 100)
%%% 1982 ( 8) 1998 ( 33) 2014 ( 84)
%%% 1983 ( 11) 1999 ( 50) 2015 ( 78)
%%% 1984 ( 19) 2000 ( 48) 2016 ( 101)
%%% 1985 ( 9) 2001 ( 41) 2017 ( 19)
%%% 1986 ( 23) 2002 ( 37) 2018 ( 1)
%%% 1987 ( 27) 2003 ( 52)
%%% 19xx ( 7)
%%%
%%% Article: 765
%%% Book: 53
%%% InCollection: 87
%%% InProceedings: 43
%%% MastersThesis: 1
%%% Misc: 12
%%% PhdThesis: 2
%%% Proceedings: 13
%%% TechReport: 51
%%% Unpublished: 743
%%%
%%% Total entries: 1770
%%%
%%% As an indication of the breadth of Jon
%%% Borwein's interests, his published articles
%%% appear in at least 135 journals, with these
%%% being the most commonly chosen (as recorded
%%% at version 1.07):
%%%
%%% ========================================
%%% count | journal
%%% ========================================
%%% 47 | The Conversation
%%% 46 | j-AMER-MATH-MONTHLY
%%% 37 | Huffington Post
%%% 36 | ArXiv e-prints
%%% 21 | j-PROC-AM-MATH-SOC
%%% 18 | j-J-CONVEX-ANAL
%%% 17 | j-J-MATH-ANAL-APPL
%%% 16 | j-EXP-MATH
%%% 14 | j-MATH-PROG
%%% 13 | j-CAN-J-MATH
%%% 13 | j-NONLINEAR-ANAL
%%% 12 | j-CAN-MATH-BULL
%%% 12 | j-TRANS-AM-MATH-SOC
%%% 11 | j-J-OPT-THEORY-APPL
%%% 11 | j-NAMS
%%% 11 | j-RAMANUJAN-J
%%% 10 | j-SIAM-J-OPT
%%% 10 | j-SET-VALUED-ANAL
%%% 8 | j-SIAM-REVIEW
%%% 8 | ArXiv Mathematics e-prints
%%% 8 | j-MATH-INTEL
%%% 7 | j-SIAM-J-CONTROL-OPTIM
%%% 7 | j-J-APPROX-THEORY
%%% 7 | j-MATH-COMPUT
%%% 6 | j-OPTIMIZATION
%%% 6 | j-BULL-AUSTRAL-MATH-SOC
%%% 6 | j-J-NONLINEAR-CONVEX-ANAL
%%% 6 | j-AUSTRALIAN-MATH-SOC-GAZ
%%% 5 | j-OPTIM-LETT
%%% 4 | j-MATH-OP-RES
%%% 4 | j-MAPLE-TECH-NEWS
%%% 4 | j-J-FUNCT-ANAL
%%% 4 | j-MATH-INEQUAL-APPL
%%% 4 | j-SIAM-NEWS
%%% 3 | j-PAC-J-MATH
%%% 3 | j-J-COMPUT-APPL-MATH
%%% 3 | ArXiv High Energy Physics --- Theory e-prints
%%% 3 | j-ELECT-J-COMB
%%% 3 | j-J-GLOBAL-OPT
%%% 3 | j-SET-VALUED-VAR-ANAL
%%% 3 | j-APPL-MATH-COMP
%%% 3 | j-INTEGERS
%%% 2 | j-J-LOND-MATH-SOC-2
%%% 2 | j-INT-J-MATH-MATH-SCI
%%% 2 | j-MATH-PROG-STUDY
%%% 2 | j-J-AUSTRAL-MATH-SOC-SER-A
%%% 2 | j-BIT
%%% 2 | j-PROC-EDINBURGH-MATH-SOC-2
%%% 2 | j-J-MATH-PHYS
%%% 2 | j-J-AUSTRAL-MATH-SOC-SER-B
%%% 2 | j-ISRAEL-J-MATH
%%% 2 | j-IMA-J-NUMER-ANAL
%%% 2 | j-J-PHYS-A
%%% 2 | j-Z-OPER-RES
%%% 2 | j-SCIENCE
%%% 2 | j-AEQUATIONES-MATHEMATICAE
%%% 2 | j-NUM-MATH
%%% 2 | j-IEEE-TRANS-NUCL-SCI
%%% 2 | j-SIGSAM
%%% 2 | j-INT-J-NUMBER-THEORY
%%% 2 | j-J-PHYS-A-MATH-THEOR
%%% 2 | Rhodes Scholar Blog
%%% 2 | j-J-AUSTRAL-MATH-SOC
%%% 2 | j-ANZIAM-J
%%% 2 | j-J-SYMBOLIC-COMP
%%% 1 | in each of 70 other journals
%%% ========================================
%%%
%%% Besides at least 504 articles, 90 blogs, and
%%% 708 invited talks on five continents, Jon
%%% Borwein also authored or edited, or was the
%%% subject of, 34 books (including new editions
%%% and translations):
%%%
%%% =================================================================================================
%%% 1987 | Pi and the AGM: a Study in Analytic Number Theory and Computational Complexity
%%% 1990 | A dictionary of real numbers
%%% 1991 | The HarperCollins dictionary of mathematics
%%% 1995 | Dizionario Collins della matematica
%%% 1995 | Shu xue ci dian
%%% 1997 | Pi, a source book
%%% 1997 | The MathResource interactive math dictionary
%%% 1998 | Pi and the AGM: A study in analytic number theory and computational complexity
%%% 1999 | Dictionary of mathematics
%%% 2000 | Convex Analysis and Nonlinear Optimization
%%% 2000 | Pi: a source book
%%% 2002 | Mathematics: Collins dictionary
%%% 2002 | Multimedia tools for communicating mathematics
%%% 2003 | Experimentation in mathematics: computational paths to discovery
%%% 2004 | Mathematics by Experiment: Plausible Reasoning in the 21st Century
%%% 2004 | Pi: a source book
%%% 2005 | Techniques of Variational Analysis
%%% 2006 | Convex analysis and nonlinear optimization
%%% 2006 | Experiments in Mathematics
%%% 2007 | Experimental Mathematics in Action
%%% 2008 | Communicating Mathematics in the Digital Era
%%% 2008 | Mathematics by Experiment
%%% 2009 | The computer as crucible: an introduction to experimental mathematics
%%% 2010 | Convex functions: constructions, characterizations and counterexamples
%%% 2010 | Experimental and computational mathematics: selected writings
%%% 2011 | An introduction to modern mathematical computing: with Maple
%%% 2011 | Experimentelle Mathematik: Eine beispielorientierte Einfuhrung
%%% 2012 | An introduction to modern mathematical computing: with Mathematicareg
%%% 2012 | Exploratory experimentation in mathematics: selected works
%%% 2013 | Computational and analytical mathematics: in honor of Jonathan Borwein's 60th Birthday
%%% 2013 | Lattice Sums: Then and Now
%%% 2014 | Neverending fractions: an introduction to continued fractions
%%% 2016 | Pi: the next generation: a sourcebook on the recent history of Pi and its computation
%%% 2016 | Tools and Mathematics
%%% =================================================================================================
%%%
%%% The tables given above have been produced
%%% automatically, and reliably, from the output
%%% of queries to an SQL database containing the
%%% entries in this bibliography.
%%%
%%% A count of recorded page ranges of the form
%%% mmm--nnn in parts 1--3 of this file finds
%%% 7939 pages in 514 documents, an average of
%%% 15.45 pages each. That is an impressive
%%% production in the mathematical literature!
%%%
%%% Entries for this bibliography have been
%%% derived from data in the BibNet Project and
%%% TeX User Group bibliography archives, and
%%% from the ACM Portal, American Physical
%%% Society (APS), American Institute of Physics
%%% (AIP), arxiv.org, Australian Mathematical
%%% Society, Cambridge Journals, Canadian
%%% Mathematical Society (CMS), Canadian
%%% Association of Physicists, Elsevier
%%% ScienceDirect, EuroPhysics, IEEE Xplore,
%%% Institute of Physics (IOP), JSTOR, MathSciNet,
%%% Nature, PubMed, Royal Society, Science,
%%% Smithsonian Astrophysical Observatory,
%%% SpringerLink, Web of Science, Wiley, and
%%% zbMATH databases. Once those resources were
%%% exhausted, the BibTeX entries produced from
%%% them were matched entry by entry with Jon
%%% Borwein's curriculum vitae in his file
%%% CV.pdf, and all previously-missing ones were
%%% converted to BibTeX form and added to this
%%% file.
%%%
%%% Numerous errors and inconsistencies in those
%%% sources have been corrected, and many
%%% heuristic checks, and spelling corrections,
%%% have been done. The companion file
%%% borwein-jonathan-m.sok contains a private
%%% spelling-exception dictionary for this file.
%%%
%%% Special thanks go to David H. Bailey of
%%% the University of California, Davis, and
%%% Karl Dilcher of Dalhousie University for
%%% uncovering many previously unrecorded works
%%% by Jonathan Borwein.
%%%
%%% TO DO: More work is still needed to locate
%%% electronic addresses for some entries. Of
%%% the 592 article entries containing Borwein in
%%% the author field, 536 have either a DOI or a
%%% URL value, and 164 have both DOI and URL
%%% values, but 56 have neither.
%%%
%%% Of the 115 Borwein entries for InXxx blocks,
%%% 61 have neither DOI nor URL values.
%%%
%%% Of the 37 Borwein entries for Book and
%%% Proceedings blocks, 17 have neither DOI nor
%%% URL values.
%%%
%%% Except for those publications in open-access
%%% journals or technical reports, document
%%% access via DOI or URL values may require an
%%% institutional journal subscription, or online
%%% payment.
%%%
%%% The checksum field above contains a CRC-16
%%% checksum as the first value, followed by the
%%% equivalent of the standard UNIX wc (word
%%% count) utility output of lines, words, and
%%% characters. This is produced by Robert
%%% Solovay's checksum utility.",
%%% }
%%% ====================================================================
@Preamble{
"\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" #
"\ifx \undefined \cdprime \def \cdprime {$''$} \fi" #
"\ifx \undefined \cftilf \def \cftil #1{\ifmmode \setbox7 \hbox{$\accent5E#1$}\else
\setbox7 \hbox{\accent5E#1}\penalty 10000 \relax \fi \raise 1\ht7
\hbox{\lower 1.15ex \hbox to 1\wd7{\hss \accent7E \hss}}\penalty 10000
\hskip-1\wd7 \penalty 10000 \box7} \fi" #
"\ifx \undefined \circled \def \circled #1{(#1)}\fi" #
"\ifx \undefined \cprime \def \cprime {$'$} \fi" #
"\ifx \undefined \coloneq \def \coloneq {\colon=} \fi" #
"\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}} \fi" #
"\ifx \undefined \mathrm \def \mathrm #1{{\rm #1}} \fi" #
"\ifx \undefined \refcno \def \refcno{Cno. } \fi" #
"\ifx \undefined \reg \def \reg {\circled{R}}\fi"
}
%%% ====================================================================
%%% Acknowledgement abbreviations:
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|http://www.math.utah.edu/~beebe/|"}
@String{ack-njh = "Nick Higham,
e-mail: \path|nick.higham@manchester.ac.uk|"}
%%% ====================================================================
%%% Institutional abbreviations:
@String{inst-CARMA = "Centre for Computer-assisted Research
Mathematics and its Applications
(CARMA), School of Mathematical and
Physical Sciences, University of
Newcastle"}
@String{inst-CARMA:adr = "Callaghan, NSW 2308, Australia"}
@String{inst-CECM = "Centre for Experimental and Constructive
Mathematics (CECM) at Simon Fraser
University (SFU)"}
@String{inst-CECM:adr = "Burnaby, BC, Canada"}
%%% ====================================================================
%%% Journal abbreviations:
@String{j-ABSTR-APPL-ANAL = "Abstract and Applied Analysis"}
@String{j-ACM-COMM-COMP-ALGEBRA = "ACM Communications in Computer Algebra"}
@String{j-ACTA-ARITHMETICA = "Acta Arithmetica"}
@String{j-ACTA-SCI-NATUR-UNIV-SUNYATSENI = "Acta Scientiarum Naturalium
Universitatis Sunyatseni. Zhongshan Daxue
Xuebao. Ziran Kexue Ban"}
@String{j-ADV-NONLINEAR-ANAL = "Advances in Nonlinear Analysis"}
@String{j-AEQUATIONES-MATHEMATICAE = "Aequationes Mathematicae"}
@String{j-AM-SCI = "American Scientist"}
@String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"}
@String{j-ANZIAM-J = "The ANZIAM Journal"}
@String{j-APPL-ANAL = "Applicable Analysis"}
@String{j-APPL-MATH-COMP = "Applied Mathematics and Computation"}
@String{j-APPL-MATH-LETT = "Applied Mathematics Letters"}
@String{j-APPL-MATH-OPTIM = "Applied Mathematics and Optimization"}
@String{j-AUSTRALIAN-MATH-SOC-GAZ = "Australian Mathematical Society Gazette"}
@String{j-BIT = "BIT (Nordisk tidskrift for
informationsbehandling)"}
@String{j-BOUND-VALUE-PROBL = "Boundary Value Problems"}
@String{j-BULL-AMS-N-S = "Bulletin of the American Mathematical
Society (new series)"}
@String{j-BULL-AUSTRAL-MATH-SOC = "Bulletin of the Australian Mathematical
Society"}
@String{j-BULL-CALCUTTA-MATH-SOC = "Bulletin of the Calcutta Mathematical Society"}
@String{j-C-R-ACAD-BULGARE-SCI = "Comptes rendus de l'Acad{\'e}mie bulgare
des sciences"}
@String{j-C-R-ACAD-SCI-CANADA = "Comptes rendus de l'Acad{\'e}mie des
sciences. Canada"}
@String{j-CAN-J-MATH = "Canadian Journal of Mathematics = Journal
canadien de math{\'e}matiques"}
@String{j-CAN-MATH-BULL = "Canadian mathematical bulletin = Bulletin
canadien de math{\'e}matiques"}
@String{j-CMS-NOTES = "Canadian Mathematical Society Notes"}
@String{j-COMMUN-CONTEMP-MATH = "Communications in Contemporary Mathematics"}
@String{j-COMP-OPTIM-APPL = "Computational optimization and
applications"}
@String{j-COMP-PHYS-COMM = "Computer Physics Communications"}
@String{j-COMPUT-SCI-ENG = "Computing in Science and Engineering"}
@String{j-COMPUTING = "Computing: Archiv f{\"u}r informatik und
numerik"}
@String{j-CONST-APPROX = "Constructive Approximation"}
@String{j-DISCRETE-MATH = "Discrete Mathematics"}
@String{j-EDUC-STUD-MATH = "Educational Studies in Mathematics"}
@String{j-ELECT-J-COMB = "Electronic Journal of Combinatorics"}
@String{j-ELECTRON-TRANS-NUMER-ANAL = "Electronic Transactions on Numerical
Analysis"}
@String{j-ENTROPY = "Entropy"}
@String{j-EUR-MATH-SOC-NEWSL = "European Mathematical Society. Newsletter"}
@String{j-EXP-MATH = "Experimental Mathematics"}
@String{j-FIB-QUART = "Fibonacci Quarterly"}
@String{j-HOUSTON-J-MATH = "Houston Journal of Mathematics"}
@String{j-IEEE-CONTROL-SYST-MAG = "IEEE Control Systems Magazine"}
@String{j-IEEE-TRANS-MED-IMAG = "IEEE Transactions on Medical Imaging"}
@String{j-IEEE-TRANS-NUCL-SCI = "IEEE Transactions on Nuclear Science"}
@String{j-IMA-J-NUMER-ANAL = "IMA Journal of Numerical Analysis"}
@String{j-INDAG-MATH = "Indagationes Mathematic{\ae}"}
@String{j-INFO-SCI = "Information Sciences"}
@String{j-INT-J-COMPUT-MATH = "International Journal of Computer
Mathematics"}
@String{j-INT-J-MATH-MATH-SCI = "International Journal of Mathematics and
Mathematical Sciences"}
@String{j-INT-J-NUMBER-THEORY = "International Journal of Number Theory"}
@String{j-INTEGERS = "Integers"}
@String{j-INVERSE-PROBL-SCI-ENG = "Inverse Problems in Science and
Engineering"}
@String{j-ISRAEL-J-MATH = "Israel Journal of Mathematics"}
@String{j-J-ALG = "Journal of Algorithms"}
@String{j-J-APPL-MATH = "Journal of Applied Mathematics"}
@String{j-J-APPROX-THEORY = "Journal of Approximation Theory"}
@String{j-J-AUSTRAL-MATH-SOC = "Journal of the Australian
Mathematical Society"}
@String{j-J-AUSTRAL-MATH-SOC-SER-A = "Journal of the Australian
Mathematical Society. Series A: Pure
Mathematics and Statistics"}
@String{j-J-AUSTRAL-MATH-SOC-SER-B = "Journal of the Australian
Mathematical Society. Series B"}
@String{j-J-COMB-THEORY-A = "Journal of Combinatorial Theory (Series A)"}
@String{j-J-COMP-MATH = "Journal of Computational Mathematics"}
@String{j-J-COMPUT-APPL-MATH = "Journal of Computational and Applied
Mathematics"}
@String{j-J-COMPUT-FINANCE = "Journal of Computational Finance"}
@String{j-J-CONVEX-ANAL = "Journal of Convex Analysis"}
@String{j-J-FUNCT-ANAL = "Journal of Functional Analysis"}
@String{j-J-GLOBAL-OPT = "Journal of Global Optimization"}
@String{j-J-HUMANIST-MATH = "Journal of Humanistic Mathematics"}
@String{j-J-INTEGER-SEQ = "Journal of Integer Sequences"}
@String{j-J-INVESTMENT-MANAGE = "Journal of Investment Management"}
@String{j-J-LOND-MATH-SOC-2 = "Journal of the London Mathematical Society
(series 2)"}
@String{j-J-MATH-ANAL-APPL = "Journal of Mathematical Analysis and
Applications"}
@String{j-J-MATH-PHYS = "Journal of Mathematical Physics"}
@String{j-J-NONLINEAR-CONVEX-ANAL = "Journal of Nonlinear and Convex Analysis"}
@String{j-J-NUMBER-THEORY = "Journal of Number Theory"}
@String{j-J-OPT-THEORY-APPL = "Journal of Optimization Theory and
Applications"}
@String{j-J-PHYS-A = "Journal of Physics A (Mathematical and
General)"}
@String{j-J-PHYS-A-MATH-THEOR = "Journal of Physics A: Mathematical and
Theoretical"}
@String{j-J-REINE-ANGEW-MATH = "{Journal f{\"u}r die reine und angewandte
Mathematik}"}
@String{j-J-SCI-COMPUT = "Journal of Scientific Computing"}
@String{j-J-SYMBOLIC-COMP = "Journal of Symbolic Computation"}
@String{j-LECT-NOTES-COMP-SCI = "Lecture Notes in Computer Science"}
@String{j-LECT-NOTES-MATH = "Lecture Notes in Mathematics"}
@String{j-MAPLE-TECH-NEWS = "Maple Technical Newsletter"}
@String{j-MATH-COMPUT = "Mathematics of Computation"}
@String{j-MATH-GAZ = "Mathematical Gazette"}
@String{j-MATH-INEQUAL-APPL = "Mathematical Inequalities \& Applications"}
@String{j-MATH-INTEL = "The Mathematical Intelligencer"}
@String{j-MATH-MAG = "Mathematics Magazine"}
@String{j-MATH-OP-RES = "Mathematics of Operations Research"}
@String{j-MATH-PROG = "Mathematical Programming"}
@String{j-MATH-PROG-STUDY = "Mathematical Programming Study"}
@String{j-MATH-SCAND = "Mathematica Scandinavica"}
@String{j-MATH-STUDENT = "The Mathematics Student"}
@String{j-METHODS-APPL-ANAL = "Methods and Applications of Analysis"}
@String{j-MICH-MATH-J = "Michigan Mathematical Journal"}
@String{j-NAMS = "Notices of the American Mathematical
Society"}
@String{j-NEUROCOMPUTING = "Neurocomputing"}
@String{j-NONLINEAR-ANAL = "Nonlinear Analysis, Theory, Methods and
Applications"}
@String{j-NUM-LIN-ALG-APPL = "Numerical Linear Algebra with Applications"}
@String{j-NUM-MATH = "Numerische Mathematik"}
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@String{j-SET-VALUED-VAR-ANAL = "Set-Valued and Variational Analysis"}
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Processing Society of Japan"}
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Mathematical Methods of Operations Research"}
@String{j-ZOR-MATH-METHODS-OPER-RES = "ZOR --- Mathematical Methods of
Operations Research"}
%%% ====================================================================
%%% Publisher abbreviations:
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@String{pub-A-K-PETERS:adr = "Wellesley, MA, USA"}
@String{pub-ACADEMIC = "Academic Press"}
@String{pub-ACADEMIC:adr = "New York, NY, USA"}
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@String{pub-ACM:adr = "New York, NY 10036, USA"}
@String{pub-AMS = "American Mathematical Society"}
@String{pub-AMS:adr = "Providence, RI, USA"}
@String{pub-CAMBRIDGE = "Cambridge University Press"}
@String{pub-CAMBRIDGE:adr = "Cambridge, UK"}
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@String{pub-NORTH-HOLLAND:adr = "Amsterdam, The Netherlands"}
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@String{pub-WILEY:adr = "New York, NY, USA"}
%%% ====================================================================
%%% Series abbreviations:
%%% ====================================================================
%%% Part 1 (of 4): Academic works by Jonathan Michael Borwein
%%%
%%% Bibliography entries, sorted by year, and then by citation label,
%%% with ``bibsort --byyear'':
@MastersThesis{Borwein:1972:MON,
author = "Jonathan Michael Borwein",
title = "Monotone Operators and Non-Linear Functional
Analysis",
type = "{M.Sc.} thesis",
school = "Oxford University",
address = "Oxford, UK",
year = "1972",
bibdate = "Thu Aug 11 17:24:59 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@PhdThesis{Borwein:1974:ORP,
author = "Jonathan Michael Borwein",
title = "Optimization with respect to partial orderings",
type = "{D.Phil.} thesis",
school = "Oxford University",
address = "Oxford, UK",
year = "1974",
bibdate = "Wed Aug 10 10:59:56 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://search.proquest.com/pqdtglobal/docview/1767375969/",
acknowledgement = ack-nhfb,
advisor = "M. A. H. (Michael Alan Howarth) Dempster",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1976:FPD,
author = "J. M. Borwein",
title = "Fractional programming without differentiability",
journal = j-MATH-PROG,
volume = "11",
number = "1",
pages = "283--290",
year = "1976",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/BF01580396",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "90C10 (65K05)",
MRnumber = "0449664",
MRreviewer = "Siegfried Schaible",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1671/;
http://link.springer.com/article/10.1007/BF01580396",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxnumber = "3",
}
@Article{Borwein:1976:NFJ,
author = "J. M. Borwein",
title = "A note on {Fritz John} sufficiency",
journal = j-BULL-AUSTRAL-MATH-SOC,
volume = "15",
number = "2",
pages = "293--296",
month = oct,
year = "1976",
CODEN = "ALNBAB",
DOI = "https://doi.org/10.1017/S0004972700022656",
ISSN = "0004-9727 (print), 1755-1633 (electronic)",
ISSN-L = "0004-9727",
MRclass = "90C30",
MRnumber = "0426851",
MRreviewer = "R. N. Kaul",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1515/;
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=4812456",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the Australian Mathematical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1976:TCC,
author = "J. Borwein and R. O'Brien",
title = "Tangent cones and convexity",
journal = j-CAN-MATH-BULL,
volume = "19",
number = "3",
pages = "257--261",
year = "1976",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1976-040-x",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "46A99 (52A05)",
MRnumber = "0454586",
MRreviewer = "A. Gopfert",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1517/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1976:VS,
author = "J. Borwein and M. Edelstein and R. O'Brien",
title = "Visibility and Starshape",
journal = j-J-LOND-MATH-SOC-2,
volume = "S2-14",
number = "2",
pages = "313--318",
month = nov,
year = "1976",
CODEN = "JLMSAK",
DOI = "https://doi.org/10.1112/jlms/s2-14.2.313",
ISSN = "0024-6107 (print), 1469-7750 (electronic)",
ISSN-L = "0024-6107",
MRclass = "46B05",
MRnumber = "0428010",
MRreviewer = "Bor-Luh Lin",
bibdate = "Fri Aug 12 16:38:27 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1670/;
http://jlms.oxfordjournals.org/content/s2-14/2/313.full.pdf+html",
acknowledgement = ack-nhfb,
ajournal = "J. Lond. Math. Soc. (2)",
fjournal = "Journal of the London Mathematical Society (series
2)",
journal-URL = "http://jlms.oxfordjournals.org/content/by/year",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1977:MCO,
author = "J. Borwein",
title = "Multivalued convexity and optimization: a unified
approach to inequality and equality constraints",
journal = j-MATH-PROG,
volume = "13",
number = "2",
pages = "183--199",
year = "1977",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/BF01584336",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "52A40 (90C25)",
MRnumber = "0451166",
MRreviewer = "J. Stoer",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1669/;
http://link.springer.com/article/10.1007/BF01584336",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1977:PEH,
author = "J. Borwein",
title = "A proof of the equivalence of {Helly}'s and
{Krasnoselski}'s theorems",
journal = j-CAN-MATH-BULL,
volume = "20",
number = "1",
pages = "35--37",
month = mar,
year = "1977",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1977-007-4",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "52A35",
MRnumber = "0478014",
MRreviewer = "John D. Baildon",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://cms.math.ca/cmb/v20/;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/canmathbull.bib",
URL = "http://docserver.carma.newcastle.edu.au/1518/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1977:PEP,
author = "J. Borwein",
title = "Proper Efficient Points for Maximizations with Respect
to Cones",
journal = j-SIAM-J-CONTROL-OPTIM,
volume = "15",
number = "1",
pages = "57--63",
month = jan,
year = "1977",
CODEN = "SJCODC",
DOI = "https://doi.org/10.1137/0315004",
ISSN = "0363-0129 (print), 1095-7138 (electronic)",
ISSN-L = "0363-0129",
MRclass = "90C30 (65K05 49B99)",
MRnumber = "0434441",
MRreviewer = "M. Rossler",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICON/15/1;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/siamjcontroloptim.bib",
URL = "http://docserver.carma.newcastle.edu.au/1667/",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Control and Optimization",
journal-URL = "http://epubs.siam.org/sicon",
journalabr = "SIAM J Control Optim",
onlinedate = "January 1977",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1977:SRV,
author = "J. Borwein and M. Edelstein and R. O'Brien",
title = "Some remarks on visibility and starshape",
journal = j-J-LOND-MATH-SOC-2,
volume = "S2-15",
number = "2",
pages = "342--344",
month = apr,
year = "1977",
CODEN = "JLMSAK",
DOI = "https://doi.org/10.1112/jlms/s2-15.2.342",
ISSN = "0024-6107 (print), 1469-7750 (electronic)",
ISSN-L = "0024-6107",
MRclass = "46A99",
MRnumber = "0442642",
MRreviewer = "Bor-Luh Lin",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1666/;
http://jlms.oxfordjournals.org/content/s2-15/2/342.full.pdf+html",
acknowledgement = ack-nhfb,
ajournal = "J. Lond. Math. Soc. (2)",
fjournal = "Journal of the London Mathematical Society (series
2)",
journal-URL = "http://jlms.oxfordjournals.org/content/by/year",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Misc{Borwein:1977:WLP,
author = "J. M. Borwein",
title = "The {William Lowell Putnam} Competition. {A} Brief
History",
howpublished = "Unpublished notes.",
pages = "9",
day = "26",
month = jan,
year = "1977",
bibdate = "Mon Nov 07 06:59:36 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "In December 1921 William Lowell Putnam, a magna cum
laude Mathematics graduate of the Harvard class of
1882, wrote in the Harvard Graduate Magazine on ``A
Suggestion For Increasing The Undergraduate Interest In
Studies''. He noted that all prizes for scholarship
were individual and suggested that ``a Harvard man
prefers for example to be a member of a tennis team to
play against Yale \ldots{} rather than to be champion
of Harvard'' and that the same principle of team work
and team competition ``which has inspired young men to
undertake and undergo so much for the sake of athletic
victories might accomplish some result in academic
fields''. These sentiments, and others which seem even
more dated, would probably have had no effect were it
not that Putnam's wife was a Lowell, was extremely rich
and was the sister of then President Abbott Lowell of
Harvard. Putnam's mother was also a Lowell while his
father was a Unitarian with all the right connections
and memberships who founded the English Speaking Union
among other organizations and wrote prodigiously on
many learned topics",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1978:CCC,
author = "J. M. Borwein and R. C. O'Brien",
title = "Cancellation characterizes convexity",
journal = "Nanta Mathematica",
volume = "11",
number = "1",
pages = "100--102",
year = "1978",
CODEN = "NAMAB2",
ISSN = "0077-2739",
MRclass = "52A20",
MRnumber = "510842",
MRreviewer = "John D. Baildon",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1659/",
acknowledgement = ack-nhfb,
ajournal = "Nanta Math.",
fjournal = "Nanyang University. Nanta Mathematica",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1978:SEF,
author = "J. M. Borwein",
title = "On strongly exposing functionals",
journal = j-PROC-AM-MATH-SOC,
volume = "69",
number = "1",
pages = "46--48",
year = "1978",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "46B99 (52A05)",
MRnumber = "0493272",
MRreviewer = "Ka Sing Lau",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1665/;
http://www.jstor.org/stable/2043185",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1978:TCS,
author = "J. M. Borwein",
title = "Tangent cones, starshape and convexity",
journal = j-INT-J-MATH-MATH-SCI,
volume = "1",
number = "4",
pages = "459--477",
year = "1978",
DOI = "https://doi.org/10.1155/S0161171278000460",
ISSN = "0161-1712 (print), 1687-0425 (electronic)",
ISSN-L = "0161-1712",
MRclass = "52A30 (90C30)",
MRnumber = "517949",
MRreviewer = "Gerald Beer",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1663/",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematics and Mathematical
Sciences",
journal-URL = "https://www.hindawi.com/journals/ijmms/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1978:WTC,
author = "J. Borwein",
title = "Weak Tangent Cones and Optimization in a {Banach}
Space",
journal = j-SIAM-J-CONTROL-OPTIM,
volume = "16",
number = "3",
pages = "512--522",
month = may,
year = "1978",
CODEN = "SJCODC",
DOI = "https://doi.org/10.1137/0316034",
ISSN = "0363-0129 (print), 1095-7138 (electronic)",
ISSN-L = "0363-0129",
MRclass = "65K05 (90C99)",
MRnumber = "0478612",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICON/16/3;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/siamjcontroloptim.bib",
URL = "http://docserver.carma.newcastle.edu.au/1664/",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Control and Optimization",
journal-URL = "http://epubs.siam.org/sicon",
journalabr = "SIAM J Control Optim",
onlinedate = "May 1978",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:1979:CD,
author = "J. M. Borwein",
title = "On convex decompositions",
year = "1979",
bibdate = "Fri Aug 12 16:51:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Accepted for publication in \booktitle{Nanta
Mathematica}, but the journal ceased publication in
1979 before the paper appeared.",
URL = "http://docserver.carma.newcastle.edu.au/1672/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1979:COA,
author = "J. M. Borwein and H. Wolkowicz",
title = "Characterizations of Optimality for the Abstract
Convex Program",
type = "Research Report",
number = "19",
institution = "Department of Mathematics, Dalhousie University",
address = "Halifax, NS, Canada",
pages = "54",
month = jul,
year = "1979",
bibdate = "Tue Nov 08 15:45:14 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib",
abstract = "This paper presents characterizations of optimality
for the convex program $$ (p) \mu = \inf \{ p(x) \colon
g(x) \in - S, x \in \Omega \} $$ when $S$ is an
arbitrary convex cone in a finite dimensional space, $
\Omega $ is a convex set and $p$ and $g$ are
respectively convex and S-convex(on $ \Omega $). These
characterizations, which include a Lagrange multiplier
and do not presume any a priori constraint
qualification, subsume those presently in the
literature.",
acknowledgement = ack-nhfb,
keywords = "abstract programming; cone of positive semi-definite
matrices; convexity; duality principles; facial
reduction; Lagrange multipliers; Slater's condition;
subgradients; symmetric matrices",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1979:COC,
author = "J. M. Borwein and H. Wolkowicz",
title = "Characterizations of optimality without constraint
qualification for the abstract convex program",
type = "Research Report",
number = "14",
institution = "Department of Mathematics, Dalhousie University",
address = "Halifax, NS, Canada",
pages = "59",
month = jun,
year = "1979",
bibdate = "Tue Nov 08 15:45:14 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1979:DTS,
author = "J. M. Borwein",
title = "Direct theorems in semi-infinite convex programming",
type = "Report",
number = "11",
institution = "Department of Mathematics, Dalhousie University",
address = "Halifax, NS, Canada",
pages = "33",
month = apr,
year = "1979",
bibdate = "Tue Nov 08 15:45:14 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "Recently Ben-Tal, Ben-Israel and Rossinger [1] have
proven a ``direct theorem'' for the existence of finite
subprograms for infinitely constrained programming
problems with finitely many variables. They did this
via a Helly-type theorem for open convex sets due to
Klee [10], [7]. The proof of Klee's theorem [10] is
somewhat difficult to follow and, in addition, requires
the use of the notion of an ``open-closed'' family of
sets. One of the purposes of this paper is to provide
an entirely self-contained proof of an extension of the
result in [1].",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1979:LLC,
author = "J. M. Borwein",
title = "The Limiting Lagrangean as a Consequence of {Helly's
Theorem}",
type = "Report",
number = "7",
institution = "Department of Mathematics, Dalhousie University",
address = "Halifax, NS, Canada",
month = mar,
year = "1979",
bibdate = "Tue Nov 08 15:34:18 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "The perturbational Lagrangean equation established by
Jeroslow in convex semi-infinite programming is derived
from Helly's Theorem and some prior results on one
dimensional perturbations of convex programs.",
acknowledgement = ack-nhfb,
keywords = "Affine Minorants; convex semi-infinite programming;
Helly's Theorem; limiting Lagrangeans; Recession
Directions",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1979:MAF,
author = "J. M. Borwein",
title = "A multivalued approach to the {Farkas} lemma",
journal = j-MATH-PROG-STUDY,
volume = "10",
pages = "42--47",
year = "1979",
CODEN = "MPSTDF",
DOI = "https://doi.org/10.1007/BFb0120842",
ISSN = "0303-3929",
MRclass = "90C99",
MRnumber = "527056",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Point-to-set maps and mathematical programming.",
URL = "http://docserver.carma.newcastle.edu.au/1660/;
http://link.springer.com/chapter/10.1007/BFb0120842",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming Study",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1979:MFP,
author = "J. M. Borwein",
booktitle = "{Third Symposium on Operations Research (Univ.
Mannheim, Mannheim, 1978), Section I}",
title = "The minimum of a family of programs",
volume = "31",
publisher = "Hain",
pages = "99--111",
year = "1979",
MRclass = "90C25",
MRnumber = "541191",
MRreviewer = "Jacques Dubois",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Operations Res. Verfahren",
acknowledgement = ack-nhfb,
addresss = "K{\"o}nigstein im Taunus, West Germany",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1979:MLP,
author = "Jonathan M. Borwein",
title = "Monochrome lines in the plane",
journal = j-MATH-MAG,
volume = "52",
number = "1",
pages = "41--45",
year = "1979",
CODEN = "MAMGA8",
DOI = "https://doi.org/10.2307/2689976",
ISSN = "0025-570X (print), 1930-0980 (electronic)",
ISSN-L = "0025-570X",
MRclass = "54B20 (57N05)",
MRnumber = "524202",
MRreviewer = "H. W. Lambert",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1662/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Magazine",
journal-URL = "http://www.maa.org/pubs/mathmag.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1979:TVS,
author = "J. M. Borwein",
title = "Two variants of {Sylvester}'s theorem",
journal = "Atlantic Mathematics Bulletin",
volume = "3",
number = "??",
pages = "11--13",
month = "????",
year = "1979",
DOI = "",
ISSN = "0705-9078",
ISSN-L = "0705-9078",
bibdate = "Fri Aug 12 16:08:43 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1658/",
acknowledgement = ack-nhfb,
ajournal = "Atlantic Math. Bull.",
fjournal = "Atlantic Mathematics Bulletin",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1979:WLS,
author = "J. M. Borwein",
title = "Weak local supportability and applications to
approximation",
journal = j-PAC-J-MATH,
volume = "82",
number = "2",
pages = "323--338",
year = "1979",
CODEN = "PJMAAI",
ISSN = "0030-8730 (print), 1945-5844 (electronic)",
ISSN-L = "0030-8730",
MRclass = "46B99 (41A25 49A27 58C20 90C30)",
MRnumber = "551692",
MRreviewer = "Ka Sing Lau",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://projecteuclid.org/euclid.pjm/1102784876",
acknowledgement = ack-nhfb,
fjournal = "Pacific Journal of Mathematics",
journal-URL = "http://msp.org/pjm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1980:GPE,
author = "J. M. Borwein",
title = "The geometry of {Pareto} efficiency over cones",
journal = j-OPTIMIZATION,
volume = "11",
number = "2",
pages = "235--248",
year = "1980",
CODEN = "OPTZDQ",
DOI = "https://doi.org/10.1080/02331938008842650",
ISSN = "0323-3898",
ISSN-L = "0233-1934",
MRclass = "90C31 (58E17 90C25 90C30)",
MRnumber = "640689",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/02331938008842650",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Operationsforschung und Statistik Series
Optimization",
onlinedate = "5 July 2007",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1980:HMC,
author = "J. Borwein and L. Keener",
title = "The {Hausdorff} metric and {{\v{C}}eby{\v{s}}ev}
centres",
journal = j-J-APPROX-THEORY,
volume = "28",
number = "4",
pages = "366--376",
year = "1980",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1016/0021-9045(80)90071-4",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "41A65 (46B20)",
MRnumber = "589992",
MRreviewer = "S. Cobza{\c{s}}",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1652/;
http://www.sciencedirect.com/science/article/pii/0021904580900714",
acknowledgement = ack-nhfb,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1980:LM,
author = "J. M. Borwein",
title = "Lexicographic multipliers",
journal = j-J-MATH-ANAL-APPL,
volume = "78",
number = "1",
pages = "309--327",
year = "1980",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247X(80)90228-0",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "90C25 (58C20)",
MRnumber = "595782",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1653/;
http://www.sciencedirect.com/science/article/pii/0022247X80902280",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1980:LMT,
author = "J. M. Borwein",
title = "A {Lagrange} Multiplier Theorem and a Sandwich Theorem
for Convex Relations",
type = "Research Report",
number = "80-1",
institution = "Department of Mathematics, Dalhousie University",
address = "Halifax, NS, Canada",
pages = "26",
day = "15",
month = jan,
year = "1980",
bibdate = "Tue Nov 08 15:45:14 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "We formulate and prove various separation principles
for convex relations taking values in an order complete
vector space. These principles subsume the standard
ones",
acknowledgement = ack-nhfb,
keywords = "convex relations; Fenchel's theorem; Lagrange
multipliers; order complete spaces; separation",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1980:NPD,
author = "J. M. Borwein",
title = "A note on perfect duality and limiting {Lagrangeans}",
journal = j-MATH-PROG,
volume = "18",
number = "1",
pages = "330--337",
year = "1980",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/BF01588327",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "90C25",
MRnumber = "571994",
MRreviewer = "N. N. Astaf{\cprime}ev",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1654/;
http://link.springer.com/article/10.1007/BF01588327",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxnumber = "3",
}
@Article{Borwein:1980:SDT,
author = "J. M. Borwein",
title = "A strong duality theorem for the minimum of a family
of convex programs",
journal = j-J-OPT-THEORY-APPL,
volume = "31",
number = "4",
pages = "453--472",
year = "1980",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00934472",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "90C25 (46G99 90C30)",
MRnumber = "600199",
MRreviewer = "Tadashi Nakamura",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1657/;
http://link.springer.com/article/10.1007/BF00934472",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Tijs:1980:SGC,
author = "S. H. Tijs and J. M. Borwein",
title = "Some Generalizations of {Carath{\'e}odory}'s Theorem
via Barycentres, with Application to Mathematical
Programming",
journal = j-CAN-MATH-BULL,
volume = "23",
number = "3",
pages = "339--346",
month = sep,
year = "1980",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1980-048-x",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "90C05 (46G99 58C20)",
MRnumber = "593393",
MRreviewer = "M. Brannigan",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://cms.math.ca/cmb/v23/;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/canmathbull.bib",
URL = "http://docserver.carma.newcastle.edu.au/1656/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1981:CCP,
author = "J. M. Borwein and H. Wolkowicz",
booktitle = "Generalized Convexity in Optimization and Economics",
title = "Cone convex programming, stability and affine
constraints",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "379--392",
year = "1981",
DOI = "",
ISBN = "",
ISBN-13 = "",
LCCN = "",
bibdate = "Mon Aug 15 15:19:56 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1981:COA,
author = "Jon M. Borwein and Henry Wolkowicz",
title = "Characterization of optimality for the abstract convex
program with finite dimensional range",
journal = j-J-AUSTRAL-MATH-SOC-SER-A,
volume = "30",
number = "4",
pages = "390--411",
month = apr,
year = "1981",
CODEN = "JAMADS",
DOI = "https://doi.org/10.1017/S1446788700017882",
ISSN = "0263-6115 (print), 2396-8192 (electronic)",
ISSN-L = "0263-6115",
MRclass = "90C48",
MRnumber = "621556 (83i:90156)",
MRreviewer = "R. L. Graves",
bibdate = "Wed Aug 31 15:25:43 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib",
URL = "http://docserver.carma.newcastle.edu.au/1649/;
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=4896312",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Australian Mathematical Society. Series
A",
journal-URL = "http://journals.cambridge.org/action/displayBackIssues?jid=JAZ",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
received = "21 March 1980",
}
@InCollection{Borwein:1981:CRO,
author = "J. M. Borwein",
booktitle = "Generalized Convexity in Optimization and Economics",
title = "Convex relations in optimization and analysis",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "335--377",
year = "1981",
ISBN = "",
ISBN-13 = "",
LCCN = "",
bibdate = "Mon Aug 15 15:17:45 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1981:DTS,
author = "J. M. Borwein",
title = "Direct theorems in semi-infinite convex programming",
journal = j-MATH-PROG,
volume = "21",
number = "1",
pages = "301--318",
year = "1981",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/BF01584251",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "90C25 (49D39 90C30)",
MRnumber = "632637",
MRreviewer = "{\c{S}}tefan {\c{T}}igan",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://link.springer.com/article/10.1007/BF01584251",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxnumber = "3",
}
@Article{Borwein:1981:FRC,
author = "Jon M. Borwein and Henry Wolkowicz",
title = "Facial reduction for a cone-convex programming
problem",
journal = j-J-AUSTRAL-MATH-SOC-SER-A,
volume = "30",
number = "3",
pages = "369--380",
month = feb,
year = "1981",
CODEN = "JAMADS",
DOI = "https://doi.org/10.1017/S1446788700017250",
ISSN = "0263-6115 (print), 2396-8192 (electronic)",
ISSN-L = "0263-6115",
MRclass = "90C25; 90C48",
MRnumber = "83b:90121 (614086)",
MRreviewer = "B. T. Polyak",
bibdate = "Wed Aug 31 16:29:21 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib",
URL = "http://docserver.carma.newcastle.edu.au/1650/;
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=5441184",
ZMnumber = "0464.90086",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Australian Mathematical Society. Series
A",
journal-URL = "http://journals.cambridge.org/action/displayBackIssues?jid=JAZ",
onlinedate = "28 July 1980",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
received = "21 March 1980",
}
@Article{Borwein:1981:LLC,
author = "J. M. Borwein",
title = "The limiting {Lagrangian} as a consequence of
{Helly}'s theorem",
journal = j-J-OPT-THEORY-APPL,
volume = "33",
number = "4",
pages = "497--513",
year = "1981",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00935755",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "90C25",
MRnumber = "616567",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1647/;
http://link.springer.com/article/10.1007/BF00935755",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1981:LMT,
author = "J. M. Borwein",
title = "A {Lagrange} multiplier theorem and a sandwich theorem
for convex relations",
journal = j-MATH-SCAND,
volume = "48",
number = "2",
pages = "189--204",
year = "1981",
CODEN = "MTSCAN",
ISSN = "0025-5521 (print), 1903-1807 (electronic)",
ISSN-L = "0025-5521",
MRclass = "49A50 (26A51 46A22 90C25); 49J45 (Optimal control
problems involving semicontinuity and convergence;
relaxation); 58C06 (Set-valued and function-space
valued mappings on manifolds); 49J27 (Optimal control
problems in abstract spaces (existence)); 46A30 (Open
mapping and closed graph theorems; completeness); 46A40
(Ordered topological linear spaces, vector lattices)",
MRnumber = "631335",
MRreviewer = "Michel Th{\'e}ra",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1646/;
http://www.mscand.dk/article/view/11911/9927",
ZMnumber = "0468.49007",
acknowledgement = ack-nhfb,
fjournal = "Mathematica Scandinavica",
journal-URL = "http://www.mscand.dk/issue/archive",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1981:RAC,
author = "Jon Borwein and Henry Wolkowicz",
title = "Regularizing the abstract convex program",
journal = j-J-MATH-ANAL-APPL,
volume = "83",
number = "2",
pages = "495--530",
year = "1981",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247X(81)90138-4",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "90C48 (90C25)",
MRnumber = "641348",
MRreviewer = "S. Zlobec",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib",
URL = "http://docserver.carma.newcastle.edu.au/1645/;
http://www.sciencedirect.com/science/article/pii/0022247X81901384",
abstract = "Characterizations of optimality for the abstract
convex program $ \mu = i n f \{ p(x) \colon g(x) \in -
S, x \in \Omega \} (P) $ where $S$ is an arbitrary
convex cone in a finite dimensional space, $ \Omega $
is a convex set, and $p$ and $g$ are respectively
convex and $S$-convex (on $ \Omega $), were given in
[10]. These characterizations hold without any
constraint qualification. They use the ``minimal cone''
$ S^f$ of $ (P)$ and the cone of directions of
constancy $ D_g = (S^f)$. In the faithfully convex case
these cones can be used to regularize $ (P)$, i.e.,
transform $ (P)$ into an equivalent program $ (P_r)$
for which Slater's condition holds. We present an
algorithm that finds both $ S^$ f and $ D_g = (S^f)$.
The main step of the algorithm consists in solving a
particular complementarity problem. We also present a
characterization of optimality for $ (P)$ in terms of
the cone of directions of constancy of a convex
functional $ D_{\phi g}^ = $ rather than $ D_g^ =
(S^f)$.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1981:SRP,
author = "J. Borwein",
title = "Some remarks on a paper of {{\c{S}. Cobza{\c{s}} on
antiproximal sets: ``Antiproximinal sets in some Banach
spaces'' [Math. Balkanica {\bf 4} (1974), 79--82;\ {MR}
{\bf 51} \#13553]}}",
journal = j-BULL-CALCUTTA-MATH-SOC,
volume = "73",
number = "1",
pages = "5--8",
year = "1981",
CODEN = "BCMSA5",
ISSN = "0008-0659",
ISSN-L = "0008-0659",
MRclass = "46B20",
MRnumber = "669750",
MRreviewer = "M. M. Day",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1648/",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the Calcutta Mathematical Society",
journal-URL = "http://bulletin.calmathsoc.org/database.php",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1982:CDP,
author = "J. M. Borwein",
title = "Continuity and differentiability properties of convex
operators",
journal = j-PROC-LONDON-MATH-SOC-3,
volume = "44",
number = "3",
pages = "420--444",
year = "1982",
CODEN = "PLMTAL",
DOI = "https://doi.org/10.1112/plms/s3-44.3.420",
ISSN = "0024-6115 (print), 1460-244x (electronic)",
ISSN-L = "0024-6115",
MRclass = "58C20 (46G99 47H99 49A51 52A07)",
MRnumber = "656244",
MRreviewer = "Jean-Paul Penot",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1640/",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the London Mathematical Society. Third
Series",
journal-URL = "http://londmathsoc.onlinelibrary.wiley.com/hub/journal/10.1112/(ISSN)1460-244X/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1982:COCa,
author = "J. M. Borwein and H. Wolkowicz",
title = "Characterizations of optimality without constraint
qualification for the abstract convex program",
journal = j-MATH-PROG-STUDY,
volume = "19",
pages = "77--100",
year = "1982",
CODEN = "MPSTDF",
ISSN = "0303-3929",
ISSN-L = "0303-3929",
MRclass = "90C25",
MRnumber = "669726",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib",
note = "Optimality and stability in mathematical
programming.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming Study",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:1982:COCb,
author = "J. M. Borwein and H. Wolkowicz",
booktitle = "{Optimality and Stability in Mathematical
Programming}",
title = "Characterizations of optimality without constraint
qualification for the abstract convex program",
publisher = pub-SV,
address = pub-SV:adr,
pages = "??--??",
year = "1982",
DOI = "https://doi.org/10.1007/BFb0120983",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0120983",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1982:HBE,
author = "Jonathan M. Borwein",
title = "On the {Hahn--Banach} extension property",
journal = j-PROC-AM-MATH-SOC,
volume = "86",
number = "1",
pages = "42--46",
year = "1982",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.2307/2044393",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "46A40 (06F20)",
MRnumber = "663863",
MRreviewer = "M. M. Day",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1982:NES,
author = "J. M. Borwein",
title = "A note on the existence of subgradients",
journal = j-MATH-PROG,
volume = "24",
number = "2",
pages = "225--228",
year = "1982",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/BF01585105",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "49A50 (90C25)",
MRnumber = "674632",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1641/;
http://link.springer.com/article/10.1007/BF01585105",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxnumber = "1",
}
@Article{Borwein:1982:NSC,
author = "J. M. Borwein",
title = "Necessary and sufficient conditions for quadratic
minimality",
journal = j-NUMER-FUNCT-ANAL-OPTIM,
volume = "5",
number = "2",
pages = "127--140",
year = "1982",
CODEN = "NFADOL",
DOI = "https://doi.org/10.1080/01630568208816135",
ISSN = "0163-0563 (print), 1532-2467 (electronic)",
ISSN-L = "0163-0563",
MRclass = "90C20",
MRnumber = "704109",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1639/",
acknowledgement = ack-nhfb,
fjournal = "Numerical Functional Analysis and Optimization. An
International Journal",
journal-URL = "http://www.tandfonline.com/loi/lnfa20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1982:NSM,
author = "J. M. Borwein",
title = "A note on {$ \varepsilon $}-subgradients and maximal
monotonicity",
journal = j-PAC-J-MATH,
volume = "103",
number = "2",
pages = "307--314",
year = "1982",
CODEN = "PJMAAI",
ISSN = "0030-8730 (print), 1945-5844 (electronic)",
ISSN-L = "0030-8730",
MRclass = "90C25 (49A50 58C20)",
MRnumber = "705231",
MRreviewer = "J. E. Spingarn",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://projecteuclid.org/euclid.pjm/1102723964",
acknowledgement = ack-nhfb,
fjournal = "Pacific Journal of Mathematics",
journal-URL = "http://msp.org/pjm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1982:SSI,
author = "J. M. Borwein and G. P. H. Styan and H. Wolkowicz",
title = "Solutions: Some Inequalities Involving Statistical
Expressions ({L. V. Foster})",
journal = j-SIAM-REVIEW,
volume = "24",
number = "3",
pages = "340--342",
month = "????",
year = "1982",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1024072",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:53:30 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/24/3;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1982",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1983:APD,
author = "J. M. Borwein",
title = "Adjoint process duality",
journal = j-MATH-OP-RES,
volume = "8",
number = "3",
pages = "403--434",
year = "1983",
CODEN = "MOREDQ",
DOI = "https://doi.org/10.1287/moor.8.3.403",
ISSN = "0364-765x (print), 1526-5471 (electronic)",
ISSN-L = "0364-765X",
MRclass = "90C25",
MRnumber = "716121",
MRreviewer = "J. E. Spingarn",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "See letter \cite{Zalinescu:1986:LEJ}.",
URL = "http://docserver.carma.newcastle.edu.au/1633/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Operations Research",
journal-URL = "http://pubsonline.informs.org/loi/moor",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1983:CCP,
author = "J. M. Borwein",
title = "Completeness and the contraction principle",
journal = j-PROC-AM-MATH-SOC,
volume = "87",
number = "2",
pages = "246--250",
year = "1983",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.2307/2043697",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "54H25 (54E40)",
MRnumber = "681829",
MRreviewer = "L. Janos",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1637/",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1983:EPE,
author = "Jonathan M. Borwein",
title = "On the existence of {Pareto} efficient points",
journal = j-MATH-OP-RES,
volume = "8",
number = "1",
pages = "64--73",
month = feb,
year = "1983",
CODEN = "MOREDQ",
DOI = "https://doi.org/10.1287/moor.8.1.64",
ISSN = "0364-765x (print), 1526-5471 (electronic)",
ISSN-L = "0364-765X",
MRclass = "90C25 (46N05 52A05)",
MRnumber = "703826",
MRreviewer = "Autorreferat",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1636/;
http://www.jstor.org/stable/3689411",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Operations Research",
journal-URL = "http://pubsonline.informs.org/loi/moor",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1983:FDS,
author = "J. M. Borwein and K. O. Kortanek",
title = "{Fenchel}-duality and separably-infinite programs",
journal = j-OPTIMIZATION,
volume = "14",
number = "1",
pages = "37--48.",
year = "1983",
CODEN = "OPTZDQ",
DOI = "https://doi.org/10.1080/02331938308842831",
ISSN = "0323-3898",
ISSN-L = "0233-1934",
MRclass = "90C25 (90C05)",
MRnumber = "694801",
MRreviewer = "W. F. Tyndall",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Operationsforschung und Statistik Series
Optimization",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1983:HSS,
author = "J. M. Borwein",
booktitle = "Semi-infinite Programming",
title = "How special is semi-infinite programming?",
publisher = pub-SV,
address = pub-SV:adr,
pages = "139--172",
year = "1983",
bibdate = "Mon Aug 15 15:11:40 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1983:NFL,
author = "J. M. Borwein",
title = "A note on the {Farkas} lemma",
journal = j-UTIL-MATH,
volume = "24",
pages = "235--241",
year = "1983",
CODEN = "UTMADA",
ISSN = "0315-3681",
MRclass = "90C05 (90C30)",
MRnumber = "724772",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1631/",
acknowledgement = ack-nhfb,
fjournal = "Utilitas Mathematica. A Canadian Journal of Applied
Mathematics, Computer Science, and Statistics",
journal-URL = "http://bkocay.cs.umanitoba.ca/utilitas/index.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1983:NMB,
author = "Jonathan Borwein and Brailey Sims",
title = "Nonexpansive mappings on {Banach} lattices",
journal = j-C-R-ACAD-SCI-CANADA,
volume = "5",
number = "1",
pages = "21--26",
year = "1983",
ISSN = "0706-1994",
MRclass = "46A40 (46B20 47H09)",
MRnumber = "690312",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1635/",
acknowledgement = ack-nhfb,
fjournal = "La Soci{\'e}t{\'e} Royale du Canada. L'Academie des
Sciences. Comptes Rendus Math{\'e}matiques.
(Mathematical Reports)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1983:PSA,
author = "J. Borwein and Gabor J. Szekely and Andras Zempleni
and Michael Barr and Edmund Butler and Allen J. Schwenk
and Thomas Q. Sibley",
title = "Problems and Solutions: Advanced Problems: 6430-6435",
journal = j-AMER-MATH-MONTHLY,
volume = "90",
number = "6",
pages = "402--403",
year = "1983",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2975584",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1540218",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1983:SIP,
author = "Jonathan M. Borwein",
booktitle = "Semi-infinite programming and applications ({Austin},
{Tex}., 1981)",
title = "Semi-infinite programming duality: how special is
it?",
volume = "215",
publisher = pub-SV,
address = pub-SV:adr,
pages = "10--36",
year = "1983",
MRclass = "49D39 (90C30)",
MRnumber = "709266",
MRreviewer = "Sven-{\.A}ke Gustafson",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Lecture Notes in Econom. and Math. Systems",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1983:VRC,
author = "J. M. Borwein and P. B. Borwein",
title = "A very rapidly convergent product expansion for $ \pi
$",
journal = j-BIT,
volume = "23",
number = "4",
pages = "538--540",
month = dec,
year = "1983",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933626",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65B99",
MRnumber = "721199, 85h:65011",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=23&issue=4;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/bit.bib",
URL = "http://docserver.carma.newcastle.edu.au/1634/;
http://link.springer.com/article/10.1007/BF01933626;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=23&issue=4&spage=538",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1984:AGM,
author = "J. M. Borwein and P. B. Borwein",
title = "The Arithmetic--Geometric Mean and Fast Computation of
Elementary Functions",
journal = j-SIAM-REVIEW,
volume = "26",
number = "3",
pages = "351--366",
month = jul,
year = "1984",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1026073",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65D20 (26A09)",
MRnumber = "750454; 86d:65029",
MRreviewer = "S. Conde",
bibdate = "Tue Mar 14 07:52:56 2017",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://epubs.siam.org/toc/siread/26/3;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/agm.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://www.jstor.org/stable/2031275",
abstract = "We produce a self contained account of the
relationship between the Gaussian arithmetic--geometric
mean iteration and the fast computation of elementary
functions. A particularly pleasant algorithm for pi is
one of the by-products.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliationaddress = "Dalhousie Univ, Halifax, NS, Can",
classification = "723; 921",
fjournal = "SIAM Review. A Publication of the Society for
Industrial and Applied Mathematics",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "AGM (Arithmetic--Geometric Mean);
arithmetic--geometric mean; calculation of pi;
computational methods; elliptic functions; Iterative
Methods; mathematical techniques; numerical
mathematics",
onlinedate = "July 1984",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1984:ANV,
author = "J. M. Borwein and D. T. Yost",
title = "Absolute norms on vector lattices",
journal = j-PROC-EDINBURGH-MATH-SOC-2,
volume = "27",
number = "2",
pages = "215--222",
month = jun,
year = "1984",
CODEN = "PEMSA3",
DOI = "https://doi.org/10.1017/S0013091500022318",
ISSN = "0013-0915 (print), 1464-3839 (electronic)",
ISSN-L = "0013-0915",
MRclass = "46A40 (46B30 90C48)",
MRnumber = "760617",
MRreviewer = "I. Namioka",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1624/;
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=3076132",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Edinburgh Mathematical Society.
Series II",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PEM",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1984:CCO,
author = "J. M. Borwein and J.-P. Penot and M. Th{\'e}ra",
title = "Conjugate convex operators",
journal = j-J-MATH-ANAL-APPL,
volume = "102",
number = "2",
pages = "399--414",
year = "1984",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247X(84)90180-X",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "90C48 (46G99 49A50)",
MRnumber = "755971",
MRreviewer = "Christian Malivert",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1620/;
http://www.sciencedirect.com/science/article/pii/0022247X8490180X",
abstract = "Convex mappings from a locally convex space X into F.
= F \cup {+\infty } are considered, where F is an
ordered topological vector space and + \infty an
arbitrary greatest element adjoined to F. In view of
applications to the polarity theory of convex
operators, the possibility is investigated of
representing a convex mapping taking values in F. as a
supremum of continuous affine mappings.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1984:CHO,
author = "J. M. Borwein and P. B. Borwein",
title = "Cubic and higher order algorithms for $ \pi $",
journal = j-CAN-MATH-BULL,
volume = "27",
number = "4",
pages = "436--443",
month = dec,
year = "1984",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1984-067-7",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "11Y16 (33A25 65D20)",
MRnumber = "763041",
MRreviewer = "L. C. Eggan",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://cms.math.ca/cmb/v27/;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/canmathbull.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
URL = "http://docserver.carma.newcastle.edu.au/1622/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1984:DLM,
author = "J. M. Borwein and H. M. Str{\'o}jwas",
title = "Directionally {Lipschitzian} mappings on {Baire}
spaces",
journal = j-CAN-J-MATH,
volume = "36",
number = "1",
pages = "95--130",
year = "1984",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1984-008-7",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
MRclass = "49A52 (26A27 58C20 90C30 90C48)",
MRnumber = "733710",
MRreviewer = "Jean-Paul Penot",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1627/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics. Journal Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:1984:EAO,
author = "J. M. Borwein and P. B. Borwein",
title = "Explicit algebraic $n$ th order approximations to pi",
crossref = "Singh:1984:ATS",
volume = "136",
pages = "247--256",
year = "1984",
DOI = "https://doi.org/10.1007/978-94-009-6466-2_12",
MRclass = "65D20",
MRnumber = "786845",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
URL = "http://link.springer.com/chapter/10.1007/978-94-009-6466-2_12",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:1984:EEH,
author = "J. M. Borwein",
editor = "????",
booktitle = "APICS Proceedings",
title = "On the existence of eigenvalues for {Hermitian}
matrices",
publisher = "????",
address = "????",
pages = "1--5",
year = "1984",
DOI = "",
ISBN = "",
ISBN-13 = "",
LCCN = "",
bibdate = "Mon Aug 15 15:10:50 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:1984:EIA,
author = "J. M. Borwein and P. B. Borwein",
title = "Elliptic integrals and approximations to $ \pi $",
month = jan,
year = "1984",
bibdate = "Mon Nov 07 17:37:11 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Typescript, with 84-01 added by hand on cover page.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1984:GLC,
author = "J. M. Borwein",
title = "Generalized linear complementarity problems treated
without fixed-point theory",
journal = j-J-OPT-THEORY-APPL,
volume = "43",
number = "3",
pages = "343--356",
year = "1984",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00934459",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "90C33 (90C25)",
MRnumber = "750013",
MRreviewer = "Ikuyo Kaneko",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://link.springer.com/article/10.1007/BF00934459",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1984:HMM,
author = "J. M. Borwein and B. Richmond",
title = "How many matrices have roots?",
journal = j-CAN-J-MATH,
volume = "36",
number = "2",
pages = "286--299",
year = "1984",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1984-018-0",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
MRclass = "15A23",
MRnumber = "749985",
MRreviewer = "J. L. Brenner",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1628/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics. Journal Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1984:ICE,
author = "J. M. Borwein",
title = "An integral characterization of {Euclidean} space",
journal = j-BULL-AUSTRAL-MATH-SOC,
volume = "29",
number = "3",
pages = "357--364",
year = "1984",
CODEN = "ALNBAB",
DOI = "https://doi.org/10.1017/S0004972700021602",
ISSN = "0004-9727 (print), 1755-1633 (electronic)",
ISSN-L = "0004-9727",
MRclass = "46C10",
MRnumber = "748728",
MRreviewer = "M. M. Day",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1623/",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the Australian Mathematical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1984:NMB,
author = "Jon M. Borwein and Brailey Sims",
title = "Nonexpansive mappings on {Banach} lattices and related
topics",
journal = j-HOUSTON-J-MATH,
volume = "10",
number = "3",
pages = "339--356",
year = "1984",
CODEN = "HJMADZ",
ISSN = "0362-1588",
MRclass = "47H10 (46A40 46B20)",
MRnumber = "763236",
MRreviewer = "Gregory B. Passty",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "https://www.math.uh.edu/~hjm/restricted/archive/v010n3/0339BORWEIN.pdf",
acknowledgement = ack-nhfb,
fjournal = "Houston Journal of Mathematics",
journal-URL = "https://www.math.uh.edu/~hjm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1984:RCC,
author = "J. M. Borwein and P. B. Borwein",
title = "Reduced Complexity Calculation of Log",
number = "DALTR 84-01",
institution = "Department of Mathematics, Dalhousie University",
address = "Halifax, NS, Canada",
pages = "17",
month = jan,
year = "1984",
bibdate = "Mon Nov 07 17:37:11 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "Various reduced complexity methods for high precision
computation of the logarithm are investigated.",
acknowledgement = ack-nhfb,
keywords = "analytic complexity; arithmetic--geometric mean;
binary splitting; bit complexity; elliptic integrals;
Fast Fourier Transform; logarithms; operational
complexity; theta functions",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Typescript, with 84-01 added by hand on cover page.",
}
@Article{Borwein:1984:SCO,
author = "J. M. Borwein",
title = "Subgradients of convex operators",
journal = j-OPTIMIZATION,
volume = "15",
number = "2",
pages = "179--191",
year = "1984",
CODEN = "OPTZDQ",
DOI = "https://doi.org/10.1080/02331938408842921",
ISSN = "0323-3898",
ISSN-L = "0233-1934",
MRclass = "90C25 (65K05)",
MRnumber = "741284",
MRreviewer = "C. A. Botsaris",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Operationsforschung und Statistik Series
Optimization",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1984:SCS,
author = "J. M. Borwein and D. W. Tingley",
title = "On Supportless Convex Sets",
type = "Report",
number = "DALTR 84-04",
institution = "Department of Mathematics, Dalhousie University",
address = "Halifax, NS, Canada",
pages = "13",
year = "1984",
bibdate = "Tue Nov 08 15:45:14 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "We give some general constructions of supportless
convex subsets of normed spaces and pose a number of
open questions.",
acknowledgement = ack-nhfb,
keywords = "Bishop-Phelps Theorem; convex sets; support points",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1984:SRP,
author = "J. M. Borwein",
title = "Stability and Regular Points of Inequality Systems",
type = "Report",
number = "DALTR 84-02",
institution = "Department of Mathematics, Dalhousie University and
Carnegie-Mellon University",
address = "Halifax, NS, Canada and Pittsburgh, PA, USA",
pages = "67",
year = "1984",
bibdate = "Tue Nov 08 15:45:14 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "We undertake a general study of regular points of
Lipschitz and strictly differentiable mappings with
applications to tangent cone analysis, inversion
theorems, perturbed optimization problems and higher
order conditions.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1984:TCS,
author = "J. M. Borwein and P. B. Borwein",
title = "A tangent cone separation principle",
type = "Report",
number = "DALTR 84-03",
institution = "Department of Mathematics, Dalhousie University",
address = "Halifax, NS, Canada",
month = jan,
year = "1984",
bibdate = "Mon Nov 07 17:37:11 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Typescript, with DALTR added by hand on cover page
before typewritten 84-03.",
}
@Article{Borwein:1984:TKN,
author = "J. M. Borwein and J. W. Nieuwenhuis",
title = "Two kinds of normality in vector optimization",
journal = j-MATH-PROG,
volume = "28",
number = "2",
pages = "185--191",
year = "1984",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/BF02612358",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "90C31",
MRnumber = "733210",
MRreviewer = "M. Ma{\v{n}}as",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1626/;
http://link.springer.com/article/10.1007/BF02612358",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1985:ATG,
author = "Jonathan M. Borwein",
booktitle = "Infinite programming ({Cambridge}, 1984)",
title = "Alternative theorems for general complementarity
problems",
volume = "259",
publisher = pub-SV,
address = pub-SV:adr,
pages = "194--203",
year = "1985",
DOI = "https://doi.org/10.1007/978-3-642-46564-2_15",
MRclass = "90C33 (52A40)",
MRnumber = "824573",
MRreviewer = "J. Parida",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Lecture Notes in Econom. and Math. Systems",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1985:CLS,
author = "David Borwein and Jonathan M. Borwein and Keith F.
Taylor",
title = "Convergence of lattice sums and {Madelung}'s
constant",
journal = j-J-MATH-PHYS,
volume = "26",
number = "11",
pages = "2999--3009",
month = nov,
year = "1985",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.526675",
ISSN = "0022-2488",
ISSN-L = "0022-2488",
MRclass = "82A67 (82A60)",
MRnumber = "808518",
MRreviewer = "Pierre Moussa",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/1985JMP....26.2999B;
http://docserver.carma.newcastle.edu.au/1618/",
abstract = "The lattice sums involved in the definition of
Madelung's constant of an NaCl-type crystal lattice in
two or three dimensions are investigated. The
fundamental mathematical questions of convergence and
uniqueness of the sum of these, not absolutely
convergent, series are considered. It is shown that
some of the simplest direct sum methods converge and
some do not converge. In particular, the very common
method of expressing Madelung's constant by a series
obtained from expanding spheres does not converge. The
concept of analytic continuation of a complex function
to provide a basis for an unambiguous mathematical
definition of Madelung's constant is introduced. By
these means, the simple intuitive direct sum methods
and the powerful integral transformation methods, which
are based on theta function identities and the Mellin
transform, are brought together. A brief analysis of a
hexagonal lattice is also given.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1985:PSA,
author = "Jon Borwein and Anatole Beck",
title = "Problems and Solutions: Advanced Problems:
6491--6492",
journal = j-AMER-MATH-MONTHLY,
volume = "92",
number = "3",
pages = "217--217",
month = mar,
year = "1985",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2322884",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1540608",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/journals/00029890.htm;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib",
note = "See also \cite{Beck:1987:PSS,Borwein:1986:PSS}.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1985:PSS,
author = "J. Borwein",
title = "Problems and Solutions: Solutions of Advanced
Problems: 6430",
journal = j-AMER-MATH-MONTHLY,
volume = "92",
number = "2",
pages = "148--149",
month = feb,
year = "1985",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2322656",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1540590",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/journals/00029890.htm;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib",
note = "See also \cite{Borwein:1983:PSA}.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1985:SCS,
author = "J. M. Borwein and D. W. Tingley",
title = "On supportless convex sets",
journal = j-PROC-AM-MATH-SOC,
volume = "94",
number = "3",
pages = "471--476",
year = "1985",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.2307/2045238",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "46B20 (46A55 52A07)",
MRnumber = "787897",
MRreviewer = "N. T. Peck",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1619/",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1985:SMI,
author = "Jon Borwein",
title = "Some modular identities of {Ramanujan} useful in
approximating $ \pi $",
journal = j-PROC-AM-MATH-SOC,
volume = "95",
number = "3",
pages = "365--371",
month = nov,
year = "1985",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.2307/2045804",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "11F03 (11J72 41A25)",
MRnumber = "806072",
MRreviewer = "Bruce C. Berndt",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1616/;
http://www.jstor.org/stable/2045804",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1985:TA,
author = "J. M. Borwein and H. M. Str{\'o}jwas",
title = "Tangential approximations",
journal = j-NONLINEAR-ANAL,
volume = "9",
number = "12",
pages = "1347--1366",
year = "1985",
CODEN = "NOANDD",
DOI = "https://doi.org/10.1016/0362-546X(85)90095-1",
ISSN = "0362-546x (print), 1873-5215 (electronic)",
ISSN-L = "0362-546X",
MRclass = "90C48 (46A55 90C25)",
MRnumber = "820646",
MRreviewer = "Christian Malivert",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1617/;
http://www.sciencedirect.com/science/article/pii/0362546X85900951",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
keywords = "epi-Lipschitzian (compactly epi-Lipschitzian; Tangent
cones; tangentially regular) set at a point;
unsupportable space",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Honor:1985:DTR,
author = "R. B. Honor",
title = "Density and transitivity results on $ l^i n f t y $
and $ l^1 $",
journal = j-J-LOND-MATH-SOC-2,
volume = "S2-32",
number = "3",
pages = "521--527",
month = dec,
year = "1985",
CODEN = "JLMSAK",
DOI = "https://doi.org/10.1112/jlms/s2-32.3.521",
ISSN = "0024-6107 (print), 1469-7750 (electronic)",
ISSN-L = "0024-6107",
bibdate = "Fri Aug 12 15:21:25 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "The `author' is an acronym for the family names of
seven people: Heydar Radjavi, Jon Borwein, Don Hadwin,
Richard O'Brien, Eric Nordgren, Mehmet Orhon, and Peter
Rose.",
URL = "http://jlms.oxfordjournals.org/content/s2-32/3/521.full.pdf+html",
acknowledgement = ack-nhfb,
ajournal = "J. Lond. Math. Soc. (2)",
fjournal = "Journal of the London Mathematical Society (series
2)",
journal-URL = "http://jlms.oxfordjournals.org/content/by/year",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Adler:1986:PSS,
author = "Irving Adler and A. A. Jagers and J. M. Borwein",
title = "Problems and Solutions: Solutions of Elementary
Problems: {E2997}",
journal = j-AMER-MATH-MONTHLY,
volume = "93",
number = "4",
pages = "304--304",
month = apr,
year = "1986",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2323694",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1540849",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/journals/00029890.htm;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib",
note = "See also \cite{Asic:1983:PSE}.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1986:ECI,
author = "J. M. Borwein and P. B. Borwein",
title = "An explicit cubic iteration for $ \pi $",
journal = j-BIT,
volume = "26",
number = "1",
pages = "123--126",
month = mar,
year = "1986",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939368",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "11Y60 (65D20)",
MRnumber = "833837, 87e:11144",
MRreviewer = "Duncan A. Buell",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=1;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/bit.bib",
URL = "http://docserver.carma.newcastle.edu.au/1609/;
http://link.springer.com/article/10.1007/BF01939368;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=1&spage=123",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1986:FMT,
author = "J. M. Borwein and D. Zhuang",
title = "On {Fan}'s minimax theorem",
journal = j-MATH-PROG,
volume = "34",
number = "2",
pages = "232--234",
year = "1986",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/BF01580587",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "90C30 (90C48)",
MRnumber = "838482",
MRreviewer = "Marco Gaviano",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1608/;
http://link.springer.com/article/10.1007/BF01580587",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1986:GDO,
author = "Jonathan M. Borwein",
title = "Generic differentiability of order-bounded convex
operators",
journal = j-J-AUSTRAL-MATH-SOC-SER-B,
volume = "28",
number = "1",
pages = "22--29",
month = jul,
year = "1986",
CODEN = "JAMMDU",
DOI = "https://doi.org/10.1017/S0334270000005166",
ISSN = "0334-2700",
MRclass = "90C25 (46G05 90C48)",
MRnumber = "846780",
MRreviewer = "Christian Malivert",
bibdate = "Fri Sep 30 10:52:51 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1607/;
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=3973752",
acknowledgement = ack-nhfb,
fjournal = "Australian Mathematical Society. Journal. Series B.
Applied Mathematics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1986:LOC,
author = "J. M. Borwein and M. A. H. Dempster",
title = "The Linear Order Complementarity Problem",
type = "Report",
number = "DALTR 86-3",
institution = "Department of Mathematics, Statistics \& Computing
Science, Dalhousie University and Balliol College,
Oxford University",
address = "Halifax, NS, Canada and Oxford, England OX1 3BJ",
pages = "47",
month = jul,
year = "1986",
bibdate = "Tue Nov 08 15:45:14 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "The classical complementarity problem in Euclidean
space can be viewed alternatively as a variational
inequality or as a lattice orthogonality problem.
Generalizations of the former have been extensively
studied, but infinite dimensional analogues of the
latter have been largely ignored. Moreover, as we show,
many well known results about the classical
complementarity problem are more appropriately viewed
order-theoretically. This is particularly true of least
element solutions, which are central to the present
study of order complementarity in vector lattices.",
acknowledgement = ack-nhfb,
keywords = "(P) operators; (Z) operators; Banach lattices;
complementarity problems; Least elements; order
complementarity",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Revision of August 1985 original.",
}
@Article{Borwein:1986:MQC,
author = "J. M. Borwein and P. B. Borwein",
title = "More quadratically converging algorithms for $ \pi $",
journal = j-MATH-COMPUT,
volume = "46",
number = "173",
pages = "247--253",
month = jan,
year = "1986",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2008229",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20",
MRnumber = "815846, 87e:65014",
MRreviewer = "M. M. Chawla",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
URL = "http://docserver.carma.newcastle.edu.au/1614/",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
B0290Z (Other numerical methods); C4130 (Interpolation
and function approximation); C4190 (Other numerical
methods)",
corpsource = "Dalhousie Univ., Halifax, NS, Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "arithmetic--geometric mean iteration; complete
elliptic; convergence of numerical methods;
Gauss--Legendre iteration; geometry; integrals;
iterative; Legendre formula; methods; pi evaluation;
quadratically converging algorithms",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
treatment = "T Theoretical or Mathematical",
}
@Article{Borwein:1986:NAS,
author = "David Borwein and Jonathan M. Borwein",
title = "A Note on Alternating Series in Several Dimensions",
journal = j-AMER-MATH-MONTHLY,
volume = "93",
number = "7",
pages = "531--539",
month = aug # "\slash " # sep,
year = "1986",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2323026",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "40B05 (40A05)",
MRnumber = "856292, 87j:40008",
MRreviewer = "F. M{\'o}ricz",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/journals/00029890.htm;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib",
URL = "http://docserver.carma.newcastle.edu.au/1610/",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1986:NDC,
author = "J. M. Borwein",
title = "Norm duality for convex processes and applications",
journal = j-J-OPT-THEORY-APPL,
volume = "48",
number = "1",
pages = "53--64",
year = "1986",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00938589",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "90C25 (46N05)",
MRnumber = "825384",
MRreviewer = "Lionel Thibault",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Fourth symposium on nonlinear programming with data
perturbations.",
URL = "http://docserver.carma.newcastle.edu.au/1613/;
http://link.springer.com/article/10.1007/BF00938589",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1986:PAB,
author = "J. M. Borwein and H. M. Str{\'o}jwas",
title = "Proximal analysis and boundaries of closed sets in
{Banach} space. {I}. {Theory}",
journal = j-CAN-J-MATH,
volume = "38",
number = "2",
pages = "431--452",
year = "1986",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1986-022-4",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
MRclass = "90C48 (46B10 49A50 58C20)",
MRnumber = "833578",
MRreviewer = "Bruce D. Craven",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1611/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics. Journal Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1986:PMO,
author = "J. M. Borwein",
title = "Partially monotone operators and the generic
differentiability of convex-concave and biconvex
mappings",
journal = j-ISRAEL-J-MATH,
volume = "54",
number = "1",
pages = "42--50",
year = "1986",
CODEN = "ISJMAP",
DOI = "https://doi.org/10.1007/BF02764875",
ISSN = "0021-2172 (print), 1565-8511 (electronic)",
ISSN-L = "0021-2172",
MRclass = "90C48 (47H05 49A51 58C20)",
MRnumber = "852468",
MRreviewer = "Jean-Paul Penot",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1605/;
http://link.springer.com/article/10.1007/BF02764875",
acknowledgement = ack-nhfb,
fjournal = "Israel Journal of Mathematics",
journal-URL = "http://link.springer.com/journal/11856",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1986:PSS,
author = "Jon Borwein and William A. Newcomb",
title = "Problems and Solutions: Solutions of Advanced
Problems: 6491",
journal = j-AMER-MATH-MONTHLY,
volume = "93",
number = "10",
pages = "822--823",
year = "1986",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2322952",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1541009",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1986:SCQ,
author = "J. M. Borwein and H. Wolkowicz",
title = "A simple constraint qualification in
infinite-dimensional programming",
journal = j-MATH-PROG,
volume = "35",
number = "1",
pages = "83--96",
year = "1986",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/BF01589443",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "90C48",
MRnumber = "842636",
MRreviewer = "W. W. Breckner",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib",
URL = "http://docserver.carma.newcastle.edu.au/1606/;
http://link.springer.com/article/10.1007/BF01589443",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1986:SRP,
author = "J. M. Borwein",
title = "Stability and regular points of inequality systems",
journal = j-J-OPT-THEORY-APPL,
volume = "48",
number = "1",
pages = "9--52",
year = "1986",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00938588",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "58C20 (46N05 90C30 90C48)",
MRnumber = "825383",
MRreviewer = "Lionel Thibault",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Fourth symposium on nonlinear programming with data
perturbations.",
URL = "http://docserver.carma.newcastle.edu.au/1612/;
http://link.springer.com/article/10.1007/BF00938588",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1987:ACO,
author = "J. M. Borwein",
title = "Automatic continuity and openness of convex
relations",
journal = j-PROC-AM-MATH-SOC,
volume = "99",
number = "1",
pages = "49--55",
month = jan,
year = "1987",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.2307/2046269",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "46A55 (47H99)",
MRnumber = "866428",
MRreviewer = "Robert T. Vescan",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1604/;
http://www.jstor.org/stable/2046269",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:1987:CCM,
author = "J. M. Borwein",
booktitle = "{Recent Advances and Historical Development of Vector
Optimization}",
title = "Convex Cones, Minimality Notions, and Consequences",
publisher = pub-SV,
address = pub-SV:adr,
pages = "??--??",
year = "1987",
DOI = "https://doi.org/10.1007/978-3-642-46618-2_3",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-46618-2_3",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1987:CMN,
author = "J. M. Borwein",
booktitle = "Recent Advances and Historic Development of Vector
Optimization",
title = "Cones, minimality notions and consequences",
publisher = pub-SV,
address = pub-SV:adr,
pages = "62--85",
year = "1987",
bibdate = "Mon Aug 15 15:09:27 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1987:DRF,
author = "J. M. Borwein and S. P. Fitzpatrick and J. R. Giles",
title = "The differentiability of real functions on normed
linear space using generalized subgradients",
journal = j-J-MATH-ANAL-APPL,
volume = "128",
number = "2",
pages = "512--534",
year = "1987",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247X(87)90203-4",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "58C20 (26E15 46G05 49A52 90C48)",
MRnumber = "917385",
MRreviewer = "W. W. Breckner",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1598/;
http://www.sciencedirect.com/science/article/pii/0022247X87902034",
abstract = "The modification of the Clarke generalized
subdifferential due to Michel and Penot is a useful
tool in determining differentiability properties for
certain classes of real functions on a normed linear
space. The G{\^a}teaux differentiability of any real
function can be deduced from the G{\^a}teaux
differentiability of the norm if the function has a
directional derivative which attains a constant related
to its generalized directional derivative. For any
distance function on a space with uniformly G{\^a}teaux
differentiable norm, the Clarke and Michel-Penot
generalized subdifferentials at points off the set
reduce to the same object and this generates a
continuity characterization for G{\^a}teaux
differentiability. However, on a Banach space with
rotund dual, the Fr{\'e}chet differentiability of a
distance function implies that it is a convex function.
A mean value theorem for the modified generalized
subdifferential has implications for G{\^a}teaux
differentiability.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1987:EIE,
author = "J. M. Borwein and I. J. Zucker",
title = "Elliptic Integral Evaluation of the Gamma Function at
Values with Small Rational Denominators",
type = "Report",
institution = "Department of Mathematics, Statistics and Computing
Science, Dalhousie University and Department of
Physics, King's College",
address = "Halifax, NS B3H 3J5, Canada and London WC2, UK",
pages = "13",
day = "2",
month = sep,
year = "1987",
bibdate = "Fri Nov 11 06:50:29 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "We produce simplified evaluations of certain complete
elliptic integrals in terms of Gamma and Beta
functions. We also provide explicit quadratically
convergent recursions for quantities including $ \Gamma
(n / 4) $ and $ \Gamma (n / 6) $.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1987:ELL,
author = "Jonathan Michael Borwein",
title = "Epi-{Lipschitz}-like sets in {Banach} space: theorems
and examples",
journal = j-NONLINEAR-ANAL,
volume = "11",
number = "10",
pages = "1207--1217",
year = "1987",
CODEN = "NOANDD",
DOI = "https://doi.org/10.1016/0362-546X(87)90008-3",
ISSN = "0362-546x (print), 1873-5215 (electronic)",
ISSN-L = "0362-546X",
MRclass = "90C48 (46G99 58C20 90C25)",
MRnumber = "913679",
MRreviewer = "J. E. Spingarn",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1599/;
http://www.sciencedirect.com/science/article/pii/0362546X87900083",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
keywords = "differential inclusions; epi-Lipschitz-like sets;
Lipschitz-like functions; locally compact subgradients;
non-support points; Nonsmooth analysis; normal cones",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1987:ERT,
author = "J. M. Borwein and P. B. Borwein",
title = "Explicit {Ramanujan}-type approximations to pi of high
order",
journal = "Proceedings of the Indian Academy of Sciences ---
Mathematical Sciences",
volume = "97",
number = "1--3",
pages = "53--59",
year = "1987",
DOI = "https://doi.org/10.1007/BF02837813",
ISSN = "0253-4142 (print), 0973-7685 (electronic)",
ISSN-L = "0253-4142",
MRclass = "11Y60",
MRnumber = "983604",
MRreviewer = "D. H. Lehmer",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Centennial issue.",
URL = "http://link.springer.com/article/10.1007/BF02837813",
acknowledgement = ack-nhfb,
ajournal = "Proc. Indian Acad. Sci. Math. Sci.",
fjournal = "Indian Academy of Sciences. Proceedings. Mathematical
Sciences",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxyear = "1988",
}
@TechReport{Borwein:1987:ESE,
author = "D. Borwein and J. M. Borwein and R. Shail and I. J.
Zucker",
title = "Energy of Static Electron Lattices",
type = "Report",
institution = "University of Western Ontario and Department of
Mathematics, Statistics and Computing Science,
Dalhousie University and University of Surrey and
University of Surrey",
address = "London, ON N6A 3K7, Canada and Halifax, NS B3H 3J5,
Canada and Guildford, UK GU2 5XH and Guildford, UK GU2
5XH",
pages = "20",
day = "11",
month = sep,
year = "1987",
bibdate = "Fri Nov 11 06:54:37 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "A new approach to evaluating the static lattice energy
of any given Wigner lattice is proposed. The method is
much simpler than the traditional one and the results
are much faster to evaluate. The new approach is
applied to two-dimensional triangular lattices where it
is shown that the triangular lattice is more stable
than the square lattice. Three dimensional hexagonal
lattices are also investigated. In addition, we have
placed many of our considerations on a rigorous
mathematical footing.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Date recorded in ambiguous form 11/9/87; entry
Borwein:1988:CCJ has 31/12/88, suggesting that the
first number is the day.",
}
@Article{Borwein:1987:PAB,
author = "J. M. Borwein and H. M. Str{\'o}jwas",
title = "Proximal analysis and boundaries of closed sets in
{Banach} space. {II}. {Applications}",
journal = j-CAN-J-MATH,
volume = "39",
number = "2",
pages = "428--472",
year = "1987",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1987-019-4",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
MRclass = "46B20 (41A65 90C48)",
MRnumber = "899844",
MRreviewer = "Bruce D. Craven",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1600/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics. Journal Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Borwein:1987:PAS,
author = "Jonathan M. Borwein and Peter B. Borwein",
title = "Pi and the {AGM}: a Study in Analytic Number Theory
and Computational Complexity",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 414",
year = "1987",
ISBN = "0-471-83138-7, 0-471-31515-X (paperback)",
ISBN-13 = "978-0-471-83138-9, 978-0-471-31515-5 (paperback)",
LCCN = "QA241 .B774 1987",
MRclass = "11Y60 (68Q30)",
MRnumber = "877728",
MRreviewer = "H. London",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
z3950.loc.gov:7090/Voyager",
series = "Canadian Mathematical Society series of monographs and
advanced texts = Monographies et {\'e}tudes de la
Soci{\'e}t{\'e} math{\'e}matique du Canada",
abstract = "Critical Acclaim for Pi and the AGM: ``Fortunately we
have the Borwein's beautiful book \ldots{} explores in
the first five chapters the glorious world so dear to
Ramanujan \ldots{} would be a marvelous text book for a
graduate course.'' --- Bulletin of the American
Mathematical Society \\
``What am I to say about this quilt of a book? One is
reminded of Debussy who, on being asked by his harmony
teacher to explain what rules he was following as he
improvised at the piano, replied, ``Mon plaisir.'' The
authors are cultured mathematicians. They have selected
what has amused and intrigued them in the hope that it
will do the same for us. Frankly, I cannot think of a
more provocative and generous recipe for writing a book
\ldots{} (it) is cleanly, even beautifully written, and
attractively printed and composed. The book is unique.
I cannot think of any other book in print which
contains more than a smidgen of the material these
authors have included. --- SIAM Review \\
``If this subject begins to sound more interesting than
it did in the last newspaper article on 130 million
digits of Pi, I have partly succeeded. To succeed
completely I will have gotten you interested enough to
read the delightful and important book by the
Borweins.'' --- American Mathematical Monthly \\
``The authors are to be commended for their careful
presentation of much of the content of Ramanujan's
famous paper, 'Modular Equations and Approximations to
Pi'. This material has not heretofore appeared in book
form. However, more importantly, Ramanujan provided no
proofs for many of the claims that he made, and so the
authors provided many of the missing details \ldots{}
The Borweins, indeed have helped us find the right
roads.'' --- Mathematics of Computation",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Chinese edition 1995.",
subject = "Number theory; Computational complexity; Elliptic
functions; Pi",
tableofcontents = "Complete Elliptic Integrals and the
Arithmetic-Geometric Mean Iteration \\
Theta Functions and the Arithmetic-Geometric Mean
Iteration \\
Jacobi's Triple-Product and Some Number Theoretic
Applications \\
Higher Order Transformations \\
Modular Equations and Algebraic Approximations to $\pi$
\\
The Complexity of Algebraic Functions \\
Algorithms for the Elementary Functions \\
General Means and Iterations \\
Some Additional Applications \\
Other Approaches to the Elementary Functions \\
Pi \\
Bibliography \\
Symbol List \\
Index",
}
@Article{Borwein:1987:PNF,
author = "J. M. Borwein and J. R. Giles",
title = "The proximal normal formula in {Banach} space",
journal = j-TRANS-AM-MATH-SOC,
volume = "302",
number = "1",
pages = "371--381",
year = "1987",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/2000915",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "49A52 (46B20 46G05)",
MRnumber = "887515",
MRreviewer = "Gianfranco Bottaro",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1602/",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1987:RRA,
author = "J. M. Borwein and P. B. Borwein",
title = "{Ramanujan}'s rational and algebraic series for {$ 1 /
\pi $}",
journal = "J. Indian Math. Soc. (N.S.)",
volume = "51",
pages = "147--160 (1988)",
year = "1987",
CODEN = "JIMTA2",
ISSN = "0019-5839",
ISSN-L = "0019-5839",
MRclass = "11Y60 (33A30)",
MRnumber = "988313",
MRreviewer = "Herman J. J. te Riele",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Ramanujan Centennial issue.",
acknowledgement = ack-nhfb,
fjournal = "The Journal of the Indian Mathematical Society. New
Series",
journal-URL = "http://www.indianmathsociety.org.in/jims.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1987:SVPa,
author = "Jonathan M. Borwein and David Preiss",
title = "A smooth variational principle with applications to
subdifferentiability and to differentiability of convex
functions",
journal = j-TRANS-AM-MATH-SOC,
volume = "303",
number = "2",
pages = "517--527",
month = oct,
year = "1987",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/2000681",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "49A27 (46B20 46G05 49A51 49A52 58C20 90C25 90C48)",
MRnumber = "902782",
MRreviewer = "B. Mordukhovich",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1597/;
http://www.jstor.org/stable/2000681",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "According to \cite{Thera:2016:HSH}, this paper is the
first published {\em smooth variational principle}.",
}
@Article{Borwein:1987:UPW,
author = "J. M. Borwein and P. B. Borwein",
title = "Unsolved Problems: The Way of All Means",
journal = j-AMER-MATH-MONTHLY,
volume = "94",
number = "6",
pages = "519--522",
month = jun # "\slash " # jul,
year = "1987",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2322842",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1541118",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/journals/00029890.htm;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib",
URL = "http://www.jstor.org/stable/2322842",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Schoenberg:1987:APS,
author = "I. J. Schoenberg and Peter B. Borwein",
title = "Advanced Problems and Solutions: Solutions: 6501",
journal = j-AMER-MATH-MONTHLY,
volume = "94",
number = "4",
pages = "390--390",
month = apr,
year = "1987",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2323115",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/journals/00029890.htm;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib",
note = "See also \cite{Schoenberg:1985:PSA}.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Ward:1987:NCF,
author = "D. E. Ward and J. M. Borwein",
title = "Nonsmooth Calculus in Finite Dimensions",
journal = j-SIAM-J-CONTROL-OPTIM,
volume = "25",
number = "5",
pages = "1312--1340",
month = sep,
year = "1987",
CODEN = "SJCODC",
DOI = "https://doi.org/10.1137/0325072",
ISSN = "0363-0129 (print), 1095-7138 (electronic)",
ISSN-L = "0363-0129",
MRclass = "58C20 (46G05 49A52 90C48)",
MRnumber = "905047, 88m:58011",
MRreviewer = "A. B. N{\'e}meth",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICON/25/5;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/siamjcontroloptim.bib",
URL = "http://docserver.carma.newcastle.edu.au/1601/",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Control and Optimization",
journal-URL = "http://epubs.siam.org/sicon",
journalabr = "SIAM J Control Optim",
onlinedate = "September 1987",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Barzilai:1988:TPS,
author = "Jonathan Barzilai and Jonathan M. Borwein",
title = "Two-Point Step Size Gradient Methods",
journal = j-IMA-J-NUMER-ANAL,
volume = "8",
number = "1",
pages = "141--148",
year = "1988",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/8.1.141",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65K05",
MRnumber = "967848, 90h:65113",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "According to \cite{Thera:2016:HSH}, Google Scholar
says that this paper has been cited more than 1300
times [checked: 1378 times as of 02 January 2017].",
}
@Article{Ben-Tal:1988:DAM,
author = "A. Ben-Tal and J. M. Borwein and M. Teboulle",
title = "A dual approach to multidimensional {$ L_p $} spectral
estimation problems",
journal = j-SIAM-J-CONTROL-OPTIM,
volume = "26",
number = "4",
pages = "985--996",
year = "1988",
CODEN = "SJCODE",
DOI = "https://doi.org/10.1137/0326053",
ISSN = "0363-0129 (print), 1095-7138 (electronic)",
ISSN-L = "0363-0129",
MRclass = "49A55 (42A05 49D29 90C25 94A11)",
MRnumber = "948654",
MRreviewer = "Krzysztof C. Kiwiel",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Control and Optimization",
journal-URL = "http://epubs.siam.org/sicon",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Borowski:1988:DM,
author = "E. J. (Ephraim J.) Borowski and Jonathan M. Borwein",
title = "Dictionary of mathematics",
publisher = "Collins",
address = "London, UK",
pages = "xi + 659",
year = "1988",
ISBN = "0-00-434347-6 (paperback)",
ISBN-13 = "978-0-00-434347-1 (paperback)",
LCCN = "QA5",
bibdate = "Mon Oct 23 07:36:34 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "With contributions by J. F. Bowers.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "Mathematics; Dictionaries",
}
@TechReport{Borwein:1988:CCJ,
author = "J. M. Borwein and P. B. Borwein",
title = "A Cubic Counterpart of {Jacobi}'s Identity and the
{AGM}",
type = "Report",
institution = "Department of Mathematics, Statistics and Computing
Science, Dalhousie University",
address = "Halifax, NS B3H 3J5, Canada",
pages = "20",
day = "31",
month = dec,
year = "1988",
bibdate = "Fri Nov 11 07:03:04 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "We produce cubic analogues of Jacobi's celebrated
theta function identity and of the
arithmetic--geometric mean iteration of Gauss and
Legendre. The iteration in question is $ a_{n + 1} =
(a_n + 2 b_n) / 3 $ and $ b_{n + 1} = \sqrt
[3]{b_n((a_n^2 + a_n b_n + b_n^2) / 3)} $. The limit of
this iteration is identified in terms of the
hypergeometric function $_2 F_1 (1 / 3, 2 / 3; 1;
\cdot)$ which supports a particularly simple cubic
transformation.",
acknowledgement = ack-nhfb,
keywords = "$\pi$; arithmetic--geometric mean (AGM); cubic
transformations; generalised elliptic functions;
hypergeometric functions; mean iterations; theta
functions",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1988:CFF,
author = "J. M. Borwein and P. B. Borwein",
title = "On the Complexity of Familiar Functions and Numbers",
journal = j-SIAM-REVIEW,
volume = "30",
number = "4",
pages = "589--601",
month = dec,
year = "1988",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1030134",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "68Q25 (03D15 11Y16)",
MRnumber = "967961, 89k:68061",
MRreviewer = "Klaus W. Wagner",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "ACM Computing Archive CD-ROM database (1991);
Compendex database;
http://epubs.siam.org/toc/siread/30/4;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://docserver.carma.newcastle.edu.au/1593/;
http://www.jstor.org/stable/2030559",
abstract = "This paper examines low-complexity approximations to
familiar functions and numbers. The intent is to
suggest that it is possible to base a taxonomy of such
functions and numbers on their computational
complexity. A central theme is that traditional methods
of approximation are often very far from optimal, while
good or optimal methods are often very far from
obvious. For most functions, provably optimal methods
are not known; however the gap between what is known
and what is possible is often small. A considerable
number of open problems are posed and a number of
related examples are presented.",
acknowledgement = ack-nhfb,
affiliationaddress = "Halifax, NS, Can",
bibno = "58008",
catcode = "G.1.2; F.2.1; F.1.3",
classification = "921",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; F.2.1 Numerical Algorithms and Problems;
F.1.3 Complexity Classes",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
Complexity Classes",
fjournal = "SIAM Review. A Publication of the Society for
Industrial and Applied Mathematics",
genterm = "algorithms; theory; performance",
guideno = "1988-13907",
journal-URL = "http://epubs.siam.org/sirev",
journalabbrev = "SIAM Rev.",
journalabr = "SIAM Rev",
jrldate = "Dec. 1988",
keywords = "Algebraic Approximation; Approximation Theory;
Computation of Digits; Familiar Functions; Low
Complexity Approximation; Mathematical Techniques;
Rational Approximation; Reduced Complexity
Approximation",
onlinedate = "December 1988",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; F. Theory of Computation; F.1
COMPUTATION BY ABSTRACT DEVICES",
}
@Article{Borwein:1988:ESE,
author = "D. Borwein and J. M. Borwein and R. Shail and I. J.
Zucker",
title = "Energy of static electron lattices",
journal = j-J-PHYS-A,
volume = "21",
number = "7",
pages = "1519--1531",
month = apr,
year = "1988",
CODEN = "JPHAC5",
DOI = "https://doi.org/10.1088/0305-4470/21/7/015",
ISSN = "0305-4470 (print), 1361-6447 (electronic)",
ISSN-L = "0305-4470",
MRclass = "82A65 (81H99)",
MRnumber = "951042",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/1988JPhA...21.1519B;
http://docserver.carma.newcastle.edu.au/1592/;
http://stacks.iop.org/0305-4470/21/1519;
http://stacks.iop.org/0305-4470/21/i=7/a=015",
acknowledgement = ack-nhfb,
fjournal = "Journal of Physics. A. Mathematical and General",
journal-URL = "http://iopscience.iop.org/1751-8121",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1988:MRT,
author = "J. M. Borwein and P. B. Borwein",
booktitle = "{Ramanujan} revisited ({Urbana-Champaign, Ill.},
1987)",
title = "More {Ramanujan}-type series for {$ 1 / \pi $}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "359--374",
year = "1988",
MRclass = "11Y60",
MRnumber = "938974",
MRreviewer = "Duncan A. Buell",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1988:RP,
author = "Jonathan M. Borwein and Peter B. Borwein",
title = "{Ramanujan} and {Pi}",
journal = j-SCI-AMER,
volume = "258",
number = "2",
pages = "112--117",
month = feb,
year = "1988",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican0288-112",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/sciam1980.bib",
note = "Japanese edition (April 1988), Russian edition (April
1988), German edition (May 1988). Reprinted in
\cite{Borwein:1991:RP,Borwein:1996:SRZ,Borwein:2001:RP,Bailey:2016:PNG}.",
URL = "http://docserver.carma.newcastle.edu.au/1379/;
http://www.nature.com/scientificamerican/journal/v258/n2/pdf/scientificamerican0288-112.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxnewdata = "1998.01.30",
}
@Article{Borwein:1988:VNS,
author = "J. M. Borwein and D. M. Zhuang",
title = "Verifiable necessary and sufficient conditions for
openness and regularity of set-valued and single-valued
maps",
journal = j-J-MATH-ANAL-APPL,
volume = "134",
number = "2",
pages = "441--459",
year = "1988",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247X(88)90034-0",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "90C48 (54C60 58C20 90C25)",
MRnumber = "961349",
MRreviewer = "Jean-Paul Penot",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1594/;
http://www.sciencedirect.com/science/article/pii/0022247X88900340",
abstract = "We provide several equivalences to the regularity of
closed set-valued maps around a point in general metric
settings. In particular, an easy to verify approximate
openness notion is shown equivalent to regularity. A
simple specialization of our theorem strengthens
Frankowska's novel ``open mapping principle.''",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Deutsch:1988:PSSa,
author = "Emeric Deutsch and Jonathan M. Borwein and Paul Cull
and G. Behrendt",
title = "Problems and Solutions: Solutions of Elementary
Problems: {E3159}",
journal = j-AMER-MATH-MONTHLY,
volume = "95",
number = "6",
pages = "557--558",
month = jun # "\slash " # jul,
year = "1988",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2322769",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1541335",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/journals/00029890.htm;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib",
note = "See also \cite{Deutsch:1986:PSE}.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1989:ACL,
author = "D. Borwein and J. M. Borwein and R. Shail",
title = "Analysis of certain lattice sums",
journal = j-J-MATH-ANAL-APPL,
volume = "143",
number = "1",
pages = "126--137",
year = "1989",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247X(89)90032-2",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "82A67 (11M99)",
MRnumber = "1019453",
MRreviewer = "A. K. Rajagopal",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1589/;
http://www.sciencedirect.com/science/article/pii/0022247X89900322",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1989:ARM,
author = "J. M. Borwein and P. B. Borwein",
title = "Approximating $ \pi $ with {Ramanujan}'s modular
equations",
journal = j-ROCKY-MOUNTAIN-J-MATH,
volume = "19",
number = "1",
pages = "93--102",
year = "1989",
CODEN = "RMJMAE",
DOI = "https://doi.org/10.1216/RMJ-1989-19-1-93",
ISSN = "0035-7596 (print), 1945-3795 (electronic)",
ISSN-L = "0035-7596",
MRclass = "11Y35 (11F11 33E05)",
MRnumber = "1016163",
MRreviewer = "Bruce C. Berndt",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Constructive Function Theory---86 Conference
(Edmonton, AB, 1986).",
acknowledgement = ack-nhfb,
fjournal = "The Rocky Mountain Journal of Mathematics",
journal-URL = "http://projecteuclid.org/euclid.rmjm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1989:ENP,
author = "Jonathan M. Borwein and Simon Fitzpatrick",
title = "Existence of nearest points in {Banach} spaces",
journal = j-CAN-J-MATH,
volume = "41",
number = "4",
pages = "702--720",
year = "1989",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1989-032-7",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
MRclass = "46B20",
MRnumber = "1012624",
MRreviewer = "Mari{\'a}n Fabian",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1582/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics. Journal Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1989:HC,
author = "J. M. Borwein and H. M. Str{\'o}jwas",
title = "The hypertangent cone",
journal = j-NONLINEAR-ANAL,
volume = "13",
number = "2",
pages = "125--144",
year = "1989",
CODEN = "NOANDD",
DOI = "https://doi.org/10.1016/0362-546X(89)90039-4",
ISSN = "0362-546x (print), 1873-5215 (electronic)",
ISSN-L = "0362-546X",
MRclass = "90C30 (47H99 49A52)",
MRnumber = "979036",
MRreviewer = "D{\cftil{o}} V{\u{a}}n Lu{\cprime}u",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1588/;
http://www.sciencedirect.com/science/article/pii/0362546X89900394",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
keywords = "directional derivatives and subgradients;
directionally Lipschitzian functions; Discrete tangent
cone formulas; epi-Lipschitzian sets; inversion
theorems; mean value theorems",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1989:LBM,
author = "Jon Borwein and Simon Fitzpatrick",
title = "Local boundedness of monotone operators under minimal
hypotheses",
journal = j-BULL-AUSTRAL-MATH-SOC,
volume = "39",
number = "3",
pages = "439--441",
year = "1989",
CODEN = "ALNBAB",
DOI = "https://doi.org/10.1017/S000497270000335X",
ISSN = "0004-9727 (print), 1755-1633 (electronic)",
ISSN-L = "0004-9727",
MRclass = "47H05",
MRnumber = "995141",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1590/",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the Australian Mathematical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1989:LOC,
author = "J. M. Borwein and M. A. H. Dempster",
title = "The linear order complementarity problem",
journal = j-MATH-OP-RES,
volume = "14",
number = "3",
pages = "534--558",
year = "1989",
CODEN = "MOREDQ",
DOI = "https://doi.org/10.1287/moor.14.3.534",
ISSN = "0364-765x (print), 1526-5471 (electronic)",
ISSN-L = "0364-765X",
MRclass = "90C33 (47H99 90C48)",
MRnumber = "1008428",
MRreviewer = "Morgan A. Hanson",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1585/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Operations Research",
journal-URL = "http://pubsonline.informs.org/loi/moor",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1989:MCK,
author = "Jonathan M. Borwein and Simon Fitzpatrick",
title = "{Mosco} convergence and the {Kadec} property",
journal = j-PROC-AM-MATH-SOC,
volume = "106",
number = "3",
pages = "843--851",
year = "1989",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.2307/2047444",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "46B20 (52A05 54C60)",
MRnumber = "969313",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1584/",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1989:MI,
author = "J. M. Borwein and P. B. Borwein",
title = "On the Mean Iteration $ (a, b) \leftarrow \big (\frac
{a + 3b}{4}, \frac {\sqrt {ab} + b}{2} \big) $",
journal = j-MATH-COMPUT,
volume = "53",
number = "187",
pages = "311--326",
month = jul,
year = "1989",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2008364",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "30D05 (33A25)",
MRnumber = "968148, 90a:30075",
MRreviewer = "Carl C. Cowen",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
URL = "http://docserver.carma.newcastle.edu.au/1586/",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Dept. of Math. Stat. and Comput. Sci., Dalhousie
Univ., Halifax, NS, Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computation; convergence of numerical methods;
converging process; iterative methods; iterative
process; limit; mean iteration; nontrivial
identifications; quadratically; symbolic; uniformizing
parameters",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
treatment = "T Theoretical or Mathematical",
}
@Article{Borwein:1989:PEN,
author = "J. M. Borwein and P. B. Borwein and K. Dilcher",
title = "Pi, {Euler} numbers, and asymptotic expansions",
journal = j-AMER-MATH-MONTHLY,
volume = "96",
number = "8",
pages = "681--687",
year = "1989",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2324715",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "40A25 (11Y60 65B15)",
MRnumber = "1019148",
MRreviewer = "Bruce C. Berndt",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1583/",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1989:RME,
author = "J. M. Borwein and P. B. Borwein and D. H. Bailey",
title = "{Ramanujan}, modular equations, and approximations to
pi, or {How} to compute one billion digits of pi",
journal = j-AMER-MATH-MONTHLY,
volume = "96",
number = "3",
pages = "201--219",
month = mar,
year = "1989",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2325206",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11Y60 (01A60 11F03 33A25)",
MRnumber = "991866",
MRreviewer = "Herman J. J. te Riele",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Reprinted in \cite{Bailey:1997:RME}.",
URL = "http://docserver.carma.newcastle.edu.au/1587/;
http://www.jstor.org/stable/2325206",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Beer:1990:MCR,
author = "Gerald Beer and Jonathan M. Borwein",
title = "{Mosco} convergence and reflexivity",
journal = j-PROC-AM-MATH-SOC,
volume = "109",
number = "2",
pages = "427--436",
year = "1990",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.2307/2048005",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "46B10 (46B20 49J45 54B20 90C25)",
MRnumber = "1012924",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1581/",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1990:BRG,
author = "Jonathan Borwein",
title = "Book Review: {{\booktitle{Generalized Concavity}}
(Mordecai Avriel, Walter E. Diewert, Siegfried
Schaible, and Israel Zang)}",
journal = j-SIAM-REVIEW,
volume = "32",
number = "4",
pages = "689--690",
month = dec,
year = "1990",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1032140",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://epubs.siam.org/toc/siread/32/4;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "December 1990",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Borwein:1990:DRN,
author = "Jonathan Borwein and Peter B. Borwein",
title = "A dictionary of real numbers",
publisher = pub-WADSWORTH,
address = pub-WADSWORTH:adr,
pages = "viii + 424",
year = "1990",
DOI = "https://doi.org/10.1007/978-1-4615-8510-7",
ISBN = "0-534-12840-8",
ISBN-13 = "978-0-534-12840-1",
LCCN = "QA47.B625 1990",
MRclass = "11-00 (11Y60 11Y70)",
MRnumber = "1030542, 91g:11001",
MRreviewer = "Jeffrey O. Shallit",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
abstract = "This dictionary was designed for researchers who have
encountered various numbers computationally and want to
know if these numbers have simple form. The book is
structured as a reverse handbook of special function
values. It lists over 100,000 eight digit real numbers
in the interval (1,0) that arise as the first eight
digits of special values of familiar functions.",
acknowledgement = ack-nhfb,
keywords = "Maple",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
reviewer = "Jeffrey O. Shallit",
}
@Article{Borwein:1990:RCM,
author = "J. M. Borwein and P. B. Borwein",
booktitle = "Computational methods and function theory
({Valpara}{\'\i}so, 1989)",
title = "A remarkable cubic mean iteration",
journal = j-LECT-NOTES-MATH,
volume = "1435",
pages = "27--31",
year = "1990",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0087894",
ISBN = "3-540-52768-0 (print), 3-540-47139-1 (e-book)",
ISBN-13 = "978-3-540-52768-8 (print), 978-3-540-47139-4
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
MRclass = "33C05",
MRnumber = "1071759 (92b:33003)",
MRreviewer = "W. H. J. Fuchs",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/lnm1990.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0087894/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0087892",
book-URL = "http://www.springerlink.com/content/978-3-540-47139-4",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:1990:SDPa,
author = "J. M. Borwein",
editor = "Gustave Choquet and others",
booktitle = "S{\'e}minaire d'initiation {\`a} l'analyze",
title = "A survey of differentiability properties of convex,
{Lipschitz} and lsc functions",
publisher = "Publ. Math. Univ. Pierre et Marie Curie",
address = "Paris, France",
pages = "??--??",
year = "1990",
DOI = "",
ISBN = "",
ISBN-13 = "",
LCCN = "",
bibdate = "Mon Aug 15 15:02:04 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "https://carma.newcastle.edu.au/jon/Preprints/Books/CUP/CUPold/convsurvey.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
pagecount = "11",
}
@TechReport{Borwein:1990:SSH,
author = "J. M. Borwein and P. B. Borwein",
title = "Strange Series and High Precision Fraud",
type = "Preliminary Report",
institution = "Department of Mathematics, Statistics and Computing
Science, Dalhousie University",
address = "Halifax, NS B3H 3J5, Canada",
pages = "28",
day = "4",
month = sep,
year = "1990",
MRclass = "11A99, 11A55 (primary), 65B10 (secondary)",
bibdate = "Fri Nov 11 07:05:53 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "We present a variety of series some of which have
simple evaluations. Others appear to have simple
evaluations when computed to several hundred or even
several million digit precision, but are in fact
frauds. Many of these examples are based on series
whose terms involve digit sums and the integer part
function.",
acknowledgement = ack-nhfb,
keywords = "approximation; continued fractions; digit series;
generating functions; high precision estimates; integer
parts; irrationality; Mahler's series; modular
transformations; transcendence",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Date recorded in ambiguous form 4/9/90; entry
Borwein:1988:CCJ has 31/12/88, suggesting that the
first number is the day.",
}
@Article{Knuth:1990:PSSa,
author = "D. E. Knuth and Jungmin Woo and Hans Kappus and J. M.
Borwein and P. B. Borwein",
title = "Problems and Solutions: Solutions of Elementary
Problems: {E3335}",
journal = j-AMER-MATH-MONTHLY,
volume = "97",
number = "10",
pages = "927",
year = "1990",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1541809",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "2-8&origin=MSN;
http://links.jstor.org/sici?sici=0002-9890(199012)97:10<927:E>2.0.CO",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Knuth:1990:PSSb,
author = "D. E. Knuth and Jungmin Woo and Hans Kappus and J. M.
Borwein and P. B. Borwein",
title = "Problems and Solutions: Solutions of Elementary
Problems: {E3335}",
journal = j-AMER-MATH-MONTHLY,
volume = "97",
number = "10",
pages = "927",
year = "1990",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1541809",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "2-8&origin=MSN;
http://links.jstor.org/sici?sici=0002-9890(199012)97:10<927:E>2.0.CO",
acknowledgement = ack-nhfb,
fjournal = "The American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Knuth:1990:PSSc,
author = "D. E. Knuth and Jungmin Woo and Hans Kappus and J. M.
Borwein and P. B. Borwein",
title = "Problems and Solutions: Solutions of Elementary
Problems: {E3335}",
journal = j-AMER-MATH-MONTHLY,
volume = "97",
number = "10",
pages = "927--927",
month = dec,
year = "1990",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2324339",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/journals/00029890.htm;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib",
note = "See also \cite{Rudin:1989:PSE}.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Borowski:1991:HDM,
author = "E. J. Borowski and J. M. Borwein",
title = "The {HarperCollins} dictionary of mathematics",
publisher = "HarperPerennial",
address = "New York, NY, USA",
pages = "xii + 659",
year = "1991",
ISBN = "0-06-461019-5, 0-00-434347-6 (paperback)",
ISBN-13 = "978-0-06-461019-3, 978-0-00-434347-1 (paperback)",
MRclass = "00A20",
MRnumber = "1210061",
MRreviewer = "F. J. Papp",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "With the assistance of J. F. Bowers, A. Robertson and
M. McQuillan, Revised reprint of the 1988 original
\cite{Borowski:1988:DM}.",
URL = "http://docserver.carma.newcastle.edu.au/1738/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Translations: Chinese (1995), Indonesian (Erlanga
Penerbit, 1995), Italian (Gremese Editore) 1995, Arabic
(Academia International) 1991",
}
@Article{Borwein:1991:CBE,
author = "Jonathan M. Borwein and Adrian S. Lewis",
title = "Convergence of best entropy estimates",
journal = j-SIAM-J-OPT,
volume = "1",
number = "2",
pages = "191--205",
year = "1991",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/0801014",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
MRclass = "41A46 (28A20 28D20)",
MRnumber = "1098426",
MRreviewer = "Tiberiu Constantinescu",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1576/",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1991:CCJ,
author = "J. M. Borwein and P. B. Borwein",
title = "A cubic counterpart of {Jacobi}'s identity and the
{AGM}",
journal = j-TRANS-AM-MATH-SOC,
volume = "323",
number = "2",
pages = "691--701",
month = feb,
year = "1991",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/2001551",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "33C75 (11F11 11Y60 33C05)",
MRnumber = "1010408",
MRreviewer = "Bruce C. Berndt",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1578/;
http://www.jstor.org/stable/2001551",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1991:CMP,
author = "Jonathan M. Borwein and Adrian S. Lewis",
title = "On the convergence of moment problems",
journal = j-TRANS-AM-MATH-SOC,
volume = "325",
number = "1",
pages = "249--271",
month = may,
year = "1991",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/2001670",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "44A60 (90C90)",
MRnumber = "1008695",
MRreviewer = "Tiberiu Constantinescu",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1579/;
http://www.jstor.org/stable/2001670",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1991:DPC,
author = "Jonathan M. Borwein",
booktitle = "S{\'e}minaire d'Initiation {\`a} l'Analyse",
title = "Differentiability properties of convex, of
{Lipschitz}, and of semicontinuous mappings on {Banach}
spaces",
volume = "104(19)",
publisher = "Universit{\'e} de Paris VI",
address = "Paris, France",
pages = "1--11",
year = "1991",
MRclass = "46G05 (26E15 46B20 46N10 49J50 58C20)",
MRnumber = "1217320",
MRreviewer = "Saheb Dayal",
bibdate = "Fri Oct 13 14:59:36 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Publ. Math. Univ. Pierre et Marie Curie",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1991:DRE,
author = "Jonathan M. Borwein and Adrian S. Lewis",
title = "Duality relationships for entropy-like minimization
problems",
journal = j-SIAM-J-CONTROL-OPTIM,
volume = "29",
number = "2",
pages = "325--338",
year = "1991",
CODEN = "SJCODE",
DOI = "https://doi.org/10.1137/0329017",
ISSN = "0363-0129 (print), 1095-7138 (electronic)",
ISSN-L = "0363-0129",
MRclass = "49N15 (90C29 90C48)",
MRnumber = "1092730",
MRreviewer = "C. P. Ortlieb",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1577/",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Control and Optimization",
journal-URL = "http://epubs.siam.org/sicon",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1991:FPI,
author = "David Borwein and Jonathan Borwein",
title = "Fixed point iterations for real functions",
journal = j-J-MATH-ANAL-APPL,
volume = "157",
number = "1",
pages = "112--126",
year = "1991",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247X(91)90139-Q",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "65H05 (39B12)",
MRnumber = "1109446",
MRreviewer = "Joe Thrash",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0022247X9190139Q",
abstract = "We give proofs of general results on the computation
of fixed points of a continuous function or a Lipschitz
function on the real line. We also show how completely
these results can fail to hold in spaces of more than
one dimension.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1991:MCS,
author = "J. M. Borwein",
booktitle = "Fixed point theory and applications ({Marseille},
1989)",
title = "Minimal {CUSCOS} and subgradients of {Lipschitz}
functions",
volume = "252",
publisher = pub-LONGMAN,
address = pub-LONGMAN:adr,
pages = "57--81",
year = "1991",
MRclass = "46G05 (47H04 49J52)",
MRnumber = "1122818",
MRreviewer = "Doug Ward",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Pitman Res. Notes Math. Ser.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1991:MCU,
author = "Jonathan Borwein and Simon Fitzpatrick and Petar
Kenderov",
title = "Minimal convex uscos and monotone operators on small
sets",
journal = j-CAN-J-MATH,
volume = "43",
number = "3",
pages = "461--476",
year = "1991",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1991-028-5",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
MRclass = "46G05 (47H05 54C99)",
MRnumber = "1118004",
MRreviewer = "Doug Ward",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1573/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics. Journal Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1991:NR,
author = "Jonathan M. Borwein and G. de Barra",
title = "Nested radicals",
journal = j-AMER-MATH-MONTHLY,
volume = "98",
number = "8",
pages = "735--739",
year = "1991",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2324426",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11A99 (11Y55 39A10 40A05)",
MRnumber = "1130684",
MRreviewer = "Heinrich Rolletschek",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1580/",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1991:PCF,
author = "Jonathan M. Borwein and Adrian S. Lewis",
editor = "J-B. Baillon and M. Th{\'e}ra",
booktitle = "Fixed point theory and applications ({Marseille},
1989)",
title = "Practical conditions for {Fenchel} duality in infinite
dimensions",
volume = "252",
publisher = pub-LONGMAN,
address = pub-LONGMAN:adr,
pages = "83--89",
year = "1991",
MRclass = "49N15 (46G99 90C45 90C48)",
MRnumber = "1122819",
MRreviewer = "Blagun Kalchev",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Pitman Lecture Notes in Mathematics",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxseries = "Pitman Res. Notes Math. Ser.",
}
@InCollection{Borwein:1991:RP,
author = "Jonathan M. Borwein and Peter B. Borwein",
title = "{Ramanujan} and {Pi}",
crossref = "Ferris:1991:WTP",
pages = "647--659",
year = "1991",
bibdate = "Fri Aug 12 15:11:12 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1379/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1991:SEC,
author = "J. M. Borwein and D. M. Zhuang",
title = "Super efficiency in convex vector optimization",
journal = j-Z-OPER-RES,
volume = "35",
number = "3",
pages = "175--184",
year = "1991",
CODEN = "ZMMRFZ",
DOI = "https://doi.org/10.1007/BF01415905",
ISSN = "0340-9422",
MRclass = "90C29",
MRnumber = "1114290",
MRreviewer = "Emil Iwanow",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://link.springer.com/article/10.1007/BF01415905",
acknowledgement = ack-nhfb,
ajournal = "Z. Oper. Res.",
fjournal = "Zeitschrift f{\"u}r Operations Research. Mathematical
Methods of Operations Research",
journal-URL = "http://link.springer.com/journal/186",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1991:SGB,
author = "J. M. Borwein and P. B. Borwein",
title = "A singular genius: [book review] {{\booktitle{The Man
Who Knew Infinity. A Life of the Indian Genius
Ramanujan}}. Robert Kanigel, Scribner, New York, 1991.
x + 438 pp. + plates, \$27.95}",
journal = j-SCIENCE,
volume = "253",
number = "5017",
pages = "334--335",
day = "19",
month = jul,
year = "1991",
CODEN = "SCIEAS",
DOI = "https://doi.org/10.1126/science.253.5017.334",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Wed Aug 10 18:35:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.jstor.org/stable/2879085;
http://www.ncbi.nlm.nih.gov/pubmed/17794700",
acknowledgement = ack-nhfb,
fjournal = "Science (New York, NY)",
journal-URL = "http://www.sciencemag.org/archive/",
onlinedate = "19 July 1991",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
publisherinfo = "17794700 ER",
}
@Article{Borwein:1992:ASW,
author = "Jonathan Borwein and Shi Tuo Lou",
title = "Asymptotics of a sequence of {Witt} vectors",
journal = j-J-APPROX-THEORY,
volume = "69",
number = "3",
pages = "326--337",
year = "1992",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1016/0021-9045(92)90006-A",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "05A16 (05E05 05E10 13K05)",
MRnumber = "1164995",
MRreviewer = "Jiang Zeng",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1565/;
http://www.sciencedirect.com/science/article/pii/002190459290006A",
abstract = "We provide asymptotic and order information about the
Witt vectors and integers dn appearing in \prod n\le
111 + dn(tnn|)=(1-t)et.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1992:BRS,
author = "Jonathan Borwein",
title = "Book Review: {{\booktitle{Set-valued analysis}}, J-P.
Aubin and H. Frankowska}",
journal = j-BULL-AMS-N-S,
volume = "26",
number = "1",
pages = "157--160",
year = "1992",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0273-0979-1992-00246-X",
ISSN = "0273-0979 (print), 1088-9485 (electronic)",
ISSN-L = "0273-0979",
MRnumber = "1567970",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Society. Bulletin. New Series",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1992:DMF,
author = "Jonathan M. Borwein and Adrian S. Lewis",
title = "Decomposition of multivariate functions",
journal = j-CAN-J-MATH,
volume = "44",
number = "3",
pages = "463--482",
year = "1992",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1992-030-9",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
MRclass = "54C05 (05C38 08A45 22C05 26B40 28A20)",
MRnumber = "1176365",
MRreviewer = "Douglass L. Grant",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1569/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics. Journal Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1992:DPC,
author = "J. Borwein",
booktitle = "Optimization and nonlinear analysis ({Haifa}, 1990)",
title = "Differentiability properties of convex, of
{Lipschitz}, and of semicontinuous mappings on {Banach}
spaces",
volume = "244",
publisher = pub-LONGMAN,
address = pub-LONGMAN:adr,
pages = "39--52",
year = "1992",
MRclass = "49J50 (46B20 46G05 47H99)",
MRnumber = "1184630",
MRreviewer = "Julian Revalski",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Pitman Res. Notes Math. Ser.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1992:FEG,
author = "J. M. Borwein and I. J. Zucker",
title = "Fast evaluation of the gamma function for small
rational fractions using complete elliptic integrals of
the first kind",
journal = j-IMA-J-NUMER-ANAL,
volume = "12",
number = "4",
pages = "519--526",
year = "1992",
CODEN = "IJNADN",
DOI = "https://doi.org/10.1093/imanum/12.4.519",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65D20",
MRnumber = "1186733",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1992:KMI,
author = "Jonathan Borwein and Simeon Reich and Itai Shafrir",
title = "{Krasnosel'ski--Mann} iterations in normed spaces",
journal = j-CAN-MATH-BULL,
volume = "35",
number = "1",
pages = "21--28",
year = "1992",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1992-003-0",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "47H09 (47H10 47H17)",
MRnumber = "1157459",
MRreviewer = "Gregory B. Passty",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1992:MHP,
author = "Jonathan M. Borwein and Mark A. Limber",
title = "{Maple} as a High Precision Calculator",
journal = j-MAPLE-TECH-NEWS,
volume = "0",
number = "8",
pages = "39--44",
month = "Fall",
year = "1992",
ISSN = "1061-5733",
ISSN-L = "1061-5733",
bibdate = "Fri May 09 22:33:19 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/maple-tech.bib",
URL = "http://www.can.nl/Systems_and_Packages/Per_Purpose/General/Maple/mtn/mtn8.html",
acknowledgement = ack-nhfb,
fjournal = "Maple technical newsletter",
journal-URL = "http://web.mit.edu/maple/www/plibrary/mtn.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1992:PFCa,
author = "Jonathan M. Borwein and Adrian S. Lewis",
title = "Partially finite convex programming. {I}. {Quasi}
relative interiors and duality theory",
journal = j-MATH-PROG,
volume = "57",
number = "1--3",
pages = "15--48",
year = "1992",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/BF01581072",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "90C48 (49J15 65K05 90C25)",
MRnumber = "1167406",
MRreviewer = "M. Teboulle",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1571/;
http://link.springer.com/article/10.1007/BF01581072",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1992:PFCb,
author = "Jonathan M. Borwein and Adrian S. Lewis",
title = "Partially finite convex programming, {Part II}:
Explicit lattice models",
journal = j-MATH-PROG,
volume = "57",
number = "1--3",
pages = "49--83",
year = "1992",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/BF01581073",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "90C48 (49N15 65K05 90C25)",
MRnumber = "1167407",
MRreviewer = "M. Teboulle",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1572/;
http://link.springer.com/article/10.1007/BF01581073",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:1992:SDP,
author = "J. M. Borwein",
editor = "A. Ioffe and M. Marcus and S. Reich",
booktitle = "Optimization and Nonlinear Analysis: Proceedings of
the {Technion} Special Semester on Nonlinear Analysis
({Spring 1990})",
title = "A survey of differentiability properties of convex,
{Lipschitz} and lsc functions",
publisher = "Longman",
address = "Essex, UK",
pages = "39--52",
year = "1992",
DOI = "",
ISBN = "",
ISBN-13 = "",
LCCN = "",
bibdate = "Mon Aug 15 14:55:03 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1992:SEC,
author = "J. M. Borwein and A. {Ben Tal} and M. Teboulle",
booktitle = "Systems and Management Science by extremal methods:
research honoring {Abraham Charnes} at age 70",
title = "Spectral estimation via convex programming",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "275--290",
year = "1992",
DOI = "",
ISBN = "",
ISBN-13 = "",
LCCN = "",
bibdate = "Mon Aug 15 14:57:23 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1992:SOC,
author = "Jonathan Borwein and Peter B. Borwein",
title = "Some Observations on Computer Aided Analysis",
journal = j-NAMS,
volume = "39",
number = "8",
pages = "825--829",
year = "1992",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "No journal online archives before 1995.",
}
@Article{Borwein:1992:SSH,
author = "J. M. Borwein and P. B. Borwein",
title = "Strange Series and High Precision Fraud",
journal = j-AMER-MATH-MONTHLY,
volume = "99",
number = "7",
pages = "622--640",
month = aug # "\slash " # sep,
year = "1992",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2324993",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "40-01 (40A05 40A25)",
MRnumber = "1176589, 93f:40001",
MRreviewer = "John A. Fridy",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/journals/00029890.htm;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1992:STS,
author = "J. M. Borwein and M. Th{\'e}ra",
title = "Sandwich theorems for semicontinuous operators",
journal = j-CAN-MATH-BULL,
volume = "35",
number = "4",
pages = "463--474",
year = "1992",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1992-061-7",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "54C08 (46A99 54C60 54C65 54F05)",
MRnumber = "1191505",
MRreviewer = "P. Maritz",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Cook:1992:PSS,
author = "Matthew Cook and Walther Janous and Marcin E. Kuczma
and David Borwein",
title = "Problems and Solutions: Solutions of Elementary
Problems: {E3388}",
journal = j-AMER-MATH-MONTHLY,
volume = "99",
number = "1",
pages = "69--70",
month = jan,
year = "1992",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2324561",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/journals/00029890.htm;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib",
note = "See also \cite{Sturm:1990:PSE}.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bauschke:1993:CNA,
author = "H. H. Bauschke and J. M. Borwein",
title = "On the convergence of {von Neumann}'s alternating
projection algorithm for two sets",
journal = j-SET-VALUED-ANAL,
volume = "1",
number = "2",
pages = "185--212",
year = "1993",
CODEN = "SVANEG",
DOI = "https://doi.org/10.1007/BF01027691",
ISSN = "0927-6947 (print), 1572-932X (electronic)",
ISSN-L = "0927-6947",
MRclass = "65J05 (41A65 47H17 65K10)",
MRnumber = "1239403",
MRreviewer = "F. Deutsch",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1555/;
http://link.springer.com/article/10.1007/BF01027691",
acknowledgement = ack-nhfb,
fjournal = "Set-Valued Analysis. An International Journal Devoted
to the Theory of Multifunctions and its Applications",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Beer:1993:MSC,
author = "Gerald Beer and Jonathan M. Borwein",
title = "{Mosco} and Slice Convergence of Level Sets and Graphs
of Linear Functionals",
journal = j-J-MATH-ANAL-APPL,
volume = "175",
number = "1",
pages = "53--67",
year = "1993",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1006/jmaa.1993.1151",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "46B99 (46N10 49J45 54A20)",
MRnumber = "1216744",
MRreviewer = "Constantin Z{\u{a}}linescu",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1562/;
http://www.sciencedirect.com/science/article/pii/S0022247X83711510",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:1993:ASS,
author = "J. M. Borwein",
title = "{Asplund} spaces are sequentially reflexive",
year = "1993",
bibdate = "Fri Aug 12 14:17:01 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Accepted for publication in the Canadian Journal of
Mathematics, but withdrawn and merged with another
paper. Jon Borwein recorded that as publication number
121, but because the article numbers changed with each
update of his CV, that number has long been
incorrect.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Research Report CORR 91-14.",
}
@Article{Borwein:1993:CDS,
author = "Jonathan M. Borwein and Adrian S. Lewis",
title = "Convergence of decreasing sequences of convex sets in
nonreflexive {Banach} spaces",
journal = j-SET-VALUED-ANAL,
volume = "1",
number = "4",
pages = "355--363",
year = "1993",
CODEN = "SVANEG",
DOI = "https://doi.org/10.1007/BF01027825",
ISSN = "0927-6947 (print), 1572-932x (electronic)",
ISSN-L = "0927-6947",
MRclass = "49J45 (46N10)",
MRnumber = "1267202",
MRreviewer = "Roberto Lucchetti",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1551/",
acknowledgement = ack-nhfb,
fjournal = "Set-Valued Analysis. An International Journal Devoted
to the Theory of Multifunctions and its Applications",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:1993:CEU,
author = "J. M. Borwein and R. K. Goodrich and M. A. Limber",
title = "A comparison of entropies in the underdetermined
moment problem",
month = may,
year = "1993",
bibdate = "Tue Aug 16 10:06:18 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1993:CFH,
author = "J. M. Borwein and M. Fabi{\'a}n",
title = "On convex functions having points of {G{\^a}teaux}
differentiability which are not points of {Fr}{\'e}chet
differentiability",
journal = j-CAN-J-MATH,
volume = "45",
number = "6",
pages = "1121--1134",
year = "1993",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1993-062-8",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
MRclass = "46B20 (46B03)",
MRnumber = "1247537",
MRreviewer = "Gilles Godefroy",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1552/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics. Journal Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1993:CNT,
author = "J. M. Borwein and P. B. Borwein",
title = "Class number three {Ramanujan} type series for $ 1 /
\pi $",
journal = j-J-COMPUT-APPL-MATH,
volume = "46",
number = "1--2",
pages = "281--290",
day = "14",
month = jun,
year = "1993",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(93)90302-R",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "11Y60 (11R11)",
MRnumber = "1222488",
MRreviewer = "Andrew Granville",
bibdate = "Sat Feb 25 12:20:57 MST 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
note = "Computational complex analysis.",
URL = "http://docserver.carma.newcastle.edu.au/1560/;
http://www.sciencedirect.com/science/article/pii/037704279390302R",
abstract = "There is a class of remarkable series for $ 1 / \pi $
of the form $ \sqrt {-C^3} / \pi = \sum_{n = 0}^\infty
\frac {A + n B}{C^{3 n}} \frac {(6n)!}{(3n)!(n!)^3} $
where $A$, $B$, $C$ are certain algebraic numbers.
These were first examined by Ramanujan. These examples
arise by computing singular invariants for j and the
constants involved will have degree equal to the class
number of the associated imaginary quadratic field. Our
intention is compute all such class number three
examples. The largest such example, with discriminant $
- 907$, adds $ 37$ additional digit accuracy per term.
A class number four example with discriminant $ 1555$
gives $ 50$ digits per term.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "class number; pi; Ramanujan; series",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1993:DKK,
author = "J. M. Borwein and J. Vanderwerff",
title = "Dual {Kadec--Klee} norms and the relationships between
{Wijsman}, slice and {Mosco} convergence",
journal = "ArXiv Mathematics e-prints",
month = feb,
year = "1993",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/1993math......2212B",
abstract = "In this paper, we completely settle several of the
open questions regarding the relationships between the
three most fundamental forms of set convergence. In
particular, it is shown that Wijsman and slice
convergence coincide precisely when the weak star and
norm topologies agree on the dual sphere. Consequently,
a weakly compactly generated Banach space admits a
dense set of norms for which Wijsman and slice
convergence coincide if and only if it is an Asplund
space. We also show that Wijsman convergence implies
Mosco convergence precisely when the weak star and
Mackey topologies coincide on the dual sphere. A
corollary of these results is that given a fixed norm
on an Asplund space, Wijsman and slice convergence
coincide if and only if Wijsman convergence implies
Mosco convergence.",
acknowledgement = ack-nhfb,
eprint = "math/9302212",
keywords = "Mathematics - Functional Analysis, 46B",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1993:FME,
author = "Jonathan M. Borwein",
title = "On the failure of maximum entropy reconstruction for
{Fredholm} equations and other infinite systems",
journal = j-MATH-PROG,
volume = "61",
number = "2, Ser. A",
pages = "251--261",
year = "1993",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/BF01582150",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "94A12 (45B05 47N99 90C48)",
MRnumber = "1240460",
MRreviewer = "Henry Wolkowicz",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1559/",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1993:GFI,
author = "J. M. Borwein and P. B. Borwein",
title = "On the generating function of the integer part: $ [n
\alpha + \gamma] $",
journal = j-J-NUMBER-THEORY,
volume = "43",
number = "3",
pages = "293--318",
year = "1993",
CODEN = "JNUTA9",
DOI = "https://doi.org/10.1006/jnth.1993.1023",
ISSN = "0022-314x (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
MRclass = "11J70 (11J91)",
MRnumber = "1212686",
MRreviewer = "A. J. van der Poorten",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1564/;
http://www.sciencedirect.com/science/article/pii/S0022314X83710231",
abstract = "We show that [long displayed formula]. Here $ p_n $
and $ q_n $ are the numerators and denominators of the
convergents of the continued fraction expansion of $
\alpha $ and $ t^n $ and $ s^n $ are particular
algorithmically generated sequences of best
approximates for the non-homogeneous Diophantine
approximation problem of minimizing $ |n \alpha +
\gamma - m| $. This generalizes results of B{\"o}hmer
and Mahler, who considered the special case where $
\gamma = 0 $. This representation allows us to easily
derive various transcendence results. For example, $
\sum^\infty_{n = 1} [n e + 12] / (2 n) $ is a Liouville
number. Indeed the first series is Liouville for
rational $z$, $ w \subset [ - 1, 1]$ with $ |z w| \neq
1$ provided $ \alpha $ has unbounded continued fraction
expansion. A second application, which generalizes a
theorem originally due to Lord Raleigh, is to give a
new proof of a theorem of Fraenkel, namely $ [n \alpha
+ \gamma]^\infty_{n = 1}$ and $ [n \alpha \prime +
\gamma \prime]^\infty_{n = 1}$ partition the
non-negative integers if and only if $ 1 / \alpha + 1 /
\alpha \prime = 1$ and $ \gamma / \alpha + \gamma
\prime / \alpha \prime = 0$ (provided some sign and
integer independence conditions are placed on $ \alpha
$, $ \beta $, $ \gamma $, $ \gamma \prime $). The
analysis which leads to the results is quite delicate
and rests heavily on a functional equation for $G$. For
this a natural generalization of the simple continued
fraction to Kronecker's forms $ |n \alpha + \gamma -
m|$ is required.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Number Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/0022314X",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1993:GSO,
author = "J. M. Borwein and M. Fabi{\'a}n",
title = "On generic second-order {G{\^a}teaux}
differentiability",
journal = j-NONLINEAR-ANAL,
volume = "20",
number = "12",
pages = "1373--1382",
year = "1993",
CODEN = "NOANDD",
DOI = "https://doi.org/10.1016/0362-546X(93)90166-P",
ISSN = "0362-546x (print), 1873-5215 (electronic)",
ISSN-L = "0362-546X",
MRclass = "46G05 (26E15 49J50 58C20)",
MRnumber = "1225345",
MRreviewer = "Marcin Studniarski",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1563/;
http://www.sciencedirect.com/science/article/pii/0362546X9390166P",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
keywords = "residual space; second-order difference quotient;
Separable space; twice G{\^a}teaux differentiability",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Research Report CORR 91-18.",
}
@Article{Borwein:1993:HAA,
author = "J. Borwein and P. Borwein and F. Garvan",
title = "Hypergeometric analogues of the arithmetic--geometric
mean iteration",
journal = j-CONST-APPROX,
volume = "9",
number = "4",
pages = "509--523",
year = "1993",
DOI = "https://doi.org/10.1007/BF01204654",
ISSN = "0176-4276 (print), 1432-0940 (electronic)",
ISSN-L = "0176-4276",
MRclass = "33C05",
MRnumber = "1237931",
MRreviewer = "Bruce C. Berndt",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1556/;
http://link.springer.com/article/10.1007/BF01204654",
acknowledgement = ack-nhfb,
fjournal = "Constructive Approximation. An International Journal
for Approximations and Expansions",
journal-URL = "http://link.springer.com/journal/365",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1993:ICM,
author = "Jonathan M. Borwein and Peter B. Borwein",
title = "Inequalities for Compound Mean Iterations with
Logarithmic Asymptotes",
journal = j-J-MATH-ANAL-APPL,
volume = "177",
number = "2",
pages = "572--582",
year = "1993",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1006/jmaa.1993.1278",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "33B99",
MRnumber = "1231502",
MRreviewer = "P. Anandani",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1553/;
http://www.sciencedirect.com/science/article/pii/S0022247X83712783",
abstract = "We consider the compound means arising as limits from
the arithmetic--geometric mean iteration and related
iterations. Each of these iterations possesses a
logarithmic asymptote. We show that these limit means
satisfy very precise inequalities. These can be deduced
in a quite uniform fashion from a `comparison lemma'
for compound means.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1993:LLFa,
author = "J. M. Borwein and M. Fabian and J. Vanderwerff",
title = "Locally {Lipschitz} Functions and Bornological
Derivatives",
journal = "ArXiv Mathematics e-prints",
month = feb,
year = "1993",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/1993math......2211B;
http://docserver.carma.newcastle.edu.au/69/",
abstract = "We study the relationships between G{\^a}teaux, weak
Hadamard and Frechet differentiability and their
bornologies for Lipschitz and for convex functions. In
particular, Frechet and weak Hadamard differentiability
coincide for all Lipschitz functions if and only if the
space is reflexive (an earlier paper of the first two
authors shows that these two notions of
differentiability coincide for continuous convex
functions if and only if the space does not contain a
copy of $ \ell_1$). We also examine when G{\^a}teaux
and weak Hadamard differentiability coincide for
continuous convex functions. For instance, spaces with
the Dunford--Pettis (Schur) property can be
characterized by the coincidence of G{\^a}teaux and
weak Hadamard (Frechet) differentiability for dual
norms.",
acknowledgement = ack-nhfb,
eprint = "math/9302211",
keywords = "Mathematics - Functional Analysis, 46B",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1993:LLFb,
author = "Jonathan M. Borwein and Marian Fabian and Jon
Vanderwerff",
title = "Locally {Lipschitz} functions and bornological
derivatives",
type = "CECM Research Report",
number = "93:012",
institution = inst-CECM,
address = inst-CECM:adr,
month = nov,
year = "1993",
bibdate = "Tue Aug 16 10:06:43 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/69/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1993:MMB,
author = "Jonathan M. Borwein and Peter B. Borwein",
title = "Mathematical Malaises: Book Review: {{\booktitle{Pi in
the sky: counting, thinking and being}}, John D.
Barrow. Clarendon (Oxford University Press), New York,
1992. xii, 317 pp., illus. \$25}",
journal = j-SCIENCE,
volume = "259",
number = "5103",
pages = "1928--1930",
day = "26",
month = mar,
year = "1993",
CODEN = "SCIEAS",
DOI = "https://doi.org/10.1126/science.259.5103.1928",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Sat Sep 03 09:11:44 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.ncbi.nlm.nih.gov/pubmed/17836254",
acknowledgement = ack-nhfb,
fjournal = "Science (New York, N.Y.)",
journal-URL = "http://www.sciencemag.org/archive/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
report-number = "Borwein, Jonathan/A-6082-2009",
}
@Article{Borwein:1993:PFP,
author = "Jonathan M. Borwein and Adrian S. Lewis",
title = "Partially-finite programming in {$ L_1 $} and the
existence of maximum entropy estimates",
journal = j-SIAM-J-OPT,
volume = "3",
number = "2",
pages = "248--267",
year = "1993",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/0803012",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
MRclass = "90C48 (49N15 65K05)",
MRnumber = "1215444",
MRreviewer = "M. Teboulle",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1558/",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1993:PSPa,
author = "Jonathan M. Borwein",
title = "Problems and Solutions: Problems: 10281",
journal = j-AMER-MATH-MONTHLY,
volume = "100",
number = "1",
pages = "76--77",
month = jan,
year = "1993",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2324828",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/journals/00029890.htm;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1993:PSPb,
author = "David Borwein and Jonathan Borwein",
title = "Problems and Solutions: Problems: 10335",
journal = j-AMER-MATH-MONTHLY,
volume = "100",
number = "8",
pages = "796--798",
month = oct,
year = "1993",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2324793",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/journals/00029890.htm;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:1993:SCR,
author = "Jonathan M. Borwein and Adrian S. Lewis",
editor = "A. Mohammad-Djafari and G. Demoments",
booktitle = "Maximum entropy and {Bayesian} methods ({Paris},
1992)",
title = "A Survey of Convergence Results for Maximum Entropy
Methods",
volume = "53",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "39--48",
year = "1993",
DOI = "https://doi.org/10.1007/978-94-017-2217-9_5",
MRclass = "49J45 (41A30 42A10)",
MRnumber = "1269789",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Fund. Theories Phys.",
URL = "http://link.springer.com/chapter/10.1007/978-94-017-2217-9_5",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Research Report CORR 92-32.",
}
@Article{Borwein:1993:SEV,
author = "J. M. Borwein and D. Zhuang",
title = "Super efficiency in vector optimization",
journal = j-TRANS-AM-MATH-SOC,
volume = "338",
number = "1",
pages = "105--122",
year = "1993",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/2154446",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "90C29 (52A41)",
MRnumber = "1098432",
MRreviewer = "Bernard Lemaire",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1993:WHS,
author = "Jonathan M. Borwein and Simon Fitzpatrick",
title = "A weak {Hadamard} smooth renorming of {$ L_1 (\Omega,
\mu) $}",
journal = j-CAN-MATH-BULL,
volume = "36",
number = "4",
pages = "407--413",
year = "1993",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1993-055-5",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "46B25 (46B03 46B20 46E30)",
MRnumber = "1245313",
MRreviewer = "W. A. J. Luxemburg",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://cms.math.ca/10.4153/CMB-1993-055-5;
http://docserver.carma.newcastle.edu.au/1554/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Byerly:1993:PSP,
author = "Robert E. Byerly and Murray S. Klamkin and A. Liu and
Stephen M. {Gagola, Jr.} and L. E. Mattics and Raphael
M. Robinson and M. Al-Ahmar and Donald E. Knuth and
Jonathan M. Borwein",
title = "Problems and Solutions: Problems: 10274--10281",
journal = j-AMER-MATH-MONTHLY,
volume = "100",
number = "1",
pages = "75--77",
year = "1993",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2324823",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1542259",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Hirschhorn:1993:CAJ,
author = "Michael Hirschhorn and Frank Garvan and Jon Borwein",
title = "Cubic analogues of the {Jacobian} theta function {$
\theta (z, q) $}",
journal = j-CAN-J-MATH,
volume = "45",
number = "4",
pages = "673--694",
month = "????",
year = "1993",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1993-038-2",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
MRclass = "33D10 (11F27)",
MRnumber = "1227653",
MRreviewer = "Bruce C. Berndt",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://cms.math.ca/cjm/v45/;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/canjmath1990.bib",
URL = "http://docserver.carma.newcastle.edu.au/1557/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics = Journal canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Richter:1993:PSP,
author = "R. Bruce Richter and Josef Siran and Carl Pomerance
and Kiran S. Kedlaya and Michael Golomb and John Sarli
and David Borwein and Jonathan Borwein and Ignacy I.
Kotlarski and Horst Alzer",
title = "Problems and Solutions: Problems: 10330--10337",
journal = j-AMER-MATH-MONTHLY,
volume = "100",
number = "8",
pages = "796--798",
year = "1993",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2324792",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1542408",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:1994:EEE,
author = "David H. Bailey and Jonathan M. Borwein and Roland
Girgensohn",
title = "Experimental evaluation of {Euler} sums",
journal = j-EXP-MATH,
volume = "3",
number = "1",
pages = "17--30",
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.1994.10504573",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11Y60",
MRnumber = "1302815",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://docserver.carma.newcastle.edu.au/60/;
http://projecteuclid.org/euclid.em/1062621000",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bauschke:1994:DAP,
author = "H. H. Bauschke and J. M. Borwein",
title = "{Dykstra}'s alternating projection algorithm for two
sets",
journal = j-J-APPROX-THEORY,
volume = "79",
number = "3",
pages = "418--443",
year = "1994",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1006/jath.1994.1136",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "41A65 (46N10 47N10)",
MRnumber = "1305442",
MRreviewer = "F. Deutsch",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1543/;
http://www.sciencedirect.com/science/article/pii/S0021904584711361",
abstract = "We analyze Dykstra's algorithm for two arbitrary
closed convex sets in a Hilbert space. Our technique
also applies to von Neumann's algorithm. Various
convergence results follow. An example allows one to
compare qualitative and quantitative behaviour of the
two algorithms. We discuss the case of finitely many
sets.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:CMI,
author = "Jonathan Borwein",
title = "A convergent mean iteration: a proof that {$ x_n
\coloneq M(x_{n - 1}, x_{n - 2}, \cdots, x_{n - k}) $}
converges",
journal = j-AEQUATIONES-MATHEMATICAE,
volume = "47",
number = "1",
pages = "115--118",
year = "1994",
CODEN = "AEMABN",
DOI = "https://doi.org/10.1007/BF01838145",
ISSN = "0001-9054 (print), 1420-8903 (electronic)",
ISSN-L = "0001-9054",
MRclass = "39B12",
MRnumber = "1251136",
MRreviewer = "Shigeru Haruki",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1541/",
acknowledgement = ack-nhfb,
fjournal = "Aequationes Mathematicae",
journal-URL = "http://link.springer.com/journal/10",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:DKK,
author = "Jon Borwein and Jon Vanderwerff",
title = "Dual {Kadec--Klee} norms and the relationships between
{Wijsman}, slice, and {Mosco} convergence",
journal = j-MICH-MATH-J,
volume = "41",
number = "2",
pages = "371--387",
year = "1994",
CODEN = "MIMJA5",
DOI = "https://doi.org/10.1307/mmj/1029005003",
ISSN = "0026-2285 (print), 1945-2365 (electronic)",
ISSN-L = "0026-2285",
MRclass = "46B10 (46B20 46N10 49J45 54B20)",
MRnumber = "1278442",
MRreviewer = "Simon Fitzpatrick",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "The Michigan Mathematical Journal",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxtitle = "{Mosco}, {Wijsman} and slice convergence in
nonreflexive {Banach} spaces",
}
@Article{Borwein:1994:ECFa,
author = "Jon Borwein and Simon Fitzpatrick and Jon
Vanderwerff",
title = "Examples of convex functions and classifications of
normed spaces",
journal = j-J-CONVEX-ANAL,
volume = "1",
number = "1",
pages = "61--73",
year = "1994",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "46B20 (26B25 46B10 46N10 52A41)",
MRnumber = "1326942",
MRreviewer = "Roland Durier",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/64/;
http://www.heldermann-verlag.de/jca/jca01/jca01004.pdf",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:EML,
author = "Jonathan M. Borwein and Adrian S. Lewis and Mark A.
Limber",
title = "Entropy Minimization with Lattice Bounds",
journal = j-J-APPROX-THEORY,
volume = "79",
number = "1",
pages = "1--16",
year = "1994",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1006/jath.1994.1110",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "41A46 (41A29 90C48)",
MRnumber = "1294317",
MRreviewer = "Dominikus Noll",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1545/;
http://www.sciencedirect.com/science/article/pii/S0021904584711105",
abstract = "We characterize solutions to the problem of minimizing
a convex integral objective function subject to a
finite number of linear constraints and requiring that
the feasible functions lie in a strip $ [\alpha, \beta]
$ where $ \alpha $ and $ \beta $ are extended real
valued measurable functions. We use the duality theory
of J. M. Borwein and A. S. Lewis (Math. Programming,
Series \{B57\} (1992), 15-48, 49-84) to show that the
solutions are of the usual form, but truncated where
they leave the strip.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:EMPa,
author = "Jonathan M. Borwein and Adrian S. Lewis and Roger D.
Nussbaum",
title = "Entropy Minimization, {$ D A D $} Problems, and Doubly
Stochastic Kernels",
journal = j-J-FUNCT-ANAL,
volume = "123",
number = "2",
pages = "264--307",
year = "1994",
CODEN = "JFUAAW",
DOI = "https://doi.org/10.1006/jfan.1994.1089",
ISSN = "0022-1236 (print), 1096-0783 (electronic)",
ISSN-L = "0022-1236",
MRclass = "47N10 (47B99 47H15 49N15 90C30)",
MRnumber = "1283029",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1546/;
http://www.sciencedirect.com/science/article/pii/S0022123684710895",
abstract = "The classical $ D A D $ problem asks, for a square
matrix $A$ with nonnegative entries, when it is
possible to find positive diagonal matrices $ D_1$ and
$ D_2$ with $ D_1 A D_2$ doubly stochastic. We consider
various continuous and measurable generalizations of
this problem. Through a fusion of variational and fixed
point techniques we obtain strong analogues of the
classical results. Our extensions appear inaccessible
by either technique separately.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Functional Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/00221236",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:FAS,
author = "Jon Borwein and Jon Vanderwerff",
title = "Further arguments for slice convergence in
nonreflexive spaces",
journal = j-SET-VALUED-ANAL,
volume = "2",
number = "4",
pages = "529--544",
year = "1994",
CODEN = "SVANEG",
DOI = "https://doi.org/10.1007/BF01033070",
ISSN = "0927-6947 (print), 1572-932x (electronic)",
ISSN-L = "0927-6947",
MRclass = "49J45 (46N10 54B20)",
MRnumber = "1308483",
MRreviewer = "Gerald Beer",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/62/",
acknowledgement = ack-nhfb,
fjournal = "Set-Valued Analysis. An International Journal Devoted
to the Theory of Multifunctions and its Applications",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:FED,
author = "Jonathan M. Borwein and Roland Girgensohn",
title = "Functional equations and distribution functions",
journal = "Results Math.",
volume = "26",
number = "3--4",
pages = "229--237",
year = "1994",
DOI = "https://doi.org/10.1007/BF03323043",
ISSN = "0378-6218",
ISSN-L = "0378-6218",
MRclass = "39B22 (39B62 60E05 62E15)",
MRnumber = "1300602",
MRreviewer = "K. Lajk{\'o}",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "For Janos Aczel's 70th birthday.",
URL = "http://docserver.carma.newcastle.edu.au/90/",
acknowledgement = ack-nhfb,
fjournal = "Results in Mathematics. Resultate der Mathematik",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:NRS,
author = "Jonathan M. Borwein and Mari{\'a}n Fabi{\'a}n",
title = "A note on regularity of sets and of distance functions
in {Banach} space",
journal = j-J-MATH-ANAL-APPL,
volume = "182",
number = "2",
pages = "566--570",
year = "1994",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1006/jmaa.1994.1104",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "49J52",
MRnumber = "1269478",
MRreviewer = "Doug Ward",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022247X84711048",
abstract = "We show that in every infinite dimensional Banach
space there is a compact set C and x in C such that C
is regular at x (in the sense of nonsmooth analysis)
but such that the associated distance function dC is
not regular at x and neither is -dC.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:SCM,
author = "J. M. Borwein and P. B. Borwein and F. G. Garvan",
title = "Some cubic modular identities of {Ramanujan}",
journal = j-TRANS-AM-MATH-SOC,
volume = "343",
number = "1",
pages = "35--47",
month = may,
year = "1994",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/2154520",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "11B65 (11F27 33D10)",
MRnumber = "1243610",
MRreviewer = "George E. Andrews",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1547/;
http://www.jstor.org/stable/2154520",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:SOD,
author = "Jonathan M. Borwein and Dominikus Noll",
title = "Second order differentiability of convex functions in
{Banach} spaces",
journal = j-TRANS-AM-MATH-SOC,
volume = "342",
number = "1",
pages = "43--81",
month = mar,
year = "1994",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/2154684",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "46G05 (26E15)",
MRnumber = "1145959",
MRreviewer = "Lud{\v{e}}k Zaj{\'{\i}}{\v{c}}ek",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1549/;
http://www.jstor.org/stable/2154684",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:SRO,
author = "Jonathan M. Borwein and Adrian S. Lewis",
title = "Strong rotundity and optimization",
journal = j-SIAM-J-OPT,
volume = "4",
number = "1",
pages = "146--158",
year = "1994",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/0804008",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
MRclass = "49K27 (90C48)",
MRnumber = "1260412",
MRreviewer = "T. Zolezzi",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1550/",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:STE,
author = "David Borwein and Jonathan M. Borwein",
title = "On Some Trigonometric and Exponential Lattice Sums",
journal = j-J-MATH-ANAL-APPL,
volume = "188",
number = "1",
pages = "209--218",
year = "1994",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1006/jmaa.1994.1422",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "11L03 (11L07)",
MRnumber = "1301727",
MRreviewer = "Gunter Dufner",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1542/;
http://www.sciencedirect.com/science/article/pii/S0022247X84714223",
abstract = "Certain two-dimensional trigonometric lattice series,
the ordinary convergence of which involves unresolved
questions of a deep and delicate number-theoretic
nature, are shown to be summable by a special Abelian
method and their Abelian sums are obtained. This is
done by first evaluating an absolutely convergent
exponential lattice series and then analytically
extending its sum.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:UCM,
author = "J. M. Borwein and W. Huang",
title = "Uniform convergence for moment problems with
{Fermi--Dirac} type entropies",
journal = j-ZOR-MATH-METHODS-OPER-RES,
volume = "40",
number = "3",
pages = "239--252",
year = "1994",
CODEN = "ZMRREP",
DOI = "https://doi.org/10.1007/BF01432968",
ISSN = "0340-9422",
MRclass = "90C45 (44A60)",
MRnumber = "1316390",
MRreviewer = "Dominikus Noll",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/70/;
http://link.springer.com/article/10.1007/BF01432968",
acknowledgement = ack-nhfb,
fjournal = "Zeitschrift f{\"u}r Operations Research. Mathematical
Methods of Operations Research",
journal-URL = "http://link.springer.com/journal/186",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:UMP,
author = "J. M. Borwein and M. A. Limber",
title = "Underdetermined moment problems: a case for convex
analysis",
journal = "SIAG/OPT",
volume = "??",
number = "5",
pages = "9--13",
month = "Fall",
year = "1994",
DOI = "",
bibdate = "Mon Aug 15 14:52:57 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Invited talk at 1994 SIAM Conference on
Optimization.",
URL = "",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Which journal is this??",
}
@InProceedings{Bailey:1995:FNI,
author = "D. H. Bailey and J. M. Borwein and R. Girgensohn",
editor = "????",
booktitle = "{SIAM Conference on Parallel Computing, San Francisco,
February 1995}",
title = "Finding new identities with supercomputers",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "??--??",
year = "1995",
bibdate = "Mon Aug 15 14:48:40 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Bauschke:1995:CLM,
author = "H. H. Bauschke and J. M. Borwein",
title = "Continuous linear monotone mappings in {Banach}
space",
type = "CECM Research Report",
number = "95:049",
institution = inst-CECM,
address = inst-CECM:adr,
month = aug,
year = "1995",
bibdate = "Tue Aug 16 10:12:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/114/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Borowski:1995:DCD,
author = "Ephraim J. Borowski and Jonathan M. Borwein",
title = "Dizionario {Collins} della matematica",
publisher = "Gremese Editore",
address = "Roma, Italy",
pages = "423",
year = "1995",
ISBN = "88-7605-813-3",
ISBN-13 = "978-88-7605-813-4",
LCCN = "????",
bibdate = "Tue Aug 16 09:08:42 MDT 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Translation to Italian by Andrea Stracca of
\cite{Borowski:1991:HDM}.",
series = "Dizionari Gremese",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "Matematica - Enciclopedie e dizionari",
}
@Book{Borowski:1995:SXC,
author = "Ephraim J. Borowski and Jonathan M. Borwein",
title = "Shu xue ci dian",
volume = "10",
publisher = "Mao tou ying chu ban",
address = "Taibei",
pages = "879",
year = "1995",
ISBN = "957-0337-14-1",
ISBN-13 = "978-957-0337-14-3",
LCCN = "????",
bibdate = "Tue Aug 16 09:05:36 MDT 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Chinese edition of \cite{Borowski:1991:HDM}.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1995:ATB,
author = "Jonathan M. Borwein and Roland Girgensohn",
title = "Addition theorems and binary expansions",
journal = j-CAN-J-MATH,
volume = "47",
number = "2",
pages = "262--273",
year = "1995",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-1995-013-4",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
MRclass = "39B62 (11A63)",
MRnumber = "1335077",
MRreviewer = "W. Herget",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1537/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics. Journal Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1995:CCH,
author = "Jonathan M. Borwein and Simon Fitzpatrick",
title = "Closed convex {Haar} null sets",
type = "CECM Research Report",
number = "95:052",
institution = inst-CECM,
address = inst-CECM:adr,
month = aug,
year = "1995",
bibdate = "Tue Aug 16 10:13:27 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/117/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:1995:CCS,
author = "J. M. Borwein and S. Fitzpatrick",
booktitle = "Proceedings of the Optimization Miniconference II",
title = "Characterization of {Clarke} subgradients among
one-dimensional multifunctions",
publisher = "University of Ballarat",
address = "Ballarat, VI, Australia",
pages = "5--12",
year = "1995",
bibdate = "Mon Aug 15 14:41:04 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/23/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1995:CLR,
author = "Jonathan M. Borwein and Jon D. Vanderwerff",
title = "Convergence of {Lipschitz} regularizations of convex
functions",
journal = j-J-FUNCT-ANAL,
volume = "128",
number = "1",
pages = "139--162",
year = "1995",
CODEN = "JFUAAW",
DOI = "https://doi.org/10.1006/jfan.1995.1026",
ISSN = "0022-1236 (print), 1096-0783 (electronic)",
ISSN-L = "0022-1236",
MRclass = "49J45 (46N10 49J52)",
MRnumber = "1317713",
MRreviewer = "Lionel Thibault",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1540/;
http://www.sciencedirect.com/science/article/pii/S0022123685710269",
abstract = "For a sequence or net of convex functions on a Banach
space, we study pointwise convergence of their
Lipschitz regularizations and convergence of their
epigraphs. The Lipschitz regularizations we will
consider are the infimal convolutions of the functions
with appropriate multiples of the norm. For a sequence
of convex functions on a separable Banach space we show
that both pointwise convergence of their Lipschitz
regularizations and Wijsman convergence of their
epigraphs are equivalent to variants of two conditions
used by Attouch and Beer to characterize slice
convergence. Results for nonseparable spaces are
obtained by separable reduction arguments. As a
by-product, slice convergence for an arbitrary net of
convex functions can be deduced from the pointwise
convergence of their regularizations precisely when the
w* and the norm topologies agree on the dual sphere.
This extends some known results and answers an open
question.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Functional Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/00221236",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1995:EEEa,
author = "David Borwein and Jonathan M. Borwein and Roland
Girgensohn",
title = "Explicit evaluation of {Euler} sums",
journal = j-PROC-EDINBURGH-MATH-SOC-2,
volume = "38",
number = "2",
pages = "277--294",
month = jun,
year = "1995",
CODEN = "PRMSA3",
DOI = "https://doi.org/10.1017/S0013091500019088",
ISSN = "0013-0915 (print), 1464-3839 (electronic)",
ISSN-L = "0013-0915",
MRclass = "11M06 (11Y60)",
MRnumber = "1335874",
MRreviewer = "Bruce C. Berndt",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/58/",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Edinburgh Mathematical Society
(2)",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PEM",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1995:FHMa,
author = "J. M. Borwein and W. Z. Huang",
title = "A fast heuristic method for polynomial moment problems
with {Boltzmann--Shannon} entropy",
journal = j-SIAM-J-OPT,
volume = "5",
number = "1",
pages = "68--99",
year = "1995",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/0805004",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
MRclass = "90C45 (44A60 65K05)",
MRnumber = "1315705",
MRreviewer = "Dominikus Noll",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1539/",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1995:FHMb,
author = "J. M. Borwein and M. N. Limber and D. Noll",
title = "Fast heuristic methods for function reconstruction
using derivative information",
journal = j-APPL-ANAL,
volume = "58",
number = "3--4",
pages = "241--261",
year = "1995",
CODEN = "APANCC",
DOI = "https://doi.org/10.1080/00036819508840375",
ISSN = "0003-6811",
ISSN-L = "0003-6811",
MRclass = "65D15 (49N15 62G05)",
MRnumber = "1383191",
MRreviewer = "Zdzis{\l}aw W. Trzaska",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1536/",
acknowledgement = ack-nhfb,
fjournal = "Applicable Analysis. An International Journal",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1995:IIS,
author = "David Borwein and Jonathan M. Borwein",
title = "On an intriguing integral and some series related to
{$ \zeta (4) $}",
journal = j-PROC-AM-MATH-SOC,
volume = "123",
number = "4",
pages = "1191--1198",
year = "1995",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.2307/2160718",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "11Y60 (11M06 11Y35 33B15 42A16)",
MRnumber = "1231029",
MRreviewer = "Henri Joris",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1538/",
abstract = "An intriguing log-cosine integral is fully analyzed
and shown to have value a rational multiple of $ \zeta
(4) $, $ \zeta $ being the Riemann zeta function. From
this we deduce by means of generating functions and
Parseval's identity the sums of certain series
previously established by a completely different
method.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1995:MCF,
author = "Jonathan M. Borwein and Kenneth R. Davidson",
booktitle = "{Canadian Mathematical Society}. 1945--1995",
title = "Mathematics in {Canada}: the future of mathematics in
{Canada} 50 years later",
volume = "1",
publisher = "Canadian Mathematical Society",
address = "Ottawa, ON, Canada",
pages = "231--268 (249--268 fran{\c{c}}iai)",
year = "1995",
MRclass = "01A80 (01A67)",
MRnumber = "1661625",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Dual English--French text.",
series = "CMS Publications",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:1995:MEMa,
author = "J. M. Borwein and P. B. Borwein and R. Girgensohn and
S. Parnes",
title = "Mathematical Experimentation and Methodology",
month = jan,
year = "1995",
bibdate = "Tue Aug 16 10:07:27 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Unpublished report.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1995:MER,
author = "J. M. Borwein and A. S. Lewis and M. N. Limber and D.
Noll",
title = "Maximum entropy reconstruction using derivative
information. {II}. {Computational} results",
journal = j-NUM-MATH,
volume = "69",
number = "3",
pages = "243--256",
year = "1995",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s002110050090",
ISSN = "0029-599x (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65K10 (65U05)",
MRnumber = "1312779",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/71/;
http://link.springer.com/article/10.1007/s002110050090",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxtitle = "Maximum entropy spectral analysis using first order
information. {Part 2}: {A} Numerical Algorithm for
{Fisher} information duality",
}
@TechReport{Borwein:1995:MSE,
author = "Jonathan M. Borwein and Peter B. Borwein and Roland
Girgensohn and S. Parnes",
title = "Making sense of experimental mathematics",
type = "CECM preprint",
number = "95:032",
institution = inst-CECM,
address = inst-CECM:adr,
year = "1995",
bibdate = "Thu Aug 11 09:31:33 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/98/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1995:SCB,
author = "Jonathan Borwein and Simon Fitzpatrick",
title = "{$ {\rm Weak}^\ast $} sequential compactness and
bornological limit derivatives",
journal = j-J-CONVEX-ANAL,
volume = "2",
number = "1--2",
pages = "59--67",
year = "1995",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "49J52 (46G05 47N10 49J40 58C20)",
MRnumber = "1363360",
MRreviewer = "Nikolay V. Zhivkov",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Dedicated to R. T. Rockafellar on his 60th birthday.",
URL = "http://www.heldermann.de/JCA/jcacon.htmvol.2_no.1+2/j4_49.ps.gz",
abstract = "In this note we give a self-contained account of the
relationship between the sequential and topological
constructions of bornological limit derivatives for
locally Lipschitzian real-valued functions on Banach
spaces.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
keywords = "Asplund space; bornological limit derivative; Clarke
subgradient; Fr{\'e}chet derivative; Gateaux
derivative; subderivative; weak Hadamard derivative;
weak* sequential compactness.; weakly compactly
generated",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
received = "6 June 1994; revised 15 November 1994",
}
@InProceedings{Borwein:1995:SEC,
author = "Jonathan M. Borwein",
editor = "Roland Durier and Chistian Michelot",
booktitle = "Recent Developments in Optimization: Seventh
{French--German} Conference on Optimization ({Dijon}
1994)",
title = "A survey of examples of convex functions and
classifications of normed spaces",
volume = "429",
publisher = pub-SV,
address = pub-SV:adr,
pages = "60--71",
year = "1995",
DOI = "https://doi.org/10.1007/978-3-642-46823-0_5",
ISBN = "3-642-46823-3",
ISBN-13 = "978-3-642-46823-0",
LCCN = "QA402.5",
MRclass = "46N10 (46B20 49J50)",
MRnumber = "1358388",
MRreviewer = "A. B. N{\'e}meth",
bibdate = "Mon Aug 15 14:50:05 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Lecture Notes in Economic and Mathematical Systems",
URL = "http://docserver.carma.newcastle.edu.au/93/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxtitle = "A survey of examples of convex functions and the
classification of {Banach} spaces",
}
@Article{Borwein:1995:SRS,
author = "Jonathan M. Borwein and Jon D. Vanderwerff",
title = "A survey on renorming and set convergence",
journal = "Topological Methods in Nonlinear Analysis",
volume = "5",
number = "2",
pages = "211--228",
year = "1995",
ISSN = "1230-3429",
ISSN-L = "1230-3429",
MRclass = "46B20 (46G05 46N10 49J45 54B20)",
MRnumber = "1374058",
MRreviewer = "David Yost",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/97/;
https://www.tmna.ncu.pl/static/files/v05n2-01.pdf",
acknowledgement = ack-nhfb,
ajournal = "Topol. Methods Nonlinear Anal.",
fjournal = "Topological Methods in Nonlinear Analysis",
journal-URL = "https://www.tmna.ncu.pl/static/archives/archives.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Limber:1995:DRF,
author = "M. A. Limber and M. N. Limber and A. Celler and J. S.
Barney and J. M. Borwein",
title = "Direct reconstruction of functional parameters for
dynamic {SPECT}",
journal = j-IEEE-TRANS-NUCL-SCI,
volume = "42",
number = "4",
pages = "1249--1256",
month = aug,
year = "1995",
CODEN = "IRNSAM",
DOI = "https://doi.org/10.1109/23.467872",
ISSN = "0018-9499 (print), 1558-1578 (electronic)",
ISSN-L = "0018-9499",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/1995ITNS...42.1249L;
http://docserver.carma.newcastle.edu.au/1535/",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Nuclear Science",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bauschke:1996:PAS,
author = "Heinz H. Bauschke and Jonathan M. Borwein",
title = "On Projection Algorithms for Solving Convex
Feasibility Problems",
journal = j-SIAM-REVIEW,
volume = "38",
number = "3",
pages = "367--426",
month = sep,
year = "1996",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/S0036144593251710",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "90C25 (47N10 49M45 65J10)",
MRnumber = "1 409 591",
MRreviewer = "F. Deutsch",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "Compendex database;
http://epubs.siam.org/toc/siread/38/3;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib;
http://www.siam.org/journals/sirev/sirev383.htm",
URL = "http://docserver.carma.newcastle.edu.au/100/;
http://epubs.siam.org/sam-bin/dbq/article/25171",
abstract = "Due to their extraordinary utility and broad
applicability in many areas of classical mathematics
and modern physical sciences (most notably,
computerized tomography), algorithms for solving convex
feasibility problems continue to receive great
attention. To unify, generalize, and review some of
these algorithms, a very broad and flexible framework
is investigated. Several crucial new concepts which
allow a systematic discussion of questions on behaviour
in general Hilbert spaces and on the quality of
convergence are brought out. Numerous examples are
given.",
acknowledgement = ack-nhfb,
affiliation = "Simon Fraser Univ",
affiliationaddress = "BC, Can",
classification = "723.2; 723.5; 921.5; 921.6; B0250 (Combinatorial
mathematics); B0260 (Optimisation techniques); B0290F
(Interpolation and function approximation); B6140C
(Optical information, image and video signal
processing); C1160 (Combinatorial mathematics); C1180
(Optimisation techniques); C1250 (Pattern recognition);
C4130 (Interpolation and function approximation)",
corpsource = "Dept. of Math. and Stat., Simon Fraser Univ., Burnaby,
BC, Canada",
fjournal = "SIAM Review. A Publication of the Society for
Industrial and Applied Mathematics",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "Algorithms; Approximation theory; Classical
mathematics; computerised tomography; Computerized
tomography; computerized tomography; convergence of
numerical methods; Convergence of numerical methods;
convex feasibility; Convex feasibility problems; Convex
inequalities; Convex programming; convex programming;
Functions; Hilbert spaces; Image reconstruction; image
reconstruction; image recovery; iterative method;
Iterative methods; iterative methods; Linear
convergence; linear convergence; linear inequality;
Mathematical programming; Problem solving; Projection
algorithms; projection algorithms; set theory;
Subgradient algorithm; subgradient algorithm",
onlinedate = "September 1996",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "According to the obituary at the AMS Web site, this is
Jon Borwein's most-cited paper. Google Scholar shows
1231 citations as of 02 January 2017, fewer than the
1378 noted in \cite{Barzilai:1988:TPS}.",
treatment = "T Theoretical or Mathematical",
}
@Article{Borwein:1996:ASC,
author = "D. Borwein and J. M. Borwein and Xianfu Wang",
title = "Approximate subgradients and coderivatives in {$ {\bf
R}^n $}",
journal = j-SET-VALUED-ANAL,
volume = "4",
number = "4",
pages = "375--398",
year = "1996",
CODEN = "SVANEG",
DOI = "https://doi.org/10.1007/BF00436112",
ISSN = "0927-6947 (print), 1572-932x (electronic)",
ISSN-L = "0927-6947",
MRclass = "49J52",
MRnumber = "1422402",
MRreviewer = "Doug Ward",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/152/;
http://link.springer.com/article/10.1007/BF00436112",
acknowledgement = ack-nhfb,
fjournal = "Set-Valued Analysis. An International Journal Devoted
to the Theory of Multifunctions and its Applications",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1996:BRE,
author = "Jonathan M. Borwein and Rob M. Corless",
title = "Book Review: {{\booktitle{The Encyclopedia of Integer
Sequences}}, by N. J. A. Sloane and Simon Plouffe.
Academic Press, San Diego, CA, 1995. \$44.95. xii + 587
pp., hardcover. ISBN 0-12-558630-2}",
journal = j-SIAM-REVIEW,
volume = "38",
number = "2",
pages = "333--337",
month = jun,
year = "1996",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1038058",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Wed Aug 31 09:45:28 2016",
bibsource = "http://epubs.siam.org/toc/siread/38/2;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://www.jstor.org/stable/2132886",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "June 1996",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1996:BSAa,
author = "J. M. Borwein and J. D. Vanderwerff",
title = "{Banach} spaces that admit support sets",
journal = j-PROC-AM-MATH-SOC,
volume = "124",
number = "3",
pages = "751--755",
year = "1996",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/S0002-9939-96-03122-X",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "46B20 (46B03)",
MRnumber = "1301010",
MRreviewer = "Catherine Finet",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/87/",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1996:BSAb,
author = "J. M. Borwein and J. D. Vanderwerff",
title = "{Banach} spaces that admit support sets",
journal = j-PROC-AM-MATH-SOC,
volume = "124",
number = "3",
pages = "751--756",
month = mar,
year = "1996",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/S0002-9939-96-03122-X",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
bibdate = "Fri Aug 12 12:16:08 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/87/;
http://www.ams.org/journals/proc/1996-124-03/S0002-9939-96-03122-X/",
abstract = "It is shown that the existence of a closed convex set
all of whose points are properly supported in a Banach
space is equivalent to the existence of a certain type
of uncountable ordered one-sided biorthogonal system.
Under the continuum hypothesis, we deduce that this
notion is weaker than the existence of an uncountable
biorthogonal system.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1996:DAM,
author = "Jonathan M. Borwein and Peter B. Borwein and Stephen
Braham and Robert Corless and Loki J{\"o}rgenson",
title = "Digitally Activated Mathematics for a Brave New {World
Wide Web}",
journal = "Education, Research and Perspectives",
volume = "23",
number = "2",
pages = "28--47",
month = dec,
year = "1996",
ISSN = "0311-2543 (print), 1446-0017 (electronic)",
ISSN-L = "0311-2543",
bibdate = "Fri Aug 12 12:03:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special issue on multimedia technologies and
education.",
URL = "http://docserver.carma.newcastle.edu.au/1533/;
http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:13132;
https://search.informit.com.au/documentSummary%3Bdn=970909729%3Bres=IELAPA",
acknowledgement = ack-nhfb,
journal-URL = "http://www.erpjournal.net/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "The journal Web site has no online archives before
year 2000.",
}
@Article{Borwein:1996:EFE,
author = "Jonathan M. Borwein and David M. Bradley and David J.
Broadhurst",
title = "Evaluations of $k$-fold {Euler\slash Zagier} sums: a
compendium of results for arbitrary $k$",
journal = "ArXiv High Energy Physics --- Theory e-prints",
month = nov,
year = "1996",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/1996hep.th...11004B;
http://arxiv.org/abs/hep-th/9611004",
abstract = "Euler sums (also called Zagier sums) occur within the
context of knot theory and quantum field theory. There
are various conjectures related to these sums whose
incompletion is a sign that both the mathematics and
physics communities do not yet completely understand
the field. Here, we assemble results for Euler/Zagier
sums (also known as multidimensional zeta/harmonic
sums) of arbitrary depth, including sign alternations.
Many of our results were obtained empirically and are
apparently new. By carefully compiling and examining a
huge data base of high precision numerical evaluations,
we can claim with some confidence that certain classes
of results are exhaustive. While many proofs are
lacking, we have sketched derivations of all results
that have so far been proved.",
acknowledgement = ack-nhfb,
eprint = "hep-th/9611004",
keywords = "High Energy Physics - Theory",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1996:ETE,
author = "Jonathan M. Borwein and Roland Girgensohn",
title = "Evaluation of triple {Euler} sums",
journal = j-ELECT-J-COMB,
volume = "3",
number = "1",
pages = "Research Paper 23",
year = "1996",
ISSN = "1077-8926 (print), 1097-1440 (electronic)",
ISSN-L = "1077-8926",
MRclass = "11M99 (11Y60)",
MRnumber = "1401442",
MRreviewer = "Bruce C. Berndt",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/118/;
http://www.combinatorics.org/Volume_3/Abstracts/v3i1r23.html",
acknowledgement = ack-nhfb,
fjournal = "Electronic Journal of Combinatorics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
pagecount = "27",
}
@Article{Borwein:1996:EUC,
author = "Jonathan M. Borwein and Jon D. Vanderwerff",
title = "Epigraphical and uniform convergence of convex
functions",
journal = j-TRANS-AM-MATH-SOC,
volume = "348",
number = "4",
pages = "1617--1631",
month = apr,
year = "1996",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.1090/S0002-9947-96-01581-4",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "49J45 (46A55 46B20 46N10 52A41)",
MRnumber = "1344203",
MRreviewer = "W. W. Breckner",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/94/;
http://www.jstor.org/stable/2155155",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1996:GCP,
author = "D. Borwein and J. M. Borwein and P. B. Borwein and R.
Girgensohn",
title = "{Giuga}'s conjecture on primality",
journal = j-AMER-MATH-MONTHLY,
volume = "103",
number = "1",
pages = "40--50",
year = "1996",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2975213",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11A25",
MRnumber = "1369150",
MRreviewer = "Andrew Granville",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/88/",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1996:MER,
author = "J. M. Borwein and A. S. Lewis and D. Noll",
title = "Maximum entropy reconstruction using derivative
information. {I}. {Fisher} information and convex
duality",
journal = j-MATH-OP-RES,
volume = "21",
number = "2",
pages = "442--468",
year = "1996",
CODEN = "MOREDQ",
DOI = "https://doi.org/10.1287/moor.21.2.442",
ISSN = "0364-765x (print), 1526-5471 (electronic)",
ISSN-L = "0364-765X",
MRclass = "90C48 (49N15)",
MRnumber = "1397223",
MRreviewer = "Vaithilingam Jeyakumar",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/82/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Operations Research",
journal-URL = "http://pubsonline.informs.org/loi/moor",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1996:MSE,
author = "Jonathan Borwein and Peter B. Borwein and Roland
Girgensohn and S. Parnes",
title = "Making sense of experimental mathematics",
journal = j-MATH-INTEL,
volume = "18",
number = "4",
pages = "12--18",
month = "Fall",
year = "1996",
CODEN = "MAINDC",
DOI = "https://doi.org/10.1007/BF03026747",
ISSN = "0343-6993 (print), 1866-7414 (electronic)",
ISSN-L = "0343-6993",
MRclass = "00A35",
MRnumber = "1413248",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/98/",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Intelligencer",
journal-URL = "http://link.springer.com/journal/283",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "This entry appears to be contained in
\cite{Octavio:1996:IT}. Is it a separate paper??",
}
@Article{Borwein:1996:PAS,
author = "Jonathan M. Borwein and Alexander Ioffe",
title = "Proximal analysis in smooth spaces",
journal = j-SET-VALUED-ANAL,
volume = "4",
number = "1",
pages = "1--24",
year = "1996",
CODEN = "SVANEG",
DOI = "https://doi.org/10.1007/BF00419371",
ISSN = "0927-6947 (print), 1572-932x (electronic)",
ISSN-L = "0927-6947",
MRclass = "49J52 (46N10 58C20)",
MRnumber = "1384247",
MRreviewer = "Philip D. Loewen",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/61/",
acknowledgement = ack-nhfb,
fjournal = "Set-Valued Analysis. An International Journal Devoted
to the Theory of Multifunctions and its Applications",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1996:PSR,
author = "Jonathan M. Borwein",
title = "Problems and Solutions: Revivals: 10281",
journal = j-AMER-MATH-MONTHLY,
volume = "103",
number = "10",
pages = "911--912",
year = "1996",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1542929",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://links.jstor.org/sici?sici=0002-9890(199612)103:10<911:1>2.0.CO%3B2-5&origin=MSN",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1996:PSS,
author = "Jonathan M. Borwein and Donald A. Darling and D. B.
Tyler",
title = "Problems and Solutions: Solutions: 10281",
journal = j-AMER-MATH-MONTHLY,
volume = "103",
number = "2",
pages = "181--183",
year = "1996",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2975121",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1542802",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1996:SRZ,
author = "Jonathan M. Borwein and Peter B. Borwein",
title = "{Srinivasa Ramanujan und die Zahl Pi}. ({German})
[{Srinivasa Ramanujan} and the number $ \pi $]",
crossref = "Faltings:1996:MM",
pages = "60--68",
year = "1996",
bibdate = "Fri Aug 12 14:57:29 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Reprint of \cite{Borwein:1988:RP}.",
URL = "http://docserver.carma.newcastle.edu.au/1379/",
acknowledgement = ack-nhfb,
language = "German",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxtitle = "{Ramanujan} and {Pi}",
}
@Article{Borwein:1996:SSA,
author = "Jonathan Borwein and David Bradley",
title = "Searching Symbolically for {Ap{\'e}ry}-like Formulae
for Values of the {Riemann} Zeta Function",
journal = j-SIGSAM,
volume = "30",
number = "2",
pages = "2--7",
month = jun,
year = "1996",
CODEN = "SIGSBZ",
DOI = "https://doi.org/10.1145/235699.235700",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Wed Aug 10 12:08:56 2016",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/sigsam.bib",
URL = "http://docserver.carma.newcastle.edu.au/170/;
http://doi.acm.org/10.1145/235699.235700",
acknowledgement = ack-nhfb,
acmid = "235700",
classcodes = "C7310 (Mathematics computing)",
corpsource = "Centre for Exp. and Constructive Math., Simon Fraser
Univ., Burnaby, BC, Canada",
fjournal = "SIGSAM Bulletin (ACM Special Interest Group on
Symbolic and Algebraic Manipulation)",
issue = "116",
issue-date = "June 1996",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
keywords = "algebra; Apery-like formulae; computer; formal proof;
functions; Riemann Zeta function; special values;
symbol manipulation; symbolic methods",
numpages = "6",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
treatment = "T Theoretical or Mathematical",
}
@Article{Borwein:1996:VSV,
author = "Jonathan M. Borwein and Qiji J. Zhu",
title = "Viscosity solutions and viscosity subderivatives in
smooth {Banach} spaces with applications to metric
regularity",
journal = j-SIAM-J-CONTROL-OPTIM,
volume = "34",
number = "5",
pages = "1568--1591",
year = "1996",
CODEN = "SJCODE",
DOI = "https://doi.org/10.1137/S0363012994268801",
ISSN = "0363-0129 (print), 1095-7138 (electronic)",
ISSN-L = "0363-0129",
MRclass = "49L25 (49J52 49N10)",
MRnumber = "1404847",
MRreviewer = "Abderrahim Jourani",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/80/",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Control and Optimization",
journal-URL = "http://epubs.siam.org/sicon",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Octavio:1996:IT,
author = "Alfredo Octavio and Jonathan Borwein and Peter B.
Borwein and Roland Girgensohn and S. Parnes",
title = "The ``indexed'' theorem",
journal = j-MATH-INTEL,
volume = "18",
number = "4",
pages = "9--18",
month = sep,
year = "1996",
CODEN = "MAINDC",
DOI = "https://doi.org/10.1007/bf03026747",
ISSN = "0343-6993 (print), 1866-7414 (electronic)",
ISSN-L = "0343-6993",
bibdate = "Thu Aug 11 09:28:04 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Intelligencer",
journal-URL = "http://link.springer.com/journal/283",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:1997:KC,
author = "David H. Bailey and Jonathan M. Borwein and Richard E.
Crandall",
title = "On the {Khintchine} constant",
journal = j-MATH-COMPUT,
volume = "66",
number = "217",
pages = "417--431",
year = "1997",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-97-00800-4",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y60 (11K50 11Y65)",
MRnumber = "1377659",
MRreviewer = "T. Mets{\"a}nkyl{\"a}",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/1997MaCom..66..417B;
http://docserver.carma.newcastle.edu.au/102/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:1997:QP,
author = "D. H. Bailey and J. M. Borwein and P. B. Borwein and
S. Plouffe",
title = "The quest for pi",
journal = j-MATH-INTEL,
volume = "19",
number = "1",
pages = "50--57",
year = "1997",
CODEN = "MAINDC",
DOI = "https://doi.org/10.1007/BF03024340",
ISSN = "0343-6993 (print), 1866-7414 (electronic)",
ISSN-L = "0343-6993",
MRclass = "01A99",
MRnumber = "1439159",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/164/",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Intelligencer",
journal-URL = "http://link.springer.com/journal/283",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Bailey:1997:RME,
author = "D. H. Bailey and J. M. Borwein and P. B. Borwein",
title = "{Ramanujan}, modular equations, and approximations to
pi or {How} to compute one billion digits of pi
[{MR0991866} (90d:11143)]",
crossref = "Borwein:1997:OMP",
pages = "35--71",
year = "1997",
ISSN = "0731-1036",
ISSN-L = "0731-1036",
MRclass = "11Y60 (01A60 11F03 33E20)",
MRnumber = "1483913",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
note = "Reprint of \cite{Borwein:1989:RME}.",
series = "CMS Conference Proceedings",
URL = "http://docserver.carma.newcastle.edu.au/1587/;
http://www.cecm.sfu.ca/organics/papers/borwein/index.html",
abstract = "The article underlying our contribution started life
in 1986 when David Bailey and Jon and Peter B. Borwein
began to write separate pieces on ``Pi and its
computation'' for the MAA Monthly. With urging from
Herb Wilf (the then editor) the authors joined forces
and a joint paper issued forth that was published in
1989. Since 1989, while the computers have continued to
improve and the computation of has continued unabated,
the underlying mathematical and computational
techniques being employed are still much as described
in the printed piece.\par
We opted to use this article as our contribution to
Organic Mathematics for several reasons: it is
reasonably accessible; it clearly allows for
``enhancement''; it was complete as a written piece and
so allowed us to concentrate on the key issues
underlying the larger project. Moreover, it tells a
3,000 year story touching many themes (from
transcendence theory, to elliptic functions, and the
Fast Fourier Transform) and involving many great
thinkers (Archimedes, Newton, Gauss, Euler, Ramanujan,
Von Neumann, Hilbert). In sum then we felt that the
article provided an exellent test-bed to try out what
would work in a multi-modal mathematical
environment.\par
A project like this presents several challenges for the
mathematician as multi-media author. First, the
technology is changing so quickly that tools uninvented
when the project began are sure to be obsolete before
it is finished. Second, it involves a super-highway to
be sure but one running through terra incognita. At
many levels one must balance the issues of form and
function, speed and scope. The version presently before
you looks little like the one of six months ago ---
small changes to the interface can greatly enhance or
reduce readability.\par
The opportunities are great. Within this article, you
will see the bust of Ramanujan. You can read quotes
from many sources and see part of the original
documents from Hermite, Shanks, von Neumann and others.
You may use ``lattice basis reduction'' over the Web;
plot and compute many fascinating functions. If you
want to try more examples the opportunities will be
there.\par
On the down side, you may plunge off into secondary
links and get lost coming back. You may find the
plethora of hypertext links and options distracting,
and the present limitations of using Maple over the
Internet frustrating.\par
Our hope is that this article and this collection will
play some role in limning the possibilities and
flagging the pot-holes of trying to use these new tools
to engage, educate and excite students, users and
producers of mathematics.",
acknowledgement = ack-nhfb,
book-URL = "http://www.cecm.sfu.ca/organics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Bauschke:1997:CSC,
author = "H. H. Bauschke and J. M. Borwein and A. S. Lewis",
editor = "Yair Censor and Simeon Reich",
booktitle = "Recent Developments in Optimization Theory and
Nonlinear Analysis",
title = "Convex sets and the cyclic projection algorithm",
volume = "204",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "1--38",
year = "1997",
bibdate = "Mon Aug 15 14:42:36 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Contemporary Mathematics",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bauschke:1997:LFM,
author = "Heinz H. Bauschke and Jonathan M. Borwein",
title = "{Legendre} functions and the method of random
{Bregman} projections",
journal = j-J-CONVEX-ANAL,
volume = "4",
number = "1",
pages = "27--67",
year = "1997",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "49M45 (65K10 90C25)",
MRnumber = "1459881",
MRreviewer = "Alfredo N. Iusem",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/96/;
http://www.heldermann-verlag.de/jca/jca04/jca04002.pdf",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Bauschke:1997:MCP,
author = "Heinz H. Bauschke and Jonathan M. Borwein and Adrian
S. Lewis",
booktitle = "Recent developments in optimization theory and
nonlinear analysis ({Jerusalem}, 1995)",
title = "The method of cyclic projections for closed convex
sets in {Hilbert} space",
volume = "204",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "1--38",
year = "1997",
DOI = "https://doi.org/10.1090/conm/204/02620",
MRclass = "49M45 (47H99 47N10 65F10 90C25)",
MRnumber = "1442992",
MRreviewer = "Alfredo N. Iusem",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Contemp. Math.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1997:ADE,
author = "J. M. Borwein and F. G. Garvan",
title = "Approximations to $ \pi $ via the {Dedekind} eta
function",
crossref = "Borwein:1997:OMP",
pages = "89--115",
year = "1997",
MRclass = "11F20 (11Y60)",
MRnumber = "1483915",
MRreviewer = "Bruce C. Berndt",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "CMS Conf. Proc.",
URL = "http://docserver.carma.newcastle.edu.au/158/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:1997:AGMa,
author = "J. M. Borwein and P. B. Borwein",
booktitle = "{Pi: A Source Book}",
title = "The Arithmetic--Geometric Mean and Fast Computation of
Elementary Functions",
publisher = pub-SV,
address = pub-SV:adr,
pages = "??--??",
year = "1997",
DOI = "https://doi.org/10.1007/978-1-4757-2736-4_56",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_56",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1997:AGMb,
author = "Jonathan A. Borwein and Petr Lison{\v{e}}k and John A.
Macdonald",
title = "Arithmetic--Geometric Means Revisited",
journal = j-MAPLE-TECH-NEWS,
volume = "4",
number = "1",
pages = "20--27",
month = "Winter",
year = "1997",
ISSN = "1061-5733",
ISSN-L = "1061-5733",
bibdate = "Wed Jul 23 09:11:50 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/maple-tech.bib",
note = "Special issue on Maple in the mathematical sciences.",
URL = "http://docserver.carma.newcastle.edu.au/4/",
acknowledgement = ack-nhfb,
fjournal = "Maple technical newsletter",
journal-URL = "http://web.mit.edu/maple/www/plibrary/mtn.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:1997:APD,
author = "J. M. Borwein and F. Garvan",
editor = "????",
booktitle = "Organic Mathematics Proceedings, {12 April 1996}",
title = "Approximating Pi with the {Dedekind} eta function",
publisher = "????",
address = "????",
pages = "??--??",
year = "1997",
ISSN = "0731-1036",
bibdate = "Mon Aug 15 14:37:48 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.cecm.sfu.ca/organics",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1997:CBS,
author = "J. Borwein and M. Fabian and J. Vanderwerff",
title = "Characterizations of {Banach} spaces via convex and
other locally {Lipschitz} functions",
journal = "Acta Math. Vietnam.",
volume = "22",
number = "1",
pages = "53--69",
year = "1997",
ISSN = "0251-4184 (print), 2315-4144 (electronic)",
ISSN-L = "0251-4184",
MRclass = "46B20 (46G99 52A41)",
MRnumber = "1479738",
MRreviewer = "Warren B. Moors",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special edition in honour of Huang Tuy's seventieth
birthday.",
URL = "http://docserver.carma.newcastle.edu.au/179/",
acknowledgement = ack-nhfb,
fjournal = "Acta Mathematica Vietnamica",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1997:CFB,
author = "Jon Borwein and Jon Vanderwerff",
title = "Convex functions on {Banach} spaces not containing {$
l_1 $}",
journal = j-CAN-MATH-BULL,
volume = "40",
number = "1",
pages = "10--18",
year = "1997",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1997-002-1",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "46B20 (46A55 46G05 46N10 52A41)",
MRnumber = "1443721",
MRreviewer = "Li Xin Cheng",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1532/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1997:DDF,
author = "J. M. Borwein and Xianfu Wang",
title = "Distinct differentiable functions may share the same
{Clarke} subdifferential at all points",
journal = j-PROC-AM-MATH-SOC,
volume = "125",
number = "3",
pages = "807--813",
year = "1997",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/S0002-9939-97-03654-X",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "49J52 (26A16 26A24 58C20)",
MRnumber = "1363449",
MRreviewer = "Doug Ward",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/112/",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1997:DEM,
author = "Jonathan Borwein and Michael Monagan",
title = "Differential Equations in {Maple}: a Short Tutorial",
journal = j-MAPLE-TECH-NEWS,
volume = "4",
number = "1",
pages = "55--58",
month = "Winter",
year = "1997",
ISSN = "1061-5733",
ISSN-L = "1061-5733",
bibdate = "Wed Jul 23 09:11:50 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/maple-tech.bib",
acknowledgement = ack-nhfb,
fjournal = "Maple technical newsletter",
journal-URL = "http://web.mit.edu/maple/www/plibrary/mtn.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1997:EDA,
author = "Jonathan Borwein and David Bradley",
title = "Empirically determined {Ap{\'e}ry}-like formulae for
{$ \zeta (4 n + 3) $}",
journal = j-EXP-MATH,
volume = "6",
number = "3",
pages = "181--194",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.1997.10504608",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11Y60 (11M06)",
MRnumber = "1481588",
MRreviewer = "F. Beukers",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://docserver.carma.newcastle.edu.au/163/;
http://projecteuclid.org/euclid.em/1047920419",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1997:EFE,
author = "Jonathan M. Borwein and David M. Bradley and David J.
Broadhurst",
title = "Evaluations of $k$-fold {Euler\slash Zagier} sums: a
compendium of results for arbitrary $k$",
journal = j-ELECT-J-COMB,
volume = "4",
number = "2",
pages = "Research Paper 5",
year = "1997",
ISSN = "1077-8926 (print), 1097-1440 (electronic)",
ISSN-L = "1077-8926",
MRclass = "11M41 (11Y60)",
MRnumber = "1444152",
MRreviewer = "Pavel Guerzhoy",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "The Wilf Festschrift (Philadelphia, PA, 1996).",
URL = "http://www.combinatorics.org/Volume_4/Abstracts/v4i2r5.html",
acknowledgement = ack-nhfb,
fjournal = "Electronic Journal of Combinatorics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
pagecount = "21",
}
@Article{Borwein:1997:ESLa,
author = "Jonathan M. Borwein and Warren B. Moors",
title = "Essentially smooth {Lipschitz} functions",
journal = j-J-FUNCT-ANAL,
volume = "149",
number = "2",
pages = "305--351",
year = "1997",
CODEN = "JFUAAW",
DOI = "https://doi.org/10.1006/jfan.1997.3101",
ISSN = "0022-1236 (print), 1096-0783 (electronic)",
ISSN-L = "0022-1236",
MRclass = "58C20 (46G05 46N10 49J52)",
MRnumber = "1472362",
MRreviewer = "Mari{\'a}n Fabian",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/95/;
http://www.sciencedirect.com/science/article/pii/S0022123697931013",
abstract = "In this paper we address some of the most fundamental
questions regarding the differentiability structure of
locally Lipschitz functions defined on separable Banach
spaces. For example, we examine the relationship
between integrability,D-representability, and strict
differentiability. In addition to this, we show that on
any separable Banach space there is a significant
family of locally Lipschitz functions that are
integrable,D-representable and possess desirable
differentiability properties. We also present some
striking applications of our results to distance
functions.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Functional Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/00221236",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1997:ESLb,
author = "Jonathan M. Borwein and Warren B. Moors",
editor = "F. Cucker and M. Shub",
booktitle = "Foundations of computational mathematics ({Rio de
Janeiro, 1997})",
title = "Essentially smooth {Lipschitz} functions: compositions
and chain rules",
publisher = pub-SV,
address = pub-SV:adr,
pages = "16--22",
year = "1997",
MRclass = "49J52 (46N10 58C20)",
MRnumber = "1661969",
MRreviewer = "Mari{\'a}n Fabian",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:1997:LFM,
author = "J. M. Borwein and W. B. Moors",
editor = "B. M. Glover and D. Ralph",
booktitle = "Proceedings of the Optimization Miniconference III,
University of Melbourne, July 1996",
title = "{Lipschitz} functions with minimal {Clarke}
subdifferential mappings",
publisher = "University of Ballarat",
address = "Ballarat, VI, Australia",
pages = "5--12",
year = "1997",
bibdate = "Mon Aug 15 14:41:04 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/178/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1997:LFP,
author = "Jonathan M. Borwein and Warren B. Moors and Xianfu
Wang",
title = "{Lipschitz} functions with prescribed derivatives and
subderivatives",
journal = j-NONLINEAR-ANAL,
volume = "29",
number = "1",
pages = "53--63",
year = "1997",
CODEN = "NOANDD",
DOI = "https://doi.org/10.1016/S0362-546X(96)00050-8",
ISSN = "0362-546x (print), 1873-5215 (electronic)",
ISSN-L = "0362-546X",
MRclass = "49J52 (46G05 47N10 58C05)",
MRnumber = "1447569",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/92/;
http://www.sciencedirect.com/science/article/pii/S0362546X96000508",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
keywords = "Clarke subgradient; differentiability; Haar-null set;
Lipschitz functions; maximal cyclically monotone
operator; minimal cusco",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Borwein:1997:MIM,
editor = "Jonathan M. Borwein and Carolyn Watters and Ephraim J.
Borowski",
title = "{The MathResource interactive math dictionary: version
1.0. The math visualizing program Newton and Leibniz
didn't have. [An essential tool for high school,
college and university students, teachers, scientists,
engineers, researchers and anyone else who uses or
studies mathematics]}",
publisher = "MathResources, Inc.",
address = "Halifax, NS, Canada",
pages = "????",
year = "1997",
ISBN = "3-540-14650-4",
ISBN-13 = "978-3-540-14650-6",
LCCN = "????",
bibdate = "Tue Aug 16 09:10:33 MDT 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
URL = "http://www.mathresources.com",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "1997 Eddie Award for best post-secondary reference
software, by Education Software Review. MathProbe Media
\& Methods 1998 Awards Portfolio winner. LetsDoMath,
2000 Technology \& Learning Award Winner. Integrated
with MapleSoft help files in Maple 9.5.",
}
@Article{Borwein:1997:NEW,
author = "Jon Borwein and Michael Monagan",
title = "A Note from the {Editors}: Winter 1997, Vol. 4, No.
1",
journal = j-MAPLE-TECH-NEWS,
volume = "4",
number = "1",
pages = "1--1",
month = "Winter",
year = "1997",
ISSN = "1061-5733",
ISSN-L = "1061-5733",
bibdate = "Wed Jul 23 09:11:50 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/maple-tech.bib",
acknowledgement = ack-nhfb,
fjournal = "Maple technical newsletter",
journal-URL = "http://web.mit.edu/maple/www/plibrary/mtn.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1997:OJP,
author = "Jonathan Borwein and Richard Smith",
title = "Online journal publication: two views from the
electronic trenches",
journal = "Canadian Journal of Communication",
volume = "22",
number = "??",
pages = "135--152",
month = "????",
year = "1997",
DOI = "",
bibdate = "Mon Aug 15 14:35:28 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://edie.cprost.sfu.ca/~scom",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Scholarly Communication in the Next Millennium, March
1997. Excerpted in extenso in Active Voice, the
national bi-monthly newsletter of the Editors'
Association of Canada.",
}
@InProceedings{Borwein:1997:PEN,
author = "J. M. Borwein and P. B. Borwein and K. Dilcher",
booktitle = "Pi: A Source Book",
title = "Pi, {Euler} Numbers, and Asymptotic Expansions",
publisher = pub-SV,
address = pub-SV:adr,
pages = "??--??",
year = "1997",
DOI = "https://doi.org/10.1007/978-1-4757-2736-4_65",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1583/;
http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_65",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1997:PSS,
author = "David Borwein and Jonathan Borwein and
Heinz-J{\"u}rgen Seiffert and Robert D. Brown and Pawel
Szeptycki",
title = "Problems and Solutions: Solutions: 10335",
journal = j-AMER-MATH-MONTHLY,
volume = "104",
number = "1",
pages = "72--74",
year = "1997",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2974831",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1542940",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:1997:RME,
author = "J. M. Borwein and P. B. Borwein and D. H. Bailey",
booktitle = "Pi: A Source Book",
title = "{Ramanujan}, Modular Equations, and Approximations to
Pi or How to Compute One Billion Digits of Pi",
publisher = pub-SV,
address = pub-SV:adr,
pages = "??--??",
year = "1997",
DOI = "https://doi.org/10.1007/978-1-4757-2736-4_64",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1587/;
http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_64",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1997:SAD,
author = "J. M. Borwein and W. Sun",
title = "The stability analysis of dynamic {SPECT} systems",
journal = j-NUM-MATH,
volume = "77",
number = "3",
pages = "283--298",
year = "1997",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s002110050287",
ISSN = "0029-599x (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65R30 (44A12 65R20 92C55)",
MRnumber = "1469673",
MRreviewer = "Dominikus Noll",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/99/;
http://link.springer.com/article/10.1007/s002110050287",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:1997:SAR,
author = "Jonathan M. Borwein and Jay Treiman and Qiji Zhu",
title = "Sensitivity analysis in reflexive {Banach} spaces",
month = aug,
year = "1997",
bibdate = "Tue Aug 16 10:14:16 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1997:SRR,
author = "J. M. Borwein and E. Wong",
editor = "L. Vinet",
booktitle = "Advances in mathematical sciences: {CRM}'s 25 years
({Montreal}, {PQ}, 1994)",
title = "A survey of results relating to {Giuga}'s conjecture
on primality",
volume = "11",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "13--27",
year = "1997",
MRclass = "11A51 (11Y11)",
MRnumber = "1479668",
MRreviewer = "Andrew Granville",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "CRM Proc. Lecture Notes",
URL = "http://docserver.carma.newcastle.edu.au/101/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1997:VAN,
author = "Jonathan M. Borwein and Qiji J. Zhu",
title = "Variational analysis in nonreflexive spaces and
applications to control problems with {$ L^1 $}
perturbations",
journal = j-NONLINEAR-ANAL,
volume = "28",
number = "5",
pages = "889--915",
year = "1997",
CODEN = "NOANDD",
DOI = "https://doi.org/10.1016/0362-546X(95)00186-Y",
ISSN = "0362-546x (print), 1873-5215 (electronic)",
ISSN-L = "0362-546X",
MRclass = "49K40",
MRnumber = "1422192",
MRreviewer = "Vera Zeidan",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/78/;
http://www.sciencedirect.com/science/article/pii/0362546X9500186Y",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
keywords = "Weak-Hadamard sub-derivatives;
Clarke-subdifferentials; control system;
$G$-subdifferentials; H{\"o}lder sub-derivatives;
infinite horizon problems; sensitivity analysis; smooth
renorms; variational principles",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1997:WOM,
author = "Jonathan M. Borwein and Peter B. Borwein and Robert M.
Corless and Loki J{\"o}rgenson and Nathalie Sinclair",
title = "What is organic mathematics?",
crossref = "Borwein:1997:OMP",
pages = "1--18",
year = "1997",
ISSN = "0731-1036",
ISSN-L = "0731-1036",
MRclass = "00A99 (00A30 01A99)",
MRnumber = "1483911",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "CMS/AMS Conference Proceedings",
URL = "http://docserver.carma.newcastle.edu.au/157/;
http://www.cecm.sfu.ca/organics",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Galvin:1997:PSP,
author = "Fred Galvin and Franz Rothe and Wen-Xiu Ma and Dan
Sachelarie and Vlad Sachelarie and Yury J. Ionin and
Robin R. Lewis and Joseph Rosenblatt and Jonathan M.
Borwein and C. G. Pinner",
title = "Problems and Solutions: Problems: 10599--10605",
journal = j-AMER-MATH-MONTHLY,
volume = "104",
number = "6",
pages = "566--567",
year = "1997",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2975086",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1543038",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1998:BHS,
author = "Jonathan M. Borwein",
title = "{Brouwer--Heyting} sequences converge",
journal = j-MATH-INTEL,
volume = "20",
number = "1",
pages = "14--15",
year = "1998",
CODEN = "MAINDC",
DOI = "https://doi.org/10.1007/BF03024393",
ISSN = "0343-6993 (print), 1866-7414 (electronic)",
ISSN-L = "0343-6993",
MRclass = "11A63",
MRnumber = "1601815",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Intelligencer",
journal-URL = "http://link.springer.com/journal/283",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1998:CAMa,
author = "Jonathan M. Borwein and David M. Bradley and David J.
Broadhurst and Petr Lison{\v{e}}k",
title = "Combinatorial aspects of multiple zeta values",
journal = "ArXiv Mathematics e-prints",
month = dec,
year = "1998",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/1998math.....12020B;
http://docserver.carma.newcastle.edu.au/201/",
abstract = "Multiple zeta values (MZVs, also called Euler sums or
multiple harmonic series) are nested generalizations of
the classical Riemann zeta function evaluated at
integer values. The fact that an integral
representation of MZVs obeys a shuffle product rule
allows the possibility of a combinatorial approach to
them. Using this approach we prove a longstanding
conjecture of Don Zagier about MZVs with certain
repeated arguments. We also prove a similar cyclic sum
identity. Finally, we present extensive computational
evidence supporting an infinite family of conjectured
MZV identities that simultaneously generalize the
Zagier identity.",
acknowledgement = ack-nhfb,
eprint = "math/9812020",
keywords = "Number Theory, Combinatorics, Numerical Analysis,
05A19, 11M99, 68R15 (Primary) 11Y99 (Secondary)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1998:CAMb,
author = "Jonathan M. Borwein and David M. Bradley and David J.
Broadhurst and Petr Lison{\v{e}}k",
title = "Combinatorial aspects of multiple zeta values",
journal = j-ELECT-J-COMB,
volume = "5",
pages = "Research Paper 38",
year = "1998",
ISSN = "1077-8926 (print), 1097-1440 (electronic)",
ISSN-L = "1077-8926",
MRclass = "11M41 (05A19 11Y60)",
MRnumber = "1637378",
MRreviewer = "Jerzy Browkin",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/201/;
http://www.combinatorics.org/Volume_5/Abstracts/v5i1r38.html",
acknowledgement = ack-nhfb,
fjournal = "Electronic Journal of Combinatorics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
pagecount = "12",
}
@Article{Borwein:1998:CHP,
author = "J. M. Borwein and R. Girgensohn and Xianfu Wang",
title = "On the construction of {H}{\"o}lder and proximal
subderivatives",
journal = j-CAN-MATH-BULL,
volume = "41",
number = "4",
pages = "497--507",
year = "1998",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-1998-065-9",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "49J52 (26A16 26A24)",
MRnumber = "1658271",
MRreviewer = "Lionel Thibault",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/186/",
acknowledgement = ack-nhfb,
fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1998:CML,
author = "David Borwein and Jonathan M. Borwein and Christopher
Pinner",
title = "Convergence of {Madelung}-like lattice sums",
journal = j-TRANS-AM-MATH-SOC,
volume = "350",
number = "8",
pages = "3131--3167",
month = aug,
year = "1998",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.1090/S0002-9947-98-01983-7",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "11P21 (11M41 11Z05 30B50 40A05)",
MRnumber = "1433111",
MRreviewer = "Hartmut Menzer",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/104/;
http://www.jstor.org/stable/117772",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1998:CMV,
author = "J. M. Borwein and Xianfu Wang",
title = "The converse of the mean value theorem may fail
generically",
journal = j-AMER-MATH-MONTHLY,
volume = "105",
number = "9",
pages = "847--848",
month = nov,
year = "1998",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2589216",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "26A24",
MRnumber = "1650850",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1530/;
http://www.jstor.org/stable/2589216",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1998:CRE,
author = "Jonathan M. Borwein and Warren B. Moors",
title = "A chain rule for essentially smooth {Lipschitz}
functions",
journal = j-SIAM-J-OPT,
volume = "8",
number = "2",
pages = "300--308",
year = "1998",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/S1052623496297838",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
MRclass = "49J52 (46N10 58C20)",
MRnumber = "1618794",
MRreviewer = "John R. Giles",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/151/",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1998:CSR,
author = "Jonathan M. Borwein and David M. Bradley and Richard
E. Crandall",
title = "Computational Strategies for the {Riemann} Zeta
Function",
type = "Report",
number = "CECM-98-118",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "68",
day = "30",
month = oct,
year = "1998",
bibdate = "Mon Oct 24 11:29:15 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://people.reed.edu/~crandall/papers/attach01.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1998:DRDa,
author = "Jonathan M. Borwein and David J. Broadhurst",
title = "Determinations of rational {Dedekind}-zeta invariants
of hyperbolic manifolds and {Feynman} knots and links",
journal = "ArXiv High Energy Physics --- Theory e-prints",
month = nov,
year = "1998",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/1998hep.th...11173B;
http://arxiv.org/abs/hep-th/9811173;
http://docserver.carma.newcastle.edu.au/213/",
abstract = "We identify 998 closed hyperbolic 3-manifolds whose
volumes are rationally related to Dedekind zeta values,
with coprime integers $a$ and $b$ giving $ a / {\rm
bvol}(M) = ( - D)^{3 / 2} / (2 \pi)^{2n - 4}
(\zeta_K(2)) / (2 \zeta (2))$ for a manifold $M$ whose
invariant trace field $K$ has a single complex place,
discriminant $D$, degree $n$, and Dedekind zeta value $
\zeta_K(2)$. The largest numerator of the 998
invariants of Hodgson--Weeks manifolds is,
astoundingly, $ a = 2^4 \times 23 \times 37 \times 691
= 9 \, 408 \, 656$; the largest denominator is merely $
b = 9$. We also study the rational invariant $ a / b$
for single-complex-place cusped manifolds,
complementary to knots and links, both within and
beyond the Hildebrand-Weeks census. Within the censi,
we identify 152 distinct Dedekind zetas rationally
related to volumes. Moreover, 91 census manifolds have
volumes reducible to pairs of these zeta values.
Motivated by studies of Feynman diagrams, we find a
10-component 24-crossing link in the case $ n = 2$ and
$ D = - 20$. It is one of 5 alternating platonic links,
the other 4 being quartic. For 8 of 10 quadratic fields
distinguished by rational relations between Dedekind
zeta values and volumes of Feynman orthoschemes, we
find corresponding links. Feynman links with $ D = -
39$ and $ D = - 84$ are missing; we expect them to be
as beautiful as the 8 drawn here. Dedekind-zeta
invariants are obtained for knots from Feynman diagrams
with up to 11 loops. We identify a sextic 18-crossing
positive Feynman knot whose rational invariant, $ a / b
= 26$, is 390 times that of the cubic 16-crossing
non-alternating knot with maximal $ D_9$ symmetry. Our
results are secure, numerically, yet appear very hard
to prove by analysis.",
acknowledgement = ack-nhfb,
eprint = "hep-th/9811173",
keywords = "High Energy Physics - Theory, Mathematics - Classical
Analysis and ODEs, Mathematics - Geometric Topology,
Mathematics - Number Theory",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1998:DRDb,
author = "Jonathan M. Borwein and David J. Broadhurst",
title = "Determinations of rational {Dedekind}-zeta invariants
of hyperbolic manifolds and {Feynman} knots and links",
type = "CECM Preprint",
number = "98:120",
institution = inst-CECM,
address = inst-CECM:adr,
month = nov,
year = "1998",
bibdate = "Tue Aug 16 10:14:52 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "arXiv preprint hep-th/9811173.",
URL = "http://docserver.carma.newcastle.edu.au/213/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1998:GYI,
author = "Jonathan M. Borwein",
title = "A generalization of {Young}'s {$ l^p $} inequality",
journal = j-MATH-INEQUAL-APPL,
volume = "1",
number = "1",
pages = "131--136",
year = "1998",
DOI = "https://doi.org/10.7153/mia-01-11",
ISSN = "1331-4343 (print), 1848-9966 (electronic)",
ISSN-L = "1331-4343",
MRclass = "90C25 (26B25 52A41)",
MRnumber = "1492917",
MRreviewer = "G{\'e}rard Lebourg",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/189/",
acknowledgement = ack-nhfb,
ajournal = "Math. Inequal. Appl.",
fjournal = "Mathematical Inequalities \& Applications",
journal-URL = "http://mia.ele-math.com/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1998:LCE,
author = "Jonathan M. Borwein and Qiji J. Zhu",
title = "Limiting convex examples for nonconvex subdifferential
calculus",
journal = j-J-CONVEX-ANAL,
volume = "5",
number = "2",
pages = "221--235",
year = "1998",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "49J52 (26B05)",
MRnumber = "1670340",
MRreviewer = "Lionel Thibault",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/191/;
http://www.heldermann-verlag.de/jca/jca05/j163.pdf",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1998:MPW,
author = "Jonathan Borwein",
title = "Mathematical Publication on the {Web}",
journal = j-SIGSAM,
volume = "32",
number = "1",
pages = "4--7",
month = mar,
year = "1998",
CODEN = "SIGSBZ",
DOI = "https://doi.org/10.1145/294833.294836",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Wed Aug 10 12:08:56 2016",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/sigsam.bib",
URL = "http://docserver.carma.newcastle.edu.au/190/;
http://doi.acm.org/10.1145/294833.294836",
acknowledgement = ack-nhfb,
acmid = "294836",
fjournal = "SIGSAM Bulletin (ACM Special Interest Group on
Symbolic and Algebraic Manipulation)",
issue = "123",
issue-date = "March 1998",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
numpages = "4",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1998:NCC,
author = "Jonathan M. Borwein and Jay S. Treiman and Qiji J.
Zhu",
title = "Necessary conditions for constrained optimization
problems with semicontinuous and continuous data",
journal = j-TRANS-AM-MATH-SOC,
volume = "350",
number = "6",
pages = "2409--2429",
year = "1998",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.1090/S0002-9947-98-01984-9",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "90C48 (49J52)",
MRnumber = "1433112",
MRreviewer = "B. Mordukhovich",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/116/",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1998:NSE,
author = "Jonathan M. Borwein and Warren B. Moors",
title = "Null sets and essentially smooth {Lipschitz}
functions",
journal = j-SIAM-J-OPT,
volume = "8",
number = "2",
pages = "309--323",
year = "1998",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/S1052623496305213",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
MRclass = "49J52 (46N10 58C20)",
MRnumber = "1618798",
MRreviewer = "John R. Giles",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/162/",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1998:NSP,
author = "Jonathan M. Borwein and Alejandro Jofr{\'e}",
title = "A nonconvex separation property in {Banach} spaces",
journal = j-Z-OPER-RES,
volume = "48",
number = "2",
pages = "169--179",
year = "1998",
CODEN = "ZMMRFZ",
DOI = "https://doi.org/10.1007/s001860050019",
ISSN = "1432-2994 (print), 1432-5217 (electronic)",
ISSN-L = "1432-2994",
MRclass = "46B20 (46A22 46N10 49J53 90C48)",
MRnumber = "1662819",
MRreviewer = "S. Simons",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Set-valued optimization.",
URL = "http://docserver.carma.newcastle.edu.au/197/",
acknowledgement = ack-nhfb,
ajournal = "ZOR---Math. Methods Oper. Res.",
fjournal = "Zeitschrift f{\"u}r Operations Research. Mathematical
Methods of Operations Research",
journal-URL = "http://link.springer.com/journal/186",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxjournal = "Math. Methods Oper. Res.",
}
@Book{Borwein:1998:PAS,
author = "Jonathan M. Borwein and Peter B. Borwein",
title = "Pi and the {AGM}: A study in analytic number theory
and computational complexity",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xvi + 414",
year = "1998",
ISBN = "0-471-83138-7, 0-471-31515-X (paperback)",
ISBN-13 = "978-0-471-83138-9, 978-0-471-31515-5 (paperback)",
MRclass = "11Y60 (11B65 68Q25)",
MRnumber = "1641658",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Reprint of the 1987 original.",
series = "Canadian Mathematical Society Series of Monographs and
Advanced Texts, 4",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
shorttableofcontents = "1. Complete Elliptic Integrals and the
Arithmetic--Geometric Mean Iteration \\
2. Theta Functions and the Arithmetic--Geometric Mean
Iteration \\
3. Jacobi's Triple-Product and Some Number Theoretic
Applications \\
4. Higher Order Transformations \\
5. Modular Equations and Algebraic Approximations to $
\pi $ \\
6. The Complexity of Algebraic Functions \\
7. Algorithms for the Elementary Functions \\
8. General Means and Iterations \\
9. Some Additional Applications \\
10. Other Approaches to the Elementary Functions \\
11. Pi",
subject = "Number theory; Computational complexity; Elliptic
functions; Pi; Nombres, Th{\'e}orie des; Complexit{\'e}
de calcul (Informatique); Fonctions elliptiques;
Computational complexity; Elliptic functions; Number
theory; Pi; Algebraische Funktion;
Arithmetisch-geometrisches Mittel; Berechnung;
Geschichte; Pi (Zahl); Nombres, Th{\'e}orie des;
Complexit{\'e} de calcul (informatique); Fonctions
elliptiques; Pi (le nombre); Arithmetisch-geometrisches
Mittel; Algebraische Funktion; Pi (Zahl); Berechnung;
Geschichte; moyenne arithm{\'e}tique; moyenne
g{\'e}om{\'e}trique; it{\'e}ration; fonction
elliptique; complexit{\'e} calcul; th{\'e}orie nombre",
tableofcontents = "1 Complete Elliptic Integrals and the
Arithmetic-Geometric Mean Iteration / 1 \\
1.1 The Arithmetic--Geometric Mean Iteration / 1 \\
1.2 Gauss's Derivation of the Fundamental Limit Formula
/ 5 \\
1.3 Basic Properties of Complete Elliptic Integrals / 7
\\
1.4 Quadratic Transformations and Iterations and a
Third Proof of the Fundamental Limit Formula / 11 \\
1.5 Jacobi's Differential Equation and a Fourth Proof
of the Fundamental Limit Theorem / 18 \\
1.6 Legendre's Relation / 23 \\
1.7 Elliptic Functions / 28 \\
2 Theta Functions and the Arithmetic--Geometric Mean
Iteration / 33 \\
2.1 A Theta Series Solution to the AGM / 33 \\
2.2 Poisson Summation / 36 \\
2.3 Poisson Summation and the AGM / 40 \\
2.4 The Derived Iteration and Some Convergence Results
/ 44 \\
2.5 Two Algorithms for 7T / 46 \\
2.6 General Theta Functions / 52 \\
2.7 The Landen Transformation / 57 \\
3 Jacobi's Triple-Product and Some Number Theoretic
Applications / 62 \\
3.1 Jacobi's Triple-Product Identity / 62 \\
3.2 Some Further Theta Function Identities / 67 \\
3.3 A Combinatorial Approach to the Triple-Product
Identity / 76 \\
3.4 Bressoud's ``Easy Proof'' of the Rogers--Ramanujan
Identities / 78 \\
3.5 Some Number Theoretic Applications / 81 \\
3.6 The Mellin Transform and the Zeta Function / 87 \\
3.7 Evaluation of Sums of Reciprocals of Fibonacci
Sequences / 91 \\
4 Higher Order Transformations / 102 \\
4.1 A First Approach to Higher Order Transformations /
102 \\
4.2 An Elementary Transcendental Approach to Higher
Order Transformations / 109 \\
4.3 Elliptic Modular Functions / 112 \\
4.4 The Modular Equations for $\lambda$ and $j$ / 119
\\
4.5 The Modular Equation in $u$--$v$ Form / 126 \\
4.6 The Multiplier / 136 \\
4.7 Cubic Modular Identities / 142 \\
5 Modular Equations and Algebraic Approximations to $
\pi $ / 152 \\
5.1 Singular Values of the Second Kind / 152 \\
5.2 Calculation of $\alpha$ / 155 \\
5.3 Further Formulae for $\alpha$ / 164 \\
5.4 Recursive Approximation to $ \pi $ / 169 \\
5.5 Generalized Elliptic Integrals and Rational and
Algebraic Series for $ 1 / \pi $ and $ 1 / K $ / 177
\\
5.6 Other Approximations / 191 \\
6 The Complexity of Algebraic Functions / 200 \\
6.1 Complexity Concerns / 200 \\
6.2 The Fast Fourier Transform (FFT) / 204 \\
6.3 Fast Multiplication / 209 \\
6.4 Newton's Method and the Complexity of Algebraic
Functions / 212 \\
7 Algorithms for the Elementary Functions / 219 \\
7.1 $ \pi $ and Log / 219 \\
7.2 Theta Function Algorithms for Log / 224 \\
7.3 The Complexity of Elementary and Elliptic Functions
/ 226 \\
8 General Means and Iterations / 230 \\
8.1 Abstract Means / 230 \\
8.2 Equivalence of Means / 239 \\
8.3 Compound Means / 243 \\
8.4 Convergence Rates and Some Examples / 249 \\
8.5 Carlson's Integrals and More Examples 256 / 281 \\
8.6 Series Expansions of Certain Means / 263 \\
8.7 Multidimensional Means and Iterations / 266 \\
8.8 Algebraic Iterations and Functional Relations / 273
\\
9 Some Additional Applications / 281 \\
9.1 Sums of Two Squares / 281 \\
9.2 (Chemical) Lattice Sums / 288 \\
9.3 Odd-Dimensional Sums and Benson's Formula / 301 \\
9.4 The Quintuple-Product Identity / 306 \\
9.5 Quintic and Septic Multipliers and Iterations / 309
\\
10 Other Approaches to the Elementary Functions / 316
\\
10.1 Classical Approximations / 316 \\
10.2 Reduced Complexity Methods / 326 \\
11 Pi / 337 \\
11.1 On the History of the Calculation of $ \pi $ / 337
\\
11.2 On the Transcendence of $ \pi $ / 347 \\
11.3 Irrationality Measures / 362 \\
Bibliography / 387 \\
Symbol List / 396 \\
Index / 405",
}
@Unpublished{Borwein:1998:TAP,
author = "Jonathan Borwein",
title = "Talking about Pi",
day = "20",
month = jan,
year = "1998",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
note = "The original URL is no longer found, but the archive
URL worked on 26-Apr-2011.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Marechal:1998:APR,
author = "P. Marechal and D. Togane and A. Celler and J. M.
Borwein",
booktitle = "{1998 IEEE Nuclear Science Symposium. Conference
Record. Toronto, ON, Canada, November 8--14, 1998}",
title = "Assessment of the performance of reconstruction
processes for computed tomography",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1353--1357",
year = "1998",
DOI = "https://doi.org/10.1109/NSSMIC.1998.774404",
ISSN = "1082-3654",
ISSN-L = "1082-3654",
bibdate = "Fri Aug 12 11:41:45 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1529/",
abstract = "This paper deals with the assessment of the
performance of reconstruction methods for computed
tomography, including filtered backprojection and
`entropy-like' methods. For each of these methods, the
influence of errors in the measured data on the
reconstructed image is analyzed. A small perturbation
of the data vector induces a perturbation of the
reconstructed object which can be computed by means of
the sensitivity matrix. Using appropriate matrix
computation techniques, an upper bound on the size of
the reconstruction error is determined, as well as the
pattern of noise in the sinogram that will result in
the largest reconstruction error. Simulations will
illustrate our analysis and demonstrate its utility in
the interpretation of computed images and in the
selection of reconstruction parameters",
acknowledgement = ack-nhfb,
keywords = "Attenuation; computed tomography; Computed tomography;
computerised tomography; Convolution; data vector;
entropy-like methods; filtered backprojection; Image
analysis; image reconstruction; Image reconstruction;
image reconstruction processes; Integral equations;
interpolation; inverse problems; Inverse problems;
iterative methods; Mathematics; matrix computation
techniques; maximum entropy methods; medical image
processing; pattern of noise; performance assessment;
positron emission tomography; Radon transforms;
Radon-type inverse problem; reconstruction error size;
reconstruction parameters selection; regularization
scheme; sensitivity analysis; sensitivity matrix;
singular value decomposition; sinogram; small
perturbation; Transforms; upper bound; X-ray
scattering",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Bauschke:1999:COM,
author = "Heinz H. Bauschke and Jonathan M. Borwein",
editor = "J. Giles and B. Ninness",
booktitle = "{Proceedings of the Centre for Mathematics and its
Applications (Australian National University) National
Symposium on Functional Analysis, Optimization and
Applications, March 1998}",
title = "Conical open mapping theorems and regularity",
volume = "36",
publisher = "????",
address = "????",
pages = "1--10",
year = "1999",
bibdate = "Mon Aug 15 14:33:16 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/208/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bauschke:1999:EAD,
author = "Heinz H. Bauschke and Dominikus Noll and Anna Celler
and Jonathan M. Borwein",
title = "An {EM} algorithm for dynamic {SPECT}",
journal = j-IEEE-TRANS-MED-IMAG,
volume = "18",
number = "3",
pages = "252--261",
month = mar,
year = "1999",
CODEN = "ITMID4",
DOI = "https://doi.org/10.1109/42.764899",
ISSN = "0278-0062 (print), 1558-254x (electronic)",
ISSN-L = "0278-0062",
bibdate = "Wed Aug 10 12:08:56 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.ncbi.nlm.nih.gov/pubmed/10363703",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Medical Imaging",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=42",
keywords = "Algorithms; arbitrary decaying activities; Cameras;
compartmental modeling; Computed tomography; dynamic
SPECT; EM algorithm; exponentials sum; Face detection;
Head; Heuristic algorithms; Humans; Instruments; M
step; medical diagnostic imaging; Models, Statistical;
Nuclear medicine; nuclear medicine; numerical tests;
Pharmaceuticals; physiological models; Positron
emission tomography; Reproducibility of Results; single
photon emission computed tomography; Single photon
emission computed tomography; Tomography,
Emission-Computed, Single-Photon; underlying
probabilistic models",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bauschke:1999:MMD,
author = "Heinz H. Bauschke and Jonathan M. Borwein",
title = "Maximal monotonicity of dense type, local maximal
monotonicity, and monotonicity of the conjugate are all
the same for continuous linear operators",
journal = j-PAC-J-MATH,
volume = "189",
number = "1",
pages = "1--20",
year = "1999",
CODEN = "PJMAAI",
DOI = "https://doi.org/10.2140/pjm.1999.189.1",
ISSN = "0030-8730 (print), 1945-5844 (electronic)",
ISSN-L = "0030-8730",
MRclass = "47H05 (47B99 49J52)",
MRnumber = "1687802",
MRreviewer = "Pando Georgiev",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/180/",
acknowledgement = ack-nhfb,
fjournal = "Pacific Journal of Mathematics",
journal-URL = "http://msp.org/pjm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bauschke:1999:SCH,
author = "Heinz H. Bauschke and Jonathan M. Borwein and Wu Li",
title = "Strong conical hull intersection property, bounded
linear regularity, {Jameson}'s property {$ (G) $}, and
error bounds in convex optimization",
journal = j-MATH-PROG,
volume = "86",
number = "1, Ser. A",
pages = "135--160",
year = "1999",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/s101070050083",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "90C46 (41A29 90C31)",
MRnumber = "1712477",
MRreviewer = "Charles K. Chui",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/195/",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming. A Publication of the
Mathematical Programming Society",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Research Report 98:107.",
}
@Book{Borowski:1999:DMa,
author = "E. J. (Ephraim J.) Borowski and Jonathan M. Borwein",
title = "Dictionary of mathematics",
publisher = "Unwin Hyman",
address = "London, UK",
pages = "660",
year = "1999",
ISBN = "0-261-67198-7",
ISBN-13 = "978-0-261-67198-0",
LCCN = "????",
bibdate = "Tue Aug 16 09:03:32 MDT 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "Mathematics; Dictionaries",
}
@Book{Borowski:1999:DMb,
author = "E. J. (Ephraim J.) Borowski and Jonathan M. Borwein",
title = "Dictionary of mathematics",
publisher = "HarperCollins",
address = "London, UK",
pages = "672",
year = "1999",
ISBN = "0-00-434347-6 (paperback)",
ISBN-13 = "978-0-00-434347-1 (paperback)",
LCCN = "????",
bibdate = "Mon Oct 23 07:36:34 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "This dictionary of mathematics contains over 9,000
definitions and 400 diagrams and covers subjects such
as abstract analysis; number theory; topology; vectors;
differential equations and more.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Originally published in \cite{Borowski:1988:DM}.",
subject = "Mathematics; Dictionaries; Mathematics.",
}
@Article{Borwein:1999:ESB,
author = "Jonathan M. Borwein and Boris S. Mordukhovich and
Yongheng Shao",
title = "On the Equivalence of Some Basic Principles in
Variational Analysis",
journal = j-J-MATH-ANAL-APPL,
volume = "229",
number = "1",
pages = "228--257",
year = "1999",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1006/jmaa.1998.6157",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "49J52 (46N10)",
MRnumber = "1664320",
MRreviewer = "Abderrahim Jourani",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/192/;
http://www.sciencedirect.com/science/article/pii/S0022247X98961571",
abstract = "The primary goal of this paper is to study
relationships between certain basic principles of
variational analysis and its applications to nonsmooth
calculus and optimization. Considering a broad class of
Banach spaces admitting smooth renorms with respect to
some bornology, we establish an equivalence between
useful versions of a smooth variational principle for
lower semicontinuous functions, an extremal principle
for nonconvex sets, and an enhanced fuzzy sum rule
formulated in terms of viscosity normals and
subgradients with controlled ranks. Further refinements
of the equivalence result are obtained in the case of a
Fr{\'e}chet differentiable norm. Based on the new
enhanced sum rule, we provide a simplified proof for
the refined sequential description of approximate
normals and subgradients in smooth spaces.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
keywords = "fuzzy calculus; generalized differentiation; Nonsmooth
analysis; smooth Banach spaces; variational and
extremal principles; viscosity normals and
subdifferentials",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1999:ETE,
author = "Jonathan M. Borwein and Robert M. Corless",
title = "Emerging tools for experimental mathematics",
journal = j-AMER-MATH-MONTHLY,
volume = "106",
number = "10",
pages = "889--909",
year = "1999",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2589743",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "68W30 (00A05 11Yxx)",
MRnumber = "1732501",
MRreviewer = "Michael M. Dediu",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/203/;
http://www.jstor.org/stable/2589743",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Research Report 98:110.",
}
@Article{Borwein:1999:GSB,
author = "Jonathan M. Borwein and Warren B. Moors and Xianfu
Wang",
title = "Generalized subdifferentials: a {Baire} categorical
approach",
journal = "C. R. Math. Acad. Sci. Soc. R. Can.",
volume = "21",
number = "4",
pages = "132--138",
year = "1999",
ISSN = "0706-1994",
MRclass = "49J52 (46G05 58C20)",
MRnumber = "1728265",
MRreviewer = "Mari{\'a}n Fabian",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/234/",
acknowledgement = ack-nhfb,
fjournal = "Comptes Rendus Math{\'e}matiques de l'Acad{\'e}mie des
Sciences. La Soci{\'e}t{\'e} Royale du Canada.
Mathematical Reports of the Academy of Science. The
Royal Society of Canada",
journal-URL = "https://mr.math.ca/article/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 99:128. The journal web site has no
online archives before volume 27 (2005).",
}
@InProceedings{Borwein:1999:ITD,
author = "J. M. Borwein and T. Stanway",
editor = "John Grant McGloughlin",
booktitle = "{Canadian Mathematics Education Study Group (CMESG)
Proceedings 1999 Annual Meeting}",
title = "The impact of technology on the doing of mathematics",
publisher = "Memorial University Press",
address = "St. Johns, NL, Canada",
pages = "3--6",
year = "1999",
bibdate = "Mon Aug 15 14:30:19 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/248/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1999:MFA,
author = "Jonathan M. Borwein and Qiji J. Zhu",
editor = "F. H. Clarke and R. J. Stern",
booktitle = "Nonlinear analysis, differential equations and control
({Montreal, QC, 1998})",
title = "Multifunctional and functional analytic techniques in
nonsmooth analysis",
volume = "528",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "61--157",
year = "1999",
MRclass = "49J52 (26A16 26E25 46N10)",
MRnumber = "1695006",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "NATO Sci. Ser. C Math. Phys. Sci.",
URL = "http://docserver.carma.newcastle.edu.au/49/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1999:PSS,
author = "Jonathan M. Borwein and C. G. Pinner and David
Bradley",
title = "Problems and Solutions: Solutions: An Infinite
Product: 10605",
journal = j-AMER-MATH-MONTHLY,
volume = "106",
number = "2",
pages = "173--174",
year = "1999",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2589069",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1543419",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1999:PSVa,
author = "Jonathan M. Borwein and Jay S. Treiman and Qiji J.
Zhu",
title = "Partially smooth variational principles and
applications",
journal = j-NONLINEAR-ANAL,
volume = "35",
number = "8",
pages = "1031--1059",
year = "1999",
CODEN = "NOANDD",
DOI = "https://doi.org/10.1016/S0362-546X(98)00113-8",
ISSN = "0362-546x (print), 1873-5215 (electronic)",
ISSN-L = "0362-546X",
MRclass = "49J53 (46T20 47H99)",
MRnumber = "1707806",
MRreviewer = "B. Mordukhovich",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/182/;
http://www.sciencedirect.com/science/article/pii/S0362546X98001138",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
keywords = "Fuzzy sum rules; Mean value inequalities and partially
smooth spaces; Smooth variational principle",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1999:SRM,
author = "Jonathan M. Borwein and Warren B. Moors and Yongheng
Shao",
title = "Subgradient representation of multifunctions",
journal = j-J-AUSTRAL-MATH-SOC-SER-B,
volume = "40",
number = "3",
pages = "301--313",
month = jan,
year = "1999",
CODEN = "JAMMDU",
DOI = "https://doi.org/10.1017/S0334270000010924",
ISSN = "0334-2700",
MRclass = "49J52 (47H04)",
MRnumber = "1674589",
MRreviewer = "Constantin Z{\u{a}}linescu",
bibdate = "Fri Sep 30 10:53:26 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Volume in honour of B. Craven and B. Mond.",
URL = "http://docserver.carma.newcastle.edu.au/184/;
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=3964380",
acknowledgement = ack-nhfb,
fjournal = "Australian Mathematical Society. Journal. Series B.
Applied Mathematics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1999:SSC,
author = "Jonathan M. Borwein and Qiji J. Zhu",
title = "A survey of subdifferential calculus with
applications",
journal = j-NONLINEAR-ANAL,
volume = "38",
number = "6",
pages = "687--773",
year = "1999",
CODEN = "NOANDD",
DOI = "https://doi.org/10.1016/S0362-546X(98)00142-4",
ISSN = "0362-546x (print), 1873-5215 (electronic)",
ISSN-L = "0362-546X",
MRclass = "49J52 (46G05 46N10 49-02 49J53 58C05)",
MRnumber = "1710152",
MRreviewer = "Philip D. Loewen",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "See addendum \cite{Borwein:2002:ASS}.",
URL = "http://docserver.carma.newcastle.edu.au/199/;
http://www.sciencedirect.com/science/article/pii/S0362546X98001424",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
keywords = "Coderivative calculus; Constrained optimization
problems; Generalized gradients; Geometric
subdifferential; Hamilton--Jacobi equations; Implicit
function theorems; Limiting coderivatives; Limiting
subdifferentials; Mean value inequalities; Mean value
theorems; Metric regularity; Open mapping; Proximal
subdifferential; Sensitivity; Smooth spaces;
Subdifferential calculus; Viscosity solutions;
Viscosity subdifferential",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Research Report 98:105.",
}
@Article{Borwein:1999:SVM,
author = "Jonathan M. Borwein and David M. Bradley and David J.
Broadhurst and Petr Lison{\v{e}}k",
title = "Special Values of Multiple Polylogarithms",
journal = "ArXiv Mathematics e-prints",
month = oct,
year = "1999",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/1999math.....10045B;
http://docserver.carma.newcastle.edu.au/200/",
abstract = "Historically, the polylogarithm has attracted
specialists and non-specialists alike with its lovely
evaluations. Much the same can be said for Euler sums
(or multiple harmonic sums), which, within the past
decade, have arisen in combinatorics, knot theory and
high-energy physics. More recently, we have been forced
to consider multidimensional extensions encompassing
the classical polylogarithm, Euler sums, and the
Riemann zeta function. Here, we provide a general
framework within which previously isolated results can
now be properly understood. Applying the theory
developed herein, we prove several previously
conjectured evaluations, including an intriguing
conjecture of Don Zagier.",
acknowledgement = ack-nhfb,
eprint = "math/9910045",
keywords = "Mathematics - Classical Analysis and ODEs, Mathematics
- Combinatorics, 40B05, 33E20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Marechal:1999:CSA,
author = "P. Marechal and D. Togane and A. Celler and J. M.
Borwein",
title = "Computation and stability analysis for regularized
tomographic reconstructions",
journal = j-IEEE-TRANS-NUCL-SCI,
volume = "46",
pages = "2177--2184",
month = dec,
year = "1999",
CODEN = "IRNSAM",
DOI = "https://doi.org/10.1109/23.819301",
ISSN = "0018-9499 (print), 1558-1578 (electronic)",
ISSN-L = "0018-9499",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/1999ITNS...46.2177M",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Nuclear Science",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:19xx:ASW,
author = "Jonathan Borwein and Lou Shitou",
title = "Asymptotics of a Sequence of {Witt} Vectors",
type = "Report",
institution = "Department of Mathematics, Statistics and Computing
Science, Dalhousie University",
address = "Halifax, NS B3H 3J5, Canada",
pages = "13",
year = "19xx",
bibdate = "Fri Nov 11 07:09:34 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "We provide asymptotic and order information about the
Witt vectors and integers $ d_n $ appearing in $
\Prod_{n \geq 1} (1 / (1 + d_n t^n / n!)) = (1 - t) e^t
$.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Undated report. The second author also appears in
journal databases with family name Lou, and personal
name Shi-Tuo.",
}
@TechReport{Borwein:19xx:CFF,
author = "J. M. Borwein and P. B. Borwein",
title = "On the Complexity of Familiar Functions and Numbers",
type = "Report",
institution = "Department of Mathematics, Statistics and Computing
Science, Dalhousie University",
address = "Halifax, NS B3H 3J5, Canada",
pages = "30",
year = "19xx",
MRclass = "6BC25, 41A30, 1OA30",
bibdate = "Fri Nov 11 07:08:04 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "This paper examines low-complexity approximations to
familiar functions and numbers. The intent is to
suggest that a taxonomy of such functions and numbers
based on their computational complexity is possible. A
central theme is that traditional methods of
approximation are often very far from optimal, while
good or optimal methods are often very far from obvious
For most functions provably optimal methods are not
known, however the gap between what is known and what
is possible is often small. A considerable number of
open problems are posed and a number of related
examples are presented.",
acknowledgement = ack-nhfb,
keywords = "$\pi$; algebraic approximation; computation of digits;
Elementary functions; low complexity approximation;
open problems; rational approximation; reduced
complexity approximation",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Undated report",
}
@Unpublished{Borwein:19xx:EIG,
author = "Jonathan M. Borwein",
title = "Elliptic Integrals and the {Gauss--Salamin} formula
for $ \pi $",
pages = "16",
year = "19xx",
bibdate = "Mon Nov 07 07:04:34 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Unpublished hand-written lecture slides at Dalhousie
University. The slides are undated, and the 10
references on the final slides include a reference to
E. Salamin (1976) and to P. Backmann's 1977 book
\booktitle{A History of Pi}.",
abstract = "$ \pi $ was first used by W. Jones (1703) as \emph{pi}
(short for periphery). Euler (1733) first popularized
it as a replacement for $p$ or $c$.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:19xx:EMI,
author = "Jonathan M. Borwein and Peter B. Borwein and Roland
Girgensohn and S. Parnes",
title = "Experimental mathematical investigation of decimal and
continued fraction expansions of select constants",
year = "19xx",
bibdate = "Thu Aug 11 09:30:52 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Unpublished.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Cited in \cite{Octavio:1996:IT}.",
}
@TechReport{Borwein:19xx:MI,
author = "J. M. Borwein and P. B. Borwein",
title = "On the Mean Iteration $ (a, b) \leftarrow ((a + 3 b) /
4, (\sqrt {ab} + b) / 2) $",
type = "Report",
institution = "Department of Mathematics, Statistics and Computing
Science, Dalhousie University",
address = "Halifax, NS B3H 3J5, Canada",
pages = "39",
year = "19xx",
bibdate = "Fri Nov 11 07:10:57 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "The iterative process $ a_{n + 1} = (a_n + 3 b_n) / 4
$, $ b_{n + 1} = (\sqrt {a_n b_n} + b_n) / 2 $ is
studied in detail. The limit of this quadratically
converging process is explicitly identified, as are the
uniformizing parameters. The role of symbolic
computation, in discovering these non-trivial
identifications, is highlighted.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Undated report",
}
@TechReport{Borwein:19xx:PCT,
author = "Jonathan M. Borwein and Peter B. Borwein",
title = "Pi and its computation: a twenty-two hundred year
quest continues: why it is now possible to calculate a
billion digits of pi",
type = "Report",
institution = "Dalhousie University",
address = "Halifax, NS, Canada",
pages = "21",
year = "19xx",
bibdate = "Mon Nov 07 07:01:20 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Undated typeset manuscript intended for
\booktitle{Scientific American}, but never published.
The latest reference is to a 1987 book.",
abstract = "Classical mathematics of Gauss, Ramanujan, and others
combines the modern theory of algorithms to
dramatically improve our understanding of this ancient
problem.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "This paper must have been written between 1987 and
1997, and before the discovery of the BBP algorithm
\cite{Bailey:1997:RCV}, because the last paragraph
says: ``It is also reasonable to speculate that
computing the $n$-th digit of $ \pi $ is not very much
easier than computing all the first $n$ digits. We
think it very probable that computing the $n$-th digit
of $ \pi $ cannot be of a lower order than
multiplication. As a consequence, we conjecture that no
one will ever determine the $ 10^{1000}$-th decimal
digit of $ \pi $.",
}
@TechReport{Borwein:19xx:WMS,
author = "J. M. Borwein and B. Richmond",
title = "When is a matrix a square?",
type = "Research report",
number = "5",
institution = "Department of Mathematics, Dalhousie University and
Department of Combinatorics and Optimization,
University of Waterloo",
address = "Halifax, NS, Canada and Waterloo, ON, Canada",
pages = "22",
year = "19xx",
bibdate = "Mon Nov 07 17:45:04 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "Necessary and sufficient conditions for an arbitrary $
n \times n $ matrix to possess a $k$-th root are given
in terms of the associated Jordan form. These
characterizations are used to give asymptotic estimates
for the relative frequency of nilpotent matrices
possessing square roots. The estimates are entirely
combinatorial in genesis.",
acknowledgement = ack-nhfb,
keywords = "asymptotic formulae; Jordan forms; partition
functions; square roots",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "There are only 5 references on the last page, the most
recent a book from 1976.",
}
@Article{Bauschke:2000:BLR,
author = "Heinz H. Bauschke and Jonathan M. Borwein and Paul
Tseng",
title = "Bounded linear regularity, strong {CHIP}, and {CHIP}
are distinct properties",
journal = j-J-CONVEX-ANAL,
volume = "7",
number = "2",
pages = "395--412",
year = "2000",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "90C48 (41A65 49J53 52A15 52A20)",
MRnumber = "1811687",
MRreviewer = "Wu Li",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.heldermann.de/JCA/JCA07/JCA072/jca07020.htm",
abstract = "Bounded linear regularity, the strong conical hull
intersection property (strong CHIP), and the conical
hull intersection property (CHIP) are properties of a
collection of finitely many closed convex intersecting
sets in Euclidean space. It was shown recently that
these properties are fundamental in several branches of
convex optimization, including convex feasibility
problems, error bounds, Fenchel duality, and
constrained approximation. It was known that regularity
implies strong CHIP. which ill turn implies CHIP;
moreover, the three properties always hold for
subspaces. The question whether or not converse
implications are true for general convex sets was
open.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 98:112.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Bauschke,
Heinz/D-5582-2009",
unique-id = "Bauschke:2000:BLR",
}
@Book{Berggren:2000:PSB,
author = "Lennart Berggren and Jonathan Borwein and Peter
Borwein",
title = "Pi: a source book",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xx + 736",
year = "2000",
DOI = "https://doi.org/10.1007/978-1-4757-3240-5",
ISBN = "0-387-98946-3 (hardcover)",
ISBN-13 = "978-0-387-98946-4 (hardcover)",
LCCN = "QA484 .P5 2000",
MRclass = "11-00 (01A05 01A75 11-03)",
MRnumber = "1746004",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
tableofcontents = "Preface \\
Acknowledgements \\
Introduction \\
The Rhind Mathematical Papyrus-Problem 50 \\
Engles / Quadrature of the Circle in Ancient Egypt \\
Archimedes / Measurement of a Circle \\
Phillips / Archimedes the Numerical Analyst \\
Lam \& Ang / Circle Measurements in Ancient China \\
The Banu Musa: The Measurement of Plane and Solid
Figures \\
Madhava's / The Power Series for Arctan and Pi \\
Hope-Jones / Ludolph van Ceulen \\
Vi{\`e}te / Variorum de Revus Mathematicis Reponsorum
Liber VII \\
Wallis / Computation of Pi by Successive Interpolations
\\
Wallis / Arithmetica Infinitorum \\
Huygens / De Circuli Magnitudine Inventa \\
Gregory / Correspondence with John Collins \\
Jones / The First Use of Pi for the Circle Ratio \\
Newton / Of The Method of Fluxions and Infinite Series
\\
Euler / Chapter 10 of Introduction to Analysis of the
Infinite \\
Lambert / M{\'e}moire Sur Quelques Propri{\'e}t{\'e}s
Remarquables Des Quantit{\'e}s Transcendentes
Circulaires et Logarithmiques \\
Lambert / Irrationality of Pi \\
Shanks / Contributions to Mathematics Comprising
Chiefly of the Rectification of the Circle to 607
Places of Decimals \\
Hermite / Sur La Fonction Exponentielle",
}
@InProceedings{Borwein:2000:AGM,
author = "J. M. Borwein and P. B. Borwein",
booktitle = "Pi: A Source Book",
title = "The Arithmetic--Geometric Mean and Fast Computation of
Elementary Functions",
publisher = pub-SV,
address = pub-SV:adr,
pages = "??--??",
year = "2000",
DOI = "https://doi.org/10.1007/978-1-4757-3240-5_56",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_56",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2000:AIR,
author = "Jonathan M. Borwein and Petr Lison{\v{e}}k",
title = "Applications of integer relation algorithms",
journal = j-DISCRETE-MATH,
volume = "217",
number = "1--3",
pages = "65--82",
year = "2000",
CODEN = "DSMHA4",
DOI = "https://doi.org/10.1016/S0012-365X(99)00256-3",
ISSN = "0012-365x (print), 1872-681x (electronic)",
ISSN-L = "0012-365X",
MRclass = "65Y15 (68W99)",
MRnumber = "1766260",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Formal power series and algebraic combinatorics
(Vienna, 1997).",
URL = "http://docserver.carma.newcastle.edu.au/198/;
http://www.sciencedirect.com/science/article/pii/S0012365X99002563",
abstract = "Let a be a vector of real numbers. By an integer
relation for a we mean a non-zero integer vector c such
that caT=0. We discuss the algorithms for finding such
integer relations from the user's point of view, by
presenting examples of their applications and by
reviewing the available software implementations.",
acknowledgement = ack-nhfb,
fjournal = "Discrete Mathematics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Research Report 97:104.",
}
@Book{Borwein:2000:CAN,
author = "Jonathan M. Borwein and Adrian S. Lewis",
title = "Convex Analysis and Nonlinear Optimization",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 273",
year = "2000",
DOI = "https://doi.org/10.1007/978-1-4757-9859-3",
ISBN = "0-387-98940-4",
ISBN-13 = "978-0-387-98940-2",
MRclass = "49-01 (46N10 47N10 49-02 49J53 90-01)",
MRnumber = "1757448",
MRreviewer = "John R. Giles",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Theory and examples.",
series = "CMS Books in Mathematics/Ouvrages de Math{\'e}matiques
de la SMC, 3",
abstract = "This book is a concise account of convex analysis, its
applications and extensions, for a broad audience.
Blurring as it does the distinctions between
mathematical optimization and modern analysis, the
elegant language of convexity and duality is
indispensable both in computational optimization and
for understanding variational properties of functions
and multifunctions. Primarily aimed at first-year
graduate students, the text consists of short,
self-contained sections, each followed by an extensive
set of exercises, many of which are guided. The book is
thus appropriate either as a class text or for
self-study.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
tableofcontents = "1: Background \\
1.1: Euclidean Spaces \\
1.2: Symmetric Matrices \\
2: Inequality Constraints \\
2.1: Optimality Conditions \\
2.2: Theorems of the Alternative \\
2.3: Max-functions \\
3: Fenchel Duality \\
3.1: Subgradients and Convex Functions \\
3.2: The Value Function \\
3.3: The Fenchel Conjugate \\
4: Convex Analysis \\
4.1: Continuity of Convex Functions \\
4.2: Fenchel Biconjugation \\
4.3: Lagrangian Duality \\
5: Special Cases \\
5.1: Polyhedral Convex Sets and Functions \\
5.2: Functions of Eigenvalues \\
5.3: Duality for Linear and Semidefinite Programming
\\
5.4: Convex Process Duality \\
6: Nonsmooth Optimization \\
6.1: Generalized Derivatives \\
6.2: Regularity and Strict Differentiability \\
6.3: Tangent Cones",
}
@Article{Borwein:2000:CBS,
author = "Jonathan M. Borwein and David J. Broadhurst and Joel
Kamnitzer",
title = "Central Binomial Sums, Multiple {Clausen} Values and
Zeta Values",
journal = "ArXiv High Energy Physics --- Theory e-prints",
month = apr,
year = "2000",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2000hep.th....4153B;
http://docserver.carma.newcastle.edu.au/243/",
abstract = "We find and prove relationships between Riemann zeta
values and central binomial sums. We also investigate
alternating binomial sums (also called Ap{\'e}ry sums).
The study of non-alternating sums leads to an
investigation of different types of sums which we call
multiple Clausen values. The study of alternating sums
leads to a tower of experimental results involving
polylogarithms in the golden ratio. In the
non-alternating case, there is a strong connection to
polylogarithms of the sixth root of unity, encountered
in the 3-loop Feynman diagrams of \url{hep-th/9803091}
and subsequently in \url{hep-ph/9910223},
\url{hep-ph/9910224}, \url{cond-mat/9911452} and
\url{hep-th/0004010}.",
acknowledgement = ack-nhfb,
eprint = "hep-th/0004153",
keywords = "High Energy Physics - Theory, Mathematics - Classical
Analysis and ODEs",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2000:CDA,
author = "Jonathan M. Borwein and Pierre Mar{\'e}chal and David
Naugler",
title = "A convex dual approach to the computation of {NMR}
complex spectra",
journal = "Math. Methods Oper. Res.",
volume = "51",
number = "1",
pages = "91--102",
year = "2000",
DOI = "https://doi.org/10.1007/s001860050004",
ISSN = "1432-2994 (print), 1432-5217 (electronic)",
ISSN-L = "1432-2994",
MRclass = "90C30",
MRnumber = "1742398",
MRreviewer = "Massimo Pappalardo",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/207/",
abstract = "The particular entropy method proposed by Hoch et al.
[7] for the computation of NMR complex spectra allows
an elegant application of the concepts of duality
theory. Correspondingly, duality theory casts new light
on their choice of entropy. The purpose of this paper
is to present the relevant theoretical developments
together with some numerical illustrations.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Methods of Operations Research",
ORCID-numbers = "Naugler, David/0000-0001-5485-0498; Borwein,
Jonathan/0000-0002-1263-0646",
remark = "CECM Research Report 98:114.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2000:CDA",
}
@Article{Borwein:2000:CEL,
author = "Jonathan Borwein and Yves Lucet and Boris
Mordukhovich",
title = "Compactly epi-{Lipschitzian} convex sets and functions
in normed spaces",
journal = j-J-CONVEX-ANAL,
volume = "7",
number = "2",
pages = "375--393",
year = "2000",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "49J53 (46B20 46N10 90C48)",
MRnumber = "1811686",
MRreviewer = "Abderrahim Jourani",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/210/;
http://www.heldermann.de/JCA/JCA07/JCA072/jca07019.htm",
abstract = "We provide several characterizations of compact
epi-Lipschitzness for closed convex sets in normed
vector spaces. In particular, we show that a closed
convex set is compactly epi-Lipschitzian if and only if
it has nonempty relative interior, finite codimension,
and spans a closed subspace. Next, we establish that
all boundary points of compactly epi-Lipschitzian sets
are proper support points. We provide the corresponding
results for functions hy using inf-convolutions and the
Legendre Fenchel transform. We also give an application
to constrained optimization with compactly
epi-Lipschitzian data via a generalized Slater
condition involving relative interiors.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 98:113.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2000:CEL",
}
@Article{Borwein:2000:CSF,
author = "Jonathan M. Borwein and John Read and Adrian S. Lewis
and Qiji Zhu",
title = "Convex spectral functions of compact operators",
journal = j-J-NONLINEAR-CONVEX-ANAL,
volume = "1",
number = "1",
pages = "17--35",
year = "2000",
ISSN = "1345-4773 (print), 1880-5221 (electronic)",
ISSN-L = "1345-4773",
MRclass = "49N15 (47N10 49J52 90C25)",
MRnumber = "1751726",
MRreviewer = "Mihai Turinici",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.ybook.co.jp/online2/jncav1.html",
acknowledgement = ack-nhfb,
fjournal = "Journal of Nonlinear and Convex Analysis. An
International Journal",
journal-URL = "http://www.ybook.co.jp/jnca.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 99:130.",
xxauthor = "Jon Borwein and Adrian Lewis and John Read and Qiji
Zhu",
}
@Article{Borwein:2000:CSR,
author = "Jonathan M. Borwein and David M. Bradley and Richard
E. Crandall",
title = "Computational strategies for the {Riemann} zeta
function",
journal = j-J-COMPUT-APPL-MATH,
volume = "121",
number = "1--2",
pages = "247--296",
month = sep,
year = "2000",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(00)00336-8",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "11M06 (11Y35 33F05)",
MRnumber = "1780051",
MRreviewer = "Cem Y. Y{\i}ld{\i}r{\i}m",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Numerical analysis in the 20th century, Vol. I,
Approximation theory.",
URL = "http://adsabs.harvard.edu/abs/2000JCoAM.121..247B;
http://docserver.carma.newcastle.edu.au/211/;
http://www.sciencedirect.com/science/article/pii/S0377042700003368",
abstract = "We provide a compendium of evaluation methods for the
Riemann zeta function, presenting formulae ranging from
historical attempts to recently found convergent series
to curious oddities old and new. We concentrate
primarily on practical computational issues, such
issues depending on the domain of the argument, the
desired speed of computation, and the incidence of what
we call ``value recycling''.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 98:118.",
}
@Article{Borwein:2000:LFM,
author = "Jonathan M. Borwein and Xianfu Wang",
title = "{Lipschitz} functions with maximal {Clarke}
subdifferentials are generic",
journal = j-PROC-AM-MATH-SOC,
volume = "128",
number = "11",
pages = "3221--3229",
year = "2000",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/S0002-9939-00-05914-1",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "49J52 (26B25 58C20)",
MRnumber = "1777577",
MRreviewer = "Jean-No{\"e}l Corvellec",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/206/",
abstract = "We show that on a separable Banach space most
Lipschitz functions have maximal Clarke subdifferential
mappings. In particular, the generic nonexpansive
function has the dual unit ball as its Clarke
subdifferential at every point. Diverse corollaries are
given.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2000:LFM",
}
@InProceedings{Borwein:2000:NCMa,
author = "J. M. Borwein and T. Stanway",
editor = "Bruce Cload and Tom Jenkyns",
booktitle = "{Proceedings of the Conference on Technology in
Mathematics Education at the Secondary and Tertiary
Levels, June 2--4, 1999 at Brock University}",
title = "Numerical and computational mathematics (at the
undergraduate level)",
publisher = "Brock University Press",
address = "St. Catharines, ON, L2S 3A1 Canada",
pages = "20--37",
year = "2000",
bibdate = "Mon Aug 15 14:24:05 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/246/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Also appeared in Cubo.",
}
@InProceedings{Borwein:2000:PEN,
author = "J. M. Borwein and P. B. Borwein and K. Dilcher",
booktitle = "Pi: A Source Book",
title = "Pi, {Euler} Numbers, and Asymptotic Expansions",
publisher = pub-SV,
address = pub-SV:adr,
pages = "??--??",
year = "2000",
DOI = "https://doi.org/10.1007/978-1-4757-3240-5_65",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1583/;
http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_65",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2000:R,
author = "Jonathan Borwein and Kwok-Kwong Stephen Choi",
title = "On the representations of $ x y + y z + z x $",
journal = j-EXP-MATH,
volume = "9",
number = "1",
pages = "153--158",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2000.10504642",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11D85",
MRnumber = "1758806",
MRreviewer = "Mao Hua Le",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://docserver.carma.newcastle.edu.au/212/;
http://projecteuclid.org/euclid.em/1046889597",
abstract = "We show that there are at most 19 integers that are
not of the form $ x y + y z + x z $ with $ x, y, z \geq
1 $. Eighteen of them are small and easily found. The
remaining possibility must be greater than $ 10^{11} $
and cannot occur if we assume the Generalized Riemann
Hypothesis.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 98:119.",
}
@InProceedings{Borwein:2000:RME,
author = "J. M. Borwein and P. B. Borwein and D. H. Bailey",
booktitle = "Pi: A Source Book",
title = "{Ramanujan}, Modular Equations, and Approximations to
Pi or How to Compute One Billion Digits of Pi",
publisher = pub-SV,
address = pub-SV:adr,
pages = "623--641",
year = "2000",
DOI = "https://doi.org/10.1007/978-1-4757-2736-4_64;
https://doi.org/10.1007/978-1-4757-3240-5_64",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1587/;
http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_64;
http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_64",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2000:SDI,
author = "Jonathan M. Borwein and Warren B. Moors",
title = "Separable determination of integrability and
minimality of the {Clarke} subdifferential mapping",
journal = j-PROC-AM-MATH-SOC,
volume = "128",
number = "1",
pages = "215--221",
month = jan,
year = "2000",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/S0002-9939-99-05001-7",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "49J52 (46N10 58C20)",
MRnumber = "1622793",
MRreviewer = "Lionel Thibault",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/196/;
http://www.jstor.org/stable/119403",
abstract = "In this paper we show that the study of integrability
and D-representability of Lipschitz functions defined
on arbitrary Banach spaces reduces to the study of
these properties on separable Banach spaces.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Research Report 97:102.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2000:SDI",
}
@Article{Borwein:2000:SM,
author = "D. Borwein and J. M. Borwein and P. Mar{\'e}chal",
title = "Surprise maximization",
journal = j-AMER-MATH-MONTHLY,
volume = "107",
number = "6",
pages = "517--527",
month = jun # "\slash " # jul,
year = "2000",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2589347",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "00A08 (03B48 90C90)",
MRnumber = "1767060",
MRreviewer = "S. Kutateladze",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/209/",
abstract = "The Surprise Examination or Unexpected Hanging Paradox
has long fascinated mathematicians and philosophers, as
the number of publications devoted to it attests. For
an exhaustive bibliography on the subject, see [1]. We
examine and solve the optimization problems arising
from an information theoretic avoidance of the Paradox.
These problems provide a very satisfactory application
of both the Kuhn-Tucker theory and of various classical
inequalities and estimation techniques. We assume some
elementary knowledge of optimization but recall the
necessary convex analytic concepts in the course of the
paper. Readers unfamiliar with this background may
simply skip a couple of proofs and a few technical
details.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 98:116.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2000:SM",
}
@Article{Theodorescu:2000:PSS,
author = "Radu Theodorescu and Jonathan M. Borwein",
title = "Problems and Solutions: Solutions: Moments of the
{Poisson} Distribution: 10738",
journal = j-AMER-MATH-MONTHLY,
volume = "107",
number = "7",
pages = "659--659",
month = aug # "\slash " # sep,
year = "2000",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2589135",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1543703",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.jstor.org/stable/2589135",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Bailey:2001:EMR,
author = "David H. Bailey and Jonathan M. Borwein",
booktitle = "Mathematics unlimited---2001 and beyond",
title = "Experimental mathematics: recent developments and
future outlook",
publisher = pub-SV,
address = pub-SV:adr,
pages = "51--66",
year = "2001",
MRclass = "00A99",
MRnumber = "1852153",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/250/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 99:143.",
}
@Article{Bauschke:2001:ESE,
author = "Heinz H. Bauschke and Jonathan M. Borwein and Patrick
L. Combettes",
title = "Essential smoothness, essential strict convexity, and
{Legendre} functions in {Banach} spaces",
journal = j-COMMUN-CONTEMP-MATH,
volume = "3",
number = "4",
pages = "615--647",
year = "2001",
DOI = "https://doi.org/10.1142/S0219199701000524",
ISSN = "0219-1997 (print), 1793-6683 (electronic)",
MRclass = "49J53 (46G05 46N10)",
MRnumber = "1869107",
MRreviewer = "S. Simons",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/232/",
abstract = "The classical notions of essential smoothness,
essential strict convexity, and Legendreness for convex
functions axe extended from Euclidean to Banach spaces.
A pertinent duality theory is developed and several
useful characterizations are given. The proofs rely on
new results on the more subtle behavior of
subdifferentials and directional derivatives at
boundary points of the domain. In weak Asplund spaces,
a new formula allows the recovery of the
subdifferential from nearby gradients. Finally, it is
shown that every Legendre function on a reflexive
Banach space is zone consistent, a fundamental property
in the analysis of optimization algorithms based on
Bregman distances. Numerous illustrating examples are
provided.",
acknowledgement = ack-nhfb,
fjournal = "Communications in Contemporary Mathematics",
journal-URL = "http://www.worldscientific.com/worldscinet/ccm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 00:156.",
researcherid-numbers = "Combettes, Patrick/A-2442-2011 Borwein,
Jonathan/A-6082-2009 Bauschke, Heinz/D-5582-2009",
unique-id = "Bauschke:2001:ESE",
}
@InProceedings{Bauschke:2001:JSC,
author = "Heinz H. Bauschke and Jonathan M. Borwein",
editor = "Dan Butnariu and Yair Censor and Simeon Reich",
booktitle = "Inherently Parallel Algorithms in Feasibility and
Optimization and their Applications ({Haifa}, 2000)",
title = "Joint and separate convexity of the {Bregman}
distance",
volume = "8",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "23--36",
year = "2001",
DOI = "https://doi.org/10.1016/S1570-579X(01)80004-5",
ISSN = "1570-579X (print), 2212-1145 (electronic)",
ISSN-L = "1570-579X",
MRclass = "90C48 (49J53 65J05 90C30)",
MRnumber = "1853214",
MRreviewer = "Simeon Reich",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Studies in Computational Mathematics",
URL = "http://docserver.carma.newcastle.edu.au/227/;
http://www.sciencedirect.com/science/article/pii/S1570579X01800045",
abstract = "Algorithms involving Bregman projections for solving
optimization problems have been receiving much
attention lately. Several of these methods rely
crucially on the joint convexity of the Bregman
distance. In this note, we study joint and separate
convexity of Bregman distances. To bring out the main
ideas more clearly, we consider first functions defined
on an open interval. Our main result states that the
Bregman distance of a given function is jointly convex
if and only if the reciprocal of its second derivative
is concave. We observe that Bregman distances induced
by the two most popular choices --- the energy and the
Boltzmann--Shannon entropy --- are limiting cases in a
profound sense. This result is generalized by weakening
assumptions on differentiability and strict convexity.
We then consider general, not necessarily separable,
convex functions. The characterization of joint
convexity has a natural and beautiful analog. Finally,
we discuss spectral functions, where the situation is
less clear. Throughout, we provide numerous examples to
illustrate our results.",
acknowledgement = ack-nhfb,
keywords = ":Bregman distance; convex function; joint convexity;
separate convexity",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2001:CBS,
author = "Jonathan Michael Borwein and David J. Broadhurst and
Joel Kamnitzer",
title = "Central binomial sums, multiple {Clausen} values, and
zeta values",
journal = j-EXP-MATH,
volume = "10",
number = "1",
pages = "25--34",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2001.10504426",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11G55 (05A10 11M06 33B99)",
MRnumber = "1821569",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://arxiv.org/abs/hep-th/0004153;
http://docserver.carma.newcastle.edu.au/243/;
http://projecteuclid.org/euclid.em/999188418",
abstract = "We find and prove relationships between Riemann zeta
values and central binomial sums. We also investigate
alternating binomial sums (also called Apery sums). The
study of nonalternating sums leads to an investigation
of different types of sums which we call multiple
Clausen values. The study of alternating sums leads to
a tower of experimental results involving
polylogarithms in the golden ratio.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2001:CBS",
}
@Article{Borwein:2001:CFL,
author = "Jonathan M. Borwein and Jon D. Vanderwerff",
title = "Convex functions of {Legendre} type in general
{Banach} spaces",
journal = j-J-CONVEX-ANAL,
volume = "8",
number = "2",
pages = "569--581",
year = "2001",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "46G99 (46N10 49J50)",
MRnumber = "1915959",
MRreviewer = "A. B. N{\'e}meth",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/228/;
http://www.heldermann.de/JCA/JCA08/JCA082/jca08030.htm",
abstract = "Convex functions of Legendre type are constructed on
arbitrary open convex sets in Banach spaces that
satisfy appropriate rotundity and smoothness
conditions. A simple direct proof of the existence of
``universal'' barriers on arbitrary open convex sets in
R-n is given.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 00:151.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2001:CFL",
}
@Article{Borwein:2001:CMCa,
author = "Jonathan M. Borwein and Peter B. Borwein",
title = "Challenges in Mathematical Computing",
journal = j-COMPUT-SCI-ENG,
volume = "3",
number = "3",
pages = "48--53",
month = may # "\slash " # jun,
year = "2001",
CODEN = "CSENFA",
DOI = "https://doi.org/10.1109/5992.919266",
ISSN = "1521-9615 (print), 1558-366X (electronic)",
ISSN-L = "1521-9615",
bibdate = "Wed Aug 10 12:08:56 2016",
bibsource = "http://www.computer.org/cse/cs1999;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/computscieng.bib",
URL = "http://dlib.computer.org/cs/books/cs2001/pdf/c3048.pdf;
http://docserver.carma.newcastle.edu.au/135/;
http://www.computer.org/cse/cs1999c3048abs.htm",
abstract = "Almost all interesting mathematical algorithmic
questions relate to NP-hard questions. Such computation
is prone to explode exponentially. The authors
anticipate the greatest benefit will come from
mathematical platforms that allow for computer-assisted
insight generation, not from solutions of
grand-challenge problems.",
acknowledgement = ack-nhfb,
fjournal = "Computing in Science and Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
keywords = "Algebra; computational complexity; Computer
architecture; Computer networks; computer-assisted
insight generation; Databases; Encyclopedias;
grand-challenge problems; HTML; Java; mathematical
algorithmic questions; mathematical computing;
mathematical platforms; Mathematics; mathematics
computing; NP-hard questions; Packaging; Statistics;
symbol manipulation",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2001:CMC",
}
@InCollection{Borwein:2001:CSF,
author = "Jonathan M. Borwein and Adrian S. Lewis and Qiji J.
Zhu",
booktitle = "Optimization and related topics
({Ballarat}/{Melbourne}, 1999)",
title = "Convex spectral functions of compact operators. {II}.
{Lower} semicontinuity and rearrangement invariance",
volume = "47",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "179--196",
year = "2001",
DOI = "https://doi.org/10.1007/978-1-4757-6099-6_12",
MRclass = "49N15 (47A10 47B10 90C25)",
MRnumber = "1893622",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Appl. Optim.",
URL = "http://docserver.carma.newcastle.edu.au/251/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2001:DIS,
author = "J. M. Borwein and S. P. Fitzpatrick",
title = "Duality inequalities and sandwiched functions",
journal = j-NONLINEAR-ANAL,
volume = "46",
number = "3",
pages = "365--380",
year = "2001",
CODEN = "NOANDD",
DOI = "https://doi.org/10.1016/S0362-546X(00)00129-2",
ISSN = "0362-546x (print), 1873-5215 (electronic)",
ISSN-L = "0362-546X",
MRclass = "49J53 (49N15 90C46)",
MRnumber = "1851858",
MRreviewer = "Roberto Lucchetti",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/204/;
http://www.sciencedirect.com/science/article/pii/S0362546X00001292",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
keywords = "Ekeland variational principle; Fenchel duality;
Mean-value inequalities; Nonconvex separation; Sandwich
theorem; Schauder fixed-point theorem",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Research Report 98:111.",
}
@Article{Borwein:2001:EM,
author = "Jonathan M. Borwein",
title = "Experimental Mathematics",
journal = j-AUSTRALIAN-MATH-SOC-GAZ,
volume = "28",
number = "??",
pages = "77--80",
month = "????",
year = "2001",
DOI = "",
ISSN = "0311-0729 (print), 1326-2297 (electronic)",
ISSN-L = "0311-0729",
bibdate = "Fri Aug 12 11:12:55 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1527/",
acknowledgement = ack-nhfb,
ajournal = "Aust. Math. Soc. Gaz.",
fjournal = "Australian Mathematical Society Gazette",
journal-URL = "http://www.austms.org.au/gazette",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2001:GSB,
author = "Jonathan M. Borwein and Warren B. Moors and Xianfu
Wang",
title = "Generalized subdifferentials: a {Baire} categorical
approach",
journal = j-TRANS-AM-MATH-SOC,
volume = "353",
number = "10",
pages = "3875--3893",
year = "2001",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.1090/S0002-9947-01-02820-3",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "49J52 (46G05 58C20)",
MRnumber = "1837212",
MRreviewer = "Mari{\'a}n Fabian",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/234/",
abstract = "We use Baire categorical arguments to construct
pathological locally Lipschitz functions. The origins
of this approach can be traced back to Banach and
Mazurkiewicz (1931) who independently used similar
categorical arguments to show that ``almost every
continuous real-valued function defined on [0,1] is
nowhere differentiable''. As with the results of Banach
and Mazurkiewicz, it appears that it is easier to show
that almost every function possesses a certain property
than to construct a single concrete example. Among the
most striking results contained in this paper are:
Almost every 1-Lipschitz function defined on a Banach
space has a Clarke subdifferential mapping that is
identically equal to the dual ball; if \{T-1;
T-2,...,T-n\} is a family of maximal cyclically
monotone operators defined on a Banach space X then
there exists a real-valued locally Lipschitz function g
such that partial derivative (0g)(x) =co \{T-1(x);
T-2(x),...,T-n(x)\} for each x is an element of X; in a
separable Banach space each non-empty weak* compact
convex subset in the dual space is identically equal to
the approximate subdifferential mapping of some
Lipschitz function and for locally Lipschitz functions
defined on separable spaces the notions of strong and
weak integrability coincide.",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 99:127.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2001:GSB",
}
@Article{Borwein:2001:RCS,
author = "D. Borwein and J. Borwein and G. Fee and R.
Girgensohn",
title = "Refined convexity and special cases of the
{Blaschke--Santalo} inequality",
journal = j-MATH-INEQUAL-APPL,
volume = "4",
number = "4",
pages = "631--638",
year = "2001",
DOI = "https://doi.org/10.7153/mia-04-56",
ISSN = "1331-4343 (print), 1848-9966 (electronic)",
ISSN-L = "1331-4343",
MRclass = "52A38 (26B25 52A40)",
MRnumber = "1859668",
MRreviewer = "Beifang Chen",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/222/",
abstract = "We derive the l(p) version of the classical
Blaschke-Santalo inequality for polar volumes as a
consequence of more subtle convexity estimates for the
volume of the p-ball in Euclidean space. We also give
analogs for the (p, q) -substitution norm.",
acknowledgement = ack-nhfb,
ajournal = "Math. Inequal. Appl.",
fjournal = "Mathematical Inequalities \& Applications",
journal-URL = "http://mia.ele-math.com/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 00:146.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2001:RCS",
}
@Article{Borwein:2001:RGC,
author = "J. M. Borwein and M. Fabian and I. Kortezov and P. D.
Loewen",
title = "The range of the gradient of a continuously
differentiable bump",
journal = j-J-NONLINEAR-CONVEX-ANAL,
volume = "2",
number = "1",
pages = "1--19",
year = "2001",
ISSN = "1345-4773 (print), 1880-5221 (electronic)",
ISSN-L = "1345-4773",
MRclass = "58C20 (46G05 49J53)",
MRnumber = "1828155",
MRreviewer = "Mari{\'a}n Fabian",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special issue for Professor Ky Fan.",
URL = "http://docserver.carma.newcastle.edu.au/231/;
http://www.ybook.co.jp/online2/opjnca/vol2/p1.html",
acknowledgement = ack-nhfb,
fjournal = "Journal of Nonlinear and Convex Analysis. An
International Journal",
journal-URL = "http://www.ybook.co.jp/jnca.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2001:RP,
author = "Jonathan M. Borwein and Peter B. Borwein",
title = "{Ramanujan} and pi",
crossref = "Berndt:2001:RES",
pages = "187--199",
year = "2001",
MRclass = "11-03 (01A70)",
MRnumber = "1862751",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Reprint of \cite{Borwein:1988:RP}.",
series = "Hist. Math.",
URL = "http://docserver.carma.newcastle.edu.au/1379/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2001:SGR,
author = "Jonathan M. Borwein and Ivaylo Kortezov",
title = "Some generic results on nonattaining functionals",
journal = j-SET-VALUED-ANAL,
volume = "9",
number = "1--2",
pages = "35--47",
year = "2001",
CODEN = "SVANEG",
DOI = "https://doi.org/10.1023/A:1011246414064",
ISSN = "0927-6947 (print), 1572-932x (electronic)",
ISSN-L = "0927-6947",
MRclass = "46N10 (49J53 54E52)",
MRnumber = "1845933",
MRreviewer = "Gargi Chakraborty",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Wellposedness in optimization and related topics
(Gargnano, 1999).",
URL = "http://docserver.carma.newcastle.edu.au/221/",
abstract = "We prove that (a) in a reflexive space, for any
linearly bounded but unbounded closed convex subset the
nonsupport functionals are a dense G(delta) subset of
the polar set, and (b) any non-semicoercive proper
convex Isc [weak*-lsc] function in a [dual] Banach
space has a generic [dense G(delta)] set of
L-infinity-perturbations which do not attain their
infimum. We also characterize the proper convex
functions that have inf-nonattaining
L-infinity-perturbations. This results also in a
criterion for reflexivity.",
acknowledgement = ack-nhfb,
fjournal = "Set-Valued Analysis. An International Journal Devoted
to the Theory of Multifunctions and its Applications",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2001:SGR",
}
@Article{Borwein:2001:SRP,
author = "David Borwein and Jonathan M. Borwein",
title = "Some remarkable properties of sinc and related
integrals",
journal = j-RAMANUJAN-J,
volume = "5",
number = "1",
pages = "73--89",
year = "2001",
CODEN = "RAJOF9",
DOI = "https://doi.org/10.1023/A:1011497229317",
ISSN = "1382-4090 (print), 1572-9303 (electronic)",
ISSN-L = "1382-4090",
MRclass = "42A38 (26D15 40A05 41A55)",
MRnumber = "1829810",
MRreviewer = "Philip Heywood",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/249/",
abstract = "Using Fourier transform techniques, we establish
inequalities for integrals of the form [GRAPHICS] We
then give quite striking closed form evaluations of
such integrals and finish by discussing various
extensions and applications.",
acknowledgement = ack-nhfb,
fjournal = "The {Ramanujan} Journal",
journal-URL = "http://link.springer.com/journal/11139",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2001:SRP",
}
@Article{Borwein:2001:STC,
author = "J. M. Borwein and X. Wang",
title = "Subdifferentiability of typical continuous functions",
journal = "Nonlinear Analysis Forum",
volume = "6",
number = "1",
pages = "49--58",
year = "2001",
ISSN = "1226-7228",
MRclass = "49J52 (26A24 46G05 46T20)",
MRnumber = "1844467",
MRreviewer = "Yan Gao",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Nonlinear analysis and its applications (St. John's,
NF, 1999).",
URL = "http://docserver.carma.newcastle.edu.au/241/;
http://prof.ks.ac.kr/bslee/naf/table/vol-0601/v0601-05a.PDF",
acknowledgement = ack-nhfb,
ajournal = "Nonlinear Anal. Forum",
fjournal = "Nonlinear Analysis Forum. An International Journal",
journal-URL = "http://prof.ks.ac.kr/bslee/naf/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2001:SVM,
author = "Jonathan M. Borwein and David M. Bradley and David J.
Broadhurst and Petr Lison{\v{e}}k",
title = "Special values of multiple polylogarithms",
journal = j-TRANS-AM-MATH-SOC,
volume = "353",
number = "3",
pages = "907--941",
month = mar,
year = "2001",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.1090/S0002-9947-00-02616-7",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "33B30 (11G55 11Y60 33E20)",
MRnumber = "1709772",
MRreviewer = "P. D. F. Ion",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.jstor.org/stable/221840",
abstract = "Historically, the polylogarithm has attracted
specialists and nonspecialists alike with its lovely
evaluations. Much the same can be said for Euler sums
(or multiple harmonic sums), which, within the past
decade, have arisen in combinatorics, knot theory and
high-energy physics. More recently, we have been forced
to consider multidimensional extensions encompassing
the classical polylogarithm, Euler sums, and the
Riemann zeta function. Here, we provide a general
framework within which previously isolated results can
now be properly understood. Applying the theory
developed herein, we prove several previously
conjectured evaluations, including an intriguing
conjecture of Don Zagier.",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2001:SVM",
}
@Article{Lindqvist:2001:PSS,
author = "Peter Lindqvist and Jaak Peetre and Jonathan M.
Borwein",
title = "Problems and Solutions: Solutions: Generalized
Trigonometric Functions: 10744",
journal = j-AMER-MATH-MONTHLY,
volume = "108",
number = "5",
pages = "473--474",
year = "2001",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2695813",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRnumber = "1544137",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Borowski:2002:MCD,
author = "Ephraim J. Borowski and Jonathan M. Borwein",
title = "Mathematics: {Collins} dictionary",
publisher = "Collins",
address = "London, UK",
edition = "Second",
pages = "633",
year = "2002",
ISBN = "0-00-710295-X",
ISBN-13 = "978-0-00-710295-2",
LCCN = "????",
bibdate = "Tue Aug 16 09:04:49 MDT 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "Mathematics; Dictionaries; Mathematik;
W{\"o}rterbuch.; Mathematics.",
}
@Article{Borwein:2002:ANB,
author = "J. M. Borwein and M. Jim{\'e}nez-Sevilla and J. P.
Moreno",
title = "Antiproximinal norms in {Banach} spaces",
journal = j-J-APPROX-THEORY,
volume = "114",
number = "1",
pages = "57--69",
year = "2002",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1006/jath.2001.3636",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "46B20 (41A65)",
MRnumber = "1880294",
MRreviewer = "Ioan {\c{S}}erb",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/233/;
http://www.sciencedirect.com/science/article/pii/S0021904501936366",
abstract = "We prove that every Banach space containing a
complemented copy of $ c_0 $ has an antiproximinal body
for a suitable norm. If, in addition, the space is
separable, there is a pair of antiproximinal norms. In
particular, in a separable polyhedral space $X$, the
set of all (equivalent) norms on $X$ having an
isomorphic antiproximinal norm is dense. In contrast,
it is shown that there are no antiproximinal norms in
Banach spaces with the convex point of continuity
property (CPCP). Other questions related to the
existence of antiproximinal bodies are also
discussed.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
received = "CECM Preprint 00:157.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2002:ANB",
}
@Article{Borwein:2002:ASS,
author = "Jonathan M. Borwein and Qiji J. Zhu",
title = "Addendum: ``{A survey of subdifferential calculus with
applications'' [Nonlinear Anal.\ {\bf 38} (1999), no.\
6, Ser.\ A: Theory Methods, 687--773; (2000j:49024)]}",
journal = j-NONLINEAR-ANAL,
volume = "49",
number = "2, Ser. A: Theory Methods",
pages = "295--296",
year = "2002",
CODEN = "NOANDD",
DOI = "https://doi.org/10.1016/S0362-546X(01)00099-2",
ISSN = "0362-546x (print), 1873-5215 (electronic)",
ISSN-L = "0362-546X",
MRclass = "49J52 (46G05 46N10 49-02 49J53 58C05)",
MRnumber = "1885123",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "See \cite{Borwein:1999:SSC}.",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2002:CBC,
author = "J. M. Borwein and J. D. Vanderwerff",
title = "On the continuity of biconjugate convex functions",
journal = j-PROC-AM-MATH-SOC,
volume = "130",
number = "6",
pages = "1797--1803",
month = jun,
year = "2002",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/S0002-9939-01-06249-9",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "46B20 (46N10 52A41)",
MRnumber = "1887028",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/230/;
http://www.jstor.org/stable/2699775",
abstract = "We show that a Banach space is a Grothendieck space if
and only if every continuous convex function on $X$ has
a continuous biconjugate function on $ X**$, thus also
answering a question raised by S. Simons. Related
characterizations and examples are given.",
acknowledgement = ack-nhfb,
article-number = "UNSP S 0002-9939(01)06249-9",
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 00:154.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2002:CBC",
}
@Article{Borwein:2002:EMI,
author = "J. M. Borwein",
title = "Experimental Mathematics and Integer Relations",
journal = "European Research Consortium for Informatics and
Mathematics, ERCIM News",
volume = "50",
number = "??",
pages = "30--31",
month = jul,
year = "2002",
bibdate = "Sat Aug 13 17:35:58 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Section Special Theme ERCIMathematics.",
acknowledgement = ack-nhfb,
journal-URL = "http://ercim-news.ercim.eu/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "The journal web sites has no online content before
volume 86, July 2011.",
}
@Article{Borwein:2002:FES,
author = "J. M. Borwein and I. Kortezov and H. Wiersma",
title = "A {$ C^1 $}-function that is even on a sphere and has
no critical points in the ball",
journal = j-J-NONLINEAR-CONVEX-ANAL,
volume = "3",
number = "1",
pages = "1--16",
year = "2002",
ISSN = "1345-4773 (print), 1880-5221 (electronic)",
ISSN-L = "1345-4773",
MRclass = "49J53 (26B35 47J30)",
MRnumber = "1895233",
MRreviewer = "S. Simons",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.ybook.co.jp/online2/jncav3.html",
acknowledgement = ack-nhfb,
fjournal = "Journal of Nonlinear and Convex Analysis. An
International Journal",
journal-URL = "http://www.ybook.co.jp/jnca.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 01:164.",
}
@Article{Borwein:2002:MVS,
author = "David Borwein and Jonathan M. Borwein and Bernard A.
{Mares, Jr.}",
title = "Multi-variable sinc integrals and volumes of
polyhedra",
journal = j-RAMANUJAN-J,
volume = "6",
number = "2",
pages = "189--208",
year = "2002",
CODEN = "RAJOF9",
DOI = "https://doi.org/10.1023/A:1015727317007",
ISSN = "1382-4090 (print), 1572-9303 (electronic)",
ISSN-L = "1382-4090",
MRclass = "52A38 (42B10)",
MRnumber = "1908197",
MRreviewer = "Carla Peri",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/56/",
abstract = "We investigate multi-variable integrals of products of
sinc functions and show how they may be interpreted as
volumes of symmetric convex polyhedra. We then derive
an explicit formula for computing such sinc integrals
and so equivalently volumes of polyhedra.",
acknowledgement = ack-nhfb,
fjournal = "The {Ramanujan} Journal",
journal-URL = "http://link.springer.com/journal/11139",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 01:159.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2002:MVS",
}
@Article{Borwein:2002:RGL,
author = "J. M. Borwein and M. Fabian and P. D. Loewen",
title = "The range of the gradient of a {Lipschitz} {$ C^1
$}-smooth bump in infinite dimensions",
journal = j-ISRAEL-J-MATH,
volume = "132",
number = "1",
pages = "239--251",
month = dec,
year = "2002",
CODEN = "ISJMAP",
DOI = "https://doi.org/10.1007/BF02784514",
ISSN = "0021-2172 (print), 1565-8511 (electronic)",
ISSN-L = "0021-2172",
MRclass = "58C05 (46B20 46G05)",
MRnumber = "1952623",
MRreviewer = "Li Xin Cheng",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/144/;
http://link.springer.com/article/10.1007/BF02784514",
abstract = "If a Banach space has a Lipschitz C-1-smooth bump
function, then it admits other bumps of the same
smoothness whose gradients exactly fill the dual unit
ball and other reasonable figures. This strengthens a
result of Azagra and Deville who were able to cover the
dual unit ball.",
acknowledgement = ack-nhfb,
fjournal = "Israel Journal of Mathematics",
journal-URL = "http://link.springer.com/journal/11856",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 01:169.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Fabian,
Marian/D-5427-2014",
unique-id = "Borwein:2002:RGL",
}
@Article{Borwein:2002:RNC,
author = "Jon Borwein and John Giles and Jon Vanderwerff",
title = "Rotund norms, {Clarke} subdifferentials and extensions
of {Lipschitz} functions",
journal = j-NONLINEAR-ANAL,
volume = "48",
number = "2",
pages = "287--301",
year = "2002",
CODEN = "NOANDD",
DOI = "https://doi.org/10.1016/S0362-546X(00)00187-5",
ISSN = "0362-546x (print), 1873-5215 (electronic)",
ISSN-L = "0362-546X",
MRclass = "49J52 (46B20)",
MRnumber = "1870757",
MRreviewer = "Lionel Thibault",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/219/;
http://www.sciencedirect.com/science/article/pii/S0362546X00001875",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
keywords = "Baire category; Clarke subdifferentials; Extensions;
Lipschitz functions; Rotund norms",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 98:126.",
}
@Article{Borwein:2002:SSC,
author = "Jonathan M. Borwein and Qiji J. Zhu",
title = "A survey of subdifferential calculus with
applications: [Nonlinear Anal. TMA {\bf 38} (1999)
687--773]",
journal = j-NONLINEAR-ANAL,
volume = "49",
number = "2",
pages = "295--296",
year = "2002",
CODEN = "NOANDD",
DOI = "https://doi.org/10.1016/S0362-546X(01)00099-2",
ISSN = "0362-546x (print), 1873-5215 (electronic)",
ISSN-L = "0362-546X",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/199/;
http://www.sciencedirect.com/science/article/pii/S0362546X01000992",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Analysis, Theory, Methods and Applications",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bauschke:2003:BMO,
author = "Heinz H. Bauschke and Jonathan M. Borwein and Patrick
L. Combettes",
title = "{Bregman} monotone optimization algorithms",
journal = j-SIAM-J-CONTROL-OPTIM,
volume = "42",
number = "2",
pages = "596--636",
year = "2003",
CODEN = "SJCODC",
DOI = "https://doi.org/10.1137/S0363012902407120",
ISSN = "0363-0129 (print), 1095-7138 (electronic)",
ISSN-L = "0363-0129",
MRclass = "90C25 (47H05 47N10 90C48)",
MRnumber = "1982285",
MRreviewer = "Simeon Reich",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/127/",
abstract = "A broad class of optimization algorithms based on
Bregman distances in Banach spaces is unified around
the notion of Bregman monotonicity. A systematic
investigation of this notion leads to a simplified
analysis of numerous algorithms and to the development
of a new class of parallel block-iterative surrogate
Bregman projection schemes. Another key contribution is
the introduction of a class of operators that is shown
to be intrinsically tied to the notion of Bregman
monotonicity and to include the operators commonly
found in Bregman optimization methods. Special emphasis
is placed on the viability of the algorithms and the
importance of Legendre functions in this regard.
Various applications are discussed.",
acknowledgement = ack-nhfb,
article-number = "PII S0363012902407120",
fjournal = "SIAM Journal on Control and Optimization",
journal-URL = "http://epubs.siam.org/sicon",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930 Borwein,
Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 02:184.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Combettes,
Patrick/A-2442-2011 Bauschke, Heinz/D-5582-2009",
unique-id = "Bauschke:2003:BMO",
}
@Article{Benoist:2003:CQV,
author = "Jo{\"e}l Benoist and Jonathan M. Borwein and Nicolae
Popovici",
title = "A characterization of quasiconvex vector-valued
functions",
journal = j-PROC-AM-MATH-SOC,
volume = "131",
number = "4",
pages = "1109--1113",
month = apr,
year = "2003",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/S0002-9939-02-06761-8",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "26B25 (49J53 90C26)",
MRnumber = "1948101",
MRreviewer = "Laura Martein",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/145/;
http://www.jstor.org/stable/1194189",
abstract = "The aim of this paper is to characterize in terms of
scalar quasiconvexity the vector-valued functions which
are $K$-quasiconvex with respect to a closed convex
cone $K$ in a Banach space. Our main result extends a
well-known characterization of $K$-quasiconvexity by
means of extreme directions of the polar cone of $K$,
obtained by Dinh The Luc in the particular case when
$K$ is a polyhedral cone generated by exactly $n$
linearly independent vectors in the Euclidean space $
R^n$.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Popovici, Nicolae/0000-0002-1842-6005 Roohi,
Mehdi/0000-0002-8444-042X Borwein,
Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 01:170.",
researcherid-numbers = "Popovici, Nicolae/G-6304-2010 Borwein,
Jonathan/A-6082-2009",
unique-id = "Benoist:2003:CQV",
}
@TechReport{Berggren:2003:PP,
author = "Lennart Berggren and Jonathan Borwein and Peter
Borwein",
title = "A Pamphlet on Pi",
type = "CECM Preprint",
number = "2003:210",
institution = inst-CECM,
address = inst-CECM:adr,
month = jun,
year = "2003",
bibdate = "Tue Aug 16 10:15:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/33/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2003:BGT,
author = "J. M. Borwein and A. L. Dontchev",
title = "On the {Bartle--Graves} theorem",
journal = j-PROC-AM-MATH-SOC,
volume = "131",
number = "8",
pages = "2553--2560",
year = "2003",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/S0002-9939-03-07229-0",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "49J53 (47J20)",
MRnumber = "1974655",
MRreviewer = "Mari{\'a}n Fabian",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "The Bartle-Graves theorem extends the Banach open
mapping principle to a family of linear and bounded
mappings, thus showing that surjectivity of each member
of the family is equivalent to the openness of the
whole family. In this paper we place this theorem in
the perspective of recent concepts and results, and
present a general Bartle-Graves theorem for set-valued
mappings. As applications, we obtain versions of this
theorem for mappings defined by systems of
inequalities, and for monotone variational
inequalities.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 02:185.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Dontchev,
Assen/J-6833-2017",
unique-id = "Borwein:2003:BGT",
}
@InCollection{Borwein:2003:BTE,
author = "Jonathan M. Borwein",
editor = "A. Michalos",
booktitle = "Royal Society of Canada Volume",
title = "The best teacher {I} ever had: personal reports from
highly productive scholars",
publisher = "Althouse Press",
address = "????",
pages = "??--??",
year = "2003",
bibdate = "Sat Aug 13 17:29:16 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2003:CEI,
author = "Jonathan Borwein and Roland Girgensohn",
title = "A class of exponential inequalities",
journal = j-MATH-INEQUAL-APPL,
volume = "6",
number = "3",
pages = "397--411",
year = "2003",
DOI = "https://doi.org/10.7153/mia-06-37",
ISSN = "1331-4343 (print), 1848-9966 (electronic)",
ISSN-L = "1331-4343",
MRclass = "26D15",
MRnumber = "1992480",
MRreviewer = "Feng Qi",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/148/",
abstract = "We prove that for reals $ x_i $ with $ \sum x_i \geq 0
$, the estimate $ \sum x_i e^{x_i} \geq (C_N / N) \sum
x_i^2 $ holds, where $ C_N = \max \{ 2, e (1 - 1 / N)
\} $. We also prove analogues for the $I$-norm and for
Lebesgue-integrable functions.",
acknowledgement = ack-nhfb,
ajournal = "Math. Inequal. Appl.",
fjournal = "Mathematical Inequalities \& Applications",
journal-URL = "http://mia.ele-math.com/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 01:174.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2003:CEI",
}
@Article{Borwein:2003:DSS,
author = "Jonathan Michael Borwein and Kwok-Kwong Stephen Choi",
title = "On {Dirichlet} series for sums of squares",
journal = j-RAMANUJAN-J,
volume = "7",
number = "1--3",
pages = "95--127",
year = "2003",
CODEN = "RAJOF9",
DOI = "https://doi.org/10.1023/A:1026230709945",
ISSN = "1382-4090 (print), 1572-9303 (electronic)",
ISSN-L = "1382-4090",
MRclass = "11M41 (11E25)",
MRnumber = "2035795",
MRreviewer = "Don Redmond",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Rankin memorial issues.",
URL = "http://docserver.carma.newcastle.edu.au/142/",
abstract = "Hardy and Wright (\booktitle{An Introduction to the
Theory of Numbers}, 5th edn., Oxford, 1979) recorded
elegant closed forms for the generating functions of
the divisor functions $ \sigma_k(n) $ and $
\sigma^2_k(n) $ in the terms of Riemann Zeta function $
\zeta (s) $ only. In this paper, we explore other
arithmetical functions enjoying this remarkable
property. In Theorem 2.1 below, we are able to
generalize the above result and prove that if $ f_i $
and $ g_i $ are completely multiplicative, then we have
[large equation] where $ L_f(s) := \sum_{n = 1}^\infty
f(n) n^{-s} $ is the Dirichlet series corresponding to
$f$. Let $ r_N(n)$ be the number of solutions of $
x_1^2 + \ldots {} + x_N^2 = n$ and $ r_{2, P}(n)$ be
the number of solutions of $ x^2 + P y^2 = n$. One of
the applications of Theorem 2.1 is to obtain closed
forms, in terms of $ \zeta (s)$ and Dirichlet
$L$-functions, for the generating functions of $
r_N(n)$, $ r_N^2 (n)$, $ r_{2, P}(n)$ and $ r_{2,
P}(n)^2$ for certain $N$ and $P$. We also use these
generating functions to obtain asymptotic estimates of
the average values for each function for which we
obtain a Dirichlet series.",
acknowledgement = ack-nhfb,
fjournal = "The {Ramanujan} Journal",
journal-URL = "http://link.springer.com/journal/11139",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 01:167.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2003:DSS",
}
@Article{Borwein:2003:LFL,
author = "J. M. Borwein and Xianfu Wang",
title = "{Lipschitz} functions on the line with prescribed
{H}{\"o}lder subdifferentials",
journal = "Advanced Studies in Contemporary Mathematics
(Kyungshang).",
volume = "7",
number = "2",
pages = "93--117",
year = "2003",
ISSN = "1229-3067",
ISSN-L = "1229-3067",
MRclass = "49J52 (26A16 26A24 26A27)",
MRnumber = "2005859",
MRreviewer = "Mari{\'a}n Fabian",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1526/",
acknowledgement = ack-nhfb,
ajournal = "Adv. Stud. Contemp. Math. (Kyungshang)",
fjournal = "Advanced Studies in Contemporary Mathematics
(Kyungshang). Memoirs of the Jangjeon Mathematical
Society",
journal-URL = "http://www.jangjeon.or.kr/etc/Search.html?division=ASCM",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Article archive requires login access.",
}
@Article{Borwein:2003:LLC,
author = "J. M. Borwein and J. Vanderwerff and Xianfu Wang",
title = "Local {Lipschitz}-constant functions and maximal
subdifferentials",
journal = j-SET-VALUED-ANAL,
volume = "11",
number = "1",
pages = "37--67",
year = "2003",
CODEN = "SVANEG",
DOI = "https://doi.org/10.1023/A:1021975622768",
ISSN = "0927-6947 (print), 1572-932X (electronic)",
ISSN-L = "0927-6947",
MRclass = "49J52 (54E40 54E52)",
MRnumber = "1954034",
MRreviewer = "John R. Giles",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://link.springer.com/article/10.1023/A%3A1021975622768",
abstract = "It is shown that if $ k(x) $ is an upper
semicontinuous and quasi lower semicontinuous function
on a Banach space $X$, then $ k(x) B - X*$ is the
Clarke subdifferential of some locally Lipschitz
function on $X$. Related results for approximate
subdifferentials are also given. Moreover, on smooth
Banach spaces, for every locally Lipschitz function
with minimal Clarke subdifferential, one can obtain a
maximal Clarke subdifferential map via its `local
Lipschitz-constant' function. Finally, some results
concerning the characterization and calculus of local
Lipschitz-constant functions are developed.",
acknowledgement = ack-nhfb,
fjournal = "Set-Valued Analysis. An International Journal Devoted
to the Theory of Multifunctions and its Applications",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 01:158.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2003:LLC",
}
@InProceedings{Borwein:2003:MDM,
author = "J. M. Borwein and T. Stanway",
title = "Managing Digital Mathematical Discourse",
crossref = "Asperti:2003:MKM",
pages = "45--55",
year = "2003",
bibdate = "Sat Aug 13 17:26:56 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "In this paper, we propose that the present state of
Mathematical Knowledge Management (MKM) derives from
two main imperatives: the desire to organize and
encapsulate mathematical knowledge after it is produced
and the desire to encapsulate the act of production.
While progress in digital network technology has
facilitated a confluence of these efforts, their
original separation imposes an approximate rubric on
MKM which may be used to help define the challenges
facing the field. We propose that one of the main
challenges lies in the question of fixed versus
flexible ontologies and the related question of
ontology resolution between applications. Finally, we
describe Emkara, an application which adopts a flexible
metadata definition in the archiving and retrieval of
digital mathematical exchanges, queries, and grey
literature.",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2003:MDM",
}
@Article{Borwein:2003:NRI,
author = "J. Borwein and R. Goebel",
title = "Notions of relative interior in {Banach} spaces",
journal = "J. Math. Sci. (NY)",
volume = "115",
number = "4",
pages = "2542--2553",
year = "2003",
CODEN = "JMTSEW",
DOI = "https://doi.org/10.1023/A:1022988116044",
ISSN = "1072-3374 (print), 1573-8795 (electronic)",
MRclass = "49J53 (46B20 90C48)",
MRnumber = "1992991",
MRreviewer = "Constantin Z{\u{a}}linescu",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special issue on optimization and related topics, 1.",
URL = "http://docserver.carma.newcastle.edu.au/138/;
http://link.springer.com/article/10.1023/A%3A1022988116044",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Sciences (New York)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 01:162.",
}
@Article{Borwein:2003:PDA,
author = "J. Borwein and R. Choksi and P. Mar{\'e}chal",
title = "Probability distributions of assets inferred from
option prices via the principle of maximum entropy",
journal = j-SIAM-J-OPT,
volume = "14",
number = "2",
pages = "464--478",
year = "2003",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/S1052623401400324",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
MRclass = "90C25 (91B28)",
MRnumber = "2048161",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/10/",
abstract = "This article revisits the maximum entropy algorithm in
the context of recovering the probability distribution
of an asset from the prices of finitely many associated
European call options via partially finite
convex-programming. We are able to provide an effective
characterization of the constraint qualification under
which the problem reduces to optimizing an explicit
function in finitely many variables. We also prove that
the value (or objective) function is lower
semicontinuous on its domain. Reference is given to a
website which exploits these ideas for the efficient
computation of the maximum entropy solution (MES).",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 02:176.",
researcherid-numbers = "Choksi, Rustum/A-9985-2009 Borwein,
Jonathan/A-6082-2009",
unique-id = "Borwein:2003:PDA",
}
@Article{Borwein:2003:SWG,
author = "Jonathan Borwein and Simon Fitzpatrick and Roland
Girgensohn",
title = "Subdifferentials whose graphs are not norm {$ \times
$} weak$^*$ closed",
journal = j-CAN-MATH-BULL,
volume = "46",
number = "4",
pages = "538--545",
month = dec,
year = "2003",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-2003-051-5",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "49J52 (46N10 47H05 90C48)",
MRnumber = "2011392",
MRreviewer = "John R. Giles",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://cms.math.ca/cmb/v46/;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/canmathbull.bib",
URL = "http://cms.math.ca/10.4153/CMB-2003-051-5;
http://docserver.carma.newcastle.edu.au/149/",
abstract = "In this note we give examples of convex functions
whose subdifferentials have unpleasant properties.
Particularly, we exhibit a proper lower semicontinuous
convex function on a separable Hilbert space such that
the graph of its subdifferential is not dosed in the
product of the norm and bounded weak topologies. We
also exhibit a set whose sequential normal cone is not
norm dosed.",
acknowledgement = ack-nhfb,
fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 01:175.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2003:SWG",
}
@Article{Kellar:2003:DCM,
author = "Melanie Kellar and Bonnie MacKay and Rui Zhang and
Carolyn Watters and David Kaufman and Jonathan
Borwein",
title = "Dynamic Composition of Math Lessons",
journal = "Journal of Educational Technology \& Society",
volume = "6",
number = "4",
pages = "100--111",
month = "????",
year = "2003",
ISSN = "1176-3647 (print), 1436-4522 (electronic)",
ISSN-L = "1176-3647",
bibdate = "Tue Feb 06 09:20:39 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1525/;
http://ifets.ieee.org/periodical/6_4/10.pdf;
http://www.jstor.org/stable/jeductechsoci.6.4.100",
acknowledgement = ack-nhfb,
journal-URL = "http://www.jstor.org/journal/jeductechsoci",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2004:BEA,
author = "David H. Bailey and Jonathan M. Borwein and Richard E.
Crandall and Carl Pomerance",
title = "On the binary expansions of algebraic numbers",
journal = "Journal de Th{\'e}orie des Nombres de {Bordeaux}",
volume = "16",
number = "3",
pages = "487--518",
year = "2004",
ISSN = "1246-7405 (print), 2118-8572 (electronic)",
ISSN-L = "1246-7405",
MRclass = "11K16 (11J25 11J91)",
MRnumber = "2144954",
MRreviewer = "John H. Loxton",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/36/;
http://jtnb.cedram.org/item?id=JTNB_2004__16_3_487_0",
acknowledgement = ack-nhfb,
ajournal = "J. Th{\'e}or. Nombres Bordeaux",
fjournal = "Journal de Th{\'e}orie des Nombres de Bordeaux",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 2003:204.",
}
@Book{Berggren:2004:PSB,
author = "Lennart Berggren and Jonathan Borwein and Peter
Borwein",
title = "Pi: a source book",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Third",
pages = "xx + 797",
year = "2004",
DOI = "https://doi.org/10.1007/978-1-4757-4217-6",
ISBN = "0-387-20571-3",
ISBN-13 = "978-0-387-20571-7",
MRclass = "11-00 (01A05 01A75 11-03)",
MRnumber = "2065455",
MRreviewer = "F. Beukers",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 2003:210.",
tableofcontents = "Preface to the Third Edition / v \\
Preface to the Second Edition / vi \\
Preface / vii \\
Acknowledgments / x \\
Introduction / xvii \\
1. The Rhind Mathematical Papyrus --- Problem 50
($\approx$1650 B.C.) / A problem dealing with the area
of a round field of given diameter / 1 \\
2. Engels / Quadrature of the Circle in Ancient Egypt
(1977) / A conjectural explanation of how the
mathematicians of ancient Egypt approximated the area
of a circle / 3 \\
3. Archimedes / Measurement of a Circle --- (-250 B.C.)
/ The seminal work in which Archimedes presents the
first true algorithm for $ \pi $ / 7 \\
4. Phillips / Archimedes the Numerical --- Analyst
(1981) / A summary of Archimedes' work on the
computation of $ \pi $ using modem notation / 15 \\
5. Lam and Ang / Circle Measurements in Ancient China
(1986) / This paper discusses and contains a
translation of Liu Hui's (3rd century) method for
evaluating $ \pi $ and also examines values for $ \pi $
given by Zu Chongzhi (429--500) / 20 \\
6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
and Solid Figures (--850) / This extract gives an
explicit statement and proof that the ratio of the
circumference to the diameter is constant / 36 \\
7. M{\=a}dhava / The Power Series for Arctan and Pi
(-1400) / These theorems by a fifteenth century Indian
mathematician give Gregory's series for arctan with
remainder terms and Leibniz's series for $ \pi $ / 45
\\
8. Hope-Jones / Ludolph (or Ludolff or Lucius) van
Ceulen (1938) / Correspondence about van Ceulen's
tombstone in reference to it containing some digits of
$ \pi $ / 51 \\
9. Vi{\`e}te / \booktitle{Variorum de Rebus
Mathematicis Reponsorum Liber VII} (1593) / Two
excerpts. One containing the first infinite expression
of $ \pi $, obtained by relating the area of a regular
$2n$-gon to that of a regular $n$-gon / 53 \\
10. Wallis. Computation of $ \pi $ by Successive
Interpolations (1655) / How Wallis derived the infinite
product for $ \pi $ that bears his name / 68 \\
11. Wallis / \booktitle{Arithmetica Infinitorum} (1655)
/ An excerpt including Prop. 189, 191 and an alternate
form of the result that gives Wm. Brounker's continued
fraction expression for $ 4 / \pi$ / ?? \\
12. Huygens / \booktitle{De Circuli Magnitudine
Inventa} (1654) / Huygens's demonstration of how to
triple the number of correct decimals over those in
Archimedes' estimate of $ \pi $ / 81 13. Gregory /
Correspondence with John Collins (1671) / A letter to
Collins in which he gives his series for arctangent,
carried to the ninth power / 87 \\
14. Roy / The Discovery of the Series Formula for $ \pi
$ by Leibniz, Gregory, and Nilakantha (1990) / A
discussion of the discovery of the series $ \pi / 4 = 1
- 1/3 + 1/5 - \cdots{} $ / 92 \\
15. Jones / The First Use of $ \pi $ for the Circle
Ratio (1706) / An excerpt from Jones' book, the
\booktitle{Synopsis Palmariorum Matheseos: or, a New
Introduction to the Mathematics}, London, 1706 / 108
\\
16. Newton / Of the Method of Fluxions and Infinite
Series (1737) / An excerpt giving Newton's calculation
of $ \pi $ to 16 decimal places / 110 \\
17. Euler / Chapter 10 of \booktitle{Introduction to
Analysis of the Infinite (On the Use of the Discovered
Fractions to Sum Infinite Series)} (1748) / This
includes many of Euler's infinite series for $ \pi $
and powers of $ \pi $ / 112 \\
18. Lambert / \booktitle{M{\'e}moire Sur Quelques
Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
Transcendentes Circulaires et Logarithmiques} (1761) /
An excerpt from Lambert's original proof of the
irrationality of $ \pi $ / 129 19. Lambert /
Irrationality of $ \pi $ (1969) / A translation and
Struik's discussion of Lambert's proof of the
irrationality of $ \pi $ / 141 \\
20. Shanks / Contributions to Mathematics Comprising
Chiefly of the Rectification of the Circle to 607
Places of Decimals (1853) / Pages from Shanks's report
of his monumental hand calculation of $ \pi $ / 147 \\
21. Hermite / \booktitle{Sur La Fonction Exponentielle}
(1873) / The first proof of the transcendence of $ e $
/ 162 \\
22. Lindemann / \booktitle{Ueber die Zahl $ \pi $}
(1882) / The first proof of the transcendence of $ \pi
$ / 194 23. Weierstrass / \booktitle{Zu Lindemann's
Abhandlung ``{\"U}ber die Ludolphsche Zahl''} (1885) /
Weierstrass' proof of the transcendence of $ \pi $ /
207 24. Hilbert / \booktitle{Ueber die Transzendenz der
Zahlen $ e $ und $ \pi $} (1893) / Hilbert's short and
elegant simplification of the transcendence proofs for
$ e $ and $ \pi $ / 226 25. Goodwin / Quadrature of the
Circle (1894) / The dubious origin of the attempted
legislation of the value of $ \pi $ in Indiana / 230
\\
26. Edington / House Bill No. 246, Indiana State
Legislature, 1897 (1935) / A summary of the action
taken by the Indiana State Legislature to fix the value
of $ \pi $ (including a copy of the actual bill that
was proposed) / 231 \\
27. Singmaster / The Legal Values of Pi (1985) / A
history of the attempt by Indiana to legislate the
value of $ \pi $ / 236 \\
28. Ramanujan / Squaring the Circle (1913) / A
geometric approximation to $ \pi $ / 240 \\
29. Ramanujan / Modular Equations and Approximations to
$ \pi $ (1914) / Ramanujan's seminal paper on pi that
includes a number of striking series and algebraic
approximations / 241 \\
30. Watson / The Marquis and the Land Agent: A Tale of
the Eighteenth Century (1933) / A Presidential address
to the Mathematical Association in which the author
gives an account of ``some of the elementary work on
arcs and ellipses and other curves which led up to the
idea of inverting an elliptic integral, and so laying
the foundations of elliptic functions and doubly
periodic functions generally.'' / ?? \\
31. Ballantine / The Best (?) Formula for Computing $
\pi $ to a Thousand Places (1939) / An early attempt to
orchestrate the calculation of $ \pi $ more cleverly /
271 \\
32. Birch / An Algorithm for Construction of Arctangent
Relations (1946) / The object of this note is to
express $ \pi / 4$ as a sum of arctan relations in
powers of 10 / 274 \\
33. Niven / A Simple Proof that $ \pi $ is Irrational
(1947) / A very concise proof of the irrationality of $
\pi $ / 276 \\
34. Reitwiesner / An ENIAC Determination of $ \pi $ and
$ e $ to 2000 Decimal Places (1950) / One of the first
computer-based computations / 277 \\
35. Schepler / The Chronology of Pi (1950) / A fairly
reliable outline of the history of $ \pi $ from 3000
B.C. to 1949 / 282 \\
36. Mahler / On the Approximation of $ \pi $ (1953) /
``The aim of this paper is to determine an explicit
lower bound free of unknown constants for the distance
of $ \pi $ from a given rational or algebraic number.''
/ 306 \\
37. Wrench, Jr. / The Evolution of Extended Decimal
Approximations to $ \pi $ (1960) / A history of the
calculation of the digits of $ \pi $ to 1960 / 319 \\
38. Shanks and Wrench, Jr. / Calculation of $ \pi $ to
100,000 Decimals (1962) / A landmark computation of $
\pi $ to more than 100,000 places / 326 39. Sweeny / On
the Computation of Euler's Constant (1963) / The
computation of Euler's constant to 3566 decimal places
/ 350 40. Baker / Approximations to the Logarithms of
Certain Rational Numbers (1964) / The main purpose of
this deep and fundamental paper is to ``deduce results
concerning the accuracy with which the natural
logarithms of certain rational numbers may be
approximated by rational numbers, or, more generally,
by algebraic numbers of bounded degree.'' / 359 \\
41. Adams / Asymptotic Diophantine Approximations to e
(1966) / An asymptotic estimate for the rational
approximation to $ e $ which disproves the conjecture
that $ e $ behaves like almost all numbers in this
respect / 368 \\
42. Mahler / Applications of Some Formulae by Hermite
to the Approximations of Exponentials of Logarithms
(1967) / An important extension of Hilbert's approach
to the study of transcendence / 372 43. Eves / In
Mathematical Circles; A Selection of Mathematical
Stories and Anecdotes (excerpt) (1969) / A collection
of mathematical stories and anecdotes about $ \pi $ /
456 \\
44. Eves / Mathematical Circles Revisited; A Second
Collection of Mathematical Stories and Anecdotes
(excerpt) (1971) / A further collection of mathematical
stories and anecdotes about $ \pi $ / 402 45. Todd /
The Lemniscate Constants (1975) / A unifying account of
some of the methods used for computing the lemniscate
constants / 412 \\
46. Salamin / Computation of $ \pi $ Using
Arithmetic--Geometric Mean (1976) / The first
quadratically converging algorithm for $ \pi $ based on
Gauss's AGM and on Legendre's relation for elliptic
integrals / 418 \\
47. Brent / Fast Multiple-Precision Evaluation of
Elementary Functions (1976) / ``This paper contains the
`Gauss--Legendre' method and some different algorithms
for $\log$ and $\exp$ (using Landen transformations).''
/ 424 \\
48. Beukers / A Note on the Irrationality of $ \zeta(2)
$ and $ \zeta(3) $ (1979) / A short and elegant
recasting of Apery's proof of the irrationality of
$\zeta(3)$ (and $\zeta(2)$) / 434 \\
49. van der Poorten / A Proof that Euler Missed
\ldots{} Apery's Proof of the Irrationality of $\zeta
(3)$ (1979) / An illuminating account of Apery's
astonishing proof of the irrationality of $\zeta (3)$ /
439 \\
50. Brent and McMillan / Some New Algorithms for
High-Precision Computation of Euler's Constant (1980) /
Several new algorithms for high-precision calculation
of Euler's constant, including one which was used to
compute 30,100 decimal places / 448 \\
51. Apostol / A Proof that Euler Missed: Evaluating
$\zeta(2)$ the Easy Way (1983) / This note shows that
one of the double integrals considered by Beukers ([48]
in the table of contents) can be used to establish
directly that $\zeta(2) = \pi^2 / 6$ / 456 \\
52. O'Shaughnessy / Putting God Back in Math (1983) /
An article about the Institute of Pi Research, an
organization that ``pokes fun at creationists by
pointing out that even the Bible makes mistakes.'' /
458 \\
53. Stern / A Remarkable Approximation to $ \pi $
(1985) / Justification of the value of $ \pi $ in the
Bible through numerological interpretations / 460 \\
54. Newman and Shanks / On a Sequence Arising in Series
for $ \pi $ (1984) / More connections between $ \pi $
and modular equations / 462 \\
55. Cox / The Arithmetic--Geometric Mean of Gauss
(1984) / An extensive study of the complex analytic
properties of the AGM / 481 \\
56. Borwein and Borwein / The Arithmetic--Geometric
Mean and Fast Computation of Elementary Functions
(1984) / The relationship between the AGM iteration and
fast computation of elementary functions (one of the
by-products is an algorithm for $ \pi $) / 537 57.
Newman / A Simplified Version of the Fast Algorithms of
Brent and Salamin (1984) / Elementary algorithms for
evaluating $ e^x $ and $ \pi $ using the Gauss AGM
without explicit elliptic function theory / 553 \\
58. Wagon / Is Pi Normal? (1985) / A discussion of the
conjecture that $ \pi $ has randomly distributed digits
/ 557 \\
59. Keith / Circle Digits: A Self-Referential Story
(1986) / A mnemonic for the first 402 decimal places of
$ \pi $ / 560 \\
60. Bailey / The Computation of $ \pi $ to 29,360,000
Decimal Digits Using Borwein's Quartically Convergent
Algorithm (1988) / The algorithms used, both for $ \pi
$ and for performing the required multiple-precision
arithmetic / 562 \\
61. Kanada / Vectorization of Multiple-Precision
Arithmetic Program and 201,326,000 Decimal Digits of $
\pi $ Calculation (1988) / Details of the computation
and statistical tests of the first 200 million digits
of $ \pi $ / 576 \\
62. Borwein and Borwein / Ramanujan and Pi (1988) /
This article documents Ramanujan's life, his ingenious
approach to calculating $ \pi $, and how his approach
is now incorporated into modern computer algorithms /
588 \\
63. Chudnovsky and Chudnovsky / Approximations and
Complex Multiplication According to Ramanujan (1988) /
This excerpt describes ``Ramanujan's original quadratic
period--quasiperiod relations for elliptic curves with
complex multiplication and their applications to
representations of fractions of $ \pi $ and other
logarithms in terms of rapidly convergent nearly
integral (hypergeometric) series.'' / 596 \\
64. Borwein, Borwein and Bailey / Ramanujan, Modular
Equations, and Approximations to Pi or How to Compute
One Billion Digits of Pi (1989) / An exposition of the
computation of $ \pi $ using mathematics rooted in
Ramanujan's work / 623 \\
65. Borwein, Borwein and Dilcher / Pi, Euler Numbers,
and Asymptotic Expansions (1989) / An explanation as to
why the slowly convergent Gregory series for $ \pi $,
truncated at 500,000 terms, gives $ \pi $ to 40 places
with only the 6th, 17th, 18th, and 29th places being
incorrect / 642 \\
66. Beukers, Bezivin, and Robba / An Alternative Proof
of the Lindemann--Weierstrass Theorem (1990) / The
Lindemann--Weierstrass theorem as a by-product of a
criterion for rationality of solutions of differential
equations / 649 \\
67. Webster / The Tale of Pi (1991) / Various anecdotes
about $ \pi $ from the 14th annual IMO Lecture to the
Royal Society / 654 \\
68. Eco / An excerpt from Foucault's Pendulum (1993) /
``The unnumbered perfection of the circle itself.'' /
658 \\
69. Keith / Pi Mnemonics and the Art of Constrained
Writing (1996) / A mnemonic for $ \pi $ based on Edgar
Allen Poe's poem ``The Raven.'' / 659 \\
70. Bailey, Borwein, and Plouffe / On the Rapid
Computation of Various Polylogarithmic Constants (1997)
/ A fast method for computing individual digits of $
\pi $ in base 2 / 663 \\
Appendix I --- On the Early History of Pi / 677 \\
Appendix II --- A Computational Chronology of Pi / 683
\\
Appendix III --- Selected Formulae for Pi / 686 \\
Appendix IV --- Translations of Viele and Huygens / 690
\\
Bibliography / 710 \\
Credits / 717 \\
A Pamphlet on Pi / 721 \\
Contents / 723 \\
1. Pi and Its Friends / 725 \\
2. Normality of Numbers / 741 \\
3. Historia Cyclometrica / 753 \\
4. Demotica Cyclometrica / 771 \\
References / 779 \\
Index / 783",
}
@InProceedings{Borwein:2004:AGMa,
author = "J. M. Borwein and P. B. Borwein",
booktitle = "Pi: A Source Book",
title = "The Arithmetic--Geometric Mean and Fast Computation of
Elementary Functions",
publisher = pub-SV,
address = pub-SV:adr,
pages = "??--??",
year = "2004",
DOI = "https://doi.org/10.1007/978-1-4757-4217-6_56",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_56",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2004:CCS,
author = "Jonathan M. Borwein and Jon D. Vanderwerff",
title = "Constructible convex sets",
journal = j-SET-VALUED-ANAL,
volume = "12",
number = "1--2",
pages = "61--77",
month = mar # "\slash " # jun,
year = "2004",
CODEN = "SVANEG",
DOI = "https://doi.org/10.1023/B:SVAN.0000023393.75251.05",
ISSN = "0927-6947 (print), 1572-932x (electronic)",
ISSN-L = "0927-6947",
MRclass = "49J53 (46B20 46N10 90C25 90C48)",
MRnumber = "2069352",
MRreviewer = "Diethard Pallaschke",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/38/",
abstract = "We investigate when closed convex sets can be written
as countable intersections of closed half-spaces in
Banach spaces. It is reasonable to consider this class
to comprise the constructible convex sets since such
sets are precisely those that can be defined by a
countable number of linear inequalities, hence are
accessible to techniques of semi-infinite convex
programming. We also explore some model theoretic
implications. Applications to set convergence are given
as limiting examples.",
acknowledgement = ack-nhfb,
fjournal = "Set-Valued Analysis. An International Journal Devoted
to the Theory of Multifunctions and its Applications",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 2003:202.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2004:CCS",
}
@Article{Borwein:2004:CMU,
author = "J. Borwein and I. Kortezov",
title = "Constructive minimal uscos",
journal = j-C-R-ACAD-BULGARE-SCI,
volume = "57",
number = "12",
pages = "9--12",
year = "2004",
CODEN = "DBANAD",
ISSN = "1310-1331 (print), 2367-5535 (electronic)",
ISSN-L = "1310-1331",
MRclass = "49J53 (54C60)",
MRnumber = "2117234",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/273/",
acknowledgement = ack-nhfb,
fjournal = "Dokladi na B\cdprime lgarskata Akademiya na Naukite.
Comptes Rendus de l'Acad{\'e}mie Bulgare des Sciences",
journal-URL = "http://www.proceedings.bas.bg/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CoLab Preprint 273. The journal web site only has an
abstract for this paper.",
xxtitle = "Constructive minimal cuscos",
}
@Article{Borwein:2004:DCM,
author = "Jonathan M. Borwein and James V. Burke and Adrian S.
Lewis",
title = "Differentiability of cone-monotone functions on
separable {Banach} space",
journal = j-PROC-AM-MATH-SOC,
volume = "132",
number = "4",
pages = "1067--1076",
month = apr,
year = "2004",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/S0002-9939-03-07149-1",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "49J50 (46G05 46N10)",
MRnumber = "2045422",
MRreviewer = "Jes{\'u}s A. Jaramillo",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1242/;
http://www.jstor.org/stable/4097135",
abstract = "Motivated by applications to (directionally) Lipschitz
functions, we provide a general result on the almost
everywhere Gateaux differentiability of real-valued
functions on separable Banach spaces, when the function
is monotone with respect to an ordering induced by a
convex cone with nonempty interior. This seemingly
arduous restriction is useful, since it covers the case
of directionally Lipschitz functions, and necessary. We
show by way of example that most results fail more
generally.",
acknowledgement = ack-nhfb,
article-number = "PII S0002-9939(03)07149-1",
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 02:183.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2004:DCM",
}
@InProceedings{Borwein:2004:DSS,
author = "Jonathan Michael Borwein and Kwok-Kwong Stephen Choi",
title = "{Dirichlet} series for squares of sums of squares: a
summary",
crossref = "Kisilevsky:2004:NTP",
volume = "36",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "27--34",
year = "2004",
MRclass = "11M41 (11E25)",
MRnumber = "2076564",
MRreviewer = "Don Redmond",
bibdate = "Sat Aug 13 17:30:35 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "CRM Proc. Lecture Notes",
ZMnumber = "1078.11055",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Borwein:2004:EMCa,
author = "Jonathan M. Borwein and David H. Bailey and Roland
Girgensohn",
title = "Experimentation in mathematics: computational paths to
discovery",
publisher = pub-A-K-PETERS,
address = pub-A-K-PETERS:adr,
pages = "x + 357",
year = "2004",
ISBN = "1-56881-136-5",
ISBN-13 = "978-1-56881-136-9",
LCCN = "QA12 .B67 2004",
MRclass = "11-01 (11Yxx 40-01 42A16 42A38 68W30)",
MRnumber = "2051473",
MRreviewer = "F. Beukers",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
shorttableofcontents = "Sequences, series, products and integrals / 1
\\
Fourier series and integrals / 69 \\
Zeta functions and multizeta functions / 131 \\
Partitions and powers / 183 \\
Primes and polynomials / 225 \\
The power of constructive proofs II / 263 \\
Numerical techniques II / 299",
tableofcontents = "",
xxyear = "2003",
}
@Article{Borwein:2004:FEA,
author = "Jonathan M. Borwein and David Borwein and William F.
Galway",
title = "Finding and excluding {$b$}-ary {Machin}-type
individual digit formulae",
journal = j-CAN-J-MATH,
volume = "56",
number = "5",
pages = "897--925",
month = "????",
year = "2004",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-2004-041-2",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
MRclass = "11Y60 (11A67 11G55 33B30)",
MRnumber = "2085627",
MRreviewer = "Greg Martin",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/canjmath.bib",
note = "This paper established the result that there are no
degree-1 BBP-type formulas for $ \pi $, except when the
base is 2 (or an integer power thereof).",
URL = "http://docserver.carma.newcastle.edu.au/47/",
abstract = "Constants with formulae of the form treated by D.
Bailey, P. Borwein, and S. Plouffe (BBP formulae to a
given base $b$) have interesting computational
properties, such as allowing single digits in their
base $b$ expansion to be independently computed, and
there are hints that they should be normal numbers,
i.e., that their base $b$ digits are randomly
distributed. We study a formally limited subset of BBP
formulae, which we call Machin-type BBP formulae, for
which it is relatively easy to determine whether or not
a given constant kappa has a Machin-type BBP formula.
In particular, given $b$ is an element of $N$, $ b >
2$, $b$ not a proper power, a $b$-ary Machin-type BBP
arctangent formula for $ \kappa $ is a formula of the
form $ \kappa = \sum_m a_m \arctan ( - b^{-m})$, $
a_m$ is an element of $Q$, while when $ b = 2$, we also
allow terms of the form $ a_m \arctan (1 / (1 - 2^m))$.
Of particular interest, we show that $ \pi $ has no
Machin-type BBP arctangent formula when $ b \neq 2$. To
the best of our knowledge, when there is no Machin-type
BBP formula for a constant then no BBP formula of any
form is known for that constant.",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics = Journal canadien de
math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 2003:195.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2004:FEB",
}
@Book{Borwein:2004:MEP,
author = "Jonathan M. Borwein and David H. Bailey",
title = "Mathematics by Experiment: Plausible Reasoning in the
{21st Century}",
publisher = pub-A-K-PETERS,
address = pub-A-K-PETERS:adr,
pages = "x + 288",
year = "2004",
ISBN = "1-56881-211-6",
ISBN-13 = "978-1-56881-211-3",
LCCN = "QA76.95 .B67 2003",
MRclass = "00A35",
MRnumber = "2033012",
MRreviewer = "John H. Mason",
bibdate = "Fri Oct 17 10:38:25 2003",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$45.00",
URL = "http://docserver.carma.newcastle.edu.au/272/",
abstract = "Using examples that truly represent the experimental
methodology, this book provides the historical context
of, and rationale behind, experimental mathematics. It
shows how today, the use of advanced computing
technology provides, mathematicians with an amazing,
previously unimaginable ``laboratory,'' in which
examples can be analyzed, new ideas tested, and
patterns discovered. This is a perfect introduction to
the history and current state of research and
technology in the growing field of experimental
mathematics.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Due to an unfortunate error, some of the citations in
the book point to the wrong item in the Bibliography.
Here is how to find the correct citation number:
[1]--[85]: Citation number is correct; [86, page 100]:
[86]; [86, page 2]: [87]; [87]--[156]: Add one to
citation number; [157]: [159]; [158, page 139]: [158];
[158, page 97]: [160]; [159]--[196]: Add two to
citation number",
tableofcontents = "What is Experimental Mathematics? \\
Experimental Mathematics in Action \\
Pi and Its Friends \\
Normality of Numbers \\
The Power of Constructive Proofs I \\
Numerical Techniques I \\
Making Sense of Experimental Math",
}
@Article{Borwein:2004:OPV,
author = "Jonathan Borwein and Lixin Cheng and Mari{\'a}n Fabian
and Julian P. Revalski",
title = "A one perturbation variational principle and
applications",
journal = j-SET-VALUED-ANAL,
volume = "12",
number = "1--2",
pages = "49--60",
year = "2004",
CODEN = "SVANEG",
DOI = "https://doi.org/10.1023/B:SVAN.0000023400.92518.cb",
ISSN = "0927-6947 (print), 1572-932x (electronic)",
ISSN-L = "0927-6947",
MRclass = "49J53 (46B20 46G05 49J40 49J50)",
MRnumber = "2069351",
MRreviewer = "John R. Giles",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/14/",
abstract = "We study a variational principle in which there is one
common perturbation function $ \phi $ for every proper
lower semicontinuous extended real-valued function $f$
defined on a metric space $X$. Necessary and sufficient
conditions are given in order for the perturbed
function $ f + \phi $ to attain its minimum. In the
case of a separable Banach space we obtain a specific
principle in which the common perturbation function is,
in addition, also convex and Hadamard-like
differentiable. This allows us to provide applications
of the principle to differentiability of convex
functions on separable and more general Banach
spaces.",
acknowledgement = ack-nhfb,
fjournal = "Set-Valued Analysis. An International Journal Devoted
to the Theory of Multifunctions and its Applications",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 2003:205.",
researcherid-numbers = "Fabian, Marian/D-5427-2014 Borwein,
Jonathan/A-6082-2009 Cheng, LX/G-3342-2010",
unique-id = "Borwein:2004:OPV",
}
@InProceedings{Borwein:2004:PEN,
author = "J. M. Borwein and P. B. Borwein and K. Dilcher",
booktitle = "Pi: A Source Book",
title = "Pi, {Euler} Numbers, and Asymptotic Expansions",
publisher = pub-SV,
address = pub-SV:adr,
pages = "??--??",
year = "2004",
DOI = "https://doi.org/10.1007/978-1-4757-4217-6_65",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1583/;
http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_65",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2004:RAFa,
author = "J. Borwein and R. Crandall and G. Fee",
title = "On the {Ramanujan} {AGM} Fraction, {I}: The
Real-Parameter Case",
journal = j-EXP-MATH,
volume = "13",
number = "3",
pages = "275--285",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2004.10504540",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11J70 (11A55 33C05 40A15)",
MRnumber = "2103326",
MRreviewer = "James G. Mc Laughlin",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://docserver.carma.newcastle.edu.au/27/;
http://projecteuclid.org/euclid.em/1103749836",
abstract = "The Ramanujan AGM continued fraction is a construct
[GRAPHIC] enjoying attractive algebraic properties,
such as a striking arithmetic-geometric mean (AGM)
relation and elegant connections with elliptic-function
theory. But the fraction also presents an intriguing
computational challenge. Herein we show how to rapidly
evaluate $R$ for any triple of positive reals $a$, $b$,
$ \eta $. Even in the problematic scenario when a
approximate to $b$ certain transformations allow rapid
evaluation. In this process we find, for example, that
when $ a_\eta = b_\eta = $ a rational number, $ R_\eta
$, is essentially an $L$-series that can be cast as a
finite sum of fundamental numbers. We ultimately
exhibit an algorithm that yields $D$ good digits of $R$
in $ O(D)$ iterations where the implied big-$O$
constant is independent of the positive-real triple
$a$, $b$, $ \eta $. Finally, we address the evidently
profound theoretical and computational dilemmas
attendant on complex parameters, indicating how one
might extend the AGM relation for complex parameter
domains.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2004:RAFa",
}
@Article{Borwein:2004:RAFb,
author = "J. Borwein and R. Crandall",
title = "On the {Ramanujan} {AGM} Fraction, {II}: The
Complex-Parameter Case",
journal = j-EXP-MATH,
volume = "13",
number = "3",
pages = "287--295",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2004.10504541",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11J70 (11A55 33C05)",
MRnumber = "2103327",
MRreviewer = "James G. Mc Laughlin",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://docserver.carma.newcastle.edu.au/29/;
http://projecteuclid.org/euclid.em/1103749837",
abstract = "The Ramanujan continued fraction is interesting in
many ways; e.g., for certain complex parameters $
(\eta, a, b) $ one has an attractive AGM relation $
R_{\eta }(a.b) + R_\eta (b, a) = 2 R_\eta ((a + b) / 2,
\sqrt {a b}) $. Alas, for some parameters the continued
fraction $ R_\eta $, does not converge; moreover, there
are converging instances where the AGM relation itself
does not hold. To unravel these dilemmas we herein
establish convergence theorems, the central result
being that $ R_1 $ converges whenever $ |a| \neq |b| $.
Such analysis leads naturally to the conjecture that
divergence occurs whenever $ a = b e^{i \phi } $ with $
c o s^2 \phi \neq 1 $ (which conjecture has been proven
in a separate work) [Borwein et al. 04b.] We further
conjecture that for $ a / b $ lying in a certain ---
and rather picturesque --- complex domain, we have both
convergence and the truth of the AGM relation.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2004:RAFb",
}
@InProceedings{Borwein:2004:RME,
author = "J. M. Borwein and P. B. Borwein and D. H. Bailey",
booktitle = "Pi: A Source Book",
title = "{Ramanujan}, Modular Equations, and Approximations to
Pi or How to Compute One Billion Digits of Pi",
publisher = pub-SV,
address = pub-SV:adr,
pages = "??--??",
year = "2004",
DOI = "https://doi.org/10.1007/978-1-4757-4217-6_64",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1587/;
http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_64",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2005:EDA,
author = "David H. Bailey and Jonathan M. Borwein and David M.
Bradley",
title = "Experimental determination of {Ap{\'e}ry}-like
identities for $ \zeta (2 n + 2) $",
journal = "ArXiv Mathematics e-prints",
month = may,
year = "2005",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2005math......5270B;
http://docserver.carma.newcastle.edu.au/295/",
abstract = "We document the discovery of two generating functions
for the Riemann zeta values $ \zeta (2 n + 2) $,
analogous to earlier work for $ \zeta (2 n + 1) $ and $
\zeta (4 n + 3) $. This continues work initiated by
Koecher and pursued further by Borwein, Bradley and
others.",
acknowledgement = ack-nhfb,
eprint = "math/0505270",
keywords = "Mathematics - Number Theory, Mathematics - Classical
Analysis and ODEs, 11M06 (Primary), 33C20 (Secondary)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2005:EME,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Experimental mathematics: examples, methods and
implications",
journal = j-NAMS,
volume = "52",
number = "5",
pages = "502--514",
year = "2005",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "00A35",
MRnumber = "2140093",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1241/;
http://www.ams.org/notices/200505/fea-borwein.pdf",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CoLab Preprint 269.",
}
@Article{Bailey:2005:FPC,
author = "D. H. Bailey and J. M. Borwein",
title = "Future Prospects for Computer-assisted Mathematics",
journal = j-CMS-NOTES,
volume = "37",
number = "8",
pages = "2--6",
month = dec,
year = "2005",
DOI = "",
ISSN = "1193-9273 (print), 1496-4295 (electronic)",
ISSN-L = "1193-9273",
bibdate = "Sat Aug 13 17:21:21 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/304/;
https://cms.math.ca/notes/v37/n8/Notesv37n8.pdf",
acknowledgement = ack-nhfb,
ajournal = "CMS Notes",
fjournal = "Canadian Mathematical Society Notes",
journal-URL = "https://cms.math.ca/notes",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2005:ADC,
author = "J. M. Borwein and K. Karamanos",
editor = "Andrew Eberhard and Nicolas Hadjisavvas and Dinh The
Luc",
booktitle = "Generalized Convexity, Generalized Monotonicity and
Applications",
title = "Algebraic Dynamics of Certain Gamma Function Values",
volume = "77",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "xi + 350",
pages = "3--21",
year = "2005",
DOI = "https://doi.org/10.1007/0-387-23639-2_1",
ISBN = "0-387-23638-4",
ISBN-13 = "978-0-387-23638-4",
MRclass = "11Y60 (33B15 37B99 37N99 94A17)",
MRnumber = "2103023",
MRreviewer = "Brian L. Burrows",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Nonconvex Optim. Appl.",
URL = "http://docserver.carma.newcastle.edu.au/256/;
http://link.springer.com/chapter/10.1007/0-387-23639-2_1",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2005:CFT,
author = "Jonathan Michael Borwein and Kwok-Kwong Stephen Choi
and Wilfried Pigulla",
title = "Continued fractions of tails of hypergeometric
series",
journal = j-AMER-MATH-MONTHLY,
volume = "112",
number = "6",
pages = "493--501",
month = jun # "\slash " # jul,
year = "2005",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/30037519",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "33C05 (40A15)",
MRnumber = "2142600",
MRreviewer = "Takao Komatsu",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/39/;
http://www.jstor.org/stable/30037519",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 2003:201.",
}
@Article{Borwein:2005:CMF,
author = "Jonathan M. Borwein and Xianfu Wang",
title = "Cone-monotone functions: differentiability and
continuity",
journal = j-CAN-J-MATH,
volume = "57",
number = "5",
pages = "961--982",
year = "2005",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-2005-037-5",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
MRclass = "49J50 (26B05 46G05 58C20)",
MRnumber = "2164591",
MRreviewer = "Lud{\v{e}}k Zaj{\'{\i}}{\v{c}}ek",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "We provide a porosity-based approach to the
differentiability and continuity of real-valued
functions on separable Banach spaces, when the function
is monotone with respect to an ordering induced by a
convex cone $K$ with non-empty interior. We also show
that the set of nowhere $K$-monotone functions has a
sigma-porous complement in the space of continuous
functions endowed with the uniform metric.",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics. Journal Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2005:CMF",
}
@Article{Borwein:2005:DCF,
author = "Jonathan M. Borwein and D. Russell Luke",
title = "Dynamics of a continued fraction of {Ramanujan} with
random coefficients",
journal = j-ABSTR-APPL-ANAL,
volume = "2005",
number = "5",
pages = "449--467",
month = "????",
year = "2005",
DOI = "https://doi.org/10.1155/AAA.2005.449",
ISSN = "1085-3375 (print), 1687-0409 (electronic)",
ISSN-L = "1085-3375",
MRclass = "11J70 (60F15)",
MRnumber = "2201037",
MRreviewer = "Mary E. Flahive",
bibdate = "Fri Aug 12 10:09:56 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2005AbApA2005..449B;
http://www.hindawi.com/journals/aaa/2005/162798/abs/",
abstract = "We study a generalization of a continued fraction of
Ramanujan with random, complex-valued coefficients. A
study of the continued fraction is equivalent to an
analysis of the convergence of certain stochastic
difference equations and the stability of random
dynamical systems. We determine the convergence
properties of stochastic difference equations and so
the divergence of their corresponding continued
fractions.",
acknowledgement = ack-nhfb,
fjournal = "Abstract and Applied Analysis",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
received = "16 November 2004",
remark = "CoLab Preprint 275",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2005:DCF",
}
@Article{Borwein:2005:EBS,
author = "Jonathan M. Borwein and Roland Girgensohn",
title = "Evaluations of binomial series",
journal = j-AEQUATIONES-MATHEMATICAE,
volume = "70",
number = "1--2",
pages = "25--36",
year = "2005",
CODEN = "AEMABN",
DOI = "https://doi.org/10.1007/s00010-005-2774-x",
ISSN = "0001-9054 (print), 1420-8903 (electronic)",
ISSN-L = "0001-9054",
MRclass = "05A10 (11B65 33B30)",
MRnumber = "2167981",
MRreviewer = "Valery V. Karachik",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/131/",
acknowledgement = ack-nhfb,
fjournal = "Aequationes Mathematicae",
journal-URL = "http://link.springer.com/journal/10",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 02:188.",
}
@Article{Borwein:2005:EDA,
author = "Jonathan M. Borwein and David M. Bradley",
title = "Empirically determined {Ap{\'e}ry}-like formulae for $
\zeta (4 n + 3) $",
journal = "ArXiv Mathematics e-prints",
month = may,
year = "2005",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2005math......5124B;
http://docserver.carma.newcastle.edu.au/163/",
abstract = "Some rapidly convergent formulae for special values of
the Riemann zeta function are given. We obtain a
generating function formula for $ \zeta (4 n + 3) $
which generalizes Ap{\'e}ry's series for $ \zeta (3) $,
and appears to give the best possible series relations
of this type, at least for $ n \lt 12 $. The formula
reduces to a finite but apparently non-trivial
combinatorial identity. The identity is equivalent to
an interesting new integral evaluation for the central
binomial coefficient. We outline a new technique for
transforming and summing certain infinite series. We
also derive a beautiful formula which provides strange
evaluations of a large new class of non-terminating
hypergeometric series. Our main results are shown to be
equivalent. At the time this article was submitted for
publication back in 1996, these results were only
conjectures, but they have subsequently been proved as
a result of work due to Gert Almkvist and Andrew
Granville.",
acknowledgement = ack-nhfb,
eprint = "math/0505124",
keywords = "Mathematics - Classical Analysis and ODEs, Mathematics
- Number Theory, 11M06",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2005:EMPa,
author = "J. M. Borwein",
title = "The Experimental Mathematician: The Pleasure of
Discovery and the Role of Proof",
journal = "International Journal of Computers for Mathematical
Learning",
volume = "10",
number = "2",
pages = "75--108",
month = may,
year = "2005",
DOI = "https://doi.org/10.1007/s10758-005-5216-x",
ISSN = "1382-3892 (print), 1573-1766 (electronic)",
ISSN-L = "1382-3892",
bibdate = "Fri Aug 12 10:49:11 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Counterpart presentation published in CMESG25
Proceedings, 2002, with lecture slides at
\url{http://www.cecm.sfu.ca/personal/jborwein/proof.pdf}.",
URL = "http://docserver.carma.newcastle.edu.au/264/;
http://link.springer.com/article/10.1007/s10758-005-5216-x;
https://web.archive.org/web/20040330173752/http://www.cecm.sfu.ca/personal/jborwein/proof.pdf",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10758",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark-1 = "CECM Preprint 02:178; 264.",
remark-2 = "Journal renamed in 2011 to \booktitle{Technology,
knowledge and learning}.",
}
@Article{Borwein:2005:KCM,
author = "Jonathan Borwein and Terry Stanway",
title = "Knowledge and Community in Mathematics",
journal = j-MATH-INTEL,
volume = "27",
number = "2",
pages = "7--16",
year = "2005",
CODEN = "MAINDC",
DOI = "https://doi.org/10.1007/BF02985788",
ISSN = "0343-6993 (print), 1866-7414 (electronic)",
ISSN-L = "0343-6993",
MRclass = "01A80 (00A05)",
MRnumber = "2156530",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/274/",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Intelligencer",
journal-URL = "http://link.springer.com/journal/283",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CoLab Preprint 274.",
}
@Article{Borwein:2005:LFM,
author = "Jonathan M. Borwein and Xianfu Wang",
title = "{Lipschitz} functions with maximal {Clarke}
subdifferentials are staunch",
journal = j-BULL-AUSTRAL-MATH-SOC,
volume = "72",
number = "3",
pages = "491--496",
year = "2005",
CODEN = "ALNBAB",
DOI = "https://doi.org/10.1017/S0004972700035322",
ISSN = "0004-9727 (print), 1755-1633 (electronic)",
ISSN-L = "0004-9727",
MRclass = "49J52 (26B05 26E25 54C30)",
MRnumber = "2199651",
MRreviewer = "Dariusz Zagrodny",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/302/;
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=4829356",
abstract = "In a recent paper we have shown that most
non-expansive Lipschitz functions (in the sense of
Baire's category) have a maximal Clarke sub
differential. In the present paper, we show that in a
separable Banach space the set of non-expansive
Lipschitz functions with a maximal Clarke
subdifferential is not only generic, but also staunch
in the space of non-expansive functions.",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the Australian Mathematical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2005:LFM",
}
@InProceedings{Borwein:2005:PFW,
author = "Jonathan M. Borwein and Mason Macklem and Jaehyun
Paek",
editor = "????",
booktitle = "SIAM Conference on Computational Science and
Engineering, Orlando, February 2005",
title = "A Prototype for the Federated World Directory of
Mathematicians",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "??--??",
year = "2005",
bibdate = "Sat Aug 13 17:23:15 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2005:SDC,
author = "Jonathan M. Borwein",
title = "The {SIAM} 100-Digit challenge: a study in
high-accuracy numerical computing",
journal = j-MATH-INTEL,
volume = "27",
number = "4",
pages = "40--48",
year = "2005",
CODEN = "MAINDC",
DOI = "https://doi.org/10.1007/BF02985860",
ISSN = "0343-6993 (print), 1866-7414 (electronic)",
ISSN-L = "0343-6993",
bibdate = "Fri Aug 12 10:34:00 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Intelligencer",
journal-URL = "http://link.springer.com/journal/283",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "D-drive preprint 285.",
}
@Article{Borwein:2005:SSA,
author = "J. M. Borwein and David M. Bradley",
title = "Searching symbolically for {Ap{\'e}ry}-like formulae
for values of the {Riemann} zeta function",
journal = "ArXiv Mathematics e-prints",
month = may,
year = "2005",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2005math......5093B;
http://docserver.carma.newcastle.edu.au/170/",
abstract = "We discuss some aspects of the search for identities
using computer algebra and symbolic methods. The focus
is on so-called Ap{\'e}ry-like formulae for special
values of the Riemann Zeta function. Much work lays
ahead in formally proving and properly classifying many
of the identities we have uncovered.",
acknowledgement = ack-nhfb,
eprint = "math/0505093",
keywords = "Mathematics - Classical Analysis and ODEs, Mathematics
- Number Theory, 11M06",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2005:TFI,
author = "Jonathan M. Borwein and David M. Bradley",
title = "On Two Fundamental Identities for {Euler} Sums",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "??--??",
month = feb,
year = "2005",
bibdate = "Tue Aug 16 10:16:43 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/math.NT/0502034/;
http://docserver.carma.newcastle.edu.au/279/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "The archive.org URL is wrong: it points to the
\title{Thirty-two Goldbach Variations} paper.",
}
@Article{Borwein:2005:TTG,
author = "J. M. Borwein and David M. Bradley",
title = "Thirty-two {Goldbach} Variations",
journal = "ArXiv Mathematics e-prints",
day = "1",
month = feb,
year = "2005",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2005math......2034B;
http://arxiv.org/abs/math/0502034;
http://docserver.carma.newcastle.edu.au/301/",
abstract = "We give thirty-two diverse proofs of a small
mathematical gem --- the fundamental Euler sum identity
$$ \zeta (2, 1) = \zeta (3) = 8 \zeta (\bar 2, 1) $$.
We also discuss various generalizations for multiple
harmonic (Euler) sums and some of their many
connections, thereby illustrating both the wide variety
of techniques fruitfully used to study such sums and
the attraction of their study.",
acknowledgement = ack-nhfb,
eprint = "math/0502034",
keywords = "Mathematics - Number Theory, 11M41",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "v1 (1 February 2005): 34 pages AMSLaTeX. v2 (3
November 2005): 41 pages AMSLaTeX. New introductory
material added and material on inequalities, Hilbert
matrix and Witten zeta functions. Errors in the second
section on Complex Line Integrals are corrected.
Published in \cite{Borwein:2006:TTG}.",
}
@Book{Borwein:2005:TVA,
author = "Jonathan M. Borwein and Qiji J. Zhu",
title = "Techniques of Variational Analysis",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vi + 362",
year = "2005",
DOI = "https://doi.org/10.1007/0-387-28271-8",
ISBN = "0-387-24298-8",
ISBN-13 = "978-0-387-24298-9",
MRclass = "49-02 (49J52 49J53 90-02)",
MRnumber = "2144010",
MRreviewer = "Richard B. Vinter",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "CMS Books in Mathematics/Ouvrages de Math{\'e}matiques
de la SMC, 20",
URL = "http://docserver.carma.newcastle.edu.au/1735/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
tableofcontents = "Front Matter / i--vi \\
Introduction and Notation / 1--4 \\
Variational Principles / 5--36 \\
Variational Techniques in Subdifferential Theory /
37--109 \\
Variational Techniques in Convex Analysis / 111--163
\\
Variational Techniques and Multifunctions / 165--241
\\
Variational Principles in Nonlinear Functional Analysis
/ 243--289 \\
Variational Techniques In the Presence of Symmetry /
291--338 \\
Back Matter / 339--362",
}
@InProceedings{Bailey:2006:EBE,
author = "D. H. Bailey and J. M. Borwein",
booktitle = "20th International Symposium on High-Performance
Computing in an Advanced Collaborative Environment
(HPCS'06)",
title = "Effective Bounds in {Euler--Maclaurin}-Based
Quadrature (Summary for {HPCS06})",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "34--34",
month = may,
year = "2006",
DOI = "https://doi.org/10.1109/HPCS.2006.22",
ISSN = "1550-5243 (print), 2378-2099 (electronic)",
ISSN-L = "1550-5243",
bibdate = "Wed Aug 10 12:08:56 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/hpcs06.pdf",
acknowledgement = ack-nhfb,
keywords = "Approximation error; Computer errors; Computer
science; Concurrent computing; Error analysis;
International collaboration; Mathematics; System
testing",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2006:EDA,
author = "David H. Bailey and Jonathan M. Borwein and David M.
Bradley",
title = "Experimental Determination of {Ap{\'e}ry}-like
Identities for $ \zeta (2 n + 2) $",
journal = j-EXP-MATH,
volume = "15",
number = "3",
pages = "281--289",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2006.10128968",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11Y60 (11M06)",
MRnumber = "2264467",
MRreviewer = "Tanguy Rivoal",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib;
http://www.tandfonline.com/toc/uexm20/15/3",
URL = "http://docserver.carma.newcastle.edu.au/295/;
http://projecteuclid.org/euclid.em/1175789759",
abstract = "We document the discovery of two generating functions
for $ \zeta (2 n + 2) $, analogous to earlier work for
$ \zeta (2 n + 1) $ and $ \zeta (4 n + 3) $, initiated
by Koecher and pursued further by Borwein, Bradley, and
others.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
onlinedate = "30 Jan 2011",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Bailey:2006:EDA",
}
@TechReport{Bailey:2006:FGE,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Finding General Explicit Formulas for {Ising} Integral
Recursions",
type = "Report",
institution = "Lawrence Berkeley National Laboratory and Faculty of
Computer Science, Dalhousie University",
address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5,
Canada",
day = "2",
month = oct,
year = "2006",
bibdate = "Fri Sep 30 08:18:51 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/ising-int.pdf",
acknowledgement = ack-nhfb,
keywords = "$K_0$ modified Bessel function; ARPREC multiprecision
software system",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2006:IIC,
author = "D. H. Bailey and J. M. Borwein and R. E. Crandall",
title = "Integrals of the {Ising} class",
journal = j-J-PHYS-A,
volume = "39",
number = "40",
pages = "12271--12302",
month = oct,
year = "2006",
CODEN = "JPHAC5",
DOI = "https://doi.org/10.1088/0305-4470/39/40/001",
ISSN = "0305-4470 (print), 1361-6447 (electronic)",
ISSN-L = "0305-4470",
MRclass = "33F05 (33F10 65D30 82B20 82B80)",
MRnumber = "2261886",
MRreviewer = "Syamal K. Sen",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://adsabs.harvard.edu/abs/2006JPhA...39..001B;
http://docserver.carma.newcastle.edu.au/324/;
http://iopscience.iop.org/article/10.1088/0305-4470/39/40/001;
http://stacks.iop.org/0305-4470/39/i=40/a=001",
abstract = "From an experimental-mathematical perspective we
analyse 'Ising-class' integrals. These are structurally
related $n$-dimensional integrals we call $ C_n$, $
D_n$, $ E_n$, where $ D_n$ is a magnetic susceptibility
integral central to the Ising theory of solid-state
physics. We first analyse $ C_n \coloneq \frac {4}{n!}
\int_0^\infty \cdots \int_0^\infty \frac { 1 } { \big
(\sum_{ j = 1 }^n (u_j + 1 / u_j) \big)^2 } \frac { d
u_1 } { u_1 } \cdots \frac { d u_n } { u_n }$.\par
We had conjectured --- on the basis of
extreme-precision numerical quadrature --- that $ C_n $
has a finite large-$n$ limit, namely $ C_\infty = 2
e^{-2} $, with $ \gamma $ being the Euler constant. On
such a numerological clue we are able to prove the
conjecture. We then show that integrals $ D_n $ and $
E_n $ both decay exponentially with $n$, in a certain
rigorous sense. While $ C_n $, $ D_n $ remain
unresolved for $ n \geq 5 $, we were able to conjecture
a closed form for $ E_5 $. Our experimental results
involved extreme-precision, multidimensional quadrature
on intricate integrands; thus, a highly parallel
computation was required.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Physics A (Mathematical and General)",
journal-URL = "http://iopscience.iop.org/1751-8121",
onlinedate = "19 September 2006",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2006:TPE,
author = "David H. Bailey and Jonathan M. Borwein and Vishaal
Kapoor and Eric W. Weisstein",
title = "Ten problems in experimental mathematics",
journal = j-AMER-MATH-MONTHLY,
volume = "113",
number = "6",
pages = "481--509",
month = jun # "\slash " # jul,
year = "2006",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/27641975",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "65-02 (11Y60 37E05 37G10 65-05 68-02)",
MRnumber = "2231135",
MRreviewer = "Vasily A. Chernecky",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1237/;
http://www.jstor.org/stable/27641975",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CoLab Preprint 270.",
}
@InCollection{Borwein:2006:AWM,
author = "Jonathan M. Borwein",
editor = "N. Sinclair and W. Higginson",
booktitle = "Mathematics and the aesthetic",
title = "Aesthetics for the working mathematician",
volume = "25",
publisher = pub-SV,
address = pub-SV:adr,
pages = "21--40",
year = "2006",
MRclass = "00A05 (00A99 11A99 11Y99)",
MRnumber = "2274212",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "CMS Books Math./Ouvrages Math. SMC",
URL = "http://docserver.carma.newcastle.edu.au/150/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 01:165.",
}
@Article{Borwein:2006:BDE,
author = "Jonathan Borwein and Vicente Montesinos and Jon
Vanderwerff",
title = "Boundedness, differentiability and extensions of
convex functions",
journal = j-J-CONVEX-ANAL,
volume = "13",
number = "3--4",
pages = "587--602",
year = "2006",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "46G05 (46N10 49J50 52A41)",
MRnumber = "2291553",
MRreviewer = "Lud{\v{e}}k Zaj{\'{\i}}{\v{c}}ek",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/288/;
http://www.heldermann.de/JCA/JCA13/JCA133/jca13046.htm",
abstract = "We survey various boundedness, differentiability and
extendibility properties of convex functions, and how
they are related to sequential convergence with respect
to various topologies in the dual space. It is also
shown that if $ X / Y $ is separable then every
continuous convex function on $Y$ can be extended to a
continuous convex function on $X$.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2006:BDE",
}
@Book{Borwein:2006:CAN,
author = "Jonathan M. Borwein and Adrian S. Lewis",
title = "Convex analysis and nonlinear optimization",
volume = "3",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xii + 310",
year = "2006",
DOI = "https://doi.org/10.1007/978-0-387-31256-9",
ISBN = "0-387-29570-4",
ISBN-13 = "978-0-387-29570-1",
MRclass = "49-01 (46N10 47N10 49-02 49J53 90-01)",
MRnumber = "2184742",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Theory and examples.",
series = "CMS Books in Mathematics\slash Ouvrages de
Math{\'e}matiques de la SMC",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
tableofcontents = "Front Matter / i--xii \\
Background / 1--14 \\
Inequality Constraints / 15--32 \\
Fenchel Duality / 33--63 \\
Convex Analysis / 65--96 \\
Special Cases / 97--122 \\
Nonsmooth Optimization / 123--152 \\
Karush--Kuhn--Tucker Theory / 153--177 \\
Fixed Points / 179--211 \\
More Nonsmooth Structure / 213--238 \\
Postscript: Infinite Versus Finite Dimensions /
239--251 \\
List of Results and Notation / 253--273 \\
Back Matter / 275--310",
}
@Article{Borwein:2006:DLP,
author = "Jonathan M. Borwein and Mason S. Macklem",
title = "The (digital) life of {Pi}",
journal = j-AUSTRALIAN-MATH-SOC-GAZ,
volume = "33",
number = "4",
pages = "243--248",
month = sep,
year = "2006",
ISSN = "0311-0729 (print), 1326-2297 (electronic)",
ISSN-L = "0311-0729",
MRclass = "11Y60 (65B99)",
MRnumber = "2259732",
MRreviewer = "Khodabakhsh Hessami Pilehrood",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/267/;
http://www.austms.org.au/Publ/Gazette/2006/Sep06/pi.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Australian Mathematical Society. Gazette",
journal-URL = "http://www.austms.org.au/gazette",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Borwein:2006:EM,
author = "Jonathan M. Borwein and David H. Bailey and Roland
Girgensohn",
title = "Experiments in Mathematics",
publisher = pub-A-K-PETERS,
address = pub-A-K-PETERS:adr,
pages = "????",
year = "2006",
ISBN = "1-56881-283-3, 1-56881-211-6, 1-56881-136-5",
ISBN-13 = "978-1-56881-283-0",
LCCN = "????",
bibdate = "Tue Aug 16 08:45:42 MDT 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Combined interactive CD version.",
abstract = "Contains the full text of: Mathematics by experiment:
plausible reasoning in the 21st century; and,
Experimentation in mathematics: computational paths to
discovery, in electronic, searchable form. Includes
hyperlinks for all cross references, Internet URLs, and
bibliographical references. Enhanced search function
helps with particular formulas or expressions.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2006:FRO,
author = "Jonathan M. Borwein",
title = "Featured Review: {{\booktitle{Oxford Users' Guide to
Mathematics}}. Edited by Eberhard Zeidler. Oxford
University Press, Oxford, 2004. \$59.50. xxii + 1285
pp., softcover. ISBN 0-19-850763-1}",
journal = j-SIAM-REVIEW,
volume = "48",
number = "3",
pages = "585--594",
month = sep,
year = "2006",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000048000003000585000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Wed Aug 31 09:49:49 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/doi/abs/10.1137/SIREAD000048000003000585000001;
http://www.jstor.org/stable/20453842",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2006:MMC,
author = "Jonathan M. Borwein",
title = "Maximal monotonicity via convex analysis",
journal = j-J-CONVEX-ANAL,
volume = "13",
number = "3--4",
pages = "561--586",
year = "2006",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "47H05 (47N10 49J53)",
MRnumber = "2291552",
MRreviewer = "Andrew C. Eberhard",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1235/;
http://www.heldermann.de/JCA/JCA13/JCA133/jca13045.htm",
abstract = "In his `23' ``Mathematische Probleme''(1) lecture to
the Paris International Congress in 1900, David Hilbert
wrote ``Besides it is an error to believe that rigor in
the proof is the enemy of simplicity.'' In this spirit,
we use simple convex analytic methods, relying on an
ingenious function due to Simon Fitzpatrick, to provide
a concise proof of the maximality of the sum of two
maximal monotone operators on reflexive Banach space
under standard transversality conditions. Many other
extension, surjectivity, convexity and local
boundedness results are likewise established.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2006:MMC",
}
@Unpublished{Borwein:2006:MS,
author = "Jonathan Borwein and Helaman Ferguson",
title = "The mathematics of salt",
month = dec,
year = "2006",
bibdate = "Tue Aug 16 10:05:43 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2006:MST,
author = "Jonathan M. Borwein",
title = "Maximality of sums of two maximal monotone operators",
journal = j-PROC-AM-MATH-SOC,
volume = "134",
number = "10",
pages = "2951--2955",
year = "2006",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/S0002-9939-06-08323-7",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "47H05 (46A22 46N10 47N10 49J53)",
MRnumber = "2231619",
MRreviewer = "Teemu Pennanen",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1234/;
http://www.jstor.org/stable/4098152",
abstract = "We use methods from convex analysis, relying on an
ingenious function of Simon Fitzpatrick, to prove
maximality of the sum of two maximal monotone operators
on reflexive Banach space under weak transversality
conditions.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2006:MST",
}
@Article{Borwein:2006:PES,
author = "David Borwein and Jonathan M. Borwein and David M.
Bradley",
title = "Parametric {Euler} sum identities",
journal = j-J-MATH-ANAL-APPL,
volume = "316",
number = "1",
pages = "328--338",
month = apr,
year = "2006",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/j.jmaa.2005.04.040",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "11M41",
MRnumber = "2201764",
MRreviewer = "Junesang Choi",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2006JMAA..316..328B;
http://docserver.carma.newcastle.edu.au/1236/;
http://www.sciencedirect.com/science/article/pii/S0022247X05003811",
abstract = "We consider some parametrized classes of multiple sums
first studied by Euler. Identities between meromorphic
functions of one or more variables in many cases
account for reduction formulae for these sums.",
acknowledgement = ack-nhfb,
eprint = "math/0505058",
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
keywords = "Euler sums; Generating functions; Multiple zeta
values; Zeta functions",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:2006:QCT,
author = "Jonathan Borwein and Peter (Liquin) Ye",
title = "Quadratic Convergence of the Tanh--Sinh Quadrature
Rule",
month = feb,
year = "2006",
bibdate = "Tue Aug 16 10:18:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
URL = "http://docserver.carma.newcastle.edu.au/342/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:2006:SCM,
author = "Jonathan M. Borwein and Chris H. Hamilton",
booktitle = "Proceedings of the 2006 International Symposium on
Symbolic and Algebraic Computation: {ISSAC 2006}",
title = "Symbolic Computation of Multidimensional {Fenchel}
Conjugates",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "23--30",
year = "2006",
DOI = "https://doi.org/10.1145/1145768.1145780",
ISBN = "1-59593-276-3",
ISBN-13 = "978-1-59593-276-1",
MRclass = "68W30 (65K10)",
MRnumber = "2289097",
bibdate = "Wed Aug 10 12:08:56 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "ISSAC '06",
URL = "http://doi.acm.org/10.1145/1145768.1145780",
acknowledgement = ack-nhfb,
acmid = "1145780",
keywords = "Fenchel conjugate, Legendre--Fenchel transform,
computer proofs, inequalities, subdifferential,
subgradient",
location = "Genoa, Italy",
numpages = "8",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2006:SFM,
author = "Jonathan Borwein",
title = "{Simon Fitzpatrick} memorial volume",
journal = j-J-CONVEX-ANAL,
volume = "13",
number = "3--4",
pages = "463--476",
year = "2006",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "01A70",
MRnumber = "2291547",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Introduction to Fitzpatrick memorial volume.",
URL = "http://www.heldermann.de/JCA/JCA13/JCA133/jca13040.htm",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2006:TTG,
author = "Jonathan M. Borwein and David M. Bradley",
title = "Thirty-two {Goldbach} variations",
journal = j-INT-J-NUMBER-THEORY,
volume = "2",
number = "1",
pages = "65--103",
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000383",
ISSN = "1793-0421 (print), 1933-8368 (electronic)",
MRclass = "11M41 (11M06)",
MRnumber = "2217795",
MRreviewer = "F. Beukers",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/301/",
abstract = "We give thirty-two diverse proofs of a small
mathematical gem --- the fundamental Euler sum identity
$ \zeta (2, 1) = \zeta (3) = 8 \zeta (\bar {2}, 1) $.
We also discuss various generalizations for multiple
harmonic (Euler) sums and some of their many
connections, thereby illustrating both the wide variety
of techniques fruitfully used to study such sums and
the attraction of their study.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory",
journal-URL = "http://www.worldscientific.com/worldscinet/ijnt",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2006:TTG",
}
@Article{Borwein:2006:VMC,
author = "Jonathan M. Borwein and Qiji J. Zhu",
title = "Variational methods in convex analysis",
journal = j-J-GLOBAL-OPT,
volume = "35",
number = "2",
pages = "197--213",
year = "2006",
CODEN = "JGOPEO",
DOI = "https://doi.org/10.1007/s10898-005-3835-3",
ISSN = "0925-5001 (print), 1573-2916 (electronic)",
ISSN-L = "0925-5001",
MRclass = "49J53 (90C25)",
MRnumber = "2242012",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special issue in honour of Alex Rubinov's 65th
birthday.",
URL = "http://docserver.carma.newcastle.edu.au/259/",
abstract = "We use variational methods to provide a concise
development of a number of basic results in convex and
functional analysis. This illuminates the parallels
between convex analysis and smooth subdifferential
theory.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Global Optimization",
fjournal = "Journal of Global Optimization. An International
Journal Dealing with Theoretical and Computational
Aspects of Seeking Global Optima and Their Applications
in Science, Management and Engineering",
journal-URL = "http://link.springer.com/journal/10898",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CoLab Preprint 259.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2006:VMC",
}
@Article{Bailey:2007:BI,
author = "D. H. Bailey and J. M. Borwein and R. E. Crandall",
title = "Box integrals",
journal = j-J-COMPUT-APPL-MATH,
volume = "206",
number = "1",
pages = "196--208",
month = sep,
year = "2007",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2006.06.010",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65D30 (11Y60 33E20 60E05)",
MRnumber = "2337437",
MRreviewer = "Michael J. Evans",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2007JCoAM.206..196B;
http://docserver.carma.newcastle.edu.au/320/;
http://www.sciencedirect.com/science/article/pii/S0377042706004250",
abstract = "By a ``box integral'' we mean here an expectation $
\bra | r \to - q \to | s \ket $ where $ r \to $ runs
over the unit $n$-cube, with $ q \to $ and $s$ fixed,
explicitly: $ \int_0^1 \cdots \int_0^1 ((r 1 - q 1) 2 +
\cdots + (r n - q n) 2) s / 2 d r 1 \ldots d r n$. The
study of box integrals leads one naturally into several
disparate fields of analysis. While previous studies
have focused upon symbolic evaluation and asymptotic
analysis of special cases (notably $ s = 1$), we work
herein more generally --- in interdisciplinary fashion
--- developing results such as: (1) analytic
continuation (in complex $s$), (2) relevant
combinatorial identities, (3) rapidly converging
series, (4) statistical inferences, (5) connections to
mathematical physics, and (6) extreme-precision
quadrature techniques appropriate for these integrals.
These intuitions and results open up avenues of
experimental mathematics, with a view to new
conjectures and theorems on integrals of this type.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "Box integrals; High-precision quadrature;
Multi-dimensional integrals",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Bailey:2007:EMA,
author = "David H. Bailey and Jonathan M. Borwein and Neil J.
Calkin and Roland Girgensohn and D. Russell Luke and
Victor Moll",
title = "Experimental Mathematics in Action",
publisher = pub-A-K-PETERS,
address = pub-A-K-PETERS:adr,
pages = "xii + 322",
year = "2007",
ISBN = "1-56881-271-X",
ISBN-13 = "978-1-56881-271-7",
LCCN = "QA8.7 .E97 2007",
bibdate = "Thu Oct 25 18:45:59 MDT 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://docserver.carma.newcastle.edu.au/1733/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "Experimental mathematics",
tableofcontents = "Preface / xi \\
1 A Philosophical Introduction / 1 \\
1.1 Introduction / 1 \\
1.2 Mathematical Knowledge as We View It / 1 \\
1.3 Mathematical Reasoning / 2 \\
1.4 Philosophy of Experimental Mathematics / 3 \\
1.5 Our Experimental Mathodology / 11 \\
1.6 Finding Things versus Proving Things / 15 \\
1.7 Conclusions / 24 \\
2 Algorithms for Experimental Mathematics I / 29 \\
2.1 The Poetry of Computation / 29 \\
2.2 High-Precision Arithmetic / 30 \\
2.3 Integer Relation Detection / 31 \\
2.4 Illustrations and Examples / 33 \\
2.5 Definite Integrals and Infinite Series Summations /
43 \\
2.6 Computation of Multivariate Zeta Values / 44 \\
2.7 Ramanujan-Type Elliptic Series / 45 \\
3 Algorithms for Experimental Mathematics II / 53 \\
3.1 True Scientific Value / 53 \\
3.2 Prime Number Computations / 55 \\
3.3 Roots of Polynomials / 58 \\
3.4 Numerical Quadrature / 61 \\
3.5 Infinite Series Summation / 67 \\
3.6 Ap{\'e}ry-Like Summations / 70 \\
4 Exploration and Discovery in Inverse Scattering / 79
\\
4.1 Metaphysics and Mechanics / 79 \\
4.2 The Physical Experiment / 80 \\
4.3 The Model / 83 \\
4.4 The Mathematical Experiment: Qualitative Inverse
Scattering / 90 \\
4.5 Current Research / 107 \\
5 Exploring Strange Functions on the Computer / 113 \\
5.1 What Is ``Strange''? / 113 \\
5.2 Nowhere Differentiable Functions / 114 \\
5.3 Bernoulli Convolutions / 126 \\
6 Random Vectors and Factoring Integers: A Case Study /
139 \\
6.1 Learning from Experience / 139 \\
6.2 Integer Factorization / 140 \\
6.3 Random Models / 143 \\
6.4 The Main Questions / 144 \\
6.5 Bounds / 145 \\
6.6 Which Model Is Best? / 149 \\
6.7 Experimental Evidence / 155 \\
6.8 Conclusions / 158 \\
7 A Selection of Integrals from a Popular Table / 161
\\
7.1 The Allure of the Integral / 161 \\
7.2 The Project and Its Experimental Nature / 163 \\
7.3 Families and Individuals / 164 \\
7.4 An Experimental Derivation of Wallis' Formula / 167
\\
7.5 A Hyperbolic Example / 170 \\
7.6 A Formula Hidden in the List / 174 \\
7.7 Some Experiments on Valuations / 177 \\
7.8 An Error in the Latest Edition / 184 \\
7.9 Some Examples Involving the Hurwitz Zeta Function /
185 \\
8 Experimental Mathematics: A Computational Conclusion
/ 189 \\
8.1 Mathematicians Are a Kind of Frenchmen / 189 \\
8.2 Putting Lessons in Action / 190 \\
8.3 Visual Computing / 191 \\
8.4 A Preliminary Example: Visualizing DNA Strands /
194 \\
8.5 What Is a Chaos Game? / 195 \\
8.6 Hilbert's Inequality and Witten's Zeta Function /
202 \\
8.7 Computational Challenge Problems / 214 \\
8.8 Last Words / 222 \\
9 Exercises / 225 \\
Exercises for Chapter 1 / 225 \\
Exercises for Chapter 2 / 231 \\
Exercises for Chapter 3 / 249 \\
Exercises for Chapter 4 / 256 \\
Exercises for Chapter 5 / 260 \\
Exercises for Chapter 6 / 262 \\
Exercises for Chapter 7 / 265 \\
Exercises for Chapter 8 / 273 \\
Additional Exercises / 280 \\
Bibliography / 301 \\
Index / 317",
}
@Article{Bailey:2007:HFI,
author = "D. H. Bailey and D. Borwein and J. M. Borwein and R.
E. Crandall",
title = "Hypergeometric Forms for {Ising}-Class Integrals",
journal = j-EXP-MATH,
volume = "16",
number = "3",
pages = "257--276",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2007.10129003",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "33E20 (33C05 33F05 33F10 65D30 82B20)",
MRnumber = "2367317",
MRreviewer = "Wadim Zudilin",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib;
http://www.tandfonline.com/toc/uexm20/16/3",
URL = "http://docserver.carma.newcastle.edu.au/326/;
http://projecteuclid.org/euclid.em/1204928528",
abstract = "We apply experimental -mathematical principles to
analyze the integrals [complex multiple integral] These
are generalizations of a previous integral $ C_n :=
C_{n, 1} $ relevant to the Ising theory of solid-state
physics [Bailey et al. 06]. We find representations of
the $ C_{n, k} $ in terms of Meijer $G$-functions and
nested Barnes integrals. Our investigations began by
computing 500-digit numerical values Of $ C_{n, k}$ for
all integers $n$, $k$, where $n$ is an element of $ [2,
12]$ and $k$ is an element of $ [0, 25]$. We found that
some $ C_{n, k}$ enjoy exact evaluations involving
Dirichlet L-functions or the Riemann zeta function. In
the process of analyzing hypergeometric
representations, we found-experimentally and
strikingly-that the $ C_{n, k}$ almost certainly
satisfy certain interindicial relations including
discrete k-recurrences. Using generating functions,
differential theory, complex analysis, and
Wilf--Zeilberger algorithms we are able to prove some
central cases of these relations.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Bailey:2007:HFI",
}
@Unpublished{Bailey:2007:HSI,
author = "D. Bailey and J. Borwein and R. Crandall and D.
Manna",
title = "{Heisenberg} spin integrals",
month = aug,
year = "2007",
bibdate = "Tue Aug 16 10:04:46 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "Preprint.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Bailey:2007:SPa,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Solution to Problem 11275",
type = "Report",
institution = "Lawrence Berkeley National Laboratory and Faculty of
Computer Science, Dalhousie University",
address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5,
Canada",
pages = "2",
day = "24",
month = feb,
year = "2007",
bibdate = "Fri Sep 30 08:29:49 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/amm-11275.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Bailey:2007:SPb,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Solution to Monthly Problem 11277",
type = "Report",
institution = "Lawrence Berkeley National Laboratory and Faculty of
Computer Science, Dalhousie University",
address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5,
Canada",
pages = "3",
day = "23",
month = mar,
year = "2007",
bibdate = "Fri Sep 30 08:30:39 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/amm-11277.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bartz:2007:FFC,
author = "Sedi Bartz and Heinz H. Bauschke and Jonathan M.
Borwein and Simeon Reich and Xianfu Wang",
title = "{Fitzpatrick} functions, cyclic monotonicity and
{Rockafellar}'s antiderivative",
journal = j-NONLINEAR-ANAL,
volume = "66",
number = "5",
pages = "1198--1223",
year = "2007",
CODEN = "NOANDD",
DOI = "https://doi.org/10.1016/j.na.2006.01.013",
ISSN = "0362-546x (print), 1873-5215 (electronic)",
ISSN-L = "0362-546X",
MRclass = "47H05 (47N10 49J53 90C25)",
MRnumber = "2286629",
MRreviewer = "Patrick L. Combettes",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1232/;
http://www.sciencedirect.com/science/article/pii/S0362546X06000435",
abstract = "Several deeper results on maximal monotone operators
have recently found simpler proofs using Fitzpatrick
functions. In this paper, we study a sequence of
Fitzpatrick functions associated with a monotone
operator. The first term of this sequence coincides
with the original Fitzpatrick function, and the other
terms turn out to be useful for the identification and
characterization of cyclic monotonicity properties. It
is shown that for any maximal cyclically monotone
operator, the pointwise supremum of the sequence of
Fitzpatrick functions is closely related to
Rockafellar's antiderivative. Several examples are
explicitly computed for the purpose of illustration. In
contrast to Rockafellar's result, a maximal
3-cyclically monotone operator need not be maximal
monotone. A simplified proof of Asplund's observation
that the rotation in the Euclidean plane by $ \pi / n $
is $n$-cyclically monotone but not $ (n + 1)$
-cyclically monotone is provided. The Fitzpatrick
family of the subdifferential operator of a sublinear
and of an indicator function is studied in detail. We
conclude with a new proof of Moreau's result concerning
the convexity of the set of proximal mappings.",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
keywords = "Convex function; Cyclically monotone operator; Fenchel
conjugate; Fitzpatrick function; Maximal monotone
operator; Subdifferential operator; Sublinear
function",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bauschke:2007:FFC,
author = "Heinz H. Bauschke and Jonathan M. Borwein and Xianfu
Wang",
title = "{Fitzpatrick} functions and continuous linear monotone
operators",
journal = j-SIAM-J-OPT,
volume = "18",
number = "3",
pages = "789--809",
year = "2007",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/060655468",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
MRclass = "47H05 (47B65 90C25)",
MRnumber = "2345969",
MRreviewer = "P. P. Zabre{\u\i}ko",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/319/",
abstract = "The notion of a maximal monotone operator is crucial
in optimization as it captures both the subdifferential
operator of a convex, lower semicontinuous, and proper
function and any (not necessarily symmetric) continuous
linear positive operator. It was recently discovered
that most fundamental results on maximal monotone
operators allow simpler proofs utilizing Fitzpatrick
functions. In this paper, we study Fitzpatrick
functions of continuous linear monotone operators
defined on a Hilbert space. A novel characterization of
skew operators is presented. A result by Brezis and
Haraux is reproved using the Fitzpatrick function. We
investigate the Fitzpatrick function of the sum of two
operators, and we show that a known upper bound is
actually exact in finite-dimensional and more general
settings. Cyclic monotonicity properties are also
analyzed, and closed forms of the Fitzpatrick functions
of all orders are provided for all rotators in the
Euclidean plane.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Bauschke,
Heinz/D-5582-2009",
unique-id = "Bauschke:2007:FFC",
}
@Article{Borwein:2007:ADMa,
author = "Jonathan Borwein and Herre Wiersma",
title = "{Asplund} decomposition of monotone operators",
journal = j-SIAM-J-OPT,
volume = "18",
number = "3",
pages = "946--960",
year = "2007",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/060658357",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
MRclass = "47H05 (47N10 49J53 52A41)",
MRnumber = "2345978",
MRreviewer = "Hong Kun Xu",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/321/",
abstract = "We establish representations of a monotone mapping as
the sum of a maximal subdifferential mapping and a
``remainder'' monotone mapping, where the remainder is
``acyclic'' in the sense that it contains no nontrivial
subdifferential component. This is the nonlinear
analogue of a skew linear operator. Examples of
indecomposable and acyclic operators are given. In
particular, we present an explicit nonlinear acyclic
operator.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2007:ADM",
}
@InCollection{Borwein:2007:ADMb,
author = "Jonathan M. Borwein",
editor = "Alain Pietrus and Michel H. Geoffroy",
booktitle = "{CSVAA} 2004---control set-valued analysis and
applications, ESAIM: Proceedings",
title = "{Asplund} decompositions of monotone operators",
volume = "17",
publisher = "EDP Sci.",
address = "Les Ulis, France",
pages = "19--25",
year = "2007",
DOI = "https://doi.org/10.1051/proc:071703",
MRclass = "47H05 (41A50 46B03 46B20 46G05 47N10 49J53)",
MRnumber = "2362689",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "ESAIM Proc.",
URL = "http://docserver.carma.newcastle.edu.au/299/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:2007:CCS,
author = "Jonathan M. Borwein and David Langstroth and Mason
Macklem and Scott Wilson and V. Jungi{\'c}",
booktitle = "{21st International Symposium on High Performance
Computing Systems and Applications. HPCS 2007,
Saskatoon, SK, Canada, 13--16 May 2007}",
title = "The Coast-to-Coast Seminar and Remote Mathematical
Collaboration",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "23--29",
month = may,
year = "2007",
DOI = "https://doi.org/10.1109/HPCS.2007.30",
bibdate = "Wed Aug 10 12:08:56 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
book-isbn = "0-7695-2813-9",
keywords = "AccessGrid; Australia; Canadian universities;
coast-to-coast seminar; Collaboration; Collaborative
work; computer aided instruction; Computer displays;
Computer networks; Dalhousie University; Distributed
computing; grid computing; groupware; Mathematics;
mathematics computing; Production; remote mathematical
collaboration; seminar series; Seminars; Simon Fraser
University; Virtual environment",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2007:CDS,
author = "Jonathan M. Borwein",
title = "A class of {Dirichlet} series integrals",
journal = j-AMER-MATH-MONTHLY,
volume = "114",
number = "1",
pages = "70--76",
month = jan,
year = "2007",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "40A10 (26A42)",
MRnumber = "2283644",
MRreviewer = "Ilaria Mantellini",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/262/;
http://www.jstor.org/stable/27642121",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CoLab Preprint 262.",
}
@InCollection{Borwein:2007:CNS,
author = "Jonathan M. Borwein and Warren B. Moors",
editor = "Elliott Pearl",
booktitle = "Open Problems in Topology {II}",
title = "Chapter 50: {Non-smooth} analysis, optimisation theory
and {Banach} space theory",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "549--559",
year = "2007",
DOI = "https://doi.org/10.1016/B978-044452208-5/50050-8",
ISBN = "0-444-52208-5",
ISBN-13 = "978-0-444-52208-5",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.sciencedirect.com/science/article/pii/B9780444522085500508",
abstract = "This chapter discusses about nonsmooth analysis,
optimization theory, and Banach space theory. A Banach
space X is called a weak Asplund space [G{\^a}teaux
differentiability space] if each continuous convex
function defined on it is G{\^a}teaux differentiable at
the points of a residual subset (that is, a subset that
contains the intersection of countably many dense open
subsets of X) [dense subset] of its domain. For a
Banach space (X, || \cdot || ), with closed unit ball
BX, the Bishop--Phelps set is the set of all linear
functionals in the dual X* that attain their maximum
value over BX; that is, the set {x* \subset X*: x*(x) =
|| x*|| for some x \subset BX}. The Bishop--Phelps
Theorem says that the Bishop--Phelps set is always
dense in X*. A Banach space X has the attainable
approximation property (AAP) if the set of support
functionals for any closed bounded convex subset W
\subseteq X is norm dense in X*. The concepts related
to the Bishop--Phelps problem and the complex
Bishop--Phelps property are also discussed. Concepts of
biorthogonal sequences and support points are also
elaborated.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2007:DCR,
author = "D. Borwein and J. Borwein and R. Crandall and R.
Mayer",
title = "On the dynamics of certain recurrence relations",
journal = j-RAMANUJAN-J,
volume = "13",
number = "1--3",
pages = "63--101",
year = "2007",
CODEN = "RAJOF9",
DOI = "https://doi.org/10.1007/s11139-006-0243-3",
ISSN = "1382-4090 (print), 1572-9303 (electronic)",
ISSN-L = "1382-4090",
MRclass = "11B37 (11A55 11Y16 37C99 37E99 39A10 65Q05)",
MRnumber = "2281157",
MRreviewer = "James G. Mc Laughlin",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/253/;
http://link.springer.com/article/10.1007/s11139-006-0243-3",
abstract = "In recent analyses [ 3, 4] the remarkable AGM
continued fraction of Ramanujan - denoted R-1(a, b) -
was proven to converge for almost all complex parameter
pairs (a, b). It was conjectured that R-1 diverges if
and only if (0 not equal a = be(i phi) with cos(2) phi
not equal 1) or (a(2) = b(2) is an element of
(-infinity, 0)). In the present treatment we resolve
this conjecture to the positive, thus establishing the
precise convergence domain for R-1. This is
accomplished by analyzing, using various special
functions, the dynamics of sequences such as (t(n))
satisfying a recurrence t(n) = (t(n-1)(n-1)
\kappa(n-1)t(n-2))/n. where \kappa(n):= a(2), b(2) as n
be even, odd respectively. As a byproduct, we are able
to give, in some cases, exact expressions for the n-th
convergent to the fraction R-1, thus establishing some
precise convergence rates. It is of interest that this
final resolution of convergence depends on rather
intricate theorems for complex-matrix products, which
theorems evidently being extensible to more general
continued fractions.",
acknowledgement = ack-nhfb,
fjournal = "The {Ramanujan} Journal",
journal-URL = "http://link.springer.com/journal/11139",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CoLab Preprint 253.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2007:DCR",
}
@TechReport{Borwein:2007:ELAa,
author = "David Borwein and Jonathan Borwein and Richard
Crandall",
title = "Effective {Laguerre} asymptotics",
type = "Report",
institution = "Department of Computer Science, Dalhousie University",
address = "Halifax, NS, Canada B3H 4R2",
year = "2007",
bibdate = "Thu Aug 11 08:24:07 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://docserver.carma.newcastle.edu.au/334/;
http://locutus.cs.dal.ca:8088/archive/00000334/;
http://web.archive.org/web/20070208032521/http://locutus.cs.dal.ca:8088/archive/00000334/",
abstract = "It is known that the generalized Laguerre polynomials
can enjoy sub-exponential growth for large primary
index. Specifically, for certain fixed parameter pairs
$ (a, z) $ one has the large-$n$ asymptotic $$ L_n^{( -
a)}( - z) \sim C(a, z) n^{-a / 2 - 1 / 4} e^{2 \sqrt
{nz}}. $$ We introduce a computationally motivated
contour integral that allows highly efficient numerical
evaluation of $ L_n$, yet also leads to general
asymptotic series over the full domain for
sub-exponential behavior. We eventually lay out a fast
algorithm for generation of the rather formidable
expansion coefficients. Along the way we address the
difficult problem of establishing effective (i.e.,
rigorous and explicit) error bounds on the general
expansion. To this end, we avoid classical
stationary-phase and steepest-descent techniques in
favor of an ``exp-arc'' method that amounts to a
natural bridge between converging series and effective
asymptotics. Finally, we exhibit an absolutely
convergent exp-arc series for Bessel-function
evaluation as an alternative to conventional
ascending-asymptotic switching.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2007:IPA,
author = "Jonathan M. Borwein and Marc Chamberland",
title = "Integer powers of arcsin",
journal = j-INT-J-MATH-MATH-SCI,
pages = "Art. ID 19381, 10",
month = jun,
year = "2007",
DOI = "https://doi.org/10.1155/2007/19381",
ISSN = "0161-1712 (print), 1687-0425 (electronic)",
ISSN-L = "0161-1712",
MRclass = "33B10 (11B65 33B30)",
MRnumber = "2320777",
MRreviewer = "Stefan Gerhold",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/287/",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematics and Mathematical
Sciences",
journal-URL = "https://www.hindawi.com/journals/ijmms/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2007:MST,
author = "Jonathan M. Borwein",
title = "Maximality of sums of two maximal monotone operators
in general {Banach} space",
journal = j-PROC-AM-MATH-SOC,
volume = "135",
number = "12",
pages = "3917--3924",
month = dec,
year = "2007",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/S0002-9939-07-08960-5",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "47H05 (46N10 52A41)",
MRnumber = "2341941",
MRreviewer = "S{\'a}ndor Z. N{\'e}meth",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/322/;
http://www.jstor.org/stable/20535029",
abstract = "We combine methods from convex analysis, based on a
function of Simon Fitzpatrick, with a fine recent idea
due to Voisei, to prove maximality of the sum of two
maximal monotone operators in Banach space under
various natural domain and transversality conditions.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2007:MST",
}
@InCollection{Borwein:2007:NAA,
author = "Jonathan M. Borwein and Warren B. Moors",
title = "Nonsmooth Analysis, Approximation Theory and {Banach}
Space Theory",
crossref = "Pearl:2007:OPT",
pages = "557--566",
year = "2007",
bibdate = "Sat Aug 13 17:04:44 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2007:PCS,
author = "Jonathan M. Borwein",
title = "Proximality and {Chebyshev} sets",
journal = j-OPTIM-LETT,
volume = "1",
number = "1",
pages = "21--32",
year = "2007",
DOI = "https://doi.org/10.1007/s11590-006-0014-5",
ISSN = "1862-4472 (print), 1862-4480 (electronic)",
ISSN-L = "1862-4472",
MRclass = "41A50 (46A55 46N10 47J20 49J53)",
MRnumber = "2357605",
MRreviewer = "John R. Giles",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/323/",
abstract = "This paper is a companion to a lecture given at the
Prague Spring School in Analysis in April 2006. It
highlights four distinct variational methods of proving
that a finite dimensional Chebyshev set is convex and
hopes to inspire renewed work on the open question of
whether every Chebyshev set in Hilbert space is
convex.",
acknowledgement = ack-nhfb,
ajournal = "Optim. Lett.",
fjournal = "Optimization Letters",
journal-URL = "http://link.springer.com/journal/11590",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2007:PCS",
}
@Article{Borwein:2007:PRB,
author = "J. M. Borwein and B. Salvy",
title = "A Proof of a Recursion for {Bessel} Moments",
journal = "ArXiv e-prints",
month = jun,
year = "2007",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2007arXiv0706.1409B;
http://docserver.carma.newcastle.edu.au/346/",
abstract = "We provide a proof of a conjecture in (Bailey,
Borwein, Borwein, Crandall 2007) on the existence and
form of linear recursions for moments of powers of the
Bessel function $ K_0 $.",
acknowledgement = ack-nhfb,
eprint = "0706.1409",
keywords = "Computer Science - Symbolic Computation, Mathematics -
Classical Analysis and ODEs",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "cs.SC",
}
@Unpublished{Borwein:2007:REM,
author = "J. M. Borwein and Mason Macklem",
title = "Retro-enhancement of Mathematical Literature",
month = mar,
year = "2007",
bibdate = "Tue Aug 16 10:05:13 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
URL = "http://docserver.carma.newcastle.edu.au/339/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2007:VPE,
author = "David Borwein and Jonathan Borwein",
title = "{van der Pol} Expansions of {$L$}-Series",
journal = j-CAN-MATH-BULL,
volume = "50",
number = "1",
pages = "11--23",
month = mar,
year = "2007",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-2007-002-0",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "11M35 (11M41)",
MRnumber = "2296621",
MRreviewer = "Saulius Zamarys",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://cms.math.ca/cmb/v50/;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/canmathbull.bib",
URL = "http://docserver.carma.newcastle.edu.au/283/",
abstract = "We provide concise series representations for various
L-series integrals. Different techniques are needed
below and above the abscissa of absolute convergence of
the underlying L-series.",
acknowledgement = ack-nhfb,
fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2007:VPE",
}
@InCollection{Bailey:2008:CAD,
author = "David H. Bailey and Jonathan M. Borwein",
booktitle = "Tapas in experimental mathematics",
title = "Computer-assisted discovery and proof",
volume = "457",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "21--52",
year = "2008",
DOI = "https://doi.org/10.1090/conm/457/08901",
MRclass = "11Y99 (68T15 68U35 68W30)",
MRnumber = "2427663",
MRreviewer = "Jeffrey O. Shallit",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Contemp. Math.",
URL = "http://docserver.carma.newcastle.edu.au/338/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Bailey:2008:EEB,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Effective Error Bounds for {Euler--Maclaurin}-Based
Quadrature Schemes",
crossref = "IEEE:2008:HIS",
pages = "??--??",
year = "2008",
bibdate = "Sat Aug 13 17:20:17 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
pagecount = "7",
}
@Article{Bailey:2008:EIE,
author = "David H. Bailey and Jonathan M. Borwein and David
Broadhurst and M. L. Glasser",
title = "Elliptic integral evaluations of {Bessel} moments and
applications",
journal = j-J-PHYS-A-MATH-THEOR,
volume = "41",
number = "20",
pages = "205203",
month = may,
year = "2008",
CODEN = "JPAMB5",
DOI = "https://doi.org/10.1088/1751-8113/41/20/205203",
ISSN = "1751-8113 (print), 1751-8121 (electronic)",
ISSN-L = "1751-8113",
MRclass = "33C10 (33E05 33F05)",
MRnumber = "2450513",
MRreviewer = "Subuhi Khan",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2008JPhA...41t5203B;
http://arxiv.org/abs/0801.0891;
http://iopscience.iop.org/article/10.1088/1751-8113/41/20/205203;
http://stacks.iop.org/1751-8121/41/i=20/a=205203",
abstract = "We record and substantially extend what is known about
the closed forms for various Bessel function moments
arising in quantum field theory, condensed matter
theory and other parts of mathematical physics. In
particular, we develop formulae for integrals of
products of six or fewer Bessel functions. In
consequence, we are able to discover and prove closed
forms for $ c_{n, k} \coloneq {\int }^\infty_0 t^k
K^n_0 (t) d t $ with integers $ n = 1, 2, 3, 4 $ and $
k \geq 0 $, obtaining new results for the even moments
$ c_{3, 2k} $ and $ c_{4, 2k} $. We also derive new
closed forms for the odd moments $ s_{n, 2k + 1}
\coloneq \int^\infty_0 t^{2k + 1} I_0 (t) K^{n - 1}_0
(t) \, d t $ with $ n = 3, 4 $ and for $ t_{n, 2k + 1}
\coloneq \int^\infty_0 t^{2k + 1} I^2_0 (t) K^{n - 2}_0
(t) \, d t $ with $ n = 5 $, relating the latter to
Green functions on hexagonal, diamond and cubic
lattices. We conjecture the values of $ s_{5, 2k + 1}
$, make substantial progress on the evaluation of $
c_{5, 2k + 1} $, $ s_{6, 2k + 1} $ and $ t_{6, 2k + 1}
$ and report more limited progress regarding $ c_{5,
2k} $, $ c_{6, 2k + 1} $ and $ c_{6, 2k} $. In the
process, we obtain eight conjectural evaluations, each
of which has been checked to 1200 decimal places. One
of these lies deep in four-dimensional quantum field
theory and two are probably provable by delicate
combinatorics. There remains a hard core of five
conjectures whose proofs would be most instructive, to
mathematicians and physicists alike.",
acknowledgement = ack-nhfb,
eid = "205203",
eprint = "0801.0891",
fjournal = "Journal of Physics. A. Mathematical and Theoretical",
journal-URL = "http://iopscience.iop.org/1751-8121",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
pagecount = "46",
primaryclass = "hep-th",
}
@InProceedings{Bailey:2008:HPC,
author = "D. H. Bailey and J. M. Borwein",
booktitle = "Proceedings of {XII} Advanced Computing and Analysis
Techniques in Physics Research",
title = "High-Precision Computation and Mathematical Physics",
publisher = "????",
address = "????",
pages = "14",
year = "2008",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2008acat.confE..14B;
http://docserver.carma.newcastle.edu.au/386/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Bailey:2008:HPH,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Highly Parallel, High-Precision Numerical
Integration",
type = "Report",
institution = "Lawrence Berkeley National Laboratory and Faculty of
Computer Science, Dalhousie University",
address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5,
Canada",
pages = "18",
day = "1",
month = apr,
year = "2008",
bibdate = "Fri Sep 30 08:30:39 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/quadparallel.pdf",
abstract = "This paper describes schemes for rapidly computing
numerical values of definite integrals to very high
accuracy (hundreds to thousands of digits) on highly
parallel computer systems. Such schemes are of interest
not only in computational physics and computational
chemistry, but also in experimental mathematics, where
high-precision numerical values of definite integrals
can be used to numerically discover new identities.
This paper presents performance results for 1-D and 2-D
integral test suites on highly parallel computer
systems. Results are also given for certain problems
that derive from mathematical physics. One of these
results confirms a conjecture to 20,000 digit accuracy.
The performance rate for this calculation is 690
Gflop/s on 1024 CPUs of a state-of-the-art parallel
system. Other results, which range in precision from
120 to 500 digits, and for 1-D, 2-D, 3-D and 4-D
integrals, derive from Ising theory. The largest of
these calculations required 28 hours on 256 CPUs. We
believe that these are the first instances of
evaluations of nontrivial 3-D and 4-D integrals to
multi-hundred-digit accuracy.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Bailey:2008:HPN,
author = "D. H. Bailey and J. M. Borwein",
booktitle = "MICA conference May 2008",
title = "High-Precision Numerical Integration: Progress and
Challenges",
publisher = "????",
address = "????",
pages = "??--??",
year = "2008",
bibdate = "Sat Aug 13 16:39:19 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1444/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Bailey:2008:PSP,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Proposed {SIAM} Problem",
type = "Report",
institution = "Lawrence Berkeley National Laboratory and Faculty of
Computer Science, Dalhousie University",
address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5,
Canada",
pages = "2",
day = "12",
month = aug,
year = "2008",
bibdate = "Fri Sep 30 08:36:07 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/siam-bessel.pdf",
abstract = "[From the introduction:] A recent paper by the present
authors, together with mathematical physicists David
Broadhurst and M. Larry Glasser, explored Bessel moment
integrals, namely definite integrals of the general
form $ \int_0^\infty t^m f^n(t) \, d t $, where the
function $ f(t) $ is one of the classical Bessel
functions [2]. In that paper, numerous previously
unknown analytic evaluations were obtained, using a
combination of analytic methods together with some
fairly high-powered numerical computations, often
performed on highly parallel computers.",
acknowledgement = ack-nhfb,
keywords = "Bessel moment integrals",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Baillie:2008:SSS,
author = "Robert Baillie and David Borwein and Jonathan M.
Borwein",
title = "Surprising sinc sums and integrals",
journal = j-AMER-MATH-MONTHLY,
volume = "115",
number = "10",
pages = "888--901",
month = dec,
year = "2008",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "33B10 (26D05 40A25 42A05)",
MRnumber = "2468551",
MRreviewer = "Valery V. Karachik",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/332/;
http://www.jstor.org/stable/27642636",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:2008:BST,
author = "J. M. Borwein and A. C. Eberhard",
title = "{Banach} spaces of type ({NI}) and monotone operators
on non-reflexive spaces",
month = jun,
year = "2008",
bibdate = "Tue Aug 16 10:02:34 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2008:CCC,
author = "J. Borwein and V. Jungi{\'c} and D. Langstroth and M.
Macklem and S. Wilson",
title = "Coast-to-Coast (C2C) Seminar: Background, History, and
Practice",
crossref = "Borwein:2008:CMD",
chapter = "9",
pages = "127--140",
year = "2008",
DOI = "https://doi.org/10.1201/b10587-12",
bibdate = "Sat Aug 13 16:51:32 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.crcnetbase.com/doi/pdfplus/10.1201/b10587-12",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2008:DRT,
author = "Jonathan M. Borwein and D. Russell Luke",
title = "Dynamics of a {Ramanujan}-type continued fraction with
cyclic coefficients",
journal = j-RAMANUJAN-J,
volume = "16",
number = "3",
pages = "285--304",
year = "2008",
CODEN = "RAJOF9",
DOI = "https://doi.org/10.1007/s11139-007-9096-7",
ISSN = "1382-4090 (print), 1572-9303 (electronic)",
ISSN-L = "1382-4090",
MRclass = "40A15 (11J70)",
MRnumber = "2429902",
MRreviewer = "Haakon S. Waadeland",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1480/",
abstract = "We study several generalizations of the AGM continued
fraction of Ramanujan inspired by a series of recent
articles in which the validity of the AGM relation and
the domain of convergence of the continued fraction
were determined for certain complex parameters (Borwein
et al., Exp. Math. 13, 275-286, 2004, Ramanujan J., in
press, 2004; Borwein and Crandall, Exp. Math. 12,
287-296, 2004). A study of the AGM continued fraction
is equivalent to an analysis of the convergence of
certain difference equations and the stability of
dynamical systems. Using the matrix analytical tools
developed in 2004, we determine the convergence
properties of deterministic difference equations and so
divergence of their corresponding continued
fractions.",
acknowledgement = ack-nhfb,
fjournal = "The {Ramanujan} Journal",
journal-URL = "http://link.springer.com/journal/11139",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CoLab Preprint 261.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2008:DRT",
}
@Article{Borwein:2008:EBF,
author = "David Borwein and Jonathan M. Borwein and O-Yeat
Chan",
title = "The evaluation of {Bessel} functions via exp-arc
integrals",
journal = j-J-MATH-ANAL-APPL,
volume = "341",
number = "1",
pages = "478--500",
month = may,
year = "2008",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/j.jmaa.2007.10.003",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "33C10 (33F05 65D20)",
MRnumber = "2394100",
MRreviewer = "Richard B. Paris",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2008JMAA..341..478B;
http://docserver.carma.newcastle.edu.au/1231/;
http://www.sciencedirect.com/science/article/pii/S0022247X07012346",
abstract = "A standard method for computing values of Bessel
functions has been to use the well-known ascending
series for small argument, and to use an asymptotic
series for large argument; with the choice of the
series changing at some appropriate argument magnitude,
depending on the number of digits required. In a recent
paper, D. Borwein, J. Borwein, and R. Crandall [D.
Borwein, J. M. Borwein, R. Crandall, Effective Laguerre
asymptotics, preprint at
http://locutus.cs.dal.ca:8088/archive/00000334/]
derived a series for an ``exp-arc'' integral which gave
rise to an absolutely convergent series for the J and I
Bessel functions with integral order. Such series can
be rapidly evaluated via recursion and elementary
operations, and provide a viable alternative to the
conventional ascending-asymptotic switching. In the
present work, we extend the method to deal with Bessel
functions of general (non-integral) order, as well as
to deal with the Y and K Bessel functions.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
keywords = "Bessel function; Exponential-hyperbolic expansions;
Uniform series expansion",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2008:ECE,
author = "J. M. Borwein and I. J. Zucker and J. Boersma",
title = "The evaluation of character {Euler} double sums",
journal = j-RAMANUJAN-J,
volume = "15",
number = "3",
pages = "377--405",
year = "2008",
CODEN = "RAJOF9",
DOI = "https://doi.org/10.1007/s11139-007-9083-z",
ISSN = "1382-4090 (print), 1572-9303 (electronic)",
ISSN-L = "1382-4090",
MRclass = "11M41 (11M06)",
MRnumber = "2390277",
MRreviewer = "Stamatis Koumandos",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/255/;
http://link.springer.com/article/10.1007/s11139-007-9083-z",
abstract = "Euler considered sums of the form [GRAPHICS] Here
natural generalizations of these sums namely [complex
equation] are investigated, where chi(p) and chi(q) are
characters, and s and t are positive integers. The
cases when p and q are either 1, 2a, 2b or -4 are
examined in detail, and closed-form expressions are
found for t = 1 and general s in terms of the Riemann
zeta function and the Catalan zeta function-the
Dirichlet series L(-4)(s) = 1(-s) - 3(-s) + 5(-s) -
7(-s) + center dot center dot center dot. Some results
for arbitrary p and q are obtained as well.",
acknowledgement = ack-nhfb,
fjournal = "The {Ramanujan} Journal",
journal-URL = "http://link.springer.com/journal/11139",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CoLab Preprint 260.",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2008:ECE",
}
@Article{Borwein:2008:ELA,
author = "David Borwein and Jonathan M. Borwein and Richard E.
Crandall",
title = "Effective {Laguerre} asymptotics",
journal = j-SIAM-J-NUMER-ANAL,
volume = "46",
number = "6",
pages = "3285--3312",
year = "2008",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/07068031X",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "33C65 (30E20 34E05)",
MRnumber = "2448665",
MRreviewer = "Yu-Qiu Zhao",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/334/",
abstract = "It is known that the generalized Laguerre polynomials
can enjoy subexponential growth for large primary
index. In particular, for certain fixed parameter pairs
(a, z) one has the large-n asymptotic behavior
L-n((-a)) (-z) similar to C(a, z)(n)(-a)/2-1/ (4)e(2)
root nz. We introduce a computationally motivated
contour integral that allows efficient numerical
Laguerre evaluations yet also leads to the complete
asymptotic series over the full parameter domain of
subexponential behavior. We present a fast algorithm
for symbolic generation of the rather formidable
expansion coefficients. Along the way we address the
difficult problem of establishing effective (i. e.,
rigorous and explicit) error bounds on the general
expansion. A primary tool for these developments is an
``exp-arc'' method giving a natural bridge between
converging series and effective asymptotics.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2008:ELA",
}
@Article{Borwein:2008:HIW,
author = "Jonathan M. Borwein",
title = "{Hilbert}'s Inequality and {Witten}'s Zeta-Function",
journal = j-AMER-MATH-MONTHLY,
volume = "115",
number = "2",
pages = "125--137",
month = feb,
year = "2008",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jan 30 12:00:30 MST 2012",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/i27642413;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib",
URL = "http://www.jstor.org/stable/27642418",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2008:IEM,
author = "Jonathan Borwein",
title = "Implications of experimental mathematics for the
philosophy of mathematics",
crossref = "Gold:2008:POD",
chapter = "2",
publisher = pub-LONGMAN,
address = pub-LONGMAN:adr,
pages = "33--61",
year = "2008",
MRclass = "00A30 (03A05)",
MRnumber = "2452073",
bibdate = "Sat Aug 13 16:37:59 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "MAA Spectrum",
URL = "http://docserver.carma.newcastle.edu.au/280/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxpages = "33--59",
}
@Book{Borwein:2008:ME,
author = "Jonathan Borwein and David Bailey",
title = "Mathematics by Experiment",
publisher = pub-A-K-PETERS,
address = pub-A-K-PETERS:adr,
edition = "Second",
pages = "xii + 377",
year = "2008",
DOI = "https://doi.org/10.1201/b10704",
ISBN = "1-56881-442-9, 1-4398-6536-1 (PDF e-book)",
ISBN-13 = "978-1-56881-442-1, 978-1-4398-6536-1 (PDF e-book)",
LCCN = "QA76.95 .B67 2008",
MRclass = "00A35 (37-04)",
MRnumber = "2473161",
MRreviewer = "Michael Otte",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Plausible reasoning in the 21st Century.",
URL = "http://docserver.carma.newcastle.edu.au/272/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
tableofcontents = "Front matter / i \\
1. What is experimental mathematics? / 1 \\
2. Experimental mathematics in action / 47 \\
3. Pi and its friends / 103 \\
4. Normality of numbers / 143 \\
5. The power of constructive proofs / 175 \\
6. Numerical techniques / 215 \\
7. Recent experiences / 243 \\
Bibliography / 349",
}
@Article{Borwein:2008:PRB,
author = "Jonathan M. Borwein and Bruno Salvy",
title = "A Proof of a Recurrence for {Bessel} Moments",
journal = j-EXP-MATH,
volume = "17",
number = "2",
pages = "223--230",
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2008.10129032",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "68W30 (33C10 33E30 33F10)",
MRnumber = "2433887",
MRreviewer = "Carsten Schneider",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib;
http://www.tandfonline.com/toc/uexm20/17/2",
URL = "http://docserver.carma.newcastle.edu.au/346/;
http://projecteuclid.org/euclid.em/1227118973",
abstract = "We provide a proof of a conjecture in [Bailey et al.
07a] on the existence and form of linear recurrences
for moments of powers of the Bessel function K-0.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Salvy, Bruno/0000-0002-4313-0679 Borwein,
Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2008:PRB",
}
@InProceedings{Borwein:2008:VPG,
author = "J. M. Borwein",
editor = "????",
booktitle = "Mathematics and Culture, La matematica: Problemi e
teoremi",
title = "La vita di pi greco. ({Italian}) [{The} life of
{Greek} pi]",
publisher = "Guilio Einaudi Editori",
address = "Turino, Italy",
pages = "??--??",
year = "2008",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
URL = "http://www.carma.newcastle.edu.au/~jb616/pi-2010.pdf",
acknowledgement = ack-nhfb,
language = "Italian",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CoLab Preprint 265",
}
@InCollection{Borwein:2008:WEM,
author = "J. M. Borwein and D. H. Bailey",
editor = "Giovanni Treccani",
booktitle = "Enciclopedia della Scienza e della Tecnica",
title = "What is Experimental Mathematics",
publisher = "????",
address = "Roma, Italia",
pages = "??--??",
year = "2008",
bibdate = "Sat Aug 13 16:32:55 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Reprint of \cite[Chapter 1]{Borwein:2004:MEP}.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxnote = "Check: is Treccani the editor or publisher?? I cannot
find this book in library catalogs or large
booksellers.",
}
@Article{Eberhard:2008:SOC,
author = "A. C. Eberhard and J. M. Borwein",
title = "Second Order Cones for Maximal Monotone Operators via
Representative Functions",
journal = j-SET-VALUED-ANAL,
volume = "16",
number = "2--3",
pages = "157--184",
year = "2008",
CODEN = "SVANEG",
DOI = "https://doi.org/10.1007/s11228-008-0075-y",
ISSN = "0927-6947 (print), 1572-932X (electronic)",
ISSN-L = "0927-6947",
MRclass = "49J53 (46N10 47H04 47H05 47N10)",
MRnumber = "2399200",
MRreviewer = "Nicolas Hadjisavvas",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/348/;
http://link.springer.com/article/10.1007/s11228-008-0075-y",
abstract = "It is shown that various first and second order
derivatives of the Fitzpatrick and Penot representative
functions for a maximal monotone operator T, in a
reflexive Banach space, can be used to represent
differential information associated with the tangent
and normal cones to the Graph T. In particular we
obtain formula for the proto-derivative, as well as its
polar, the normal cone to the graph of T. First order
derivatives are shown to be useful in recognising
points of single-valuedness of T. We show that a strong
form of proto-differentiability to the graph of T, is
often associated with single-valuedness of T.",
acknowledgement = ack-nhfb,
fjournal = "Set-Valued Analysis. An International Journal Devoted
to the Theory of Multifunctions and its Applications",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Eberhard, Andrew/0000-0003-2977-3456 Borwein,
Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Eberhard,
Andrew/B-5576-2013",
unique-id = "Eberhard:2008:SOC",
}
@Article{Bailey:2009:EMCa,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Experimental mathematics and computational
statistics",
journal = "Wiley Interdisciplinary Reviews: Computational
Statistics",
volume = "1",
number = "1",
pages = "12--24",
year = "2009",
DOI = "https://doi.org/10.1002/wics.1",
ISSN = "1939-0068 (print), 1939-5108 (electronic)",
ISSN-L = "1939-0068",
bibdate = "Thu Aug 11 11:01:49 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1227/",
abstract = "The field of statistics has long been noted for
techniques to detect patterns and regularities in
numerical data. In this article, we explore connections
between statistics and the emerging field of
experimental mathematics. These include both
applications of experimental mathematics in statistics
as well as statistical methods applied to computational
mathematics.",
acknowledgement = ack-nhfb,
keywords = "experimental mathematics, numerical integration,
numerical analysis, computational statistics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Bailey:2009:EMCb,
author = "D. H. Bailey and J. M. Borwein",
booktitle = "Online Encyclopedia of Computational Statistics. {A}
{Wiley} Interdisciplinary Review",
title = "Experimental Mathematics and Computational
Statistics",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "??--??",
month = jul,
year = "2009",
DOI = "",
LCCN = "",
bibdate = "Fri Aug 12 09:29:41 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://ca.wiley.com/WileyCDA/Section/id-390445.html;
http://docserver.carma.newcastle.edu.au/1227/;
http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470973889.html",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Probably identical to \cite{Bailey:2009:EMCa}. Appears
to be first edition, but not available at publisher
site.",
xxISBN = "0-470-97388-9 (second edition)",
xxisbn-13 = "978-0-470-97388-2 (second edition)",
}
@Article{Bailey:2009:HPH,
author = "David Bailey and Jonathan Borwein",
title = "Highly parallel, high precision integration",
journal = "International Journal of Computational Science and
Engineering",
volume = "4",
number = "??",
pages = "??--??",
month = "????",
year = "2009",
ISSN = "1742-7185 (print), 1742-7193 (electronic)",
ISSN-L = "1742-7185",
bibdate = "Fri Aug 12 09:16:29 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/294/",
acknowledgement = ack-nhfb,
journal-URL = "http://www.inderscience.com/jhome.php?jcode=ijcse",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "I cannot find this article at the publisher site,
which lacks metadata by volume, and fails to find
author or title values.",
}
@Article{Bailey:2009:PAD,
author = "David H. Bailey and Jonathan M. Borwein",
title = "{PSLQ}: an Algorithm to Discover to Integer
Relations",
journal = "Computeralgebra Rundbrief",
volume = "45",
number = "??",
pages = "8--11",
month = oct,
year = "2009",
ISSN = "0933-5994",
ISSN-L = "0933-5994",
bibdate = "Sat Aug 13 16:11:51 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.fachgruppe-computeralgebra.de/cms/tiki-index.php?page=Rundbrief",
acknowledgement = ack-nhfb,
journal-URL = "http://www.fachgruppe-computeralgebra.de/rundbrief/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2009:RQR,
author = "D. H. Bailey and J. M. Borwein and R. E. Crandall",
title = "Resolution of the {Quinn--Rand--Strogatz} Constant of
Nonlinear Physics",
journal = j-EXP-MATH,
volume = "18",
number = "1",
pages = "107--116",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2009.10128885",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11Y60 (11M35 11Z05)",
MRnumber = "2548991",
MRreviewer = "Herman J. J. te Riele",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib;
http://www.tandfonline.com/toc/uexm20/18/1",
URL = "http://docserver.carma.newcastle.edu.au/345/;
http://projecteuclid.org/euclid.em/1243430534",
abstract = "Herein we develop connections between zeta functions
and some recent ``mysterious'' constants of nonlinear
physics. In an important analysis of coupled Winfree
oscillators, Quinn, Rand, and Strogatz [Quinn et al.
07] developed a certain N-oscillator scenario whose
bifurcation phase offset small phi is implicitly
defined, with a conjectured asymptotic behavior sin phi
similar to 1 - c(1)/N, with experimental estimate c(1)
= 0.605443657.... We are able to derive the exact
theoretical value of this ``QRS constant'' c(1) as a
real zero of a particular Hurwitz zeta function. This
discovery enables, for example, the rapid resolution of
cl to extreme precision. Results and conjectures are
provided in regard to higher-order terms of the sin phi
asymptotic, and to yet more physics constants emerging
from the original QRS work.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Bailey:2009:RQR",
}
@TechReport{Bailey:2009:SMPa,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Solution to {{\booktitle{Monthly}}} Problem \#11418",
type = "Report",
institution = "Lawrence Berkeley National Laboratory and Faculty of
Computer Science, Dalhousie University and School of
Mathematical and Physical Sciences, University of
Newcastle",
address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5,
Canada and Callaghan, NSW 2308, Australia",
day = "6",
month = jul,
year = "2009",
bibdate = "Fri Sep 30 08:40:15 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/amm-11418.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "The report evaluates the integral $ J =
\int_\infty^\infty \frac {t^2 \sech^2(t)}{a - \tanh
(t)} \, d t $ for complex $ |a| > 1 $.",
}
@TechReport{Bailey:2009:SMPb,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Solutions to {{\booktitle{Monthly}}} Problems 11456
and 11457",
type = "Report",
institution = "Lawrence Berkeley National Laboratory and Faculty of
Computer Science, Dalhousie University",
address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5,
Canada",
pages = "2",
day = "10",
month = oct,
year = "2009",
bibdate = "Fri Sep 30 08:34:31 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/amm-11456.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Borwein:2009:CCI,
author = "Jonathan M. Borwein and Keith J. Devlin",
title = "The computer as crucible: an introduction to
experimental mathematics",
publisher = pub-A-K-PETERS,
address = pub-A-K-PETERS:adr,
pages = "xi + 158",
year = "2009",
ISBN = "1-56881-343-0",
ISBN-13 = "978-1-56881-343-1",
LCCN = "QA8.7 .B67 2009",
MRclass = "00A35 (11-04 11Y16 11Y60)",
MRnumber = "2464847",
MRreviewer = "Samuel S. Wagstaff, Jr.",
bibdate = "Tue Nov 10 17:48:24 MST 2009",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://docserver.carma.newcastle.edu.au/1730/;
http://www.loc.gov/catdir/toc/fy0904/2008022180.html",
acknowledgement = ack-nhfb,
libnote = "Not in my library.",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "Experimental mathematics",
tableofcontents = "What is experimental mathematics? \\
What is the quadrillionth decimal place of $pi$? \\
What is that number? \\
The most important function in mathematics \\
Evaluate the following integral \\
Serendipity \\
Calculating [pi] \\
The computer knows more math than you do \\
Take it to the limit \\
Danger! Always exercise caution when using the computer
\\
Stuff we left out (until now)",
}
@InProceedings{Borwein:2009:DAD,
author = "J. M. Borwein",
title = "Digitally-assisted discovery and proof",
crossref = "Lin:2009:PPM",
pages = "I.3--I.11",
year = "2009",
bibdate = "Sat Aug 13 16:21:36 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Plenary address.",
URL = "http://docserver.carma.newcastle.edu.au/390/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2009:DCF,
author = "Jonathan Borwein and Jon Vanderwerff",
title = "Differentiability of conjugate functions and perturbed
minimization principles",
journal = j-J-CONVEX-ANAL,
volume = "16",
number = "3--4",
pages = "707--711",
year = "2009",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "49K40 (46G05 46N10 49J50 52A41 58E30 90C46)",
MRnumber = "2583890",
MRreviewer = "Philip D. Loewen",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/383/;
http://www.heldermann.de/JCA/JCA16/JCA163/jca16042.htm",
abstract = "We survey the tight connection between
differentiability of conjugate functions and perturbed
optimization principles",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2009:DCF",
xxpages = "699--706",
}
@Article{Borwein:2009:EBS,
author = "Jonathan M. Borwein and Neil J. Calkin and Dante
Manna",
title = "{Euler--Boole} summation revisited",
journal = j-AMER-MATH-MONTHLY,
volume = "116",
number = "5",
pages = "387--412",
year = "2009",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/193009709X470290",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11B68 (11B73 26A06)",
MRnumber = "2510837",
MRreviewer = "Samuel S. Wagstaff, Jr.",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2009:MME,
author = "Jonathan M. Borwein",
title = "Maths Matters: Exploratory experimentation:
digitally-assisted discovery and proof",
journal = j-AUSTRALIAN-MATH-SOC-GAZ,
volume = "36",
number = "3",
pages = "166--175",
month = jul,
year = "2009",
ISSN = "0311-0729 (print), 1326-2297 (electronic)",
ISSN-L = "0311-0729",
MRclass = "00A35 68W30 97U50 00A30",
MRnumber = "2543725",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
ZMnumber = "1175.00028",
acknowledgement = ack-nhfb,
fjournal = "The Australian Mathematical Society. Gazette",
journal-URL = "http://www.austms.org.au/gazette",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark-1 = "This material is largely excerpted from a longer paper
written for ICMI Study 19 `On Proof and Proving in
Mathematics Education', and a plenary talk given in May
2009 at the corresponding Workshop at National Taiwan
Normal University. [NHFB remarks: It appears that the
longer paper did not appear in ICMI [International
Commission on Mathematical Instruction] Study 19, which
is published in \booktitle{ZDM Mathematics Education}
{\bf 40}(2) May 2008,
\url{http://link.springer.com/journal/11858/40/2/page/1},
and in the Chinese\slash English proceedings with ISBN
986-01-8210-8.]",
remark-2 = "From page 166: ``The computer offers to provide
scaffolding both to enhance mathematical reasoning and
to restrain mathematical error.''",
remark-3 = "From page 174: ``We live in an information-rich,
judgement-poor world and the explosion of information
and tools is not going to diminish.''",
}
@InCollection{Borwein:2009:NCM,
author = "Jonathan Borwein and Rafal Goebel",
booktitle = "Optimization",
title = "On the nondifferentiability of cone-monotone functions
in {Banach} spaces",
volume = "32",
publisher = pub-SV,
address = pub-SV:adr,
pages = "3--14",
year = "2009",
DOI = "https://doi.org/10.1007/978-0-387-98096-6_1",
MRclass = "49J50 (47G10 47N10)",
MRnumber = "2599222",
MRreviewer = "John R. Giles",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Springer Optim. Appl.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 02:179.",
}
@Article{Borwein:2009:PCM,
author = "Jonathan M. Borwein",
title = "{{\booktitle{The Princeton companion to mathematics}}.
Timothy Gowers, with June Barrow Green and Imre Leader.
Princeton University Press, Princeton, NJ, 2008.
\$99.00. xxii + 1034 pp., hardcover. ISBN 978-0-691-1
1880-2. [book review of \refcno 2467561]}",
journal = j-SIAM-REVIEW,
volume = "51",
number = "4",
pages = "790--794",
month = dec,
year = "2009",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/SIREAD000051000004000785000001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "00A17",
MRnumber = "2573944",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://docserver.carma.newcastle.edu.au/1228/;
http://www.jstor.org/stable/25662346",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2009:SCC,
author = "Jonathan M. Borwein and Warren B. Moors",
title = "Stability of closedness of convex cones under linear
mappings",
journal = j-J-CONVEX-ANAL,
volume = "16",
number = "3--4",
pages = "699--705",
year = "2009",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "47N10 (90C25 90C31)",
MRnumber = "2583889",
MRreviewer = "John R. Giles",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1229/;
http://www.heldermann.de/JCA/JCA16/JCA163/jca16041.htm",
abstract = "In this paper we reconsider the question of when the
continuous linear image of a closed convex cone is
closed in Euclidean space. In particular, we show that
although it is not true that the closedness of the
image is preserved under small perturbations of the
linear mappings it is ``almost'' true that the
closedness of the image is preserved under small
perturbations, in the sense that, for ``almost all''
linear mappings from R(n) into R(m) if the image of the
cone is closed then there is a small neighbourhood
around it whose members also preserve the closedness of
the cone.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2009:SCC",
xxpages = "707--713",
}
@Article{Borwein:2009:SFC,
author = "Jonathan M. Borwein and Chris H. Hamilton",
title = "Symbolic {Fenchel} conjugation",
journal = j-MATH-PROG,
volume = "116",
number = "1--2",
pages = "17--35",
year = "2009",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/s10107-007-0134-4",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "90-04 (44A15 49J52 65K10 90C25 90C46)",
MRnumber = "2421271",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special issue in honor of Alfred Auslender.",
URL = "http://docserver.carma.newcastle.edu.au/1479/",
abstract = "Of key importance in convex analysis and optimization
is the notion of duality, and in particular that of
Fenchel duality. This work explores improvements to
existing algorithms for the symbolic calculation of
subdifferentials and Fenchel conjugates of convex
functions defined on the real line. More importantly,
these algorithms are extended to enable the symbolic
calculation of Fenchel conjugates on a class of
real-valued functions defined on the real line. More
importantly, these algorithms are extended to enable
the symbolic calculation of Fenchel conjugates on a
class of real-valued functions defined on R(n). These
algorithms are realized in the form of the Maple
package SCAT.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
fjournal = "Mathematical Programming. A Publication of the
Mathematical Programming Society",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2009:SFC",
}
@Article{Borwein:2009:UBC,
author = "Jonathan M. Borwein and O-Yeat Chan",
title = "Uniform bounds for the complementary incomplete gamma
function",
journal = j-MATH-INEQUAL-APPL,
volume = "12",
number = "1",
pages = "115--121",
year = "2009",
DOI = "https://doi.org/10.7153/mia-12-10",
ISSN = "1331-4343 (print), 1848-9966 (electronic)",
ISSN-L = "1331-4343",
MRclass = "33B20",
MRnumber = "2489355",
MRreviewer = "Necdet Batir",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/335/",
abstract = "We prove upper and lower bounds for the complementary
incomplete gamma function Gamma(a, z) with complex
parameters a and z. Our bounds are refined within the
circular hyperboloid of one sheet \{(a, z) : vertical
bar z vertical bar > c vertical bar a - 1 vertical
bar\} with a real and z complex. Our results show that
within the hyperboloid, vertical bar Gamma(a,
z)vertical bar is of order vertical bar Z vertical
bar(a-1)e(-Re(z)), and extends an upper estimate of
Natalini and Palumbo to complex values of z.",
acknowledgement = ack-nhfb,
ajournal = "Math. Inequal. Appl.",
fjournal = "Mathematical Inequalities \& Applications",
journal-URL = "http://mia.ele-math.com/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2009:UBC",
}
@Article{Borwein:2009:UCF,
author = "J. Borwein and A. J. Guirao and P. H{\'a}jek and J.
Vanderwerff",
title = "Uniformly convex functions on {Banach} spaces",
journal = j-PROC-AM-MATH-SOC,
volume = "137",
number = "3",
pages = "1081--1091",
year = "2009",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/S0002-9939-08-09630-5",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "46B20 (46G05 46N10 49J50 52A41 90C48)",
MRnumber = "2457450",
MRreviewer = "Doug Ward",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/340/",
abstract = "Given a Banach space $ (X, || \cdot ||) $, we study
the connection between uniformly convex functions $ f
\colon X \to R $ bounded above by $ || \cdot ||^p $ and
the existence of norms on $X$ with moduli of convexity
of power type. In particular, we show that there exists
a uniformly convex function $ f \colon X \to R$ bounded
above $ || \cdot ||^2$ if and only if $X$ admits an
equivalent norm with modulus of convexity of power type
2",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Hajek,
Petr/D-5429-2014",
unique-id = "Borwein:2009:UCF",
}
@Article{Jackson:2009:JER,
author = "Allyn Jackson",
title = "{John Ewing} retires from the {AMS}",
journal = j-NAMS,
volume = "56",
number = "1",
pages = "48--51",
month = jan,
year = "2009",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibdate = "Tue Aug 16 09:18:13 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "With contributions by Jonathan Borwein and Jane
Kister.",
URL = "",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Bacak:2010:DCF,
author = "M. Bac{\'a}k and J. Borwein and B. Sims",
title = "Differentiability of convex functions in {CAT(0)}
spaces.",
month = aug,
year = "2010",
bibdate = "Tue Aug 16 10:01:41 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bacak:2010:ICL,
author = "Miroslav Ba{\v{c}}{\'a}k and Jonathan M. Borwein and
Andrew Eberhard and Boris S. Mordukhovich",
title = "Infimal convolutions and {Lipschitzian} properties of
subdifferentials for prox-regular functions in
{Hilbert} spaces",
journal = j-J-CONVEX-ANAL,
volume = "17",
number = "3--4",
pages = "737--763",
year = "2010",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "49J52 (46G05)",
MRnumber = "2731276",
MRreviewer = "Shawn Xianfu Wang",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special volume in honour of Hedi Attouch.",
URL = "http://docserver.carma.newcastle.edu.au/1224/;
http://www.heldermann.de/JCA/JCA17/JCA173/jca17049.htm",
abstract = "In this paper we study infimal convolutions of
extended-real-valued functions in Hilbert spaces paying
a special attention to the rather broad and remarkable
class of prox-regular functions. Such functions have
been well recognized as highly important in many
aspects of variational analysis and its applications in
both finite-dimensional and infinite-dimensional
settings. Based on advanced variational techniques, we
discover some new subdifferential properties of infimal
convolutions and apply them to the study of
Lipschitzian behavior of subdifferentials for
prox-regular functions in Hilbert spaces. It is shown,
in particular, that the fulfillment of a natural
Lipschitz-like property for (set-valued)
subdifferentials of prox-regular functions forces such
functions, under weak assumptions, actually to be
locally smooth with single-valued subdifferentials
reduced to Lipschitz continuous gradient mappings.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Eberhard, Andrew/0000-0003-2977-3456 Borwein,
Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Eberhard, Andrew/B-5576-2013",
unique-id = "Bacak:2010:ICL",
}
@Article{Bailey:2010:ATB,
author = "D. H. Bailey and J. M. Borwein and R. E. Crandall",
title = "Advances in the theory of box integrals",
journal = j-MATH-COMPUT,
volume = "79",
number = "271",
pages = "1839--1866",
month = jul,
year = "2010",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-10-02338-0",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y60 (65D30)",
MRnumber = "2630017",
MRreviewer = "Michael J. Evans",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/389/;
http://www.jstor.org/stable/20779125",
abstract = "Box integrals--expectations $ \langle \vert \vec r
\vert^s \rangle $ or $ \langle \vert \vec r - \vec q
\vert^s \rangle $ over the unit $ n$-cube--have over
three decades been occasionally given closed forms for
isolated $ n, s$. By employing experimental mathematics
together with a new, global analytic strategy, we prove
that for each of $ n = 1, 2, 3, 4$ dimensions the box
integrals are for any integer $ s$ hypergeometrically
closed (hyperclosed'') in an explicit sense we clarify
herein. For $ n = 5$ dimensions, such a complete
hyperclosure proof is blocked by a single, unresolved
integral we call $ {\mathcal K}_5$; although we do
prove that all but a finite set of ($ n = 5$) cases
enjoy hyperclosure. We supply a compendium of exemplary
closed forms that arise naturally from the theory.",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "D-drive preprint 389 (March 2009).",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Bailey:2010:ATB",
}
@InCollection{Bailey:2010:ECO,
author = "David H. Bailey and Jonathan M. Borwein",
booktitle = "Gems in experimental mathematics",
title = "Experimental computation with oscillatory integrals",
volume = "517",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "25--40",
year = "2010",
DOI = "https://doi.org/10.1090/conm/517/10131",
MRclass = "11Y35 (42B20)",
MRnumber = "2731059",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Contemp. Math.",
URL = "http://docserver.carma.newcastle.edu.au/391/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2010:EMMa,
author = "David H. Bailey and Jonathan M. Borwein and David J.
Broadhurst and Wadim Zudilin",
title = "Experimental Mathematics and Mathematical Physics",
journal = "ArXiv e-prints",
month = may,
year = "2010",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1005.0414B;
http://docserver.carma.newcastle.edu.au/1215/",
abstract = "One of the most effective techniques of experimental
mathematics is to compute mathematical entities such as
integrals, series or limits to high precision, then
attempt to recognize the resulting numerical values.
Recently these techniques have been applied with great
success to problems in mathematical physics. Notable
among these applications are the identification of some
key multi-dimensional integrals that arise in Ising
theory, quantum field theory and in magnetic spin
theory.",
acknowledgement = ack-nhfb,
eprint = "1005.0414",
keywords = "Mathematical Physics, High Energy Physics -
Phenomenology, Mathematics - Classical Analysis and
ODEs, Mathematics - Number Theory",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math-ph",
}
@InCollection{Bailey:2010:EMMb,
author = "David H. Bailey and Jonathan M. Borwein and David
Broadhurst and Wadim Zudilin",
booktitle = "Gems in experimental mathematics",
title = "Experimental mathematics and mathematical physics",
volume = "517",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "41--58",
year = "2010",
DOI = "https://doi.org/10.1090/conm/517/10132",
MRclass = "33F05 (11Y60 33F10 65D30)",
MRnumber = "2731060",
MRreviewer = "Zhonghua Li",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Contemp. Math.",
URL = "http://docserver.carma.newcastle.edu.au/1215/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Bailey:2010:SMP,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Solution to {{\booktitle{Monthly}}} Problem 11515",
type = "Report",
institution = "Lawrence Berkeley National Laboratory and School of
Mathematical and Physical Sciences, University of
Newcastle",
address = "Berkeley, CA 94720, USA and Callaghan, NSW 2308,
Australia",
pages = "2",
day = "15",
month = jun,
year = "2010",
bibdate = "Fri Sep 30 08:23:00 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/amm-11515.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "The problem of evaluating $ S(t) = \sum_{n = 1}^\infty
4^n \sin^4 (t / 2^n) $ is shown to be equal to the
simple closed form $ T(t) = t^2 - \sin^2 (t) $.",
}
@Book{Borwein:2010:CFC,
author = "Jonathan M. Borwein and Jon D. Vanderwerff",
title = "Convex functions: constructions, characterizations and
counterexamples",
volume = "109",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "x + 521",
year = "2010",
DOI = "https://doi.org/10.1017/CBO9781139087322",
ISBN = "0-521-85005-3",
ISBN-13 = "978-0-521-85005-6",
MRclass = "49-02 (46B20 46N10 49J53 52A41 90C25)",
MRnumber = "2596822",
MRreviewer = "Heinz H. Bauschke",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Encyclopedia of Mathematics and its Applications",
URL = "http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139087322",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
tableofcontents = "Frontmatter / i--vi \\
Contents / vii--viii \\
Preface / ix--x \\
1: Why convex? / 1--17 \\
2: Convex functions on Euclidean spaces / 18--93 \\
3: Finer structure of Euclidean spaces / 94--125 \\
4: Convex functions on Banach spaces / 126--208 \\
5: Duality between smoothness and strict convexity /
209--275 \\
6: Further analytic topics / 276--337 \\
7: Barriers and Legendre functions / 338--376 \\
8: Convex functions and classifications of Banach
spaces / 377--402 \\
9: Monotone operators and the Fitzpatrick function /
403--459 \\
10: Further remarks and notes / 460--482 \\
List of symbols / 483--484 \\
References / 485--507",
}
@Article{Borwein:2010:DTM,
author = "Jonathan M. Borwein and O-Yeat Chan",
title = "Duality in tails of multiple-zeta values",
journal = j-INT-J-NUMBER-THEORY,
volume = "6",
number = "3",
pages = "501--514",
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003058",
ISSN = "1793-0421 (print), 1933-8368 (electronic)",
MRclass = "11M32 (33C20 33F05)",
MRnumber = "2652893",
MRreviewer = "Zhonghua Li",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1218/",
abstract = "Duality relations are deduced for tails of
multiple-zeta values using elementary methods. These
formulas extend the classical duality formulas for
multiple-zeta values.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Number Theory",
journal-URL = "http://www.worldscientific.com/worldscinet/ijnt",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Borwein:2010:DTM",
}
@Book{Borwein:2010:ECM,
author = "Jonathan Borwein and Peter B. Borwein",
title = "Experimental and computational mathematics: selected
writings",
publisher = "Perfectly Scientific Press",
address = "Portland, OR, USA",
pages = "viii + 297",
year = "2010",
ISBN = "1-935638-05-X",
ISBN-13 = "978-1-935638-05-6",
MRclass = "11-06 (11-04 33-06)",
MRnumber = "2841256",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2010:ENE,
author = "Jonathan M. Borwein and Scott Sciffer",
booktitle = "Nonlinear analysis and optimization {II}.
{Optimization}",
title = "An explicit non-expansive function whose
subdifferential is the entire dual ball",
volume = "514",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "99--103",
year = "2010",
DOI = "https://doi.org/10.1090/conm/514/10101",
MRclass = "49J52",
MRnumber = "2668255",
MRreviewer = "Shawn Xianfu Wang",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Contemp. Math.",
URL = "http://docserver.carma.newcastle.edu.au/385/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2010:FCV,
author = "Jonathan M. Borwein",
booktitle = "Variational analysis and generalized differentiation
in optimization and control",
title = "Future challenges for variational analysis",
volume = "47",
publisher = pub-SV,
address = pub-SV:adr,
pages = "95--107",
year = "2010",
DOI = "https://doi.org/10.1007/978-1-4419-0437-9_4",
MRclass = "49J53",
MRnumber = "2766756",
MRreviewer = "B. Mordukhovich",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Springer Optim. Appl.",
URL = "http://docserver.carma.newcastle.edu.au/396/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2010:FLF,
author = "Jonathan M. Borwein and Jon Vanderwerff",
title = "{Fr{\'e}chet--Legendre} functions and reflexive
{Banach} spaces",
journal = j-J-CONVEX-ANAL,
volume = "17",
number = "3--4",
pages = "915--924",
year = "2010",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "52A41 (46G05 46N10 49J53 90C25)",
MRnumber = "2731284",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special volume in honour of Hedi Attouch.",
URL = "http://www.heldermann.de/JCA/JCA17/JCA173/jca17057.htm",
abstract = "A 2001 article by Bauschke, Borwein and Combettes [2]
showed how to extend naturally the classical
definitions of essential smoothness and essential
strict convexity from functions on R(n) in a compatible
fashion to any Banach space. They were able, among
other things, to show that substantial duality results
hold for Legendre functions in reflexive spaces. That
article focused on essential smoothness in the Gateaux
sense. Our goal herein is to show that similar results
hold for Frechet smoothness and to study related
properties of such functions on reflexive Banach
spaces.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Borwein:2010:FLF",
}
@Article{Borwein:2010:FYM,
author = "Jonathan M. Borwein",
title = "Fifty years of maximal monotonicity",
journal = j-OPTIM-LETT,
volume = "4",
number = "4",
pages = "473--490",
year = "2010",
DOI = "https://doi.org/10.1007/s11590-010-0178-x",
ISSN = "1862-4472 (print), 1862-4480 (electronic)",
ISSN-L = "1862-4472",
MRclass = "47H05 (47H09 49-02 49J53 90C25 90C33)",
MRnumber = "2719898",
MRreviewer = "Simeon Reich",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1221/",
abstract = "Maximal monotone operator theory is about to turn (or
just has turned) 50. I intend to briefly survey the
history of the subject. I shall try to explain why
maximal monotone operators are both interesting and
important-culminating with a description of the
remarkable progress made during the past decade.",
acknowledgement = ack-nhfb,
ajournal = "Optim. Lett.",
fjournal = "Optimization Letters",
journal-URL = "http://link.springer.com/journal/11590",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Borwein:2010:FYM",
}
@Article{Borwein:2010:HDB,
author = "Jonathan M. Borwein and O-Yeat Chan and R. E.
Crandall",
title = "Higher-Dimensional Box Integrals",
journal = j-EXP-MATH,
volume = "19",
number = "4",
pages = "431--446",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2010.10390634",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "33B30",
MRnumber = "2778656",
MRreviewer = "Cristinel Mortici",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib;
http://www.tandfonline.com/toc/uexm20/19/4",
URL = "http://docserver.carma.newcastle.edu.au/1223/;
http://projecteuclid.org/euclid.em/1317758103",
abstract = "Herein, with the aid of substantial symbolic
computation, we solve previously open problems in the
theory of n-dimensional box integrals B(n)(s) :=
, (r) over
bar is an element of [0, 1](n). In particular, we
resolve an elusive integral called kappa(5) that
previously acted as a ``blockade'' against closed-form
evaluation in n = 5 dimensions. In consequence, we now
know that B(n) (integer) can be given a closed form for
n = 1, 2, 3, 4, 5. We also find the general residue at
the pole at s = n, this leading to new relations and
definite integrals; for example, we are able to give
the first nontrivial closed forms for six-dimensional
box integrals and to show hyperclosure of B(6)(even).
The Clausen function and its generalizations play a
central role in these higher-dimensional evaluations.
Our results provide stringent test scenarios for
symbolic-algebra simplification methods.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Borwein:2010:HDB",
}
@InProceedings{Borwein:2010:MEPa,
author = "J. M. Borwein",
booktitle = "ICME10 Proceedings, July 2010",
title = "Mathematics by Experiment: Plausible Reasoning in the
21st Century",
publisher = "????",
address = "????",
pages = "??--??",
year = "2010",
bibdate = "Sat Aug 13 16:42:06 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/272/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CoLab Preprint 272.",
}
@Article{Borwein:2010:NSF,
author = "David Borwein and Jonathan M. Borwein and Isaac E.
Leonard",
title = "{$ L_p $} norms and the sinc function",
journal = j-AMER-MATH-MONTHLY,
volume = "117",
number = "6",
pages = "528--539",
year = "2010",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/000298910X492817",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "26A09",
MRnumber = "2662705",
MRreviewer = "Timo A. J. Tossavainen",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "It's everywhere! It's everywhere! .... In this note we
give elementary proofs of some of the striking
asymptotic properties of the p-norm of the ubiquitous
sinc function. Based on experimental evidence we
conjecture some enticing further properties of the
p-norm as a function of p. See, for example,
http://www.carma.newcastle.edu.au/(similar
to)jb616/oscillatory.pdf.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Borwein:2010:PNS",
}
@InCollection{Borwein:2010:RWP,
author = "Jonathan M. Borwein and Dirk Nuyens and Armin Straub
and James Wan",
booktitle = "{22nd International Conference on Formal Power Series
and Algebraic Combinatorics (FPSAC 2010)}",
title = "Random walks in the plane",
publisher = "Assoc. Discrete Math. Theor. Comput. Sci.",
address = "Nancy, France",
pages = "191--202",
year = "2010",
MRclass = "05C81 (05A15)",
MRnumber = "2673835",
MRreviewer = "Manuel Batista Branco",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Discrete Math. Theor. Comput. Sci. Proc., AN",
acknowledgement = ack-nhfb,
book-URL = "http://math.sfsu.edu/fpsac/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2010:SCC,
author = "Jonathan M. Borwein and Warren B. Moors",
title = "Stability of closedness of convex cones under linear
mappings {II}",
journal = "Journal of Nonlinear Analysis and Optimization: Theory
\& Applications",
volume = "1",
number = "1",
pages = "1--7",
year = "2010",
ISSN = "1906-9685",
ISSN-L = "1906-9685",
MRclass = "49J53 (47N10 90C05 90C31)",
MRnumber = "2911681",
MRreviewer = "John R. Giles",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1226/;
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/5",
acknowledgement = ack-nhfb,
ajournal = "J. Nonlinear Anal. Optim.",
fjournal = "Journal of Nonlinear Analysis and Optimization. Theory
and Applications",
journal-URL = "http://www.sci.nu.ac.th/jnao",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:2010:TTT,
author = "Jonathan M. Borwein",
title = "Talking to {Telstra}: Two weeks spent with
{Australia}'s largest {Telco}",
day = "27",
month = sep,
year = "2010",
bibdate = "Tue Aug 16 10:00:52 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Response to Australian Communications and Media
Authority (ACMA) enquiry, Reconnecting the Customer,
Sept 27, 2010.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "The background for this document is provided by Jon's
daughter, Naomi, in a talk at his funeral, and recorded
at
\url{http://jonborwein.org/2016/08/my-father-by-naomi-borwein/}:
``In 2010 Jon changed his Internet and telephone
provider to Telstra, the leading national
telecommunications provider in Australia. Telstra
started by providing service to J Brow-ein, and things
went down hill from there. So Jon chronicled his
month-long quest to fix his Internet and telephone
connection in a highly amusing, but frustratingly
bureaucratic, sixty page document. It ended up being
obligatory reading for all the vice presidents at
Telstra, and was sent as part of a package to the
Australian Government's royal commission on the
dysfunction of Big Telcos in the country. This was
under the umbrella of the Australian Communications and
Media Authority, which is an Australian Government
statutory authority. Jon was personally thanked in the
final report that was lodged in parliament.''",
}
@Article{Bacak:2011:DCL,
author = "Miroslav Ba{\v{c}}{\'a}k and Jonathan M. Borwein",
title = "On difference convexity of locally {Lipschitz}
functions",
journal = j-OPTIMIZATION,
volume = "60",
number = "8--9",
pages = "961--978",
year = "2011",
CODEN = "OPTZDQ",
DOI = "https://doi.org/10.1080/02331931003770411",
ISSN = "0233-1934, 0323-3898",
ISSN-L = "0233-1934",
MRclass = "49J53 (49-02)",
MRnumber = "2860286",
MRreviewer = "Shawn Xianfu Wang",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1446/",
abstract = "We survey and enhance salient parts of the literature
about difference convex (DC) functions with specific
regard to current knowledge and applications of DC
functions.",
acknowledgement = ack-nhfb,
fjournal = "Optimization",
fjournal = "Optimization. A Journal of Mathematical Programming
and Operations Research",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Bacak:2011:DCL",
}
@TechReport{Bailey:2011:CPI,
author = "David H. Bailey and Jonathan M. Borwein and Andrew
Mattingly and Glenn Wightwick",
title = "The Computation of Previously Inaccessible Digits of $
\pi^2 $ and {Catalan}'s Constant",
type = "Report",
institution = "Lawrence Berkeley National Laboratory; Centre for
Computer Assisted Research Mathematics and its
Applications (CARMA), University of Newcastle; IBM
Australia",
address = "Berkeley, CA, USA; Callaghan, NSW 2308, Australia; St.
Leonards, NSW 2065, Australia; Pyrmont, NSW 2009,
Australia",
pages = "18",
day = "11",
month = apr,
year = "2011",
bibdate = "Sat Apr 23 08:58:45 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
URL = "http://crd.lbl.gov/~dhbailey/dhbpapers/bbp-bluegene.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Submitted to Notices of the AMS.",
}
@TechReport{Bailey:2011:EAN,
author = "David H. Bailey and Jonathan M. Borwein and Cristian
S. Calude and Michael J. Dinneen and Monica Dumitrescu
and Alex Yee",
title = "An Empirical Approach to the Normality of $ \pi $",
type = "Report",
number = "CDMTCS-413",
institution = "Centre for Discrete Mathematics and Theoretical
Computer Science, University of Auckland",
address = "Auckland, New Zealand",
pages = "i + 31",
month = nov,
year = "2011",
bibdate = "Tue Aug 23 06:50:08 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1382/;
http://www.cs.auckland.ac.nz/research/groups/CDMTCS/researchreports/?download&paper_file=413",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2011:EEC,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Exploratory experimentation and computation",
journal = j-NAMS,
volume = "58",
number = "10",
pages = "1410--1419",
month = oct,
year = "2011",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "00A35",
MRnumber = "2884022",
MRreviewer = "Eduard Glas",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Chinese translation in Mathematical Advances in
Translation (Chinese Academy of Science), June 2012.",
URL = "http://docserver.carma.newcastle.edu.au/1396/",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Bailey:2011:GMD,
author = "David H. Bailey and Jonathan M. Borwein",
title = "The Greatest Mathematical Discovery?",
type = "Report",
institution = "Lawrence Berkeley National Laboratory and Centre for
Computer Assisted RMA, University of Newcastle",
address = "Berkeley, CA 94720, USA and Callaghan, NSW 2308,
Australia",
pages = "10",
day = "8",
month = may,
year = "2011",
bibdate = "Fri Aug 12 18:29:28 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.davidhbailey.com/dhbpapers/decimal.pdf",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic history",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2011:HPN,
author = "D. H. Bailey and J. M. Borwein",
title = "High-precision numerical integration: Progress and
challenges",
journal = j-J-SYMBOLIC-COMP,
volume = "46",
number = "7",
pages = "741--754",
month = jul,
year = "2011",
CODEN = "JSYCEH",
DOI = "https://doi.org/10.1016/j.jsc.2010.08.010",
ISSN = "0747-7171 (print), 1095-855x (electronic)",
ISSN-L = "0747-7171",
MRclass = "65D30 (65Y05 68W30)",
MRnumber = "2795208",
MRreviewer = "G. A. Evans",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
note = "Special Issue in Honour of Keith Geddes on his 60th
Birthday.",
URL = "http://docserver.carma.newcastle.edu.au/1444/;
http://www.sciencedirect.com/science/article/pii/S0747717110001409",
abstract = "One of the most fruitful advances in the field of
experimental mathematics has been the development of
practical methods for very high-precision numerical
integration, a quest initiated by Keith Geddes and
other researchers in the 1980s and 1990s. These
techniques, when coupled with equally powerful integer
relation detection methods, have resulted in the
analytic evaluation of many integrals that previously
were beyond the realm of symbolic techniques. This
paper presents a survey of the current state-of-the-art
in this area (including results by the present authors
and others), mentions some new results, and then
sketches what challenges lie ahead.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171/",
keywords = "High-precision arithmetic; Ising theory; Numerical
integration; Quadrature; Quantum field theory",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bauschke:2011:BBT,
author = "H. H. Bauschke and J. M. Borwein and X. Wang and L.
Yao",
title = "The {Br{\'e}zis--Browder} Theorem in a general
{Banach} space",
journal = "ArXiv e-prints",
month = oct,
year = "2011",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2011arXiv1110.5706B",
abstract = "During the 1970s Br{\'e}zis and Browder presented a
now classical characterization of maximal monotonicity
of monotone linear relations in reflexive spaces. In
this paper, we extend and refine their result to a
general Banach space.",
acknowledgement = ack-nhfb,
eprint = "1110.5706",
keywords = "Mathematics - Functional Analysis, 47A06 (Primary),
47H05, 47B65 (Secondary), 47N10, 90C25",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Article{Bauschke:2011:CPM,
author = "H. H. Bauschke and J. M. Borwein and X. Wang and L.
Yao",
title = "Construction of pathological maximally monotone
operators on non-reflexive {Banach} spaces",
journal = "ArXiv e-prints",
month = aug,
year = "2011",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2011arXiv1108.1463B;
http://docserver.carma.newcastle.edu.au/1090/",
abstract = "In this paper, we construct maximally monotone
operators that are not of Gossez's dense-type (D) in
many nonreflexive spaces. Many of these operators also
fail to possess the Br{\o}nsted--Rockafellar (BR)
property. Using these operators, we show that the
partial inf-convolution of two BC--functions will not
always be a BC--function. This provides a negative
answer to a challenging question posed by Stephen
Simons. Among other consequences, we deduce that every
Banach space which contains an isomorphic copy of the
James space $ \mathbf {J} $ or its dual $ \mathbf {J}^*
$, or $ c_0 $ or its dual $ \ell^1 $, admits a non type
(D) operator.",
acknowledgement = ack-nhfb,
eprint = "1108.1463",
keywords = "Mathematics - Functional Analysis, Primary 47A06,
47H05, Secondary 47B65, 47N1, 90C25",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Article{Bauschke:2011:EMM,
author = "H. H. Bauschke and J. M. Borwein and X. Wang and L.
Yao",
title = "Every maximally monotone operator of
{Fitzpatrick--Phelps} type is actually of dense type",
journal = "ArXiv e-prints",
month = apr,
year = "2011",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2011arXiv1104.0750B;
http://docserver.carma.newcastle.edu.au/1442/",
abstract = "We show that every maximally monotone operator of
Fitzpatrick--Phelps type defined on a real Banach space
must be of dense type. This provides an affirmative
answer to a question posed by Stephen Simons in 2001
and implies that various important notions of
monotonicity coincide.",
acknowledgement = ack-nhfb,
eprint = "1104.0750",
keywords = "Mathematics - Functional Analysis, Primary 47H05,
Secondary 46B10, 47N10, 90C25",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Article{Bauschke:2011:MML,
author = "Heinz H. Bauschke and Jonathan M. and Xianfu Wang and
Liangjin Yao",
title = "For maximally monotone linear relations, dense type,
negative-infimum type, and {Fitzpatrick--Phelps} type
all coincide with monotonicity of the adjoint",
journal = "ArXiv e-prints",
pages = "15",
day = "21",
month = mar,
year = "2011",
bibdate = "Tue Aug 16 09:57:56 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2011arXiv1103.6239B;
http://arxiv.org/abs/1103.6239",
abstract = "It is shown that, for maximally monotone linear
relations defined on a general Banach space, the
monotonicities of dense type, of negative-infimum type,
and of Fitzpatrick--Phelps type are the same and
equivalent to monotonicity of the adjoint. This result
also provides affirmative answers to two problems: one
posed by Phelps and Simons, and the other by Simons.",
acknowledgement = ack-nhfb,
eprint = "1103.6239",
keywords = "Mathematics - Functional Analysis, Primary 47A06,
47H05, Secondary 47B65, 47N10, 90C25",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Article{Bauschke:2011:MOB,
author = "H. H. Bauschke and J. M. Borwein and X. Wang and L.
Yao",
title = "Monotone operators and ``bigger conjugate''
functions",
journal = "ArXiv e-prints",
month = aug,
year = "2011",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2011arXiv1108.2578B;
http://docserver.carma.newcastle.edu.au/1477/",
abstract = "We study a question posed by Stephen Simons in his
2008 monograph involving ``bigger conjugate'' (BC)
functions and the partial infimal convolution. As
Simons demonstrated in his monograph, these function
have been crucial to the understanding and advancement
of the state-of-the-art of harder problems in monotone
operator theory, especially the sum problem. In this
paper, we provide some tools for further analysis of
BC--functions which allow us to answer Simons' problem
in the negative. We are also able to refute a similar
but much harder conjecture which would have generalized
a classical result of Br{\'e}zis, Crandall and Pazy.
Our work also reinforces the importance of
understanding unbounded skew linear relations to
construct monotone operators with unexpected
properties.",
acknowledgement = ack-nhfb,
eprint = "1108.2578",
keywords = "Mathematics - Functional Analysis, Primary 47A06,
47H05, Secondary 47B65, 47N10, 90C25",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Article{Borwein:2011:CBF,
author = "Jonathan M. Borwein and Simeon Reich and Shoham
Sabach",
title = "A characterization of {Bregman} firmly nonexpansive
operators using a new monotonicity concept",
journal = j-J-NONLINEAR-CONVEX-ANAL,
volume = "12",
number = "1",
pages = "161--184",
year = "2011",
ISSN = "1345-4773 (print), 1880-5221 (electronic)",
ISSN-L = "1345-4773",
MRclass = "47H05 (26B25 47H09 94A17)",
MRnumber = "2816416",
MRreviewer = "Patrick L. Combettes",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1445/",
abstract = "The property of nonexpansivity (1-Lipschitz) is very
important in the analysis of many optimization
problems. In this paper we study a more general notion
of nonexpansivity - Bregman nonexpansivity. We present
a characterization of Bregman firmly nonexpansive
operators in general reflexive Banach spaces. This
characterization allows us to construct Bregman firmly
nonexpansive operators explicitly. We provide several
examples of such operators with respect to the
Boltzmann-Shannon entropy and the Fermi-Dirac entropy
in Euclidean spaces. We also compute resolvents with
respect to these functions.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Nonlinear and Convex Analysis",
fjournal = "Journal of Nonlinear and Convex Analysis. An
International Journal",
journal-URL = "http://www.ybook.co.jp/jnca.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Borwein:2011:CBF",
}
@InCollection{Borwein:2011:DRA,
author = "Jonathan M. Borwein and Brailey Sims",
title = "The {Douglas--Rachford} Algorithm in the Absence of
Convexity",
crossref = "Bauschke:2011:FPA",
pages = "93--109",
year = "2011",
DOI = "https://doi.org/10.1007/978-1-4419-9569-8_6",
MRclass = "47N10 (47H10 47J25 65J15 90C26)",
MRnumber = "2858834",
MRreviewer = "A. G. Kartsatos",
bibdate = "Sat Aug 13 16:00:55 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Springer Optim. Appl.",
URL = "http://link.springer.com/chapter/10.1007/978-1-4419-9569-8_6",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2011:DSU,
author = "Jonathan M. Borwein and A. Straub and J. Wan and Wadim
Zudilin",
title = "Densities of short uniform random walks",
journal = "ArXiv e-prints",
month = mar,
year = "2011",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2011arXiv1103.2995B;
http://docserver.carma.newcastle.edu.au/1388/",
abstract = "We study the densities of uniform random walks in the
plane. A special focus is on the case of short walks
with three or four steps and less completely those with
five steps. As one of the main results, we obtain a
hypergeometric representation of the density for four
steps, which complements the classical elliptic
representation in the case of three steps. It appears
unrealistic to expect similar results for more than
five steps. New results are also presented concerning
the moments of uniform random walks and, in particular,
their derivatives. Relations with Mahler measures are
discussed.",
acknowledgement = ack-nhfb,
eprint = "1103.2995",
keywords = "Mathematics - Classical Analysis and ODEs, Mathematics
- Number Theory, 60G50 (Primary) 33C20, 34M25, 44A10
(Secondary)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.CA",
}
@Book{Borwein:2011:EMB,
author = "Jonathan Borwein and Keith Devlin",
title = "{Experimentelle Mathematik: Eine beispielorientierte
Einf{\"u}hrung}. ({German}) [{Experimental}
mathematics: an example-oriented introduction]",
publisher = "Spektrum Akademischer Verlag",
address = "Heidelberg, Germany",
pages = "xii + 158",
year = "2011",
DOI = "https://doi.org/10.1007/978-3-8274-2662-8",
ISBN = "3-8274-2661-8, 3-8274-2662-6 (e-book)",
ISBN-13 = "978-3-8274-2661-1, 978-3-8274-2662-8 (e-book)",
LCCN = "QA8.7 .B67 2011",
MRclass = "00A35 (01A75 11-04 11Y16 11Y60)",
MRnumber = "3052999",
bibdate = "Thu Aug 11 17:05:04 MDT 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "German translation by Roland Girgensohn of
\cite{Borwein:2009:CCI}, with updates.",
URL = "http://link.springer.com/book/10.1007/978-3-8274-2662-8",
acknowledgement = ack-nhfb,
language = "German",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Life Science and Basic Disciplines (German Language)
(Springer-11777).",
subject = "Mathematics, general; Computermathematik",
tableofcontents = "Front Matter / i--xii \\
Was ist Experimentelle Mathematik? / 1-16 \\
Was ist die billiardste Dezimalstelle von $\pi$? /
17---28 \\
Was ist diese Zahl? / 29--38 \\
Die wichtigste Funktion in der Mathematik / 39--48 \\
Werten Sie das folgende Integral aus! / 49--60 \\
Gl{\"u}ckstreffer / 61--69 \\
Berechnungen von $\pi$ / 71--79 \\
Der Computer kennt mehr Mathematik als Sie / 81--91 \\
Treib es bis zum Limit! / 93--104 \\
Vorsicht! Gefahr beim Gebrauch des Computers! /
105--113 \\
Was wir Ihnen bisher nicht verraten haben / 115--130
\\
Back Matter / 131--158",
}
@InCollection{Borwein:2011:ERF,
author = "Jonathan M. Borwein and D. Russell Luke",
title = "Entropic Regularization of the $ \ell_0 $ Function",
crossref = "Bauschke:2011:FPA",
pages = "65--92",
year = "2011",
DOI = "https://doi.org/10.1007/978-1-4419-9569-8_5",
MRclass = "49M20 (49N15 65K10 90C30)",
MRnumber = "2858833",
MRreviewer = "Aris Daniilidis",
bibdate = "Sat Aug 13 16:00:55 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Springer Optim. Appl.",
URL = "http://docserver.carma.newcastle.edu.au/1451/;
http://link.springer.com/chapter/10.1007/978-1-4419-9569-8_5",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2011:IFS,
author = "Jonathan Michael Borwein",
title = "{{\it Implicit functions and solution mappings}} [book
review of \refcno 2515104]",
journal = j-IEEE-CONTROL-SYST-MAG,
volume = "31",
number = "1",
pages = "74--77",
year = "2011",
CODEN = "ISMAD7",
DOI = "https://doi.org/10.1109/MCS.2010.939261",
ISSN = "1066-033X (print), 1941-000X (electronic)",
ISSN-L = "1066-033X",
MRclass = "00A17",
MRnumber = "2789813",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Control Systems Magazine",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Borwein:2011:IMM,
author = "Jonathan M. Borwein and Matthew P. Skerritt",
title = "An introduction to modern mathematical computing: with
{Maple}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 216",
year = "2011",
DOI = "https://doi.org/10.1007/978-1-4614-0122-3",
ISBN = "1-4614-0121-6",
ISBN-13 = "978-1-4614-0121-6",
LCCN = "QA76.6 .B665 2011",
MRclass = "65-01 (15-01 26-01 68-01)",
MRnumber = "2808248",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
series = "Springer Undergraduate Texts in Mathematics and
Technology",
URL = "http://docserver.carma.newcastle.edu.au/1727/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
tableofcontents = "Front Matter / i--xvi \\
Number Theory / 1--65 \\
Calculus / 67--128 \\
Linear Algebra / 129--185 \\
Visualization and Geometry: A Postscript / 187--201 \\
Back Matter / 211--216",
}
@Article{Borwein:2011:LEW,
author = "J. M. Borwein",
title = "Letter to the {Editor}: Why are mathematics papers so
dull?",
journal = j-SIAM-NEWS,
volume = "44",
number = "6",
pages = "7--7",
month = jul # "\slash " # aug,
year = "2011",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Sat Aug 13 15:55:33 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.siam.org/news/news.php?id=1903",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2011:LHM,
author = "Jonathan M. Borwein and Judy-Anne Osborn",
title = "{{\booktitle{Loving and hating mathematics}}, by
Reuben Hersh and Vera John-Steiner. Princeton and
Oxford: Princeton University Press, 2010, 428 pp.,
US\$29.95. ISBN-10: 0-691-14247-5, ISBN-13:
978-0-691-14247-0 [book review of \refcno 2731560]}",
journal = j-MATH-INTEL,
volume = "33",
number = "4",
pages = "63--69",
month = dec,
year = "2011",
CODEN = "MAINDC",
DOI = "https://doi.org/10.1007/s00283-011-9260-1",
ISSN = "0343-6993 (print), 1866-7414 (electronic)",
ISSN-L = "0343-6993",
MRclass = "00A17",
MRnumber = "2906477",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://link.springer.com/article/10.1007/s00283-011-9260-1",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Intelligencer",
journal-URL = "http://link.springer.com/journal/283",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2011:LSEa,
author = "J. M. Borwein and A. Straub",
title = "Log-sine evaluations of {Mahler} measures",
journal = "ArXiv e-prints",
month = mar,
year = "2011",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2011arXiv1103.3893B",
abstract = "We provide evaluations of several recently studied
higher and multiple Mahler measures using log-sine
integrals. This is complemented with an analysis of
generating functions and identities for log-sine
integrals which allows the evaluations to be expressed
in terms of zeta values or more general polylogarithmic
terms. The machinery developed is then applied to
evaluation of further families of multiple Mahler
measures.",
acknowledgement = ack-nhfb,
eprint = "1103.3893",
keywords = "Mathematics - Classical Analysis and ODEs,
Mathematical Physics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.CA",
}
@Article{Borwein:2011:LSEb,
author = "D. Borwein and J. M. Borwein and A. Straub and J.
Wan",
title = "Log-sine evaluations of {Mahler} measures, {II}",
journal = "ArXiv e-prints",
month = mar,
year = "2011",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2011arXiv1103.3035B;
http://docserver.carma.newcastle.edu.au/1435/",
abstract = "We continue the analysis of higher and multiple Mahler
measures using log-sine integrals as started in
``Log-sine evaluations of Mahler measures'' and
``Special values of generalized log-sine integrals'' by
two of the authors. This motivates a detailed study of
various multiple polylogarithms and worked examples are
given. Our techniques enable the reduction of several
multiple Mahler measures, and supply an easy proof of
two conjectures by Boyd.",
acknowledgement = ack-nhfb,
eprint = "1103.3035",
keywords = "Mathematics - Classical Analysis and ODEs,
Mathematical Physics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.CA",
}
@TechReport{Borwein:2011:MHM,
author = "Jonathan M. Borwein and Wadim Zudilin",
title = "Math Honours: Multiple Zeta Values",
type = "Classroom notes",
institution = "Centre for Computer Assisted RMA, University of
Newcastle",
address = "Callaghan, NSW 2308, Australia",
pages = "65",
day = "19",
month = oct,
year = "2011",
bibdate = "Fri Nov 04 16:04:34 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://carma.newcastle.edu.au/MZVs/mzv.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
tableofcontents = "1. Introduction to multiple zeta values (MZVs) \\
2. Method of partial fractions \\
3. Algebra of MZVs \\
4. Generalized polylogarithms and generating functions
of MZVs \\
5. Duality theorem. Sum theorem and Ohno's relations
\\
6. Quasi-shuffle products. Derivations \\
7. $q$-Analogues of MZVs \\
8. Other extensions and open questions",
}
@InProceedings{Borwein:2011:MMS,
author = "Jonathan Borwein",
booktitle = "Proceedings of the 2011 International Workshop on
Symbolic--Numeric Computation",
title = "{Mahler} Measures, Short Walks and Log-sine Integrals:
A Case Study in Hybrid Computation",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "1--1",
year = "2011",
DOI = "https://doi.org/10.1145/2331684.2331685",
ISBN = "1-4503-0515-6",
ISBN-13 = "978-1-4503-0515-0",
bibdate = "Wed Aug 10 12:08:56 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "SNC '11",
URL = "http://doi.acm.org/10.1145/2331684.2331685",
acknowledgement = ack-nhfb,
acmid = "2331685",
keywords = "Mahler measures, log-sine integral, short walks",
location = "San Jose, California",
numpages = "1",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2011:MOE,
author = "J. M. Borwein and R. Burachik and L. Yao",
title = "Monotone Operators without Enlargements",
journal = "ArXiv e-prints",
day = "11",
month = oct,
year = "2011",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2011arXiv1110.3102B;
http://arxiv.org/abs/1110.3102;
http://docserver.carma.newcastle.edu.au/1447/",
abstract = "Enlargements have proven to be useful tools for
studying maximally monotone mappings. It is therefore
natural to ask in which cases the enlargement does not
change the original mapping. Svaiter has recently
characterized non-enlargeable operators in reflexive
Banach spaces and has also given some partial results
in the nonreflexive case. In the present paper, we
provide another characterization of non-enlargeable
operators in nonreflexive Banach spaces under a
closedness assumption on the graph. Furthermore, and
still for general Banach spaces, we present a new proof
of the maximality of the sum of two maximally monotone
linear relations. We also present a new proof of the
maximality of the sum of a maximally monotone linear
relation and a normal cone operator when the domain of
the linear relation intersects the interior of the
domain of the normal cone.",
acknowledgement = ack-nhfb,
eprint = "1110.3102",
keywords = "Mathematics - Functional Analysis, Mathematics -
Optimization and Control, Primary 47A06, 47H05,
Secondary 47B65, 47N10, 90C25",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
pagecount = "26",
primaryclass = "math.FA",
}
@Unpublished{Borwein:2011:MOT,
author = "Jonathan M. Borwein and Andrew Eberhard and Liangjin
Yao",
title = "Monotone operators of type {FPV}",
month = aug,
year = "2011",
bibdate = "Tue Aug 16 09:59:46 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2011:MRGa,
author = "David Borwein and Jonathan M. Borwein and M. Larry
Glasser and James G. Wan",
title = "Moments of {Ramanujan}'s generalized elliptic
integrals and extensions of {Catalan}'s constant",
journal = j-J-MATH-ANAL-APPL,
volume = "384",
number = "2",
pages = "478--496",
year = "2011",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/j.jmaa.2011.06.001",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "33E05 (33C05)",
MRnumber = "2825201",
MRreviewer = "Diego E. Dominici",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1443/;
http://www.sciencedirect.com/science/article/pii/S0022247X1100549X",
abstract = "We undertake a thorough investigation of the moments
of Ramanujan's alternative elliptic integrals and of
related hypergeometric functions. Along the way we are
able to give some surprising closed forms for
Catalan-related constants and various new
hypergeometric identities.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
keywords = "Catalan's constant; Elliptic integrals; Hypergeometric
functions; Moments",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:2011:PSE,
author = "D. Borwein and Jonathan M. Borwein",
title = "Proof of some experimentally conjectured formulas for
$ \pi $",
type = "Preprint",
institution = "Department of Mathematics, University of Western
Ontario and Centre for Computer-assisted Research
Mathematics and its Applications (CARMA), School of
Mathematical and Physical Sciences, University of
Newcastle",
address = "London, ON, Canada and Callaghan, NSW 2308,
Australia",
day = "4",
month = dec,
year = "2011",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
abstract = "A recent paper by M. Jauregui and C. Tsallis
\cite{Jauregui:2010:NRD}, which explores applications
of the $q$-exponential function and formal
representations of the Dirac function, contains a set
of experimentally discovered formulae for $ \pi $ as
finite series of gamma function ratios. Herein, we
prove rigorously these identities as special cases of
Pfaff--Saalsch{\"u}tz evaluation for $_3 F_2 ({a, b, c}
\atop {d, e} | 1)$ functions. We likewise prove and
extend a corresponding integral identity given in
\cite{Jauregui:2010:NRD}.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2011:SAP,
author = "Jonathan M. Borwein and Dirk Nuyens and Armin Straub
and James Wan",
title = "Some arithmetic properties of short random walk
integrals",
journal = j-RAMANUJAN-J,
volume = "26",
number = "1",
pages = "109--132",
year = "2011",
CODEN = "RAJOF9",
DOI = "https://doi.org/10.1007/s11139-011-9325-y",
ISSN = "1382-4090 (print), 1572-9303 (electronic)",
ISSN-L = "1382-4090",
MRclass = "60G50 (33C20)",
MRnumber = "2837721",
MRreviewer = "Florian Sobieczky",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1440/",
ZMnumber = "1233.60024",
abstract = "We study the moments of the distance traveled by a
walk in the plane with unit steps in random directions.
While this historically interesting random walk is well
understood from a modern probabilistic point of view,
our own interest is in determining explicit closed
forms for the moment functions and their arithmetic
values at integers when only a small number of steps is
taken. As a consequence of a more general evaluation, a
closed form is obtained for the average distance
traveled in three steps. This evaluation, as well as
its proof, rely on explicit combinatorial properties,
such as recurrence equations of the even moments (which
are lifted to functional equations). The corresponding
general combinatorial and analytic features are
collected and made explicit in the case of 3 and 4
steps. Explicit hypergeometric expressions are given
for the moments of a 3-step and 4-step walk and a
general conjecture for even length walks is made.",
acknowledgement = ack-nhfb,
fjournal = "The {Ramanujan} Journal",
journal-URL = "http://link.springer.com/journal/11139",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Nuyens, Dirk/0000-0002-4555-2314 Borwein,
Jonathan/0000-0002-1263-0646 Straub,
Armin/0000-0001-6802-6053",
researcherid-numbers = "Nuyens, Dirk/A-7426-2016",
unique-id = "Borwein:2011:SAP",
}
@Article{Borwein:2011:SVGa,
author = "Jonathan M. Borwein and Armin Straub",
title = "Special Values of Generalized Log-sine Integrals",
journal = "ArXiv e-prints",
month = mar,
year = "2011",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2011arXiv1103.4298B;
http://docserver.carma.newcastle.edu.au/1398/",
abstract = "We study generalized log-sine integrals at special
values. At $ \pi $ and multiples thereof explicit
evaluations are obtained in terms of Nielsen
polylogarithms at $ \pm 1 $. For general arguments we
present algorithmic evaluations involving Nielsen
polylogarithms at related arguments. In particular, we
consider log-sine integrals at $ \pi / 3 $ which
evaluate in terms of polylogarithms at the sixth root
of unity. An implementation of our results for the
computer algebra systems Mathematica and SAGE is
provided.",
acknowledgement = ack-nhfb,
eprint = "1103.4298",
keywords = "Mathematics - Classical Analysis and ODEs, Computer
Science - Symbolic Computation, Mathematical Physics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.CA",
}
@InProceedings{Borwein:2011:SVGb,
author = "Jonathan M. Borwein and Armin Straub",
booktitle = "Proceedings of the 36th International Symposium on
Symbolic and Algebraic Computation",
title = "Special Values of Generalized Log-sine Integrals",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "43--50",
year = "2011",
DOI = "https://doi.org/10.1145/1993886.1993899",
ISBN = "1-4503-0675-6",
ISBN-13 = "978-1-4503-0675-1",
MRclass = "11R06 (33B99 68W30)",
MRnumber = "2895193",
bibdate = "Wed Aug 10 12:08:56 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
note = "Awarded ISSAC 2011 Best SIGSAM-ACM Student Paper
Prize.",
series = "ISSAC '11",
URL = "http://docserver.carma.newcastle.edu.au/1398/;
http://doi.acm.org/10.1145/1993886.1993899",
acknowledgement = ack-nhfb,
acmid = "1993899",
keywords = "Clausen functions, log-sine integrals, multiple
polylogarithms, multiple zeta values",
location = "San Jose, California, USA",
numpages = "8",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Alladi:2012:PRA,
author = "Krishnaswami Alladi and George E. Andrews and Jonathan
M. Borwein",
title = "Preface to {Ramanujan}'s 125th anniversary special
issue",
journal = j-RAMANUJAN-J,
volume = "29",
number = "1--3",
pages = "1--2",
month = dec,
year = "2012",
CODEN = "RAJOF9",
DOI = "https://doi.org/10.1007/s11139-012-9448-9",
ISSN = "1382-4090 (print), 1572-9303 (electronic)",
ISSN-L = "1382-4090",
MRclass = "11-06 (01A70)",
MRnumber = "2994085",
bibdate = "Fri Aug 12 08:52:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://link.springer.com/article/10.1007/s11139-012-9448-9",
acknowledgement = ack-nhfb,
fjournal = "The {Ramanujan} Journal",
journal-URL = "http://link.springer.com/journal/11139",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Amdeberhan:2012:FEC,
author = "Tewodros Amdeberhan and David Borwein and Jonathan M.
Borwein and Armin Straub",
title = "On formulas for $ \pi $ experimentally conjectured by
{Jauregui--Tsallis}",
journal = j-J-MATH-PHYS,
volume = "53",
number = "7",
pages = "073708",
month = jul,
year = "2012",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.4735283",
ISSN = "0022-2488",
ISSN-L = "0022-2488",
MRclass = "33C20 (11Y60 30D15 33C45)",
MRnumber = "2985267",
MRreviewer = "Tatiana Hessami Pilehrood",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2012JMP....53g3708A;
http://docserver.carma.newcastle.edu.au/1378/",
abstract = "In a recent study of representing Dirac's delta
distribution using q-exponentials, Jauregui and Tsallis
experimentally discovered formulae for $ \pi $ as
hypergeometric series as well as certain integrals.
Herein, we offer rigorous proofs of these identities
using various methods and our primary intent is to lay
down an illustration of the many technical
underpinnings of such evaluations. This includes an
explicit discussion of creative telescoping and
Carlson's Theorem. We also generalize the
Jauregui--Tsallis identities to integrals involving
Chebyshev polynomials. In our pursuit, we provide an
interesting tour through various topics from classical
analysis to the theory of special functions.",
acknowledgement = ack-nhfb,
article-number = "073708",
eid = "073708",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
onlinedate = "Sep 2012",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646 Straub,
Armin/0000-0001-6802-6053",
pagecount = "15",
unique-id = "Amdeberhan:2012:FPE",
}
@Article{AragonArtacho:2012:GCN,
author = "F. J. {Arag{\'o}n Artacho} and J. M. Borwein",
title = "Global convergence of a non-convex {Douglas--Rachford}
iteration",
journal = "ArXiv e-prints",
month = mar,
year = "2012",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2012arXiv1203.2392A;
http://docserver.carma.newcastle.edu.au/1061/",
abstract = "We establish a region of convergence for the
proto-typical non-convex Douglas--Rachford iteration
which finds a point on the intersection of a line and a
circle. Previous work on the non-convex iteration [2]
was only able to establish local convergence, and was
ineffective in that no explicit region of convergence
could be given.",
acknowledgement = ack-nhfb,
eprint = "1203.2392",
keywords = "Mathematics - Optimization and Control",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.OC",
}
@Article{Bailey:2012:AIS,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Ancient {Indian} Square Roots: An Exercise in Forensic
Paleo-Mathematics",
journal = j-AMER-MATH-MONTHLY,
volume = "119",
number = "8",
pages = "646--657",
month = oct,
year = "2012",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/amer.math.monthly.119.08.646",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "01A32",
MRnumber = "2988227",
MRreviewer = "S. G. Dani",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/10.4169/amermathmont.119.issue-8;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://docserver.carma.newcastle.edu.au/1385/;
http://www.jstor.org/stable/10.4169",
abstract = "This article examines the computation of square roots
in ancient India in the context of the discovery of
positional decimal arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Bailey:2012:AIS",
}
@Article{Bailey:2012:EAN,
author = "David H. Bailey and Jonathan M. Borwein and Cristian
S. Calude and Michael J. Dinneen and Monica Dumitrescu
and Alex Yee",
title = "An Empirical Approach to the Normality of $ \pi $",
journal = j-EXP-MATH,
volume = "21",
number = "4",
pages = "375--384",
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2012.665333",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11K16 (03D32 11A63)",
MRnumber = "3004253",
MRreviewer = "John H. Loxton",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
URL = "http://docserver.carma.newcastle.edu.au/1382/",
abstract = "Using the results of several extremely large recent
computations [Yee and Kondo 11], we tested positively
the normality of a prefix of roughly four trillion
hexadecimal digits of p. This result was used by a
Poisson process model of normality of p: in this model,
it is extraordinarily unlikely that p is not
asymptotically normal base 16, given the normality of
its initial segment.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Calude, Cristian Sorin/0000-0002-8711-6799 Borwein,
Jonathan/0000-0002-1263-0646",
unique-id = "Bailey:2012:EAN",
}
@Article{Bailey:2012:EEC,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Exploration, Experimentation and Computation",
journal = "International Advances in Mathematics",
volume = "31",
number = "1",
pages = "1--14",
month = jan,
year = "2012",
ISSN = "1003-3092",
ISSN-L = "1003-3092",
bibdate = "Fri Sep 30 08:44:21 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Chinese translation of \cite{Bailey:2011:EEC}.",
URL = "http://www.davidhbailey.com/dhbpapers/expexp-chinese.pdf",
acknowledgement = ack-nhfb,
language = "Chinese",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Bailey:2012:EEM,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Exploratory experimentation in mathematics: selected
works",
publisher = "Perfectly Scientific Press",
address = "Portland, OR, USA",
pages = "364",
year = "2012",
ISBN = "1-935638-24-6",
ISBN-13 = "978-1-935638-24-7",
LCCN = "QA76.95 .B34 2012",
bibdate = "Tue Aug 16 08:41:02 MDT 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "Mathematics; Experiments; Experiments.",
}
@Article{Bailey:2012:HHC,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Hand-to-hand combat with thousand-digit integrals",
journal = "Journal of Computational Science",
volume = "3",
number = "3",
pages = "77--86",
year = "2012",
DOI = "https://doi.org/10.1016/j.jocs.2010.12.004",
ISSN = "1877-7503 (print), 1877-7511 (electronic)",
ISSN-L = "1877-7503",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Scientific Computation Methods and Applications.",
URL = "http://docserver.carma.newcastle.edu.au/1393/;
http://www.sciencedirect.com/science/article/pii/S1877750310000773",
abstract = "In this paper we describe numerical investigations of
definite integrals that arise by considering the
moments of multi-step uniform random walks in the
plane, together with a closely related class of
integrals involving the elliptic functions K, K', E and
E'. We find that in many cases such integrals can be
``experimentally'' evaluated in closed form or that
intriguing linear relations exist within a class of
similar integrals. Discovering these identities and
relations often requires the evaluation of integrals to
extreme precision, combined with large-scale runs of
the ``PSLQ'' integer relation algorithm. This paper
presents details of the techniques used in these
calculations and mentions some of the many difficulties
that can arise.",
acknowledgement = ack-nhfb,
keywords = "Elliptic integrals; Experimental mathematics;
High-precision computing; Numerical integration; Random
walks",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2012:HPC,
author = "David H. Bailey and Roberto Barrio and Jonathan M.
Borwein",
title = "High-precision computation: Mathematical physics and
dynamics",
journal = j-APPL-MATH-COMP,
volume = "218",
number = "20",
pages = "10106--10121",
day = "15",
month = jun,
year = "2012",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2012.03.087",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
MRclass = "65Y04 (68M07)",
MRnumber = "2921767",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://docserver.carma.newcastle.edu.au/775/;
http://www.sciencedirect.com/science/article/pii/S0096300312003505",
abstract = "At the present time, IEEE 64-bit floating-point
arithmetic is sufficiently accurate for most scientific
applications. However, for a rapidly growing body of
important scientific computing applications, a higher
level of numeric precision is required. Such
calculations are facilitated by high-precision software
packages that include high-level language translation
modules to minimize the conversion effort. This paper
presents an overview of recent applications of these
techniques and provides some analysis of their
numerical requirements. We conclude that high-precision
arithmetic facilities are now an indispensable
component of a modern large-scale scientific computing
environment.",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
keywords = "Dynamical systems; Experimental mathematics;
High-precision computation; Mathematical physics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Barrio, Roberto/L-4983-2014",
}
@Misc{Bailey:2012:MPI,
author = "David H. Bailey and Jonathan Borwein",
title = "Mathematician\slash physicist\slash inventor {Richard
Crandall} dies at 64",
howpublished = "Web blog.",
day = "21",
month = dec,
year = "2012",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://experimentalmath.info/blog/2012/12/mathematicianphysicistinventor-richard-crandall-dies-at-64/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Bailey:2012:ND,
author = "David H. Bailey and Jonathan M. Borwein and Cristian
S. Calude and Michael J. Dinneen and Monica Dumitrescu
and Alex Yee",
editor = "David H. Bailey and Jonathan M. Borwein",
booktitle = "Exploratory Experimentation in Mathematics: Selected
Works",
title = "Normality and the Digits of $ \pi $",
publisher = "Perfectly Scientific Press",
address = "Portland, OR, USA",
day = "3",
month = feb,
year = "2012",
bibdate = "Fri Sep 30 08:47:20 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/normality-digits-pi.pdf",
abstract = "The question of whether (and why) the digits of
well-known constants of mathematics are statistically
random in some sense has long fascinated
mathematicians. Indeed, one prime motivation in
computing and analyzing digits of $ \pi $ is to explore
the age-old question of whether and why these digits
appear ``random.'' The first computation on ENIAC in
1949 of $ \pi $ to 2037 decimal places was proposed by
John von Neumann to shed some light on the distribution
of $ \pi $ (and of $e$) [8, pp. 277--281].",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Bailey:2012:NP,
author = "D. H. Bailey and J. M. Borwein and C. S. Calude and M.
J. Dinneen and M. Dumitrescu and A. Yee",
title = "Normality and pi",
month = feb,
year = "2012",
bibdate = "Tue Aug 16 09:57:02 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
URL = "http://www.carma.newcastle.edu.au/jon/normality-long.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2012:NSC,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Nonnormality of {Stoneham} constants",
journal = j-RAMANUJAN-J,
volume = "29",
number = "1--3",
pages = "409--422",
year = "2012",
CODEN = "RAJOF9",
DOI = "https://doi.org/10.1007/s11139-012-9417-3",
ISSN = "1382-4090 (print), 1572-9303 (electronic)",
ISSN-L = "1382-4090",
MRclass = "11K16 (11K31)",
MRnumber = "2994109",
MRreviewer = "Robert F. Tichy",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1386/",
ZMnumber = "1336.11055",
abstract = "This paper examines ``Stoneham constants,'' namely
real numbers of the form , for coprime integers ba
parts per thousand yen2 and ca parts per thousand yen2.
These are of interest because, according to previous
studies, alpha (b,c) is known to be b-normal, meaning
that every m-long string of base-b digits appears in
the base-b expansion of the constant with precisely the
limiting frequency b (-m) . So, for example, the
constant is 2-normal. More recently it was established
that alpha (b,c) is not bc-normal, so, for example,
alpha (2,3) is provably not 6-normal. In this paper, we
extend these findings by showing that alpha (b,c) is
not B-normal, where B=b (p) c (q) r, for integers b and
c as above, p,q,ra parts per thousand yen1, neither b
nor c divide r, and the condition D=c (q/p) r (1/p) /b
(c-1)< 1 is satisfied. It is not known whether or not
this is a complete catalog of bases to which alpha
(b,c) is nonnormal. We also show that the sum of two
B-nonnormal Stoneham constants as defined above,
subject to some restrictions, is B-nonnormal.",
acknowledgement = ack-nhfb,
fjournal = "The {Ramanujan} Journal",
journal-URL = "http://link.springer.com/journal/11139",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Bailey:2012:NSC",
}
@TechReport{Bailey:2012:SMP,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Solution to Monthly Problem 11650",
type = "Report",
institution = "Lawrence Berkeley National Laboratory and Centre for
Computer Assisted Research Mathematics and its
Applications (CARMA), University of Newcastle and King
Abdulaziz University",
address = "Berkeley, CA 94720, USA and Callaghan, NSW 2308,
Australia and Jeddah 80200, Saudi Arabia.",
pages = "2",
day = "14",
month = jun,
year = "2012",
bibdate = "Fri Sep 30 08:56:31 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/amm-11650.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Misc{Bailey:2012:YMA,
author = "David Bailey and Jonathan Borwein",
title = "Is your mate actually a computer? {Would} you pass the
{``Turing test''}?",
howpublished = "Web blog.",
day = "27",
month = apr,
year = "2012",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib",
URL = "http://experimentalmath.info/blog/2012/04/will-computers-soon-pass-the-turing-test/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bauschke:2012:BBT,
author = "Heinz H. Bauschke and Jonathan M. Borwein and Xianfu
Wang and Liangjin Yao",
title = "The {Br{\'e}zis--Browder} theorem in a general
{Banach} space",
journal = j-J-FUNCT-ANAL,
volume = "262",
number = "12",
pages = "4948--4971",
year = "2012",
CODEN = "JFUAAW",
DOI = "https://doi.org/10.1016/j.jfa.2012.03.023",
ISSN = "0022-1236 (print), 1096-0783 (electronic)",
ISSN-L = "0022-1236",
MRclass = "47H05 (47H04 49N15)",
MRnumber = "2916057",
MRreviewer = "Simeon Reich",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022123612001462",
abstract = "During the 1970s Br{\'e}zis and Browder presented a
now classical characterization of maximal monotonicity
of monotone linear relations in reflexive spaces. In
this paper, we extend (and refine) their result to a
general Banach space. We also provide an affirmative
answer to a problem posed by Phelps and Simons.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Functional Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/00221236",
keywords = "Adjoint; Br{\'e}zis--Browder Theorem; Linear relation;
Monotone operator; Operator of type (D); Operator of
type (FP); Operator of type (NI); Set-valued operator;
Skew operator; Symmetric operator",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bauschke:2012:CPM,
author = "Heinz H. Bauschke and Jonathan M. Borwein and Xianfu
Wang and Liangjin Yao",
title = "Construction of pathological maximally monotone
operators on non-reflexive {Banach} spaces",
journal = j-SET-VALUED-VAR-ANAL,
volume = "20",
number = "3",
pages = "387--415",
year = "2012",
DOI = "https://doi.org/10.1007/s11228-012-0209-0",
ISSN = "1877-0533 (print), 1877-0541 (electronic)",
ISSN-L = "1877-0533",
MRclass = "47H05 (47A06 47B65)",
MRnumber = "2949634",
MRreviewer = "Simeon Reich",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1108.1463;
http://docserver.carma.newcastle.edu.au/1090/",
abstract = "In this paper, we construct maximally monotone
operators that are not of Gossez's dense-type (D) in
many nonreflexive spaces. Many of these operators also
fail to possess the Bronsted-Rockafellar (BR) property.
Using these operators, we show that the partial
inf-convolution of two BC-functions will not always be
a BC-function. This provides a negative answer to a
challenging question posed by Stephen Simons. Among
other consequences, we deduce-in a uniform fashion-that
every Banach space which contains an isomorphic copy of
the James space or its dual , or c (0) or its dual
a''''(1), admits a non type (D) operator. The existence
of non type (D) operators in spaces containing a''''(1)
or c (0) has been proved recently by Bueno and
Svaiter.",
acknowledgement = ack-nhfb,
fjournal = "Set-Valued and Variational Analysis",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Bauschke,
Heinz/0000-0002-4155-9930",
unique-id = "Bauschke:2012:CPM",
}
@Article{Bauschke:2012:EMM,
author = "Heinz H. Bauschke and Jonathan M. Borwein and Xianfu
Wang and Liangjin Yao",
title = "Every maximally monotone operator of
{Fitzpatrick--Phelps} type is actually of dense type",
journal = j-OPTIM-LETT,
volume = "6",
number = "8",
pages = "1875--1881",
year = "2012",
DOI = "https://doi.org/10.1007/s11590-011-0383-2",
ISSN = "1862-4472 (print), 1862-4480 (electronic)",
ISSN-L = "1862-4472",
MRclass = "47H05 (47H04 49J53)",
MRnumber = "2996490",
MRreviewer = "Patrick L. Combettes",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1104.0750;
http://docserver.carma.newcastle.edu.au/1442/",
abstract = "We show that every maximally monotone operator of
Fitzpatrick-Phelps type defined on a real Banach space
must be of dense type. This provides an affirmative
answer to a question posed by Stephen Simons in 2001
and implies that various important notions of
monotonicity coincide.",
acknowledgement = ack-nhfb,
ajournal = "Optim. Lett.",
fjournal = "Optimization Letters",
journal-URL = "http://link.springer.com/journal/11590",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646 Bauschke,
Heinz/0000-0002-4155-9930",
unique-id = "Bauschke:2012:EMM",
}
@Article{Borwein:2012:CUC,
author = "Jonathan M. Borwein and Jon Vanderwerff",
title = "Constructions of Uniformly Convex Functions",
journal = j-CAN-MATH-BULL,
volume = "55",
number = "4",
pages = "697--707",
month = dec,
year = "2012",
CODEN = "CMBUA3",
DOI = "https://doi.org/10.4153/CMB-2011-049-2",
ISSN = "0008-4395 (print), 1496-4287 (electronic)",
ISSN-L = "0008-4395",
MRclass = "49J53 (46G05 52A41 90C25)",
MRnumber = "2994675",
MRreviewer = "Constantin Z{\u{a}}linescu",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://cms.math.ca/cmb/v55/;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/canmathbull.bib",
URL = "http://docserver.carma.newcastle.edu.au/778/",
abstract = "We give precise conditions under which the composition
of a norm with a convex function yields a uniformly
convex function on a Banach space. Various applications
are given to functions of power type. The results are
dualized to study uniform smoothness and several
examples are provided.",
acknowledgement = ack-nhfb,
fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cmb/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2012:CZD,
author = "J. M. Borwein and R. S. Burachik and L. Yao",
title = "Conditions for zero duality gap in convex
programming",
journal = "ArXiv e-prints",
month = nov,
year = "2012",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2012arXiv1211.4953B;
http://docserver.carma.newcastle.edu.au/1465/",
abstract = "We introduce and study a new dual condition which
characterizes zero duality gap in nonsmooth convex
optimization. We prove that our condition is weaker
than all existing constraint qualifications, including
the closed epigraph condition. Our dual condition was
inspired by, and is weaker than, the so-called
Bertsekas' condition for monotropic programming
problems. We give several corollaries of our result and
special cases as applications. We pay special attention
to the polyhedral and sublinear cases, and their
implications in convex optimization.",
acknowledgement = ack-nhfb,
eprint = "1211.4953",
keywords = "Mathematics - Functional Analysis, Mathematics -
Optimization and Control, 49J52, 48N15 (Primary) 90C25,
90C30, 90C46 (Secondary)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Article{Borwein:2012:DSU,
author = "Jonathan M. Borwein and Armin Straub and James Wan and
Wadim Zudilin",
title = "Densities of short uniform random walks",
journal = j-CAN-J-MATH,
volume = "64",
number = "5",
pages = "961--990",
year = "2012",
CODEN = "CJMAAB",
DOI = "https://doi.org/10.4153/CJM-2011-079-2",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
MRclass = "60G50 (11R06 33C20 82B41)",
MRnumber = "2979573",
MRreviewer = "Aklilu Zeleke",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "With an appendix by Don Zagier.",
URL = "http://arxiv.org/abs/1103.2995;
http://docserver.carma.newcastle.edu.au/1388/",
abstract = "We study the densities of uniform random walks in the
plane. A special focus is on the case of short walks
with three or four steps and, less completely, those
with five steps. As one of the main results, we obtain
a hypergeometric representation of the density for four
steps, which complements the classical elliptic
representation in the case of three steps. It appears
unrealistic to expect similar results for more than
five steps. New results are also presented concerning
the moments of uniform random walks and, in particular,
their derivatives. Relations with Mahler measures are
discussed.",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics. Journal Canadien de
Math{\'e}matiques",
journal-URL = "http://cms.math.ca/cjm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Straub, Armin/0000-0001-6802-6053 Zudilin,
Wadim/0000-0001-9551-2903",
unique-id = "Borwein:2012:DSU",
}
@InCollection{Borwein:2012:EED,
author = "Jonathan Michael Borwein",
title = "Exploratory Experimentation: Digitally-assisted
Discovery and Proof",
crossref = "Hanna:2012:PPM",
pages = "69--96",
year = "2012",
DOI = "https://doi.org/10.1007/978-94-007-2129-6_4",
bibdate = "Sat Aug 13 15:47:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/393/;
http://link.springer.com/chapter/10.1007/978-94-007-2129-6_4",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Borwein:2012:IMM,
author = "Jonathan M. Borwein and Matthew P. Skerritt",
title = "An introduction to modern mathematical computing: with
{Mathematica}\reg{}",
publisher = pub-SV,
address = pub-SV:adr,
year = "2012",
DOI = "https://doi.org/10.1007/978-1-4614-4253-0",
ISBN = "1-4614-4252-4 (print), 1-4614-4253-2 (e-book)",
ISBN-13 = "978-1-4614-4252-3 (print), 978-1-4614-4253-0
(e-book)",
ISSN = "1867-5506 (print), 1867-5514 (electronic)",
ISSN-L = "1867-5506",
LCCN = "QA76.95 .B67 2012",
bibdate = "Tue Aug 16 08:35:55 MDT 2016",
bibsource = "fsz3950.oclc.org:210/WorldCato;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
series = "Springer undergraduate texts in mathematics and
technology",
URL = "http://public.eblib.com/choice/publicfullrecord.aspx?p=1030664",
abstract = "Thirty years ago, mathematical computation was
difficult to perform and thus used sparingly. However,
mathematical computation has become far more accessible
due to the emergence of the personal computer, the
discovery of fiber-optics and the consequent
development of the modern internet, and the creation of
Maple, Mathematica, and Matlab. An Introduction to
Modern Mathematical Computing: With Mathematica looks
beyond teaching the syntax and semantics of Mathematica
and similar programs, and focuses on why they are
necessary tools for anyone who engages in mathematics.
It is an essential read for mathematicians, mathematics
educators, computer scientists, engineers, scientists,
and anyone who wishes to expand their knowledge of
mathematics. This volume will also explain how to
become an ``experimental mathematician,'' and will
supply useful information about how to create better
proofs. The text covers material in elementary number
theory, calculus, multivariable calculus, introductory
linear algebra, and visualization and interactive
geometric computation. It is intended for
upper-undergraduate students, and as a reference guide
for anyone who wishes to learn to use the Mathematica
program. Also by J. M. Borwein and M. B. Skerritt: An
Introduction to Modern Mathematical Computing: With
Maple c2011, ISBN: 978-1-4614-0121-6, 216 p. and 81
color illustrations.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "Mathematics; Data processing; Computer science;
Mathematics.; Data processing.",
tableofcontents = "Number theory \\
Calculus \\
Linear algebra \\
Visualization and geometry: a postscript",
}
@TechReport{Borwein:2012:LPA,
author = "Jonathan M. Borwein",
title = "The Life of Pi: From {Archimedes} to {ENIAC} and
Beyond",
type = "Report",
institution = "Centre for Computer Assisted Research Mathematics and
its Applications (CARMA), University of Newcastle",
address = "Callaghan, NSW 2308, Australia",
pages = "30",
day = "19",
month = jun,
year = "2012",
bibdate = "Sat Sep 03 16:38:50 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Prepared for Berggren Festschrift. Updated and revised
version of \cite{Borwein:2008:VPG}.",
URL = "http://carma.newcastle.edu.au/jon/pi-2012.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2012:LSEa,
author = "Jonathan M. Borwein and Armin Straub",
title = "Log-sine evaluations of {Mahler} measures",
journal = j-J-AUSTRAL-MATH-SOC,
volume = "92",
number = "1",
pages = "15--36",
year = "2012",
CODEN = "JAUMAX",
DOI = "https://doi.org/10.1017/S1446788712000067",
ISSN = "1446-7887 (print), 1446-8107 (electronic)",
ISSN-L = "1446-7887",
MRclass = "33E20 (11R06 33F10)",
MRnumber = "2945674",
MRreviewer = "Qiang Wu",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1384/;
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8610681",
abstract = "We provide evaluations of several recently studied
higher and multiple Mahler measures using log-sine
integrals. This is complemented with an analysis of
generating functions and identities for log-sine
integrals which allows the evaluations to be expressed
in terms of zeta values or more general polylogarithmic
terms. The machinery developed is then applied to
evaluation of further families of multiple Mahler
measures.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Australian Mathematical Society",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Straub, Armin/0000-0001-6802-6053 Borwein,
Jonathan/0000-0002-1263-0646",
unique-id = "Borwein:2012:LSE",
}
@Article{Borwein:2012:LSEb,
author = "David Borwein and Jonathan M. Borwein and Armin Straub
and James Wan",
title = "Log-sine evaluations of {Mahler} measures, {II}",
journal = j-INTEGERS,
volume = "12",
number = "6",
pages = "1179--1212",
year = "2012",
CODEN = "INTEHN",
DOI = "https://doi.org/10.1515/integers-2012-0035",
ISSN = "1867-0652 (print), 1867-0660 (electronic)",
MRclass = "11R06",
MRnumber = "3011556",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1103.3035;
http://docserver.carma.newcastle.edu.au/1435/",
acknowledgement = ack-nhfb,
fjournal = "Integers",
journal-URL = "http://www.degruyter.com/view/j/integ",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2012:LTI,
author = "J. M. Borwein and L. Yao",
title = "{Legendre}-type integrands and convex integral
functions",
journal = "ArXiv e-prints",
month = aug,
year = "2012",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2012arXiv1208.5217B;
http://docserver.carma.newcastle.edu.au/1455/",
abstract = "In this paper, we study the properties of integral
functionals induced on $ L^1_{E(S, \mu)} $ by closed
convex functions on a Euclidean space $E$. We give
sufficient conditions for such integral functions to be
strongly rotund (well-posed). We show that in this
generality functions such as the Boltzmann--Shannon
entropy and the Fermi--Dirac entropy are strongly
rotund. We also study convergence in measure and give
various limiting counterexample.",
acknowledgement = ack-nhfb,
eprint = "1208.5217",
keywords = "Mathematics - Functional Analysis, Mathematics -
Optimization and Control, Primary 46B20, 34H05,
Secondary 47H05, 47N10, 90C25",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Article{Borwein:2012:MEF,
author = "Jonathan M. Borwein",
title = "Maximum entropy and feasibility methods for convex and
nonconvex inverse problems",
journal = j-OPTIMIZATION,
volume = "61",
number = "1",
pages = "1--33",
year = "2012",
CODEN = "OPTZDQ",
DOI = "https://doi.org/10.1080/02331934.2011.632502",
ISSN = "0233-1934, 0323-3898",
ISSN-L = "0233-1934",
MRclass = "49-02 (45Q05 49J53 90C25 94A17)",
MRnumber = "2875572",
MRreviewer = "Patrick L. Combettes",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1439/",
abstract = "We discuss informally two approaches to solving convex
and nonconvex feasibility problems - via entropy
optimization and via algebraic iterative methods. We
shall highlight the advantages and disadvantages of
each and give various related applications and limiting
examples. While some of the results are very classical,
they are not as well-known to practitioners as they
should be. A key role is played by the Fenchel
conjugate.",
acknowledgement = ack-nhfb,
fjournal = "Optimization",
fjournal = "Optimization. A Journal of Mathematical Programming
and Operations Research",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Borwein:2012:MEF",
}
@Unpublished{Borwein:2012:MMO,
author = "Jonathan M. Borwein and Liangjin Yao",
title = "Maximally monotone operators of negative infimum type
are of dense type: the proof revisited",
month = jun,
year = "2012",
bibdate = "Tue Aug 16 09:56:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2012:MSM,
author = "J. M. Borwein and L. Yao",
title = "Maximality of the sum of a maximally monotone linear
relation and a maximally monotone operator",
journal = "ArXiv e-prints",
month = dec,
year = "2012",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2012arXiv1212.4266B;
http://docserver.carma.newcastle.edu.au/1483/",
abstract = "The most famous open problem in Monotone Operator
Theory concerns the maximal monotonicity of the sum of
two maximally monotone operators provided that
Rockafellar's constraint qualification holds. In this
paper, we prove the maximal monotonicity of $ A + B $
provided that $ A, B $ are maximally monotone and $A$
is a linear relation, as soon as Rockafellar's
constraint qualification holds: $ \dom A \cap \inte
\dom B \neq \varnothing $. Moreover, $ A + B$ is of
type (FPV).",
acknowledgement = ack-nhfb,
eprint = "1212.4266",
keywords = "Mathematics - Functional Analysis, Mathematics -
Optimization and Control, Primary 47A06, 47H05,
Secondary 47B65, 47N10, 90C25",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Article{Borwein:2012:OMT,
author = "Jonathan Borwein and Veselin Jungi{\'c}",
title = "Organic Mathematics: then and now",
journal = j-NAMS,
volume = "59",
number = "3",
pages = "416--419",
month = mar,
year = "2012",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibdate = "Sat Aug 13 15:39:26 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1397/;
http://www.ams.org/notices/201203/rtx120300416p.pdf",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2012:RCS,
author = "Jonathan Borwein and Peter B. Borwein and Veselin
Jungi{\'c}",
title = "Remote Collaboration: Six Years of the Coast-To-Coast
Seminar Series",
journal = "Science Communication",
volume = "34",
number = "3",
pages = "419--428",
month = jun,
year = "2012",
DOI = "https://doi.org/10.1177/1075547012443020",
ISSN = "1075-5470 (print), 1552-8545 (electronic)",
ISSN-L = "1075-5470",
bibdate = "Fri Aug 12 08:54:03 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1387/;
http://scx.sagepub.com/content/34/3/419.abstract",
abstract = "In this article, the authors describe the
Coast-to-Coast Seminar Series, a pan-Canadian
scientific event that has been running since 2005. A
short history of the series and a listing of the
various stages of its development and related
challenges in communicating complex scientific topics
to audiences at a number of remote sites is provided.
In particular, the authors revisit the original goals
of the series and discuss in detail its actual
outcomes. They finish by mentioning some present and
future applications of their experience as organizers
of the series.",
acknowledgement = ack-nhfb,
journal-URL = "http://scx.sagepub.com/content/by/year",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Borwein:2012:RCS",
}
@InCollection{Borwein:2012:REA,
author = "Jonathan M. Borwein and Judy-anne Osborn",
title = "Response to {``Experimental Approaches to Theoretical
Thinking \ldots{}''}",
crossref = "Hanna:2012:PPM",
pages = "??--??",
year = "2012",
bibdate = "Sat Aug 13 15:47:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "I cannot find this a the publisher Web site??",
}
@Article{Borwein:2012:RPMa,
author = "J. M. Borwein and L. Yao",
title = "Recent progress on Monotone Operator Theory",
journal = "ArXiv e-prints",
month = oct,
year = "2012",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2012arXiv1210.3401B;
http://docserver.carma.newcastle.edu.au/1457/",
abstract = "In this paper, we survey recent progress on the theory
of maximally monotone operators in general Banach
space. We also extend various of the results and leave
some open questions.",
acknowledgement = ack-nhfb,
eprint = "1210.3401",
keywords = "Mathematics - Functional Analysis, Mathematics -
Optimization and Control, 47H05 (Primary) 46B10, 47A06,
47B65, 47N10, 90C25 (Secondary)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Article{Borwein:2012:RPS,
author = "Jonathan M. Borwein",
title = "{Ramanujan} and {Pi}: {Srinivasa Ramanujan}: Going
strong at 125",
journal = j-NAMS,
volume = "59",
number = "11",
pages = "534--537",
month = nov,
year = "2012",
CODEN = "AMNOAN",
DOI = "",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibdate = "Fri Aug 12 08:47:51 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1379/",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2012:SRC,
author = "J. M. Borwein and L. Yao",
title = "Some results on the convexity of the closure of the
domain of a maximally monotone operator",
journal = "ArXiv e-prints",
month = may,
year = "2012",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2012arXiv1205.4482B;
http://docserver.carma.newcastle.edu.au/1373/",
abstract = "We provide a concise analysis about what is known
regarding when the closure of the domain of a maximally
monotone operator on an arbitrary real Banach space is
convex. In doing so, we also provide an affirmative
answer to a problem posed by Simons.",
acknowledgement = ack-nhfb,
eprint = "1205.4482",
keywords = "Mathematics - Functional Analysis, 47H05 (Primary)
26B25, 47A05, 47B65 (Secondary)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Article{Borwein:2012:SS,
author = "David Borwein and Jonathan M. Borwein and Armin
Straub",
title = "A sinc that sank",
journal = j-AMER-MATH-MONTHLY,
volume = "119",
number = "7",
pages = "535--549",
year = "2012",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/amer.math.monthly.119.07.535",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "33B10 (26A09)",
MRnumber = "2956424",
MRreviewer = "M{\'a}rcia Kashimoto",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1391/",
abstract = "We resolve and further study a sinc integral
evaluation, first posed in this MONTHLY in [1967, p.
1015], which was solved in [1968, p. 914] and withdrawn
in [1970, p. 657]. After a short introduction to the
problem and its history, we give a general evaluation
which we make entirely explicit in the case of the
product of three sinc functions. Finally, we exhibit
some more general structure of the integrals in
question.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Borwein:2012:SS",
}
@Article{Borwein:2012:STMa,
author = "J. M. Borwein and L. Yao",
title = "Structure theory for maximally monotone operators with
points of continuity",
journal = "ArXiv e-prints",
month = mar,
year = "2012",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2012arXiv1203.1101B;
http://docserver.carma.newcastle.edu.au/1375/",
abstract = "In this paper, we consider the structure of maximally
monotone operators in Banach space whose domains have
nonempty interior and we present new and explicit
structure formulas for such operators. Along the way,
we provide new proofs of the norm-to-weak$^*$
closedness and of property (Q) for these operators (as
recently proven by Voisei). Various applications and
limiting examples are given.",
acknowledgement = ack-nhfb,
eprint = "1203.1101",
keywords = "Mathematics - Functional Analysis, Mathematics -
Optimization and Control, Primary 47H05, Secondary
47B65, 47N10, 90C25",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Article{Piantadosi:2012:CME,
author = "Julia Piantadosi and Phil Howlett and Jonathan
Borwein",
title = "Copulas with maximum entropy",
journal = j-OPTIM-LETT,
volume = "6",
number = "1",
pages = "99--125",
year = "2012",
DOI = "https://doi.org/10.1007/s11590-010-0254-2",
ISSN = "1862-4472 (print), 1862-4480 (electronic)",
ISSN-L = "1862-4472",
MRclass = "60E05 (62H05 90C25)",
MRnumber = "2886586",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1394/",
abstract = "We shall find a multi-dimensional checkerboard copula
of maximum entropy that matches an observed set of
grade correlation coefficients. This problem is
formulated as the maximization of a concave function on
a convex polytope. Under mild constraint qualifications
we show that a unique solution exists in the core of
the feasible region. The theory of Fenchel duality is
used to reformulate the problem as an unconstrained
minimization which is well solved numerically using a
Newton iteration. Finally, we discuss the numerical
calculations for some hypothetical examples and
describe how this work can be applied to the modelling
and simulation of monthly rainfall.",
acknowledgement = ack-nhfb,
ajournal = "Optim. Lett.",
fjournal = "Optimization Letters",
journal-URL = "http://link.springer.com/journal/11590",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Howlett, Phil/0000-0003-2382-8137 Borwein,
Jonathan/0000-0002-1263-0646",
unique-id = "Piantadosi:2012:CME",
}
@Article{Piantadosi:2012:MEM,
author = "Julia Piantadosi and Phil Howlett and Jonathan Borwein
and John Henstridge",
title = "Maximum entropy methods for generating simulated
rainfall",
journal = j-NUMER-ALGEBRA-CONTROL-OPTIM,
volume = "2",
number = "2",
pages = "233--256",
year = "2012",
DOI = "https://doi.org/10.3934/naco.2012.2.233",
ISSN = "2155-3289 (print), 2155-3297 (electronic)",
ISSN-L = "2155-3297",
MRclass = "62H05 (52A41 65C05)",
MRnumber = "2929449",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ajournal = "Numer. Algebra Control Optim.",
fjournal = "Numerical Algebra, Control and Optimization",
journal-URL = "http://aimsciences.org/journals/home.jsp?journalID=22",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{AragonArtacho:2013:ACA,
author = "F. J. {Arag{\'o}n Artacho} and J. M. Borwein and V.
Mart{\'\i}n-M{\'a}rquez and L. Yao",
title = "Applications of Convex Analysis within Mathematics",
journal = "ArXiv e-prints",
month = feb,
year = "2013",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2013arXiv1302.1978A;
http://docserver.carma.newcastle.edu.au/1513/",
abstract = "In this paper, we study convex analysis and its
theoretical applications. We first apply important
tools of convex analysis to Optimization and to
Analysis. We then show various deep applications of
convex analysis and especially infimal convolution in
Monotone Operator Theory. Among other things, we
recapture the Minty surjectivity theorem in Hilbert
space, and present a new proof of the sum theorem in
reflexive spaces. More technically, we also discuss
autoconjugate representers for maximally monotone
operators. Finally, we consider various other
applications in mathematical analysis.",
acknowledgement = ack-nhfb,
eprint = "1302.1978",
keywords = "Mathematics - Functional Analysis, Mathematics -
Optimization and Control, Primary 47N10, 90C25,
Secondary 47H05, 47A06, 47B65",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Article{AragonArtacho:2013:DRF,
author = "F. J. {Arag{\'o}n Artacho} and J. M. Borwein and M. K.
Tam",
title = "{Douglas--Rachford} Feasibility Methods for Matrix
Completion Problems",
journal = "ArXiv e-prints",
month = aug,
year = "2013",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2013arXiv1308.4243A",
abstract = "In this paper we give general recommendations for
successful application of the Douglas--Rachford
reflection method to convex and non-convex real
matrix-completion problems. These guidelines are
demonstrated by various illustrative examples.",
acknowledgement = ack-nhfb,
eprint = "1308.4243",
keywords = "Mathematics - Optimization and Control",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.OC",
}
@Article{AragonArtacho:2013:GCN,
author = "Francisco J. {Arag{\'o}n Artacho} and Jonathan M.
Borwein",
title = "Global convergence of a non-convex {Douglas--Rachford}
iteration",
journal = j-J-GLOBAL-OPT,
volume = "57",
number = "3",
pages = "753--769",
year = "2013",
CODEN = "JGOPEO",
DOI = "https://doi.org/10.1007/s10898-012-9958-4",
ISSN = "0925-5001 (print), 1573-2916 (electronic)",
ISSN-L = "0925-5001",
MRclass = "47J25 (47H10 90C26)",
MRnumber = "3119379",
MRreviewer = "Patrick L. Combettes",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1203.2392;
http://docserver.carma.newcastle.edu.au/1061/",
acknowledgement = ack-nhfb,
fjournal = "Journal of Global Optimization. An International
Journal Dealing with Theoretical and Computational
Aspects of Seeking Global Optima and Their Applications
in Science, Management and Engineering",
journal-URL = "http://link.springer.com/journal/10898",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{AragonArtacho:2013:RRDa,
author = "F. J. {Arag{\'o}n Artacho} and J. M. Borwein and M. K.
Tam",
title = "Recent Results on {Douglas--Rachford} Methods for
Combinatorial Optimization Problems",
journal = "ArXiv e-prints",
month = may,
year = "2013",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2013arXiv1305.2657A;
http://docserver.carma.newcastle.edu.au/1510/",
abstract = "We discuss recent positive experiences applying convex
feasibility algorithms of Douglas--Rachford type to
highly combinatorial and far from convex problems.",
acknowledgement = ack-nhfb,
eprint = "1305.2657",
keywords = "Mathematics - Optimization and Control, Mathematics -
Combinatorics, 90C27, 90C59, 47N10",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.OC",
}
@Article{AragonArtacho:2013:RRDb,
author = "Francisco J. {Arag{\'o}n Artacho} and Jonathan M.
Borwein and Matthew K. Tam",
title = "Recent results on {Douglas--Rachford} methods",
journal = j-SERDICA-MATH-J,
volume = "39",
number = "3--4",
pages = "313--330",
year = "2013",
ISSN = "1310-6600",
MRclass = "90C27 (90C59)",
MRnumber = "3203190",
MRreviewer = "Patrick L. Combettes",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.math.bas.bg/serdica/",
acknowledgement = ack-nhfb,
fjournal = "Serdica. Mathematical Journal. Serdika. Matematichesko
Spisanie",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{AragonArtacho:2013:WRN,
author = "Francisco J. {Arag{\'o}n Artacho} and David H. Bailey
and Jonathan M. Borwein and Peter B. Borwein",
title = "Walking on Real Numbers",
journal = j-MATH-INTEL,
volume = "35",
number = "1",
pages = "42--60",
month = mar,
year = "2013",
CODEN = "MAINDC",
DOI = "https://doi.org/10.1007/s00283-012-9340-x",
ISSN = "0343-6993 (print), 1866-7414 (electronic)",
ISSN-L = "0343-6993",
MRclass = "11Y60 (60A99 60F05)",
MRnumber = "3041991",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://docserver.carma.newcastle.edu.au/1475/;
http://gigapan.com/gigapans/106803;
http://link.springer.com/article/10.1007%2Fs00283-012-9340-x;
http://www.davidhbailey.com/dhbpapers/tools-walk.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Intelligencer",
journal-URL = "http://link.springer.com/journal/283",
keywords = "Catalan's constant; Champernowne numbers; continued
fractions; Copeland--Erd{\H{o}}s numbers; DNA genome
numbers; dragon curves; Erd{\H{o}}s--Borwein numbers;
Euler--Mascherino constant ($\gamma$); expected
random-walk distance; exponential constant ($e$);
Fibonacci constant ($F$); Gauss--Kuzmin distribution;
irrational numbers; Koch snowflakes; Liouville number
($\lambda_2$); logarithmic constant ($\log 2$);
Minkowski--Bouligand dimension; normal numbers;
normalized random-walk distance; paper-folding
constant; paper-folding numbers; pi (number); random
walks; Riemann zeta numbers ($\zeta(n)$);
self-similarity; Stoneham numbers; strong normality;
Thue--Morse numbers; transcendental numbers; turtle
plots",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2013:CLS,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Compressed lattice sums arising from the {Poisson}
equation",
journal = j-BOUND-VALUE-PROBL,
volume = "75",
number = "1",
pages = "1--18",
year = "2013",
DOI = "https://doi.org/10.1186/1687-2770-2013-75",
ISSN = "1687-2770",
MRclass = "35J15 (35C10)",
MRnumber = "3055839",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special volume in honour of Hari Srivastava.",
URL = "http://boundaryvalueproblems.springeropen.com/articles/10.1186/1687-2770-2013-75;
http://docserver.carma.newcastle.edu.au/1476/;
http://www.boundaryvalueproblems.com/content/2013/1/75",
abstract = "In recent years attention has been directed to the
problem of solving the Poisson equation, either in
engineering scenarios (computational) or in regard to
crystal structure (theoretical). Methods: In (Bailey et
al. in J. Phys. A, Math. Theor. 46:115201, 2013,
doi:10.1088/1751-8113/46/11/115201) we studied a class
of lattice sums that amount to solutions of Poisson's
equation, utilizing some striking connections between
these sums and Jacobi I-function values, together with
high-precision numerical computations and the PSLQ
algorithm to find certain polynomials associated with
these sums. We take a similar approach in this study.
Results: We were able to develop new closed forms for
certain solutions and to extend such analysis to
related lattice sums. We also alluded to results for
the compressed sum phi(2)(x,y,d):=1/pi(2) Sigma(m,n is
an element of O) cos(pi mx)cos(pi n root dy)/m(2) +
dn(2) , (1) where , x, y are real numbers and denotes
the odd integers. In this paper we first survey the
earlier work and then discuss the sum (1) more
completely. Conclusions: As in the previous study, we
find some surprisingly simple closed-form evaluations
of these sums. In particular, we find that in some
cases these sums are given by , where A is an algebraic
number. These evaluations suggest that a deep theory
interconnects all such summations.",
acknowledgement = ack-nhfb,
ajournal = "Bound. Value Probl.",
article-number = "75",
fjournal = "Boundary Value Problems",
journal-URL = "http://boundaryvalueproblems.springeropen.com/",
onlinedate = "13 May 2013",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Bailey:2013:CLS",
}
@Unpublished{Bailey:2013:CPF,
author = "D. H. Bailey and J. M. Borwein and M. {L{\'o}pez de
Prado} and Qiji Zhu",
title = "Computing the Probability of Over-Fitting in the
Back-Testing and Optimization of Investment
Strategies",
month = sep,
year = "2013",
bibdate = "Tue Aug 16 09:54:19 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
URL = "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2308659",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2013:CPI,
author = "David H. Bailey and Jonathan M. Borwein and Andrew
Mattingly and Glenn Wightwick",
title = "The computation of previously inaccessible digits of
{$ \pi^2 $} and {Catalan}'s constant",
journal = j-NAMS,
volume = "60",
number = "7",
pages = "844--854",
year = "2013",
CODEN = "AMNOAN",
DOI = "https://doi.org/10.1090/noti1015",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "11Y60 (65-04)",
MRnumber = "3086394",
MRreviewer = "Michael M. Dediu",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1436/;
http://www.ams.org/notices/201307/rnoti-p844.pdf",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2013:DPR,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Are the Digits of Pi Random?",
journal = "Huffington Post",
day = "16",
month = apr,
year = "2013",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
URL = "http://www.huffingtonpost.com/david-h-bailey/are-the-digits-of-pi-random_b_3085725.html",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2013:EFS,
author = "David H. Bailey and Jonathan M. Borwein and Richard E.
Crandall and Michael G. Rose",
title = "Expectations on fractal sets",
journal = j-APPL-MATH-COMP,
volume = "220",
number = "??",
pages = "695--721",
day = "1",
month = sep,
year = "2013",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2013.06.078",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
MRclass = "28A80 (60G18 60G50)",
MRnumber = "3091892",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1454/;
http://www.sciencedirect.com/science/article/pii/S0096300313007273",
abstract = "Using fractal self-similarity and
functional-expectation relations, the classical theory
of box integrals -- being expectations on unit
hypercubes -- is extended to a class of fractal
``string-generated Cantor sets'' (SCSs) embedded in
unit hypercubes of arbitrary dimension. Motivated by
laboratory studies on the distribution of brain
synapses, these SCSs were designed for dimensional
freedom -- a suitable choice of generating string
allows for fine-tuning the fractal dimension of the
corresponding set. We also establish closed forms for
certain statistical moments on SCSs, develop a
precision algorithm for high embedding dimensions, and
report various numerical results. The underlying
numerical quadrature issues are in themselves quite
challenging.",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
keywords = "Expectations; Fractals; Monte Carlo methods; Numerical
quadrature; Self-similarity",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Bailey:2013:HPA,
author = "David H. Bailey and Jonathan M. Borwein",
title = "High-Precision Arithmetic: Opportunities and
Challenges",
month = aug,
year = "2013",
bibdate = "Tue Aug 16 09:53:03 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2013:LSA,
author = "David H. Bailey and Jonathan M. Borwein and Richard E.
Crandall and I. John Zucker",
title = "Lattice sums arising from the {Poisson} equation",
journal = j-J-PHYS-A-MATH-THEOR,
volume = "46",
number = "11",
pages = "115201",
month = mar,
year = "2013",
CODEN = "JPAMB5",
DOI = "https://doi.org/10.1088/1751-8113/46/11/115201",
ISSN = "1751-8113 (print), 1751-8121 (electronic)",
ISSN-L = "1751-8113",
MRclass = "35J05 (11Y40 35C05)",
MRnumber = "3030150",
bibdate = "Fri Sep 30 09:24:58 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://adsabs.harvard.edu/abs/2013JPhA...46k5201B;
http://docserver.carma.newcastle.edu.au/1458/;
http://iopscience.iop.org/article/10.1088/1751-8113/46/11/115201;
http://stacks.iop.org/1751-8121/46/i=11/a=115201;
http://www.davidhbailey.com/dhbpapers/PoissonLattice.pdf",
abstract = "In recent times, attention has been directed to the
problem of solving the Poisson equation, either in
engineering scenarios (computational) or in regard to
crystal structure (theoretical). Herein we study a
class of lattice sums that amount to Poisson solutions,
namely the $n$-dimensional forms $ \phi_n(r_1, \dots,
r_n) = \frac {1}{\pi^2} \sum_{ m_1, \dots, m_n {\rm
odd}} \frac { e^{ i \pi (m_1 r_1 + \cdots + m_n
r_n)}}{m_1^2 + \cdots + m_n^2} $. \par
By virtue of striking connections with Jacobi $ \thetav
$-function values, we are able to develop new closed
forms for certain values of the coordinates r$_k$, and
extend such analysis to similar lattice sums. A primary
result is that for rational $x$, $y$, the natural
potential $ \phiv_2 (x, y)$ is $ \frac {1}{\pi } \log
A$ where $A$ is an algebraic number. Various extensions
and explicit evaluations are given. Such work is made
possible by number-theoretical analysis, symbolic
computation and experimental mathematics, including
extensive numerical computations using up to
20,000-digit arithmetic.",
acknowledgement = ack-nhfb,
eid = "115201",
fjournal = "Journal of Physics A: Mathematical and Theoretical",
journal-URL = "http://iopscience.iop.org/1751-8121",
onlinedate = "25 February 2013",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
pagecount = "31",
unique-id = "Bailey:2013:LSA",
}
@InCollection{Bailey:2013:NNP,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Normal numbers and pseudorandom generators",
crossref = "Bailey:2013:CAM",
volume = "50",
pages = "1--18",
year = "2013",
DOI = "https://doi.org/10.1007/978-1-4614-7621-4_1",
MRclass = "11K16 (11A63 11K45)",
MRnumber = "3108419",
MRreviewer = "John H. Loxton",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
series = "Springer Proc. Math. Stat.",
URL = "http://docserver.carma.newcastle.edu.au/1448/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2013:OSD,
author = "D. H. Bailey and J. M. Borwein and Victoria Stodden",
title = "Opinion: Set the default to ``open''",
journal = j-NAMS,
volume = "60",
number = "6",
pages = "679--680",
month = jun # "\slash " # jul,
year = "2013",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibdate = "Sat Aug 13 15:29:13 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.ams.org/notices/201306/rnoti-p679.pdf",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Commentary on reproducibility in Computational and
Experimental Mathematics.",
}
@TechReport{Bailey:2013:PDU,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Pi Day is upon us again and we still do not know if Pi
is normal",
type = "Report",
institution = "Lawrence Berkeley National Laboratory and Centre for
Computer Assisted Research Mathematics and its
Applications (CARMA), University of Newcastle",
address = "Berkeley, CA 94720, USA and Callaghan, NSW 2308,
Australia",
pages = "20",
day = "29",
month = may,
year = "2013",
bibdate = "Fri Aug 12 18:29:28 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
URL = "http://www.carma.newcastle.edu.au/jon/pi-monthly.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Bailey:2013:SDRa,
author = "D. H. Bailey and J. Borwein and R. J. LeVeque and W.
Rider and W. Stein and V. Stodden",
title = "Setting the Default to Reproducible. {Report} on the
{ICERM} Workshop: Reproducibility in Computational and
Experimental Mathematics, {December 10--14, 2012}",
month = jan,
year = "2013",
bibdate = "Tue Aug 16 09:54:58 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint in collaboration with the workshop
participants.",
URL = "http://www.carma.newcastle.edu.au/jon/icerm12.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bauschke:2013:MOB,
author = "Heinz H. Bauschke and Jonathan M. Borwein and Xianfu
Wang and Liangjin Yao",
title = "Monotone operators and ``bigger conjugate''
functions",
journal = j-J-CONVEX-ANAL,
volume = "20",
number = "1",
pages = "143--155",
year = "2013",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "47H05 (47N10 49J53)",
MRnumber = "3086445",
MRreviewer = "Aris Daniilidis",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1477/;
http://www.heldermann.de/JCA/JCA20/JCA201/jca20009.htm",
abstract = "We study a question posed by Stephen Simons in his
2008 monograph involving ``bigger conjugate'' (BC)
functions and the partial infimal convolution. As
Simons demonstrated in his monograph, these function
have been crucial to the understanding and advancement
of the state-of-the-art of harder problems in monotone
operator theory, especially the sum problem. In this
paper, we provide some tools for further analysis of
BC-functions which allow us to answer Simons' problem
in the negative. We are also able to refute a similar
but much harder conjecture which would have generalized
a classical result of Brezis, Crandall and Pazy. Our
work also reinforces the importance of understanding
unbounded skew linear relations to construct monotone
operators with unexpected properties.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Bauschke:2013:MOB",
}
@Article{Borwein:2013:ACR,
author = "J. M. Borwein and G. Li and L. Yao",
title = "Analysis of the convergence rate for the cyclic
projection algorithm applied to basic semi-algebraic
convex sets",
journal = "ArXiv e-prints",
month = apr,
year = "2013",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2013arXiv1304.7965B;
http://docserver.carma.newcastle.edu.au/1508/",
abstract = "In this paper, we study the rate of convergence of the
cyclic projection algorithm applied to finitely many
basic semi-algebraic convex sets. We establish an
explicit convergence rate estimate which relies on the
maximum degree of the polynomials that generate the
basic semi-algebraic convex sets and the dimension of
the underlying space. We achieve our results by
exploiting the algebraic structure of the basic
semi-algebraic convex sets.",
acknowledgement = ack-nhfb,
eprint = "1304.7965",
keywords = "Mathematics - Functional Analysis, Mathematics -
Optimization and Control, Primary 41A25, 90C25,
Secondary 41A50, 90C31",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Unpublished{Borwein:2013:C,
author = "J. M. Borwein",
title = "CARMA",
pages = "70--72",
month = jul,
year = "2013",
bibdate = "Sat Aug 13 15:27:06 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "One of a small selected number of researchers featured
in an issue with a focus on ``Mathematics, Statistics,
Numerical and Computational Mathematics,''
International Innovation.",
URL = "http://www.international-innovation-northamerica.com",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "The URL domain no longer exists, and the reference
from CV.pdf is uncertain.",
}
@Article{Borwein:2013:CDRa,
author = "J. M. Borwein and M. K. Tam",
title = "A Cyclic {Douglas--Rachford} Iteration Scheme",
journal = "ArXiv e-prints",
month = mar,
year = "2013",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2013arXiv1303.1859B;
http://docserver.carma.newcastle.edu.au/1469/",
abstract = "In this paper we present two Douglas--Rachford
inspired iteration schemes which can be applied
directly to $N$-set convex feasibility problems in
Hilbert space. Our main results are weak convergence of
the methods to a point whose nearest point projections
onto each of the $N$ sets coincide. For affine
subspaces, convergence is in norm. Initial results from
numerical experiments, comparing our methods to the
classical (product-space) Douglas--Rachford scheme, are
promising.",
acknowledgement = ack-nhfb,
eprint = "1303.1859",
keywords = "Mathematics - Optimization and Control, Mathematics -
Functional Analysis",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.OC",
}
@Article{Borwein:2013:CDRb,
author = "J. M. Borwein and M. K. Tam",
title = "The Cyclic {Douglas--Rachford} Method for Inconsistent
Feasibility Problems",
journal = "ArXiv e-prints",
month = oct,
year = "2013",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2013arXiv1310.2195B",
abstract = "We analyse the behaviour of the newly introduced
cyclic Douglas--Rachford algorithm for finding a point
in the intersection of a finite number of closed convex
sets. This work considers the case in which the target
intersection set is possibly empty.",
acknowledgement = ack-nhfb,
eprint = "1310.2195",
keywords = "Mathematics - Optimization and Control",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.OC",
}
@Article{Borwein:2013:CFW,
author = "Jonathan M. Borwein and Richard E. Crandall",
title = "Closed forms: what they are and why we care",
journal = j-NAMS,
volume = "60",
number = "1",
pages = "50--65",
month = jan,
year = "2013",
CODEN = "AMNOAN",
DOI = "https://doi.org/10.1090/noti936",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "33F05",
MRnumber = "3052463",
MRreviewer = "Allan J. Mac Leod",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/767/;
http://www.ams.org/notices/201301/rnoti-p50.pdf",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2013:CIL,
author = "Jonathan Borwein and Christopher Maitland and Matthew
Skerritt",
title = "Computation of an improved lower bound to {Giuga}'s
primality conjecture",
journal = j-INTEGERS,
volume = "13",
pages = "Paper No. A67, 14",
year = "2013",
CODEN = "INTEHN",
ISSN = "1553-1732",
MRclass = "11A25",
MRnumber = "3118385",
MRreviewer = "Samuel S. Wagstaff, Jr.",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1511/",
acknowledgement = ack-nhfb,
fjournal = "Integers. Electronic Journal of Combinatorial Number
Theory",
journal-URL = "http://www.degruyter.com/view/j/integ",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2013:CLB,
author = "Jonathan M. Borwein and Matthew Skerritt and
Christopher Maitland",
title = "Computation of a lower bound to {Giuga}'s primality
conjecture",
journal = j-INTEGERS,
volume = "13",
number = "??",
pages = "??--??",
month = "????",
year = "2013",
CODEN = "INTEHN",
DOI = "",
ISSN = "1867-0652 (print), 1867-0660 (electronic)",
bibdate = "Fri Aug 12 08:29:15 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1511/",
acknowledgement = ack-nhfb,
fjournal = "Integers",
journal-URL = "http://www.degruyter.com/view/j/integ",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2013:EWC,
author = "Jonathan Borwein and Michael Rose",
title = "Explainer: what is Chaos Theory",
crossref = "Tressider:2013:EDV",
pages = "??--??",
year = "2013",
bibdate = "Sat Aug 13 15:19:55 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "https://theconversation.com/explainer-what-is-chaos-theory-10620",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Book{Borwein:2013:LST,
author = "J. M. Borwein and M. L. Glasser and R. C. McPhedran
and J. G. Wan and I. J. Zucker",
title = "Lattice Sums: Then and Now",
volume = "150",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xx + 368",
year = "2013",
DOI = "https://doi.org/10.1017/CBO9781139626804",
ISBN = "1-107-03990-8",
ISBN-13 = "978-1-107-03990-2",
MRclass = "11Mxx (11H06 11K99 11Lxx 11P21 82D25)",
MRnumber = "3135109",
MRreviewer = "S. L. Kalla",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "With a foreword by Helaman Ferguson and Claire
Ferguson.",
series = "Encyclopedia of Mathematics and its Applications",
URL = "http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139626804",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
tableofcontents = "Frontmatter / i--iv \\
Dedication / v--vi \\
Contents / vii--x \\
Foreword by Helaman and Claire Ferguson / xi--xvi \\
Preface / xvii--xx \\
1: Lattice sums / 1--86 \\
2: Convergence of lattice sums and Madelung's constant
/ 87--124 \\
3: Angular lattice sums / 125--156 \\
4: Use of Dirichlet series with complex characters /
157--185 \\
5: Lattice sums and Ramanujan's modular equations /
186--201 \\
6: Closed-form evaluations of three- and
four-dimensional sums / 202--225 \\
7: Electron sums / 226--246 \\
8: Madelung sums in higher dimensions / 247--293 \\
9: Seventy years of the Watson integrals / 294--323 \\
Appendix / 324--349 \\
References / 350--363 \\
Index / 364--368",
}
@Article{Borwein:2013:LSW,
author = "D. Borwein and J. M. Borwein and A. Straub",
title = "On lattice sums and {Wigner} limits",
journal = "ArXiv e-prints",
month = oct,
year = "2013",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2013arXiv1310.1423B;
http://docserver.carma.newcastle.edu.au/1509/",
abstract = "Wigner limits are given formally as the difference
between a lattice sum, associated to a positive
definite quadratic form, and a corresponding multiple
integral. To define these limits, which arose in work
of Wigner on the energy of static electron lattices, in
a mathematically rigorous way one commonly truncates
the lattice sum and the corresponding integral and
takes the limit along expanding hypercubes or other
regular geometric shapes. We generalize the known
mathematically rigorous two and three dimensional
results regarding Wigner limits, as laid down in
[Analysis of certain lattice sums, D. Borwein, J. M.
Borwein, and R. Shail, 1989], to integer lattices of
arbitrary dimension. In doing so, we also resolve a
problem posed in Chapter 7 of [Lattice Sums: Then and
Now, J. M. Borwein, L. Glasser, R. McPhedran, J. G.
Wan, and I. J. Zucker, 2013]. For the sake of clarity,
we begin by considering the simpler case of cubic
lattice sums first, before treating the case of
arbitrary quadratic forms. We also consider limits
taken along expanding hyperballs with respect to
general norms, and connect with classical topics such
as Gauss's circle problem. An appendix is included to
recall certain properties of Epstein zeta functions
that are either used in the paper or serve to provide
perspective.",
acknowledgement = ack-nhfb,
eprint = "1310.1423",
keywords = "Mathematical Physics, Mathematics - Classical Analysis
and ODEs, Mathematics - Number Theory",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math-ph",
}
@Article{Borwein:2013:MMS,
author = "Jonathan M. Borwein and Armin Straub",
title = "{Mahler} measures, short walks and log-sine
integrals",
journal = j-THEOR-COMP-SCI,
volume = "479",
pages = "4--21",
year = "2013",
CODEN = "TCSCDI",
DOI = "https://doi.org/10.1016/j.tcs.2012.10.025",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
MRclass = "11R06 (11M32 33E20 60G50 68W30)",
MRnumber = "3034554",
MRreviewer = "Kevin G. Hare",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Symbolic-Numerical Algorithms.",
URL = "http://docserver.carma.newcastle.edu.au/1383/;
http://www.sciencedirect.com/science/article/pii/S0304397512009462",
abstract = "The Mahler measure of a polynomial in several
variables has been a subject of much study over the
past thirty years --- very few closed forms are proven
but more are conjectured. In the case of multiple
Mahler measures more tractable but interesting families
exist. Using values of log-sine integrals we provide
systematic evaluations of various higher and multiple
Mahler measures. The evaluations in terms of log-sine
integrals become particularly useful in light of the
fact that log-sine integrals may be automatically
reexpressed as polylogarithmic values. We present this
correspondence along with related generating functions
for log-sine integrals. Our initial interest in
considering Mahler measures stems from a study of
uniform random walks in the plane as first introduced
by Pearson. The main results on the moments of the
distance traveled by an n -step walk, as well as the
corresponding probability density functions, are
reviewed. It is the derivative values of the moments
that are Mahler measures. This work would be impossible
without very extensive symbolic and numeric
computations. It also makes frequent use of the new
NIST Handbook of Mathematical Functions and similar
tools. Our intention is to show off the interplay
between numeric and symbolic computing while exploring
the three mathematical topics in the title.",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2013:MOE,
author = "Jonathan M. Borwein and Regina S. Burachik and
Liangjin Yao",
title = "Monotone operators without enlargements",
crossref = "Bailey:2013:CAM",
volume = "50",
pages = "79--103",
year = "2013",
DOI = "https://doi.org/10.1007/978-1-4614-7621-4_5",
MRclass = "47H05",
MRnumber = "3108423",
MRreviewer = "Heinz H. Bauschke",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Springer Proc. Math. Stat.",
URL = "http://docserver.carma.newcastle.edu.au/1447/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2013:MSM,
author = "Jonathan M. Borwein and Liangjin Yao",
title = "Maximality of the sum of a maximally monotone linear
relation and a maximally monotone operator",
journal = j-SET-VALUED-VAR-ANAL,
volume = "21",
number = "4",
pages = "603--616",
year = "2013",
DOI = "https://doi.org/10.1007/s11228-013-0259-y",
ISSN = "1877-0533 (print), 1877-0541 (electronic)",
ISSN-L = "1877-0533",
MRclass = "47H05 (47A05 47B65 90C25)",
MRnumber = "3134450",
MRreviewer = "Radu Ioan Bo{\c{t}}",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1212.4266;
http://docserver.carma.newcastle.edu.au/1483/",
abstract = "The most famous open problem in Monotone Operator
Theory concerns the maximal monotonicity of the sum of
two maximally monotone operators provided that
Rockafellar's constraint qualification holds. In this
paper, we prove the maximal monotonicity of A + B
provided that A, B are maximally monotone and A is a
linear relation, as soon as Rockafellar's constraint
qualification holds: . Moreover, A + B is of type
(FPV).",
acknowledgement = ack-nhfb,
ajournal = "Set-Valued Var. Anal.",
fjournal = "Set-Valued and Variational Analysis",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Borwein:2013:MSM",
}
@Article{Borwein:2013:NCR,
author = "J. M. Borwein and B. Sims and M. K. Tam",
title = "Norm Convergence of Realistic Projection and
Reflection Methods",
journal = "ArXiv e-prints",
month = dec,
year = "2013",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2013arXiv1312.7323B;
http://docserver.carma.newcastle.edu.au/1493/",
abstract = "We provide sufficient conditions for norm convergence
of various projection and reflection methods, as well
as giving limiting examples regarding convergence
rates.",
acknowledgement = ack-nhfb,
eprint = "1312.7323",
keywords = "Mathematics - Optimization and Control",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.OC",
}
@Article{Borwein:2013:STMa,
author = "J. M. Borwein and L. Yao",
title = "Sum theorems for maximally monotone operators of type
({FPV})",
journal = "ArXiv e-prints",
month = may,
year = "2013",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2013arXiv1305.6691B;
http://docserver.carma.newcastle.edu.au/1503/",
abstract = "The most important open problem in Monotone Operator
Theory concerns the maximal monotonicity of the sum of
two maximally monotone operators provided that the
classical Rockafellar's constraint qualification holds.
In this paper, we establish the maximal monotonicity of
$ A + B $ provided that $A$ and $B$ are maximally
monotone operators such that $ \sta (\dom A) \cap \inte
\dom B \neq \varnothing $, and $A$ is of type (FPV). We
show that when also $ \dom A$ is convex, the sum
operator: $ A + B$ is also of type (FPV). Our result
generalizes and unifies several recent sum theorems.",
acknowledgement = ack-nhfb,
eprint = "1305.6691",
keywords = "Mathematics - Functional Analysis, Primary 47H05,
Secondary 49N15, 52A41, 90C25",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Article{Borwein:2013:STMb,
author = "Jonathan M. Borwein and Liangjin Yao",
title = "Structure theory for maximally monotone operators with
points of continuity",
journal = j-J-OPT-THEORY-APPL,
volume = "157",
number = "1",
pages = "1--24",
year = "2013",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/s10957-012-0162-y",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "47H05 (46N10)",
MRnumber = "3034040",
MRreviewer = "Radu Ioan Bo{\c{t}}",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1203.1101;
http://docserver.carma.newcastle.edu.au/1375/",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2013:TSF,
author = "Jonathan M. Borwein and Armin Straub and James Wan",
title = "Three-Step and Four-Step Random Walk Integrals",
journal = j-EXP-MATH,
volume = "22",
number = "1",
pages = "1--14",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2013.748379",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "60G50 (33C20 33E05)",
MRnumber = "3038778",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://docserver.carma.newcastle.edu.au/763/",
abstract = "We investigate the moments of 3-step and 4-step
uniform random walks in the plane. In particular, we
further analyze a formula conjectured in [Borwein etal.
11] expressing 4-step moments in terms of 3-step
moments. Diverse related results including
hypergeometric and elliptic closed forms for W-4(+/- 1)
are given, and two new conjectures are recorded.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Straub, Armin/0000-0001-6802-6053",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Borwein:2013:TSF",
}
@Article{Borwein:2013:VMP,
author = "Jonathan M. Borwein and Qiji J. Zhu",
title = "Variational methods in the presence of symmetry",
journal = j-ADV-NONLINEAR-ANAL,
volume = "2",
number = "3",
pages = "271--307",
year = "2013",
DOI = "https://doi.org/10.1515/anona-2013-1001",
ISSN = "2191-9496 (print), 2191-950X (electronic)",
ISSN-L = "2191-9496",
MRclass = "49J53 (58E30)",
MRnumber = "3089743",
MRreviewer = "Nicolas Hadjisavvas",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1514/",
abstract = "The purpose of this paper is to survey and to provide
a unified framework to connect a diverse group of
results, currently scattered in the literature, that
can be usefully viewed as consequences of applying
variational methods to problems involving symmetry.
Here, variational methods refer to mathematical
treatment by way of constructing an appropriate action
function whose critical points-or saddle
points-correspond to or contain the desired
solutions.",
acknowledgement = ack-nhfb,
ajournal = "Adv. Nonlinear Anal.",
fjournal = "Advances in Nonlinear Analysis",
journal-URL = "http://www.degruyter.com/view/j/anona",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "Borwein:2013:VMP",
}
@InProceedings{Piantadosi:2013:GSR,
author = "Julia Piantadosi and Phil Howlett and Jonathan Borwein
and John Henstridge",
title = "Generation of simulated rainfall data at different
time-scales",
crossref = "Bean:2013:MDM",
pages = "??--??",
year = "2013",
bibdate = "Sat Aug 13 15:52:53 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1381/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Piantadosi:2013:MSS,
author = "Julia Piantadosi and Phil Howlett and Jonathan
Borwein",
title = "Modelling and simulation of seasonal rainfall",
type = "Report",
institution = "MODSIM/ASOR",
address = "Adelaide, SA, Australia",
pages = "??",
month = dec,
year = "2013",
bibdate = "Sat Aug 13 15:15:53 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1453/",
acknowledgement = ack-nhfb,
keywords = "Australian Society for Operations Research (ASOR)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Stodden:2013:SDR,
author = "Victoria Stodden and Jonathan Borwein and David H.
Bailey",
title = "``{Setting} the Default to Reproducible'' in
Computational Science Research",
journal = j-SIAM-NEWS,
volume = "46",
number = "5",
pages = "4--6",
month = jun,
year = "2013",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Fri Sep 02 07:29:13 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "https://sinews2.siam.org/DetailsPage/tabid/607/ArticleID/351/%E2%80%9CSetting-the-Default-to-Reproducible%E2%80%9D-in-Computational-Science-Research.aspx",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{AragonArtacho:2014:DRF,
author = "Francisco J. {Arag{\'o}n Artacho} and Jonathan M.
Borwein and Matthew K. Tam",
title = "{Douglas--Rachford} Feasibility Methods for Matrix
Completion Problems",
journal = j-ANZIAM-J,
volume = "55",
number = "4",
pages = "299--326",
month = apr,
year = "2014",
CODEN = "AJNOA2",
DOI = "https://doi.org/10.1017/S1446181114000145",
ISSN = "1446-1811 (print), 1446-8735 (electronic)",
ISSN-L = "1446-1811",
MRclass = "47J25 (15A83 65K05 90C59)",
MRnumber = "3257300",
MRreviewer = "Heinz H. Bauschke",
bibdate = "Fri Sep 30 10:50:24 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1308.4243;
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9347336",
abstract = "In this paper, we give general recommendations for
successful application of the Douglas--Rachford
reflection method to convex and nonconvex real matrix
completion problems. These guidelines are demonstrated
by various illustrative examples.",
acknowledgement = ack-nhfb,
fjournal = "The ANZIAM Journal. The Australian \& New Zealand
Industrial and Applied Mathematics Journal",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Aragon Artacho, Francisco Javier/C-2531-2012;
Tam, Matthew/G-8127-2013",
unique-id = "ISI:000343750400001",
}
@Article{AragonArtacho:2014:RRD,
author = "Fran {Arag{\'o}n Artacho} and Jonathan M. Borwein and
Matthew Tam",
title = "Recent Results on {Douglas--Rachford} Methods for
Combinatorial Optimization Problems",
journal = j-J-OPT-THEORY-APPL,
volume = "163",
number = "1",
pages = "1--30",
month = oct,
year = "2014",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/s10957-013-0488-0",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "47J25 (90C27)",
MRnumber = "3260973",
MRreviewer = "Heinz H. Bauschke",
bibdate = "Fri Aug 12 08:22:52 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1305.2657;
http://docserver.carma.newcastle.edu.au/1510/",
abstract = "We discuss recent positive experiences applying convex
feasibility algorithms of Douglas--Rachford type to
highly combinatorial and far from convex problems.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Aragon Artacho, Francisco
Javier/0000-0002-2445-8011",
researcherid-numbers = "Tam, Matthew/G-8127-2013; Aragon Artacho,
Francisco Javier/C-2531-2012",
unique-id = "ISI:000342442600001",
}
@Article{Artacho:2014:ACA,
author = "Francisco J. Arag{\'o}n Artacho and Jonathan M.
Borwein and Victoria Mart{\'{\i}}n-M{\'a}rquez and
Liangjin Yao",
title = "Applications of convex analysis within mathematics",
journal = j-MATH-PROG,
volume = "148",
number = "1--2",
pages = "49--88",
month = dec,
year = "2014",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/s10107-013-0707-3",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "47N10 (47A06 47B65 47H05 90C25)",
MRnumber = "3274845",
MRreviewer = "Aris Daniilidis",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special volume of Serdica Mathematical Journal in
honour of Asen Dontchev.",
URL = "http://arxiv.org/abs/1302.1978;
http://docserver.carma.newcastle.edu.au/1513/",
abstract = "In this paper, we study convex analysis and its
theoretical applications. We first apply important
tools of convex analysis to Optimization and to
Analysis. We then show various deep applications of
convex analysis and especially infimal convolution in
Monotone Operator Theory. Among other things, we
recapture the Minty surjectivity theorem in Hilbert
space, and present a new proof of the sum theorem in
reflexive spaces. More technically, we also discuss
autoconjugate representers for maximally monotone
operators. Finally, we consider various other
applications in mathematical analysis.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming. A Publication of the
Mathematical Optimization Society",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011
Martin Marquez, Victoria/0000-0002-8963-9825",
researcherid-numbers = "Martin-Marquez, Victoria/H-1047-2015; Aragon
Artacho, Francisco Javier/C-2531-2012",
unique-id = "ISI:000344809700003",
}
@Article{Artacho:2014:RRD,
author = "Francisco J. Arag{\'o}n Artacho and Jonathan M.
Borwein and Matthew K. Tam",
title = "Recent results on {Douglas--Rachford} methods for
combinatorial optimization problems",
journal = j-J-OPT-THEORY-APPL,
volume = "163",
number = "1",
pages = "1--30",
year = "2014",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/s10957-013-0488-0",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "47J25 (90C27)",
MRnumber = "3260973",
MRreviewer = "Heinz H. Bauschke",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1510/",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2014:ASL,
author = "David H. Bailey and Jonathan M. Borwein and Alexander
D. Kaiser",
title = "Automated simplification of large symbolic
expressions",
journal = j-J-SYMBOLIC-COMP,
volume = "60",
number = "??",
pages = "120--136",
year = "2014",
CODEN = "JSYCEH",
DOI = "https://doi.org/10.1016/j.jsc.2013.09.001",
ISSN = "0747-7171 (print), 1095-855x (electronic)",
ISSN-L = "0747-7171",
MRclass = "68W30",
MRnumber = "3131383",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/mathematica.bib",
URL = "http://docserver.carma.newcastle.edu.au/1456/;
http://www.sciencedirect.com/science/article/pii/S074771711300117X",
abstract = "We present a set of algorithms for automated
simplification of symbolic constants of the form
Sigma(i)alpha(i)chi(i), with a; rational and x;
complex. The included algorithms, called SimplifySum(2)
and implemented in Mathematica, remove redundant terms,
attempt to make terms and the full expression real, and
remove terms using repeated application of the
multipair PSLQ integer relation detection algorithm.
Also included are facilities for making substitutions
according to user-specified identities. We illustrate
this toolset by giving some real-world examples of its
usage, including one, for instance, where the tool
reduced a symbolic expression of approximately 100000
characters in size enough to enable manual manipulation
to one with just four simple terms.",
abstract = "We present a set of algorithms for automated
simplification of symbolic constants of the form $
\sum_i \alpha_i x_i $ with $ \alpha_i $ rational and $
x_i $ complex. The included algorithms, called
SimplifySum (available from
\url{https://github.com/alexkaiser/SimplifySum}), and
implemented in Mathematica, remove redundant terms,
attempt to make terms and the full expression real, and
remove terms using repeated application of the
multipair PSLQ integer relation detection algorithm.
Also included are facilities for making substitutions
according to user-specified identities. We illustrate
this toolset by giving some real-world examples of its
usage, including one, for instance, where the tool
reduced a symbolic expression of approximately 100\,000
characters in size enough to enable manual manipulation
to one with just four simple terms.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "Computer algebra systems; Error correction;
Experimental mathematics; Simplification",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000328661000009",
}
@Article{Bailey:2014:CTE,
author = "David H. Bailey and Jonathan M. Borwein and Richard E.
Crandall",
title = "Computation and theory of extended
{Mordell--Tornheim--Witten} sums",
journal = j-MATH-COMPUT,
volume = "83",
number = "288",
pages = "1795--1821",
month = jul,
year = "2014",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-2014-02768-3",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33B15 (11M32 33F05 65D20 65D30)",
MRnumber = "3194130",
MRreviewer = "Mehdi Hassani",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.ams.org/mcom/2014-83-288;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://docserver.carma.newcastle.edu.au/1459/;
http://www.ams.org/journals/mcom/2014-83-288/S0025-5718-2014-02768-3;
http://www.ams.org/journals/mcom/2014-83-288/S0025-5718-2014-02768-3/S0025-5718-2014-02768-3.pdf",
abstract = "We consider some fundamental generalized
Mordell--Tornheim--Witten (MTW) zeta-function values
along with their derivatives, and explore connections
with multiple-zeta values (MZVs). To achieve this, we
make use of symbolic integration, high precision
numerical integration, and some interesting
combinatorics and special-function theory. Our original
motivation was to represent unresolved constructs such
as Eulerian log-gamma integrals. We are able to resolve
all such integrals in terms of an MTW basis. We also
present, for a substantial subset of MTW values,
explicit closed-form expressions. In the process, we
significantly extend methods for high-precision
numerical computation of polylogarithms and their
derivatives with respect to order.",
acknowledgement = ack-nhfb,
article-number = "PII S 0025-5718(2014)02768-3",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000337230000010",
}
@TechReport{Bailey:2014:OCC,
author = "David H. Bailey and Jonathan M. Borwein and Olga
Caprotti and Ursula Martin and Bruno Salvy and Michela
Taufer",
title = "Opportunities and Challenges in 21st Century
Mathematical Computation: {ICERM} Workshop Report,
{July 10--14, 2014}",
institution = "????",
address = "????",
pages = "18",
day = "28",
month = aug,
year = "2014",
bibdate = "Tue Aug 16 09:53:29 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint in collaboration with the workshop
participants.",
URL = "http://www.davidhbailey.com/dhbpapers/ICERM-2014.pdf",
abstract = "``Experimental mathematics'' has emerged in the past
25 years or so to become a competitive paradigm for
research in the mathematical sciences. A workshop held
at the Institute for Computational and Experimental
Research in Mathematics (ICERM), July 21--25, 2014,
explored emerging challenges of experimental
mathematics in the rapidly changing era of modern
computer technology. This report summarizes the
workshop findings",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2014:OCE,
author = "D. H. Bailey and J. M. Borwein",
title = "Opportunities and Challenges in Experimental
Mathematics",
journal = j-SIAM-NEWS,
volume = "47",
number = "9",
pages = "4, 8",
month = "????",
year = "2014",
DOI = "",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Sat Aug 13 13:56:34 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/icerm-summ.pdf",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2014:PDUa,
author = "David H. Bailey and Jonathan Borwein",
title = "{Pi Day} is upon us again and we still do not know if
pi is normal",
journal = j-AMER-MATH-MONTHLY,
volume = "121",
number = "3",
pages = "191--206",
month = mar,
year = "2014",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/amer.math.monthly.121.03.191",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11K16 (11A63)",
MRnumber = "3168990",
MRreviewer = "Manfred G. Madritsch",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/10.4169/amermathmont.121.issue-03;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
note = "Chinese translation in Mathematical Advances in
Translation (Chinese Academy of Science) [metadata
unknown].",
URL = "http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.121.03.191.pdf",
abstract = "The digits of pi have intrigued both the public and
research mathematicians from the beginning of time.
This article briefly reviews the history of this
venerable constant, and then describes some recent
research on the question of whether pi is normal, or,
in other words,. whether its digits are statistically
random in a specific sense.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000332922000001",
}
@Article{Bailey:2014:PDUb,
author = "David H. Bailey and Jonathan M. Borwein",
title = "{Pi Day} is upon us again, and we still do not know if
pi is normal",
journal = "Mathematical Advances of Translation",
volume = "33",
number = "??",
pages = "222--235",
month = "????",
year = "2014",
bibdate = "Fri Sep 30 08:59:40 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Chinese translation of \cite{Bailey:2014:PDUa}.",
acknowledgement = ack-nhfb,
language = "Chinese",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "TO DO: Find ISSN of this journal; it is not found in
major library catalogs.",
}
@Article{Bailey:2014:PMF,
author = "David H. Bailey and Jonathan M. Borwein and Marcos
{L{\'o}pez de Prado} and Qiji Jim Zhu",
title = "Pseudo-mathematics and financial charlatanism: the
effects of backtest overfitting on out-of-sample
performance",
journal = j-NAMS,
volume = "61",
number = "5",
pages = "458--471",
month = may,
year = "2014",
CODEN = "AMNOAN",
DOI = "https://doi.org/10.1090/noti1105",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "91G70 (62P05 91G80)",
MRnumber = "3203237",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1506/;
http://www.ams.org/notices/201405/rnoti-p458.pdf",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2014:RTP,
author = "D. H. Bailey and J. M. Borwein",
title = "The recent trademarking of Pi: a troubling precedent",
journal = j-NAMS,
volume = "61",
number = "10",
pages = "121--124",
month = nov,
year = "2014",
CODEN = "AMNOAN",
DOI = "",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibdate = "Fri Aug 12 07:48:44 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/id/eprint/1501;
http://www.ams.org/notices/201410/rnoti-p1224.pdf",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2014:ACR,
author = "Jonathan M. Borwein and Guoyin Li and Liangjin Yao",
title = "Analysis of the convergence rate for the cyclic
projection algorithm applied to basic semialgebraic
convex sets",
journal = j-SIAM-J-OPT,
volume = "24",
number = "1",
pages = "498--527",
year = "2014",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/130919052",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
MRclass = "47J25 (90C25 90C31)",
MRnumber = "3180867",
MRreviewer = "Francisco J. Arag{\'o}n Artacho",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1304.7965;
http://docserver.carma.newcastle.edu.au/1508/",
abstract = "In this paper, we study the rate of convergence of the
cyclic projection algorithm applied to finitely many
basic semialgebraic convex sets. We establish an
explicit convergence rate estimate which relies on the
maximum degree of the polynomials that generate the
basic semialgebraic convex sets and the dimension of
the underlying space. We achieve our results by
exploiting the algebraic structure of the basic
semialgebraic convex sets.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
ORCID-numbers = "Li, Guoyin/0000-0002-2099-7974",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Li, Guoyin/B-7866-2009",
unique-id = "ISI:000333761700020",
}
@Article{Borwein:2014:CDR,
author = "Jonathan M. Borwein and Matthew K. Tam",
title = "A cyclic {Douglas--Rachford} iteration scheme",
journal = j-J-OPT-THEORY-APPL,
volume = "160",
number = "1",
pages = "1--29",
year = "2014",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/s10957-013-0381-x",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "47J25 (90C25 90C48)",
MRnumber = "3149115",
MRreviewer = "Francisco J. Arag{\'o}n Artacho",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1303.1859;
http://docserver.carma.newcastle.edu.au/1469/",
abstract = "In this paper, we present two Douglas--Rachford
inspired iteration schemes which can be applied
directly to N-set convex feasibility problems in
Hilbert space. Our main results are weak convergence of
the methods to a point whose nearest point projections
onto each of the N sets coincide. For affine subspaces,
convergence is in norm. Initial results from numerical
experiments, comparing our methods to the classical
(product-space) Douglas--Rachford scheme, are
promising.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Tam, Matthew/G-8127-2013",
unique-id = "ISI:000330586300001",
}
@Article{Borwein:2014:CZD,
author = "Jonathan M. Borwein and Regina S. Burachik and
Liangjin Yao",
title = "Conditions for zero duality gap in convex
programming",
journal = j-J-NONLINEAR-CONVEX-ANAL,
volume = "15",
number = "1",
pages = "167--190",
year = "2014",
ISSN = "1345-4773 (print), 1880-5221 (electronic)",
ISSN-L = "1345-4773",
MRclass = "49J52 (49N15 90C25 90C46)",
MRnumber = "3184756",
MRreviewer = "Rafa{\l} K. Goebel",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1211.49533;
http://docserver.carma.newcastle.edu.au/1465/",
abstract = "We introduce and study a new dual condition which
characterizes zero duality gap in nonsmooth convex
optimization. We prove that our condition is less
restrictive than all existing constraint
qualifications, including the closed epigraph
condition. Our dual condition was inspired by, and is
less restrictive than, the so-called Bertsekas'
condition for monotropic programming problems. We give
several corollaries of our result and special cases as
applications. We pay special attention to the
polyhedral and sublinear cases, and their implications
in convex optimization.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Nonlinear and Convex Analysis. An
International Journal",
journal-URL = "http://www.ybook.co.jp/jnca.html",
ORCID-numbers = "Burachik, Regina/0000-0003-1332-6213",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Burachik, Regina/A-9859-2008",
unique-id = "ISI:000331342600012",
}
@Article{Borwein:2014:DNS,
author = "David Borwein and Jonathan Borwein",
title = "Deriving New Sinc Results from Old",
journal = j-AMER-MATH-MONTHLY,
volume = "121",
number = "8",
pages = "700--705",
month = oct,
year = "2014",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/amer.math.monthly.121.08.700",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "52A38 (33B10 42A99 51M25)",
MRnumber = "3318479",
MRreviewer = "Victor V. Pambuccian",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.jstor.org/stable/10.4169/amermathmont.121.issue-08;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib",
URL = "http://docserver.carma.newcastle.edu.au/1502/;
http://www.jstor.org/stable/10.4169/amer.math.monthly.121.08.700",
abstract = "From previously established results in [2], we develop
a simple proof of Keith Ball's expression in [1] for
the volume of the intersection of an (n -
1)-dimensional hyperplane with an n-dimensional cube,
as well as a simple proof of the formula given by Frank
and Riede in [5] for that volume.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000343376800004",
}
@InCollection{Borwein:2014:ECVa,
author = "Jonathan M. Borwein",
title = "Experimental Computation and Visual Theorems",
crossref = "Hong:2014:MSI",
pages = "1--8",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-662-44199-2_1",
MRclass = "46-02 (65-02 68U01)",
MRnumber = "3334735",
MRreviewer = "Matti Vuorinen",
bibdate = "Sat Aug 13 13:54:11 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2014:LAE,
author = "Jonathan M. Borwein",
title = "The Life of $ \pi $: From {Archimedes} to {ENIAC} and
Beyond",
crossref = "Sidoli:2014:ATB",
pages = "531--561",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-642-36736-6_24",
MRclass = "01A20 (11Y60)",
MRnumber = "3203895",
MRreviewer = "Leo Corry",
bibdate = "Sat Aug 13 15:11:22 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Extended and updated version of
\cite{Borwein:2008:VPG}.",
URL = "http://www.carma.newcastle.edu.au/~jb616/pi-2010.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2014:LKMa,
author = "Jonathan M. Borwein and Yann Bugeaud and Michael
Coons",
title = "The legacy of {Kurt Mahler}",
journal = j-EUR-MATH-SOC-NEWSL,
volume = "91",
pages = "19--23",
month = mar,
year = "2014",
ISSN = "1027-488X",
ISSN-L = "1027-488X",
MRclass = "01A70",
MRnumber = "3202400",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.ems-ph.org/journals/journal.php?jrn=news",
acknowledgement = ack-nhfb,
fjournal = "European Mathematical Society. Newsletter",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxpages = "12--16",
}
@Article{Borwein:2014:LKMb,
author = "Jonathan M. Borwein and Yann Bugeaud and Michael
Coons",
title = "The legacy of {Kurt Mahler}",
journal = j-AUSTRALIAN-MATH-SOC-GAZ,
volume = "41",
number = "1",
pages = "11--21",
month = mar,
year = "2014",
ISSN = "0311-0729 (print), 1326-2297 (electronic)",
ISSN-L = "0311-0729",
MRclass = "01A70",
MRnumber = "3221622",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.austms.org.au/Publ/Gazette/2014/Mar14/Mahler.pdf",
ZMnumber = "1308.01014",
acknowledgement = ack-nhfb,
fjournal = "The Australian Mathematical Society. Gazette",
journal-URL = "http://www.austms.org.au/gazette",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2014:LPA,
author = "Jonathan M. Borwein",
title = "The Life of Pi: From {Archimedes} to {ENIAC} and
Beyond",
crossref = "Sidoli:2014:ATB",
pages = "531--561",
year = "2014",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
URL = "http://docserver.carma.newcastle.edu.au/265/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2014:LSW,
author = "David Borwein and Jonathan M. Borwein and Armin
Straub",
title = "On lattice sums and {Wigner} limits",
journal = j-J-MATH-ANAL-APPL,
volume = "414",
number = "2",
pages = "489--513",
year = "2014",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/j.jmaa.2014.01.008",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "11D09 (11H06 11L03)",
MRnumber = "3167976",
MRreviewer = "Ross C. McPhedran",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1310.1423;
http://docserver.carma.newcastle.edu.au/1509/;
http://www.sciencedirect.com/science/article/pii/S0022247X14000134",
abstract = "Wigner limits are given formally as the difference
between a lattice sum, associated to a positive
definite quadratic form, and a corresponding multiple
integral. To define these limits, which arose in work
of Wigner on the energy of static electron lattices, in
a mathematically rigorous way one commonly truncates
the lattice sum and the corresponding integral and
takes the limit along expanding hypercubes or other
regular geometric shapes. We generalize the known
mathematically rigorous two- and three-dimensional
results regarding Wigner limits, as laid down in [3],
to integer lattices of arbitrary dimension. In doing
so, we also resolve a problem posed in [6, Chapter 7].
For the sake of clarity, we begin by considering the
simpler case of cubic lattice sums first, before
treating the case of arbitrary quadratic forms. We also
consider limits taken along expanding hyperballs with
respect to general norms, and connect with classical
topics such as Gauss's circle problem. Appendix A is
included to recall certain properties of Epstein zeta
functions that are either used in the paper or serve to
provide perspective.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
keywords = "Analytic continuation; Lattice sums; Wigner electron
sums",
ORCID-numbers = "Straub, Armin/0000-0001-6802-6053",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000334651500001",
}
@Article{Borwein:2014:LTI,
author = "Jonathan M. Borwein and Liangjin Yao",
title = "{Legendre}-type integrands and convex integral
functions",
journal = j-J-CONVEX-ANAL,
volume = "21",
number = "1",
pages = "261--288",
year = "2014",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "46B20 (47H05 49K10)",
MRnumber = "3235316",
MRreviewer = "Jes{\'u}s Ferrer",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1208.5217;
http://docserver.carma.newcastle.edu.au/1455/;
http://www.heldermann.de/JCA/JCA21/JCA211/jca21015.htm",
abstract = "In this paper, we study the properties of integral
functionals induced on L-E(1)(S, mu) by closed convex
functions on a Euclidean space E. We give sufficient
conditions for such integral functions to be strongly
rotund (well-posed). We show that in this generality
functions such as the Boltzmann-Shannon entropy and the
Fermi-Dirac entropy are strongly rotund. We also study
convergence in measure and give various limiting
counterexamples.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000337215600015",
}
@Article{Borwein:2014:MSS,
author = "Jonathan Borwein and Phil Howlett and Julia
Piantadosi",
title = "Modelling and Simulation of Seasonal Rainfall Using
the Principle of Maximum Entropy",
journal = j-ENTROPY,
volume = "16",
number = "2",
pages = "747--769",
month = feb,
year = "2014",
CODEN = "ENTRFG",
DOI = "https://doi.org/10.3390/e16020747",
ISSN = "1099-4300",
ISSN-L = "1099-4300",
MRclass = "62P12 (62H05)",
MRnumber = "3177597",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2014Entrp..16..747B;
http://docserver.carma.newcastle.edu.au/1507/;
http://www.mdpi.com/1099-4300/16/",
abstract = "We use the principle of maximum entropy to propose a
parsimonious model for the generation of simulated
rainfall during the wettest three-month season at a
typical location on the east coast of Australia. The
model uses a checkerboard copula of maximum entropy to
model the joint probability distribution for total
seasonal rainfall and a set of two-parameter gamma
distributions to model each of the marginal monthly
rainfall totals. The model allows us to match the grade
correlation coefficients for the checkerboard copula to
the observed Spearman rank correlation coefficients for
the monthly rainfalls and, hence, provides a model that
correctly describes the mean and variance for each of
the monthly totals and also for the overall seasonal
total. Thus, we avoid the need for a posteriori
adjustment of simulated monthly totals in order to
correctly simulate the observed seasonal statistics.
Detailed results are presented for the modelling and
simulation of seasonal rainfall in the town of Kempsey
on the mid-north coast of New South Wales. Empirical
evidence from extensive simulations is used to validate
this application of the model. A similar analysis for
Sydney is also described.",
acknowledgement = ack-nhfb,
fjournal = "Entropy",
fjournal = "Entropy. An International and Interdisciplinary
Journal of Entropy and Information Studies",
ORCID-numbers = "Howlett, Phil/0000-0003-2382-8137",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000334246400007",
}
@Book{Borwein:2014:NFI,
author = "Jonathan M. Borwein and Alfred Jacobus van der Poorten
and Jeffrey Outlaw Shallit and Wadim Zudilin",
title = "Neverending Fractions: an Introduction to Continued
Fractions",
volume = "23",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "x + 212",
year = "2014",
DOI = "https://doi.org/10.1017/CBO9780511902659",
ISBN = "0-521-18649-8",
ISBN-13 = "978-0-521-18649-0",
LCCN = "QA295 .B667 2014",
MRclass = "11A55 (11J70 40-01 40A15)",
MRnumber = "3468515",
bibdate = "Thu Jun 12 08:53:05 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
series = "Australian Mathematical Society lecture series",
URL = "http://docserver.carma.newcastle.edu.au/1722/;
http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511902659",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "Continued fractions; Processes, Infinite; Fractions",
tableofcontents = "Preface \\
1. Some preliminaries from number theory \\
2. Continued fractions, as they are \\
3. Metric theory of continued fractions \\
4. Quadratic irrationals through a magnifier \\
5. Hyperelliptic curves and Somos sequences \\
6. From folding to Fibonacci \\
7. The integer part of $q \alpha + \beta$ \\
8. The Erd{\H{o}}s--Moser equation \\
9. Irregular continued fractions \\
Appendix. Selected continued fractions \\
Bibliography \\
Index",
}
@InProceedings{Borwein:2014:RMIa,
author = "J. M. Borwein and M. K. Tam",
booktitle = "{CIMPA school Generalized Nash Equilibrium Problems,
Bilevel programming and MPEC New Delhi, India, December
2012}",
title = "Reflection methods for inverse problems with
applications to protein conformation determination",
publisher = "????",
address = "????",
pages = "??--??",
year = "2014",
DOI = "",
ISBN = "",
ISBN-13 = "",
LCCN = "",
bibdate = "Fri Aug 12 18:37:52 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1678/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2014:RMIb,
author = "J. M. Borwein and M. K. Tam",
title = "Reflection methods for inverse problems with
application to protein conformation determination",
journal = "ArXiv e-prints",
month = aug,
year = "2014",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2014arXiv1408.4213B;
http://docserver.carma.newcastle.edu.au/1678/",
abstract = "The Douglas--Rachford reflection method is a general
purpose algorithm useful for solving the feasibility
problem of finding a point in the intersection of
finitely many sets. In this chapter we demonstrate that
applied to a specific problem, the method can benefit
from heuristics specific to said problem which exploit
its special structure. In particular, we focus on the
problem of protein conformation determination
formulated within the framework of matrix completion,
as was considered in a recent paper of the present
authors.",
acknowledgement = ack-nhfb,
eprint = "1408.4213",
keywords = "Mathematics - Optimization and Control",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.OC",
}
@Article{Borwein:2014:ROM,
author = "J. M. Borwein and Brailey Sims",
title = "Review of {{\booktitle{Origins of Mathematical Words:
A Comprehensive Dictionary of Latin, Greek and Arabic
Roots}} by Anthony lo Bello. The John Hopkins
University Press, 2013}",
journal = j-AUSTRALIAN-MATH-SOC-GAZ,
volume = "41",
number = "2",
pages = "116--118",
month = may,
year = "2014",
ISSN = "0311-0729 (print), 1326-2297 (electronic)",
ISSN-L = "0311-0729",
bibdate = "Tue Aug 16 09:16:30 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.austms.org.au/Publ/Gazette/2014/May14/BkRev.pdf",
acknowledgement = ack-nhfb,
ajournal = "Aust. Math. Soc. Gaz.",
fjournal = "Australian Mathematical Society Gazette",
journal-URL = "http://www.austms.org.au/gazette",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2014:SLM,
author = "David Borwein and Jonathan M. Borwein and Brailey
Sims",
title = "On the solution of linear mean recurrences",
journal = j-AMER-MATH-MONTHLY,
volume = "121",
number = "6",
pages = "486--498",
month = jun # "\slash " # jul,
year = "2014",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/amer.math.monthly.121.06.486",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "39B12 (15B51 65Q30)",
MRnumber = "3225456",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1505/;
http://www.jstor.org/stable/10.4169",
abstract = "Motivated by questions of algorithm analysis, we
provide several distinct approaches to determining
convergence and limit values for a class of linear
iterations.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000337330700002",
}
@Article{Borwein:2014:SRC,
author = "Jonathan M. Borwein and Liangjin Yao",
title = "Some results on the convexity of the closure of the
domain of a maximally monotone operator",
journal = j-OPTIM-LETT,
volume = "8",
number = "1",
pages = "237--246",
year = "2014",
DOI = "https://doi.org/10.1007/s11590-012-0564-7",
ISSN = "1862-4472 (print), 1862-4480 (electronic)",
ISSN-L = "1862-4472",
MRclass = "47H05 (26B25 47B65)",
MRnumber = "3152913",
MRreviewer = "Aris Daniilidis",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1205.4482;
http://docserver.carma.newcastle.edu.au/1373/",
abstract = "We provide a concise analysis about what is known
regarding when the closure of the domain of a maximally
monotone operator on an arbitrary real Banach space is
convex. In doing so, we also provide an affirmative
answer to a problem posed by Simons.",
acknowledgement = ack-nhfb,
ajournal = "Optim. Lett.",
fjournal = "Optimization Letters",
journal-URL = "http://link.springer.com/journal/11590",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000330434600019",
}
@Article{Borwein:2014:STMa,
author = "Jonathan M. Borwein and Liangjin Yao",
title = "Sum theorems for maximally monotone operators of type
({FPV})",
journal = j-J-AUSTRAL-MATH-SOC,
volume = "97",
number = "1",
pages = "1--26",
year = "2014",
CODEN = "JAUMAX",
DOI = "https://doi.org/10.1017/S1446788714000056",
ISSN = "1446-7887 (print), 1446-8107 (electronic)",
ISSN-L = "1446-7887",
MRclass = "47H05 (49J53 90C25 90C48)",
MRnumber = "3233391",
MRreviewer = "Radu Ioan Bo{\c{t}}",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://arxiv.org/abs/1305.6691;
http://docserver.carma.newcastle.edu.au/1503/;
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9306990",
abstract = "The most important open problem in monotone operator
theory concerns the maximal monotonicity of the sum of
two maximally monotone operators provided that the
classical Rockafellar's constraint qualification holds.
In this paper, we establish the maximal monotonicity of
A + B provided that A and B are maximally monotone
operators such that star(dom A) boolean AND int dom B
not equal phi, and A is of type (FPV). We show that
when also dom A is convex, the sum operator A + B is
also of type (FPV). Our result generalizes and unifies
several recent sum theorems.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Australian Mathematical Society",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000343185700001",
}
@Article{James:2014:STR,
author = "D. James and N. Wilkins-Diehr and V. Stodden and D.
Colbry and C. Rosales and M. Fahey and J. Shi and R. F.
Silva and K. Lee and R. Roskies and L. Loewe and S.
Lindsey and R. Kooper and L. Barba and D. Bailey and J.
Borwein and O. Corcho and E. Deelman and M. Dietze and
B. Gilbert and J. Harkes and S. Keele and P. Kumar and
J. Lee and E. Linke and R. Marciano and L. Marini and
C. Mattman and D. Mattson and K. McHenry and R. McLay
and S. Miguez and B. Minsker and M. Perez-Hernandez and
D. Ryan and M. Rynge and I. Santana-Perez and M.
Satyanarayanan and G. {St.Clair} and K. Webster and E.
Hovig and D. S. Katz and S. Kay and G. Sandve and D.
Skinner and G. Allen and J. Cazes and K. W. Cho and J.
Fonseca and L. Hwang and L. Koesterke and P. Patel and
L. Pouchard and E. Seidel and I. Suriarachchi",
title = "Standing Together for Reproducibility in Large-Scale
Computing: Report on {reproducibility@XSEDE}",
journal = "ArXiv e-prints",
month = dec,
year = "2014",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2014arXiv1412.5557J",
abstract = "This is the final report on reproducibility@XSEDE, a
one-day workshop held in conjunction with XSEDE14, the
annual conference of the Extreme Science and
Engineering Discovery Environment (XSEDE). The
workshop's discussion-oriented agenda focused on
reproducibility in large-scale computational research.
Two important themes capture the spirit of the workshop
submissions and discussions: (1) organizational
stakeholders, especially supercomputer centers, are in
a unique position to promote, enable, and support
reproducible research; and (2) individual researchers
should conduct each experiment as though someone will
replicate that experiment. Participants documented
numerous issues, questions, technologies, practices,
and potentially promising initiatives emerging from the
discussion, but also highlighted four areas of
particular interest to XSEDE: (1) documentation and
training that promotes reproducible research; (2)
system-level tools that provide build- and run-time
information at the level of the individual job; (3) the
need to model best practices in research collaborations
involving XSEDE staff; and (4) continued work on
gateways and related technologies. In addition, an
intriguing question emerged from the day's
interactions: would there be value in establishing an
annual award for excellence in reproducible research?",
acknowledgement = ack-nhfb,
eprint = "1412.5557",
keywords = "Computer Science - Distributed, Parallel, and Cluster
Computing, 68N01, D.2.9",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "cs.DC",
}
@Unpublished{Piantadosi:2014:MSS,
author = "Julia Piantadosi and Phil Howlett and Jonathan
Borwein",
title = "Modelling and simulation of seasonal rainfall using
checkerboard copulas of maximum entropy",
year = "2014",
bibdate = "Tue Aug 16 09:36:53 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Submitted eMathematics and Computers in Simulation
MATCOM, May 2014.",
URL = "http://docserver.carma.newcastle.edu.au/1694/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{AragonArtacho:2015:GBD,
author = "F. J. {Arag{\'o}n Artacho} and J. M. Borwein and M. K.
Tam",
title = "Global Behavior of the {Douglas--Rachford} Method for
a Nonconvex Feasibility Problem",
journal = "ArXiv e-prints",
month = jun,
year = "2015",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2015arXiv150609026A;
http://docserver.carma.newcastle.edu.au/1701/",
abstract = "In recent times the Douglas--Rachford algorithm has
been observed empirically to solve a variety of
nonconvex feasibility problems including those of a
combinatorial nature. For many of these problems
current theory is not sufficient to explain this
observed success and is mainly concerned with questions
of local convergence. In this paper we analyze global
behavior of the method for finding a point in the
intersection of a half-space and a potentially
non-convex set which is assumed to satisfy a
well-quasi-ordering property or a property weaker than
compactness. In particular, the special case in which
the second set is finite is covered by our framework
and provides a prototypical setting for combinatorial
optimization problems.",
acknowledgement = ack-nhfb,
eprint = "1506.09026",
keywords = "Mathematics - Optimization and Control, 90C26, 65K05",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.OC",
}
@Article{Bailey:2015:CCI,
author = "D. H. Bailey and J. M. Borwein",
title = "{Crandall}'s computation of the incomplete {Gamma}
function and the {Hurwitz} zeta function, with
applications to {Dirichlet} {$L$}-series",
journal = j-APPL-MATH-COMP,
volume = "268",
number = "??",
pages = "462--477",
day = "1",
month = oct,
year = "2015",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2015.06.048",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
MRclass = "33B30 (11M41 40A25)",
MRnumber = "3399433",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
http://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315008292",
abstract = "This paper extends tools developed by Crandall (2012)
[16] to provide robust, high-precision methods for
computation of the incomplete Gamma function and the
Lerch transcendent. We then apply these to the
corresponding computation of the Hurwitz zeta function
and so of Dirichlet $L$-series and character
polylogarithms.",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
keywords = "Character polylogarithms; Dirichlet L-series; Hurwitz
zeta function; Incomplete gamma function; Lerch
transcendent function; Polylogarithms",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000361769000039",
}
@InCollection{Bailey:2015:COG,
author = "D. H. Bailey and J. M. Borwein",
title = "Computation as an ontological game changer: The impact
of modern mathematical computation tools on the
ontology of mathematics",
crossref = "Davis:2015:MSS",
pages = "25--67",
year = "2015",
DOI = "https://doi.org/10.1007/978-3-319-21473-3_3",
bibdate = "Fri Aug 12 18:52:16 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-319-21473-3_3",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2015:CTM,
author = "D. H. Bailey and J. M. Borwein",
title = "Computation and theory of {Mordell--Tornheim--Witten}
sums {II}",
journal = j-J-APPROX-THEORY,
volume = "197",
number = "??",
pages = "115--140",
month = sep,
year = "2015",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1016/j.jat.2014.10.004",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "11M41 (33B30 33F05 65D20)",
MRnumber = "3351543",
MRreviewer = "Mehdi Hassani",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special Issue Dedicated to Dick Askey on the occasion
of his 80th birthday.",
URL = "http://docserver.carma.newcastle.edu.au/1494/;
http://www.carma.newcastle.edu.au/jon/MTW2.pdf;
http://www.sciencedirect.com/science/article/pii/S0021904514001841",
abstract = "In Bailey et al. [8] the current authors, along with
the late and much-missed Richard Crandall (1947--2012),
considered generalized Mordell--Tornheim--Witten (MTW)
zeta-function values along with their derivatives, and
explored connections with multiple-zeta values (MZVs).
This entailed use of symbolic integration, high
precision numerical integration, and some interesting
combinatorics and special-function theory. The original
motivation was to represent objects such as Eulerian
log-gamma integrals; and all such integrals were
expressed in terms of a MTW basis. Herein, we extend
the research envisaged in Bailey et al. [8] by
analyzing the relations between a significantly more
general class of MTW sums. This has required
significantly more subtle scientific computation and
concomitant special function theory.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000356633800008",
}
@InCollection{Bailey:2015:EAM,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Experimental Applied Mathematics",
crossref = "Higham:2015:PCA",
pages = "925--933",
year = "2015",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/bibnet/subjects/companion-applied-mathematics.bib",
note = "Entry VIII.6.",
URL = "http://docserver.carma.newcastle.edu.au/1460/",
acknowledgement = ack-nhfb # " and " # ack-njh,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Bailey:2015:ECO,
author = "David H. Bailey and Jonathan M. Borwein",
booktitle = "Mathematics, substance and surmise",
title = "Experimental computation as an ontological game
changer: the impact of modern mathematical computation
tools on the ontology of mathematics",
publisher = pub-SV,
address = pub-SV:adr,
pages = "25--67",
year = "2015",
MRclass = "00A35 (03B35 68W30)",
MRnumber = "3467267",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/ontology.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2015:ELG,
author = "David H. Bailey and David Borwein and Jonathan M.
Borwein",
title = "On {Eulerian} log-gamma integrals and
{Tornheim--Witten} zeta functions",
journal = j-RAMANUJAN-J,
volume = "36",
number = "1--2",
pages = "43--68",
month = feb,
year = "2015",
DOI = "https://doi.org/10.1007/s11139-012-9427-1",
ISSN = "1382-4090 (print), 1572-9303 (electronic)",
ISSN-L = "1382-4090",
MRclass = "11M35 (11M32 33B15 33F05)",
MRnumber = "3296709",
MRreviewer = "Renata Macaitien{\.e}",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1377/",
ZMnumber = "06398825",
abstract = "Stimulated by earlier work by Moll and his coworkers
(Amdeberhan et al., Proc. Am. Math. Soc., {\bf 139}(2):
535--545, 2010), we evaluate various basic log Gamma
integrals in terms of partial derivatives of
Tornheim--Witten zeta functions and their extensions
arising from evaluations of Fourier series. In
particular, we fully evaluate $ \mathcal {LG}(n) =
\int_0^1 \log^n \Gamma (x) \, d x $ for $ 1 \leq n \leq
4 $ and make some comments regarding the general case.
The subsidiary computational challenges are
substantial, interesting and significant in their own
right.",
acknowledgement = ack-nhfb,
fjournal = "The {Ramanujan} Journal",
journal-URL = "http://link.springer.com/journal/11139",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000347701700003",
}
@Article{Bailey:2015:HPA,
author = "David H. Bailey and Jonathan M. Borwein",
title = "High-precision arithmetic in mathematical physics",
journal = "Mathematics",
volume = "3",
number = "2",
pages = "337--367",
month = jun,
year = "2015",
DOI = "https://doi.org/10.3390/math3020337",
ISSN = "2227-7390",
ISSN-L = "2227-7390",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mdpi.com/2227-7390/3/2/337",
abstract = "For many scientific calculations, particularly those
involving empirical data, IEEE 32-bit floating-point
arithmetic produces results of sufficient accuracy,
while for other applications IEEE 64-bit floating-point
is more appropriate. But for some very demanding
applications, even higher levels of precision are often
required. This article discusses the challenge of
high-precision computation, in the context of
mathematical physics, and highlights what facilities
are required to support future computation, in light of
emerging developments in computer architecture.",
acknowledgement = ack-nhfb,
journal-URL = "http://www.mdpi.com/journal/mathematics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000364229100010",
xxpublisher = "Multidisciplinary Digital Publishing Institute",
}
@TechReport{Bailey:2015:OTD,
author = "David H. Bailey and Jonathan M. Borwein and Amir
Salehipour and Marcos {L{\'o}pez de Prado} and Qiji
Zhu",
title = "Online tools for demonstration of backtest
overfitting",
institution = "Lawrence Berkeley National Laboratory and four
others",
address = "Berkeley, CA 94720, USA and others",
pages = "13",
day = "29",
month = nov,
year = "2015",
MRclass = "60E, 62C, 91G10, 91G60, 91G70",
bibdate = "Fri Sep 30 09:04:44 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://ssrn.com/abstract=2597421",
abstract = "In mathematical finance, backtest overfitting relates
to the usage of historical market data (a backtest) to
develop an investment strategy, where the strategy
profits from random patterns rather than variables
signals. Backtest overfitting is now thought to be a
primary reason why quantitative investment models and
strategies that look good on paper often disappoint in
practice.\par
In this study we introduce two online tools, the
Backtest Overfitting Demonstration Tool, or BODT for
short, and the Tenure Maker Simulation Tool, or TMST,
which illustrate the impact of backtest overfitting on
investment models and strategies. We describe BODT and
TSMT, the experiments they perform, together with
technical details such as the evaluation metrics and
parameters used.",
acknowledgement = ack-nhfb,
keywords = "Backtest overfitting, multiple testing, Sharpe Ratio,
Deflated Sharpe Ratio, investment strategy",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2015:CAGa,
author = "J. M. Borwein and O. Giladi",
title = "Convex analysis in groups and semigroups: a sampler",
journal = "ArXiv e-prints",
month = oct,
year = "2015",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2015arXiv151004480B;
http://docserver.carma.newcastle.edu.au/1693/",
abstract = "We define convexity canonically in the setting of
monoids. We show that many classical results from
convex analysis hold for functions defined on such
groups and semigroups, rather than only on vector
spaces. Some examples and counter-examples are also
discussed.",
acknowledgement = ack-nhfb,
eprint = "1510.04480",
keywords = "Mathematics - Optimization and Control",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.OC",
}
@Article{Borwein:2015:CDR,
author = "Jonathan M. Borwein and Matthew K. Tam",
title = "The cyclic {Douglas--Rachford} method for inconsistent
feasibility problems",
journal = j-J-NONLINEAR-CONVEX-ANAL,
volume = "16",
number = "4",
pages = "573--584",
month = "????",
year = "2015",
DOI = "",
ISSN = "1345-4773 (print), 1880-5221 (electronic)",
ISSN-L = "1345-4773",
MRclass = "47J25 (47H09 47H10)",
MRnumber = "3343161",
MRreviewer = "Jean Mawhin",
bibdate = "Fri Sep 30 09:55:02 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1496/;
http://www.ybook.co.jp/online2/jncav16-4.html",
abstract = "We analyse the behaviour of the newly introduced
cyclic Douglas--Rachford algorithm for finding a point
in the intersection of a finite number of closed convex
sets. This work considers the case in which the target
intersection set is possibly empty.",
acknowledgement = ack-nhfb,
affiliation = "Borwein, JM (Reprint Author), Univ Newcastle, CARMA
Ctr, Callaghan, NSW 2308, Australia. Borwein, Jonathan
M.; Tam, Matthew K., Univ Newcastle, CARMA Ctr,
Callaghan, NSW 2308, Australia.",
fjournal = "Journal of Nonlinear and Convex Analysis. An
International Journal",
journal-URL = "http://www.ybook.co.jp/jnca.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000355240900001",
xxpages = "537--584",
xxtitle = "The cyclic {Douglas--Rachford} feasibility method:
behaviour on infeasible problems",
}
@Article{Borwein:2015:CRA,
author = "J. M. Borwein and G. Li and M. K. Tam",
title = "Convergence rate analysis for averaged fixed point
iterations in the presence of H{\"o}lder regularity",
journal = "ArXiv e-prints",
month = oct,
year = "2015",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2015arXiv151006823B;
http://docserver.carma.newcastle.edu.au/1690/",
abstract = "In this paper, we establish sublinear and linear
convergence of fixed point iterations generated by
averaged operators in a Hilbert space. Our results are
achieved under a bounded H{\"o}lder regularity
assumption which generalizes the well-known notion of
bounded linear regularity. As an application of our
results, we provide a convergence rate analysis for
Krasnoselskii--Mann iterations, the cyclic projection
algorithm, and the Douglas--Rachford feasibility
algorithm along with some variants. In the important
case in which the underlying sets are convex sets
described by convex polynomials in a finite dimensional
space, we show that the H{\"o}lder regularity
properties are automatically satisfied, from which
sublinear convergence follows.",
acknowledgement = ack-nhfb,
eprint = "1510.06823",
keywords = "Mathematics - Optimization and Control",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.OC",
}
@Unpublished{Borwein:2015:CU,
author = "Jonathan M. Borwein and Brailey Sims",
title = "Convexity in ultraproducts",
month = aug,
year = "2015",
bibdate = "Tue Aug 16 09:40:17 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2015:DCP,
author = "Jonathan M. Borwein and D. Russell Luke",
title = "Duality and Convex Programming",
crossref = "Scherzer:2015:HMM",
volume = "1",
pages = "257--304",
year = "2015",
DOI = "https://doi.org/10.1007/978-1-4939-0790-8_7",
MRclass = "94A08",
MRnumber = "3560070",
MRreviewer = "Nicolas Hadjisavvas",
bibdate = "Sat Aug 13 16:07:59 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1217/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2015:DSU,
author = "J. M. Borwein and A. Straub and C. Vignat",
title = "Densities of short uniform random walks in higher
dimensions",
journal = "ArXiv e-prints",
month = aug,
year = "2015",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2015arXiv150804729B;
http://docserver.carma.newcastle.edu.au/1699/",
abstract = "We study arithmetic properties of short uniform random
walks in arbitrary dimensions, with a focus on explicit
(hypergeometric) evaluations of the moment functions
and probability densities in the case of up to five
steps. Somewhat to our surprise, we are able to provide
complete extensions to arbitrary dimensions for most of
the central results known in the two-dimensional
case.",
acknowledgement = ack-nhfb,
eprint = "1508.04729",
keywords = "Mathematics - Classical Analysis and ODEs, Mathematics
- Number Theory",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.CA",
}
@InCollection{Borwein:2015:FM,
author = "Jonathan M. Borwein",
title = "The Future of Mathematics: 1965 to 2065",
crossref = "Kennedy:2015:CAM",
publisher = pub-MATH-ASSOC-AMER,
address = pub-MATH-ASSOC-AMER:adr,
pages = "313--329",
year = "2015",
MRclass = "00A35",
MRnumber = "3408151",
bibdate = "Fri Aug 12 19:11:45 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1720/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxpages = "313--330",
}
@Article{Borwein:2015:LKM,
author = "Jonathan M. Borwein and Yann Bugeaud and Michael
Coons",
title = "The legacy of {Kurt Mahler}",
journal = j-NAMS,
volume = "62",
number = "5",
pages = "526--531",
month = may,
year = "2015",
CODEN = "AMNOAN",
DOI = "https://doi.org/10.1090/noti1241",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "01A70, 01A75 (Collected or selected works), 11-03",
MRnumber = "3328921",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
ZMnumber = "1338.01030",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:2015:MCR,
author = "D. Borwein and J. M. Borwein and B. Sims",
title = "Monotonicity of certain {Riemann} sums",
year = "2015",
bibdate = "Tue Aug 16 09:36:05 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Submitted, Mathematics Magazine, January 2015.",
URL = "http://docserver.carma.newcastle.edu.au/1692/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2015:MMI,
author = "Jonathan M. Borwein and Joydeep Dutta",
title = "Maximal Monotone Inclusions and {Fitzpatrick}
Functions",
journal = j-J-OPT-THEORY-APPL,
volume = "??",
number = "??",
pages = "1--28",
year = "2015",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/s10957-015-0813-x",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special issue of JOTA on Nondifferentiable
Optimization and Nonsmooth Analysis, dedicated to
Vladimir Demyanov.",
URL = "http://docserver.carma.newcastle.edu.au/1715/;
http://link.springer.com/article/10.1007/s10957-015-0813-x",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2015:NCR,
author = "Jonathan M. Borwein and Brailey Sims and Matthew K.
Tam",
title = "Norm convergence of realistic projection and
reflection methods",
journal = j-OPTIMIZATION,
volume = "64",
number = "1",
pages = "161--178",
month = jan,
year = "2015",
CODEN = "OPTZDQ",
DOI = "https://doi.org/10.1080/02331934.2014.947499",
ISSN = "0233-1934, 0323-3898",
ISSN-L = "0233-1934",
MRclass = "47J25 (47H09 47H10 90C25 90C48)",
MRnumber = "3293546",
MRreviewer = "Patrick L. Combettes",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1493/",
abstract = "We provide sufficient conditions for norm convergence
of various projection and reflection methods, as well
as giving limiting examples regarding convergence
rates.",
acknowledgement = ack-nhfb,
fjournal = "Optimization",
fjournal = "Optimization. A Journal of Mathematical Programming
and Operations Research",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Tam, Matthew/G-8127-2013",
unique-id = "ISI:000346849000011",
}
@Article{Borwein:2015:NPD,
author = "J. M. Borwein and O. Giladi",
title = "Nearest points and delta convex functions in {Banach}
spaces",
journal = "ArXiv e-prints",
month = oct,
year = "2015",
bibdate = "Fri Sep 30 09:28:29 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint of \cite{Borwein:2016:NPD}.",
URL = "http://adsabs.harvard.edu/abs/2015arXiv151004471B",
abstract = "Given a closed set $C$ in a Banach space $ (X, ||
\cdot ||)$, a point $ x \in X$ is said to have a
nearest point in $C$ if there exists $ z \in C$ such
that $ d_C(x) = || x - z || $, where $ d_C$ is the
distance of $x$ from $C$. We shortly survey the problem
of studying how large is the set of points in $X$ which
have nearest points in $C$. We then discuss the topic
of delta-convex functions and how it is related to
finding nearest points.",
acknowledgement = ack-nhfb,
eprint = "1510.04471",
fjournal = "Bulletin of the Australian Mathematical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ",
keywords = "Mathematics - Functional Analysis",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
unique-id = "ISI:000372529100012",
}
@Article{Borwein:2015:PPA,
author = "Jonathan M. Borwein and Scott T. Chapman",
title = "{I} prefer Pi: Addenda",
journal = j-AMER-MATH-MONTHLY,
volume = "122",
number = "8",
pages = "800--800",
month = oct,
year = "2015",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/amer.math.monthly.122.8.800",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11A05 (11Z05)",
MRnumber = "3399115",
bibdate = "Fri Aug 12 07:42:48 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "See \cite{Borwein:2015:PPB}. The addenda correct
formulas (4) and (12), references [34] and [74], and
add a new reference.",
URL = "http://www.jstor.org/stable/10.4169/amer.math.monthly.122.8.800",
ZMnumber = "1328.01077",
abstract = "In the rush to prepare our March 2015 article on Pi
[1], several infelicities escaped our eye. Herein we
repair the damage.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000363911100013",
}
@Article{Borwein:2015:PPB,
author = "Jonathan M. Borwein and Scott T. Chapman",
title = "{I} prefer Pi: a brief history and anthology of
articles in the {{\booktitle{American Mathematical
Monthly}}}",
journal = j-AMER-MATH-MONTHLY,
volume = "122",
number = "3",
pages = "195--216",
month = mar,
year = "2015",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/amer.math.monthly.122.03.195",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "01A05 (11Z05)",
MRnumber = "3327710",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "See addenda \cite{Borwein:2015:PPA}.",
URL = "http://docserver.carma.newcastle.edu.au/1615/;
http://www.jstor.org/stable/10.4169",
abstract = "In celebration of both a special ``big'' $ \pi $ Day
(3/14/15) and the 2015 centennial of the Mathematical
Association of America, we review the illustrious
history of the constant $ \pi $ in the pages of the
American Mathematical Monthly.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000369889300002",
}
@Article{Borwein:2015:RNP,
author = "Jonathan M. Borwein and Armin Straub",
title = "Relations for {Nielsen} polylogarithms",
journal = j-J-APPROX-THEORY,
volume = "193",
number = "??",
pages = "74--88",
month = may,
year = "2015",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1016/j.jat.2013.07.003",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "33B30",
MRnumber = "3324564",
MRreviewer = "Junesang Choi",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special Issue Dedicated to Dick Askey on the occasion
of his 80th birthday.",
URL = "http://docserver.carma.newcastle.edu.au/1500/;
http://www.sciencedirect.com/science/article/pii/S0021904513001202",
abstract = "Polylogarithms appear in many diverse fields of
mathematics. Herein, we investigate relations amongst
the restricted class of Nielsen-type (essentially,
height one) polylogarithms, both generic and at special
arguments including the sixth roots of unity. Numerical
computations suggest that the collected relations,
partially motivated by a previous study of the authors
on log-sine integrals, are complete except in the case
when the argument is the fundamental sixth root of
unity. For use in other applications, all our results
are implemented and accessible for use in symbolic
computation or to facilitate numeric computation. In
particular, the relations are explicitly exhibited in
the case of low weights.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
keywords = "Clausen functions; Log-sine integrals; Multiple
polylogarithms; Multiple zeta values",
ORCID-numbers = "Straub, Armin/0000-0001-6802-6053",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000352676400006",
}
@InProceedings{Borwein:2015:RPM,
author = "Jonathan M. Borwein and Liangjin Yao",
title = "Recent progress on monotone operator theory",
crossref = "Reich:2015:IPO",
pages = "51--81",
year = "2015",
DOI = "https://doi.org/10.1090/conm/636/12728",
MRclass = "47H05 (46B10 47-02)",
MRnumber = "3155360",
MRreviewer = "Behzad Djafari-Rouhani",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1457/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2015:SRC,
author = "Jonathan M. Borwein and Ohad Giladi",
title = "Some remarks on convex analysis in topological
groups",
journal = "ArXiv e-prints",
month = oct,
year = "2015",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2015arXiv151004487B;
http://docserver.carma.newcastle.edu.au/1697/",
abstract = "We discuss some key results from convex analysis in
the setting of topological groups and monoids. These
include separation theorems, Krein--Milman type
theorems, and minimax theorems.",
acknowledgement = ack-nhfb,
eprint = "1510.04487",
keywords = "Mathematics - Optimization and Control, Mathematics -
Functional Analysis",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.OC",
}
@InCollection{Borwein:2015:WWH,
author = "Jonathan M. Borwein",
title = "Who We Are and How We Got That Way?",
crossref = "Casazza:2015:M",
pages = "140--156",
year = "2015",
bibdate = "Sat Aug 13 13:47:19 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/777/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Artacho:2016:GBD,
author = "Francisco J. Arag{\'o}n Artacho and Jonathan M.
Borwein and Matthew K. Tam",
title = "Global behavior of the {Douglas--Rachford} method for
a nonconvex feasibility problem",
journal = j-J-GLOBAL-OPT,
volume = "65",
number = "2",
pages = "309--327",
month = jun,
year = "2016",
CODEN = "JGOPEO",
DOI = "https://doi.org/10.1007/s10898-015-0380-6",
ISSN = "0925-5001 (print), 1573-2916 (electronic)",
ISSN-L = "0925-5001",
MRclass = "90C26 (65K05)",
MRnumber = "3498569",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1701/",
abstract = "In recent times the Douglas--Rachford algorithm has
been observed empirically to solve a variety of
nonconvex feasibility problems including those of a
combinatorial nature. For many of these problems
current theory is not sufficient to explain this
observed success and is mainly concerned with questions
of local convergence. In this paper we analyze global
behavior of the method for finding a point in the
intersection of a half-space and a potentially
non-convex set which is assumed to satisfy a
well-quasi-ordering property or a property weaker than
compactness. In particular, the special case in which
the second set is finite is covered by our framework
and provides a prototypical setting for combinatorial
optimization problems.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Global Optimization. An International
Journal Dealing with Theoretical and Computational
Aspects of Seeking Global Optima and Their Applications
in Science, Management and Engineering",
journal-URL = "http://link.springer.com/journal/10898",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Aragon Artacho, Francisco
Javier/0000-0002-2445-8011",
researcherid-numbers = "Aragon Artacho, Francisco Javier/C-2531-2012",
unique-id = "ISI:000377611500007",
}
@InCollection{Bailey:2016:AIS,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Ancient {Indian} Square Roots: An Exercise in Forensic
Paleo-Mathematics",
crossref = "Selin:2016:EHS",
pages = "305--310",
year = "2016",
DOI = "https://doi.org/10.1007/978-94-007-7747-7_10265",
bibdate = "Fri Aug 12 18:58:22 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Redacted from \cite{Bailey:2012:AIS}.",
URL = "http://docserver.carma.newcastle.edu.au/1385/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2016:BOF,
author = "David H. Bailey and Jonathan M. Borwein and Amir
Salehipour and Marcos {L{\'o}pez de Prado} and Qiji
Zhu",
title = "Backtest Overfitting in Financial Markets",
journal = "Automated Trader Magazine",
volume = "39",
number = "Q1",
pages = "52--57",
month = "????",
year = "2016",
bibdate = "Fri Aug 12 07:28:28 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1713/;
http://www.automatedtrader.net/articles/strategies/155469/backtest-overfitting-in-financial-markets",
acknowledgement = ack-nhfb,
journal-URL = "http://www.automatedtrader.net/home.xhtm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2016:CDA,
author = "David H. Bailey and Jonathan M. Borwein and Jason
Kimberley and Watson Ladd",
title = "Computer Discovery and Analysis of Large {Poisson}
Polynomials",
journal = j-EXP-MATH,
volume = "??",
number = "??",
pages = "??--??",
month = "",
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2016.1180565",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
bibdate = "Fri Aug 12 07:21:56 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1689/;
http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1180565",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
onlinedate = "24 August 2016",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxtitle = "Discovery and Analysis of Large {Poisson} Polynomials
Using the {MPFUN--MPFR} Arbitrary Precision Software",
}
@TechReport{Bailey:2016:CEEa,
author = "D. H. Bailey and J. M. Borwein",
title = "Computation and experimental evaluation of
{Mordell--Tornheim--Witten} sum derivatives",
institution = "University of California at Davis and Centre for
Computer Assisted Research Mathematics and its
Applications (CARMA), University of Newcastle",
address = "Davis, CA, USA and Callaghan, NSW 2308, Australia",
pages = "9",
day = "16",
month = aug,
year = "2016",
bibdate = "Tue Aug 16 09:37:31 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/omega-numerics.pdf",
abstract = "In previous studies the present authors and others
have studied in have studied Mordell--Tornheim--Witten
sums and their connections with multiple-zeta values.
In this note we describe the numerical computation of
derivatives at zero of a specialization originating in
[14] and studied further in [10, 15, 11], and the
experimental evaluation of these numerical values in
terms of well-known constants.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2016:CEEb,
author = "D. H. Bailey and J. M. Borwein",
title = "Computation and experimental evaluation of
{Mordell--Tornheim--Witten} sum derivatives",
journal = j-EXP-MATH,
volume = "??",
number = "??",
pages = "??--??",
month = "????",
year = "2016",
CODEN = "????",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
bibdate = "Tue Aug 16 09:37:31 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/omega-numerics.pdf",
abstract = "In previous studies the present authors and others
have studied in have studied Mordell--Tornheim--Witten
sums and their connections with multiple-zeta values.
In this note we describe the numerical computation of
derivatives at zero of a specialization originating in
[14] and studied further in [10, 15, 11], and the
experimental evaluation of these numerical values in
terms of well-known constants.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Bailey:2016:CPI,
author = "David H. Bailey and Jonathan M. Borwein and Andrew
Mattingly and Glenn Wightwick",
title = "The computation of previously inaccessible digits of $
\pi $",
crossref = "Bailey:2016:PNG",
pages = "327--339",
year = "2016",
DOI = "https://doi.org/10.1007/978-3-319-32377-0_20",
bibdate = "Tue Mar 14 11:34:57 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/agm.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2016:CSC,
author = "D. H. Bailey and J. M. Borwein",
title = "Computation and structure of character polylogarithms
with applications to character
{Mordell--Tornheim--Witten} sums",
journal = j-MATH-COMPUT,
volume = "85",
number = "297",
pages = "295--324",
year = "2016",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/mcom/2974",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11L40 (33F05)",
MRnumber = "3404451",
MRreviewer = "Karin Halupczok",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.ams.org/mcom/2016-85-297;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://docserver.carma.newcastle.edu.au/1492/;
http://www.ams.org/journals/mcom/2016-85-297/S0025-5718-2015-02974-3;
http://www.ams.org/journals/mcom/2016-85-297/S0025-5718-2015-02974-3/S0025-5718-2015-02974-3.pdf;
http://www.ams.org/mathscinet/search/author.html?authorName=Borwein%2C%20J.%20M.;
http://www.ams.org/mathscinet/search/author.html?mrauthid=29355;
http://www.carma.newcastle.edu.au/jon/MTWIII.pdf",
abstract = "This paper extends tools developed to study character
polylogarithms. These objects are used to compute
Mordell--Tornheim--Witten character sums and to explore
their connections with multiple-zeta values (MZVs) and
with their character analogues.",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000362848100011",
}
@InCollection{Bailey:2016:EMS,
author = "D. H. Bailey and J. M. Borwein",
booktitle = "7th European Mathematics Congress (EMC) on Mathematics
in the Society of the Future",
title = "Experimental Mathematics in the Society of the
Future",
publisher = "European Mathematical Society",
address = "Z{\"u}rich, Switzerland",
pages = "??--??",
year = "2016",
DOI = "https://doi.org/10.4171/164-1/2",
ISBN = "",
ISBN-13 = "",
LCCN = "",
MRclass = "00A35",
MRnumber = "3497586",
bibdate = "Fri Aug 12 18:35:05 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1675/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Bailey:2016:FRS,
author = "David H. Bailey and Jonathan M. Borwein and Victoria
Stodden",
editor = "Harald Atmanspacher and Sabine Maasen",
booktitle = "Reproducibility: Principles, Problems, Practices, and
Prospects",
title = "Facilitating Reproducibility in Scientific Computing:
Principles and Practice",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "205--231",
year = "2016",
DOI = "https://doi.org/10.1002/9781118865064.ch9",
ISBN = "1-118-86506-5",
ISBN-13 = "978-1-118-86506-4",
bibdate = "Thu Aug 11 11:01:49 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "This book was awarded the 2017 Prose Award
(``Honorable Mention'') in the category ``Textbook /
Best in Physical Sciences and Mathematics''; see
\url{https://proseawards.com/winners/2017-award-winners/}
and
\url{http://experimentalmath.org/2017/02/reproducibility-principles-problems-practices-and-prospects/}.",
abstract = "This chapter discusses the roots of the
reproducibility problem in scientific computing, and
summarizes some possible solutions that have been
suggested in the community. Statistical overfitting can
be thought of as an instance of ``selection bias'',
wherein one presents the results of only those tests
that support well one's hypothesis. The problem of
statistical overfitting in computational science is
perhaps best illustrated in the field of mathematical
finance. Present-day researchers are not as fully aware
of the potential pitfalls of performance reporting. In
any event, various high-performance computing
researchers have noted a resurrection of some of these
questionable practices. Using high-precision arithmetic
(higher than the standard IEEE 64-bit arithmetic) is
often quite useful in ameliorating numerical
difficulties and enhancing reproducibility. Very
high-precision floating-point arithmetic is essential
to obtain reproducible results in experimental
mathematics and in related mathematical physics
applications. The chapter also discusses
reproducibility in symbolic computing.",
acknowledgement = ack-nhfb,
keywords = "high-performance computing; high-precision arithmetic;
mathematical physics; numerical reproducibility;
performance reporting; scientific computing;
statistical overfitting; symbolic computing",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Bailey:2016:HHI,
author = "D. Bailey and J. Borwein and M. {L{\'o}pez de Prado}
and A. Salehipour and Qiji Zhu",
title = "How hard is it to avoid backtest overfitting?",
year = "2016",
bibdate = "Tue Aug 16 09:31:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Submitted to Applied Mathematical Finance, July
2016.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2016:RCS,
author = "David H. Bailey and Jonathan M. Borwein and Richard P.
Brent and Mohsen Reisi",
title = "Reproducibility in Computational Science: A Case
Study: Randomness of the Digits of Pi",
journal = j-EXP-MATH,
volume = "22",
number = "??",
pages = "1--8",
month = "",
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2016.1163755",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
bibdate = "Fri Aug 12 07:22:53 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
note = "See \cite{Ganz:2014:DES}.",
URL = "http://docserver.carma.newcastle.edu.au/1695/;
http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1163755",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
onlinedate = "24 August 2016",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "This paper reproduces work in \cite{Ganz:2014:DES},
and then shows that the report in that paper of
nonrandomness of digits of $ \pi $ is an artifact of an
unlucky choice of sample block sizes. Statistics from
several different block sizes support the widely-held,
but still unproven, belief that $ \pi $ is a normal
number (where all digits occur with equal
probability).",
xxauthor = "David H. Bailey and Jonathan M. Borwein and Richard P.
Brent and Mohsen Reisi Ardali",
}
@Article{Bailey:2016:SPD,
author = "D. Bailey and J. Borwein and M. {L{\'o}pez de Prado}",
title = "Stock portfolio design and backtest overfitting",
journal = j-J-INVESTMENT-MANAGE,
volume = "??",
number = "??",
pages = "??--??",
month = "????",
year = "2016",
DOI = "",
ISSN = "1545-9144 (print), 1545-9152 (electronic)",
ISSN-L = "1545-9144",
bibdate = "Fri Aug 12 07:17:41 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1684/;
http://www.davidhbailey.com/dhbpapers/stockfund.pdf",
acknowledgement = ack-nhfb,
fjournal = "Journal of Investment Management",
journal-URL = "https://www.joim.com/library-archives/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
pagecount = "16",
}
@Misc{Bailey:2016:SPP,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Sphere packing problem solved in $8$ and $ 24$
dimensions",
howpublished = "Blog posting",
day = "1",
month = apr,
year = "2016",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/kepler.bib",
note = "See research papers
\cite{Viazovska:2016:SPP,Cohn:2016:SPP}.",
URL = "http://experimentalmath.info/blog/2016/04/sphere-packing-problem-solved-in-8-and-24-dimensions/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2016:AGM,
author = "J. M. Borwein and P. B. Borwein",
title = "The arithmetic--geometric mean and fast computation of
elementary functions (1984)",
crossref = "Bailey:2016:PNG",
publisher = pub-SV,
address = pub-SV:adr,
pages = "79--96",
year = "2016",
DOI = "https://doi.org/10.1007/978-3-319-32377-0_4",
bibdate = "Thu Aug 11 09:36:22 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-319-32377-0_4",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2016:AO,
author = "J. M. Borwein",
title = "Adventures with the {OEIS}",
journal = j-RAMANUJAN-J,
volume = "??",
number = "??",
pages = "??--??",
month = "????",
year = "2016",
DOI = "",
ISSN = "1382-4090 (print), 1572-9303 (electronic)",
ISSN-L = "1382-4090",
bibdate = "Fri Aug 12 07:16:30 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1686/",
acknowledgement = ack-nhfb,
fjournal = "The {Ramanujan} Journal",
journal-URL = "http://link.springer.com/journal/11139",
keywords = "Neil J. A. Sloane; OEIS (Online Encyclopedia of
Integer Sequences)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:2016:BOM,
author = "J. M. Borwein and K. Dilcher and H. Tomkins",
title = "The behaviour at the origin of multiple {Witten} zeta
functions",
month = jul,
year = "2016",
bibdate = "Tue Aug 16 09:38:11 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "In preparation.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2016:CAGa,
author = "J. M. Borwein and O. Giladi",
title = "Convex Analysis in Groups and Semigroups: a Sampler",
journal = "Mathematical Programming Series B",
volume = "??",
number = "??",
pages = "1--44",
month = "",
year = "2016",
DOI = "https://doi.org/10.1007/s10107-016-1010-x",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
bibdate = "Fri Aug 12 07:24:09 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1693/;
http://link.springer.com/article/10.1007/s10107-016-1010-x",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10107",
onlinedate = "30 April 2016",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2016:CFD,
author = "Jonathan M. Borwein and Corwin W. Sinnamon",
title = "A closed form for the density functions of random
walks in odd dimensions",
journal = j-BULL-AUSTRAL-MATH-SOC,
volume = "93",
number = "2",
pages = "330--339",
month = apr,
year = "2016",
CODEN = "ALNBAB",
DOI = "https://doi.org/10.1017/S0004972715001112",
ISSN = "0004-9727 (print), 1755-1633 (electronic)",
ISSN-L = "0004-9727",
MRclass = "60G50 (33C20)",
MRnumber = "3480942",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1702/;
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=10230818",
abstract = "We derive an explicit piecewise-polynomial closed form
for the probability density function of the distance
travelled by a uniform random walk in an
odd-dimensional space.",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the Australian Mathematical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000372529100017",
}
@Article{Borwein:2016:CLA,
author = "Jonathan M. Borwein and Neil J. Calkin and Scott B.
Lindstrom and Andrew Mattingly",
title = "Continued Logarithms and Associated Continued
Fractions",
journal = j-EXP-MATH,
volume = "26",
number = "4",
pages = "412--429",
month = sep,
year = "2016",
DOI = "https://doi.org/10.1080/10586458.2016.1195307",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11J70 (11Y65, 11A55)",
bibdate = "Sat Oct 21 17:29:42 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://docserver.carma.newcastle.edu.au/1687/",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
keywords = "continued fractions; continued logarithms;
Gauss-Kuzmin distribution; Khintchine's constant;
logarithmic Khintchine numbers",
onlinedate = "16 September 2016",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Presented as a colloquium at the University of Western
Ontario, London, ON, Canada prior to publication.",
}
@Unpublished{Borwein:2016:CRA,
author = "Jonathan M. Borwein and Gouyin Li and Matthew Tam",
title = "Convergence rate analysis for averaged fixed point
iterations in the presence of {H{\"o}lder} regularity",
year = "2016",
bibdate = "Tue Aug 16 09:34:36 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Revised SIAM Optimization, April 2016.",
URL = "http://arxiv.org/abs/1510.06823;
http://docserver.carma.newcastle.edu.au/1690/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:2016:DFE,
author = "J. M. Borwein and Karl Dilcher",
title = "Derivatives and Fast Evaluation of the {Witten} Zeta
Function",
year = "2016",
bibdate = "Tue Aug 16 09:34:04 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Submitted to the Ramanujan Journal, April 2016.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2016:DSU,
author = "Jonathan M. Borwein and Armin Straub and Christophe
Vignat",
title = "Densities of short uniform random walks in higher
dimensions",
journal = j-J-MATH-ANAL-APPL,
volume = "437",
number = "1",
pages = "668--707",
month = may,
year = "2016",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/j.jmaa.2016.01.017",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "60G50 (33C20)",
MRnumber = "3451989",
MRreviewer = "Enzo Orsingher",
bibdate = "Fri Aug 12 07:29:41 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1699/;
http://www.sciencedirect.com/science/article/pii/S0022247X16000421",
abstract = "We study arithmetic properties of short uniform random
walks in arbitrary dimensions, with a focus on explicit
(hypergeometric) evaluations of the moment functions
and probability densities in the case of up to five
steps. Somewhat to our surprise, we are able to provide
complete extensions to arbitrary dimensions for most of
the central results known in the two-dimensional
case.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
keywords = "Bessel integrals; Generalised hypergeometric
functions; Narayana numbers; Short random walks",
ORCID-numbers = "Straub, Armin/0000-0001-6802-6053",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000369676700037",
}
@Unpublished{Borwein:2016:EAI,
author = "Jonathan M. Borwein and Michael Rose",
booktitle = "",
title = "Expectations over attractors of iterated function
systems",
month = "????",
year = "2016",
bibdate = "Tue Aug 16 09:35:26 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Submitted JMAA, June 2016.",
URL = "http://docserver.carma.newcastle.edu.au/1680/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2016:EAM,
author = "J. M. Borwein and A. Straub",
booktitle = "Mathematical Beauties 2016 Calendar",
title = "Entry for {August} on {``Moments of random walks''}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "??--??",
year = "2016",
bibdate = "Fri Aug 12 18:36:34 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:2016:EBD,
author = "J. M. Borwein and Ohad Giladi",
title = "Ergodic behaviour of a {Douglas--Rachford} operator
away from the origin",
year = "2016",
bibdate = "Tue Aug 16 09:33:31 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Submitted to the Journal of Global Optimization, May
2016.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2016:EM,
author = "Jonathan Borwein",
title = "Experimental Mathematics",
crossref = "Calude:2016:HFC",
pages = "141--156",
year = "2016",
DOI = "https://doi.org/10.1142/9781783266449_0010",
bibdate = "Fri Aug 12 18:39:34 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1527/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2016:EMP,
author = "Jonathan Borwein",
title = "The Experimental Mathematician: The Pleasure of
Discovery and the Role of Proof",
journal = j-CMS-NOTES,
volume = "48",
number = "6",
pages = "10--13",
month = dec,
year = "2016",
ISSN = "0045-5164",
ISSN-L = "0045-5164",
bibdate = "Sat Jan 07 11:42:46 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Excerpts from a 2002 CMESG Plenary Lecture given by
the author.",
URL = "http://cms.math.ca/notes/v48/n6/Notesv48n6.pdf",
acknowledgement = ack-nhfb,
fjournal = "Canadian Mathematical Society Notes",
journal-URL = "https://cms.math.ca/notes",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Published posthumously.",
}
@Article{Borwein:2016:GCLa,
author = "J. M. Borwein and K. G. Hare and J. G. Lynch",
title = "Generalized Continued Logarithms and Related Continued
Fractions",
journal = "ArXiv e-prints",
month = jun,
year = "2016",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://adsabs.harvard.edu/abs/2016arXiv160606984B",
abstract = "We study continued logarithms as introduced by Bill
Gosper and studied by J. Borwein et. al.. After
providing an overview of the type I and type II
generalizations of binary continued logarithms
introduced by Borwein et. al., we focus on a new
generalization to an arbitrary integer base $b$. We
show that all of our so-called type III continued
logarithms converge and all rational numbers have
finite type III continued logarithms. As with simple
continued fractions, we show that the continued
logarithm terms, for almost every real number, follow a
specific distribution. We also generalize Khinchine's
constant from simple continued fractions to continued
logarithms, and show that these logarithmic Khinchine
constants have an elementary closed form. Finally, we
show that simple continued fractions are the limiting
case of our continued logarithms, and briefly consider
how we could generalize past continued logarithms.",
acknowledgement = ack-nhfb,
eprint = "1606.06984",
keywords = "Mathematics - Number Theory",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
primaryclass = "math.NT",
}
@Unpublished{Borwein:2016:GCLb,
author = "J. M. Borwein and K. Hare and J. Lynch",
title = "Generalized Continued Logarithms and Related Continued
Fractions",
year = "2016",
bibdate = "Tue Aug 16 09:32:55 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Submitted to Math of Computation, June 2016.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:2016:GDR,
author = "J. Borwein and S. Lindstrom and A. Schneider and B.
Sims and M. Skerritt",
title = "Generalisation of the {Douglas--Rachford} method from
simple spheres to ellipses and $p$-spheres",
month = jun,
year = "2016",
bibdate = "Tue Aug 16 09:39:37 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2016:LFOb,
author = "J. M. Borwein and Scott Lindstrom",
title = "The {Lambert} {$W$} Function and other Special
Functions in Analysis and Optimization",
journal = "Pure and Applied Functional Analysis",
volume = "1",
number = "3",
pages = "??--??",
month = "????",
year = "2016",
DOI = "",
bibdate = "Fri Aug 12 07:19:41 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "TO DO: Find CODEN, ISSN, etc.??",
}
@InCollection{Borwein:2016:LPA,
author = "Jonathan M. Borwein",
title = "The Life of Pi: From {Archimedes} to {ENIAC} and
Beyond",
crossref = "Bailey:2016:PNG",
pages = "443--474",
year = "2016",
bibdate = "Thu Aug 11 15:18:03 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/265/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2016:MLO,
author = "Jonathan M. Borwein and Scott B. Lindstrom",
title = "Meetings with {Lambert} {$ {\cal W} $} and other
special functions in optimization and analysis",
journal = "Pure and Applied Functional Analysis",
volume = "1",
number = "3",
pages = "361--396",
year = "2016",
ISSN = "2189-3756 (print), 2189-3764 (electronic)",
MRclass = "33E99 (49N15 68W30 90C25)",
MRnumber = "3622396",
bibdate = "Fri Sep 30 09:40:16 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
ZMnumber = "06629180",
acknowledgement = ack-nhfb,
ajournal = "Pure Appl. Funct. Anal.",
fjournal = "Pure and Applied Functional Analysis",
language = "English",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2016:MMI,
author = "J. M. Borwein and J. Dutta",
title = "Maximal monotone inclusions and {Fitzpatrick}
functions",
journal = j-J-OPT-THEORY-APPL,
volume = "171",
number = "3",
pages = "757--784",
month = dec,
year = "2016",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/s10957-015-0813-x",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "49J52 (90C30)",
MRnumber = "3575644",
bibdate = "Thu Feb 16 20:11:36 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "In this paper, we study maximal monotone inclusions
from the perspective of gap functions. We propose a
very natural gap function for an arbitrary maximal
monotone inclusion and will demonstrate how naturally
this gap function arises from the Fitzpatrick function,
which is a convex function, used to represent maximal
monotone operators. This allows us to use the powerful
strong Fitzpatrick inequality to analyse solutions of
the inclusion. We also study the special cases of a
variational inequality and of a generalized variational
inequality problem. The associated notion of a scalar
gap is also considered in some detail. Corresponding
local and global error bounds are also developed for
the maximal monotone inclusion.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000389232900002",
}
@Article{Borwein:2016:NPD,
author = "Jonathan M. Borwein and Ohad Giladi",
title = "Nearest points and delta convex functions in {Banach}
spaces",
journal = j-BULL-AUSTRAL-MATH-SOC,
volume = "93",
number = "2",
pages = "283--294",
month = apr,
year = "2016",
CODEN = "ALNBAB",
DOI = "https://doi.org/10.1017/S000497271500101X",
ISSN = "0004-9727 (print), 1755-1633 (electronic)",
ISSN-L = "0004-9727",
MRclass = "46B20 (41A29)",
MRnumber = "3480938",
MRreviewer = "Mari{\'a}n Fabian",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=10230840",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the Australian Mathematical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2016:PEN,
author = "J. M. Borwein and P. B. Borwein and K. Dilcher",
title = "Pi, {Euler} numbers, and asymptotic expansions",
crossref = "Bailey:2016:PNG",
pages = "197--205",
year = "2016",
bibdate = "Thu Aug 11 15:18:03 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1583/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2016:PPB,
author = "Jonathan M. Borwein and Scott T. Chapman",
title = "{I} prefer Pi: a brief history and anthology of
articles in the {{\booktitle{American Mathematical
Monthly}}}",
crossref = "Bailey:2016:PNG",
pages = "475--499",
year = "2016",
bibdate = "Thu Aug 11 15:18:03 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1615/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2016:RME,
author = "J. M. Borwein and P. B. Borwein and D. H. Bailey",
title = "{Ramanujan}, Modular Equations, and Approximations to
Pi or How to Compute One Billion Digits of Pi",
crossref = "Bailey:2016:PNG",
pages = "175--195",
year = "2016",
bibdate = "Thu Aug 11 15:18:03 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1587/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:2016:RP,
author = "Jonathan M. Borwein and Peter B. Borwein",
title = "{Ramanujan} and {Pi}",
crossref = "Bailey:2016:PNG",
pages = "165--174",
year = "2016",
bibdate = "Thu Aug 11 15:18:03 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Reprint of \cite{Borwein:1988:RP}.",
URL = "http://docserver.carma.newcastle.edu.au/1379/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2016:SRC,
author = "Jonathan M. Borwein and Ohad Giladi",
title = "Some Remarks on Convex Analysis in Topological
Groups",
journal = j-J-CONVEX-ANAL,
volume = "23",
number = "2",
pages = "313--332",
month = "????",
year = "2016",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
MRclass = "49J52 Nonsmooth analysis (other weak concepts of
optimality), 22A10, 49J35, 49J27",
MRnumber = "3509663",
MRreviewer = "Constantin Z{\u{a}}linescu",
bibdate = "Sat Aug 13 09:28:34 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1697/;
http://www.heldermann.de/JCA/JCA23/JCA232/jca23012.htm",
ZMnumber = "06610407",
abstract = "We discuss some key results from convex analysis in
the setting of topological groups and monoids. These
include separation theorems, Krein-Milman type
theorems, and minimax theorems.",
acknowledgement = ack-nhfb,
fjournal = "Journal of convex analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000379735400001",
}
@Article{Borwein:2016:SRL,
author = "Jonathan M. Borwein and Ohad Giladi",
title = "Some Remarks on Locally Convex Groups",
journal = j-J-CONVEX-ANAL,
volume = "??",
number = "??",
pages = "??--??",
month = "",
year = "2016",
DOI = "",
ISSN = "0944-6532 (print), 2363-6394 (electronic)",
bibdate = "Fri Aug 12 07:26:11 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "",
acknowledgement = ack-nhfb,
fjournal = "Journal of convex analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Is this the same as \cite{Borwein:2016:SRC}??",
}
@Article{Borwein:2016:SWC,
author = "J. M. Borwein",
title = "A short walk can be beautiful",
journal = j-J-HUMANIST-MATH,
volume = "6",
number = "1",
pages = "5--28",
month = jan,
year = "2016",
DOI = "https://doi.org/10.5642/jhummath.201601.07",
ISSN = "2159-8118",
ISSN-L = "2159-8118",
bibdate = "Fri Aug 12 07:32:51 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1712/",
abstract = "The story I tell is of research undertaken, with
students and colleagues, in the last six or so years on
short random walks. As the research progressed, my
criteria for beauty changed. Things seemingly
remarkable became simple and other seemingly simple
things became more remarkable as our analytic and
computational tools were refined, and understanding
improved. I intentionally display some rather advanced
mathematics as it is my contention - as with classical
music that one can learn to appreciate and enjoy
complex formulas without needing to understand them
deeply.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Humanistic Mathematics",
journal-URL = "http://scholarship.claremont.edu/jhm/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000388610000006",
}
@Article{Borwein:2016:VAL,
author = "J. M. Borwein and Qiji (Jim) Zhu",
title = "A variational approach to {Lagrange} multipliers",
journal = j-J-OPT-THEORY-APPL,
volume = "171",
number = "3",
pages = "727--756",
month = dec,
year = "2016",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/s10957-015-0756-2",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "90C25; 90C46; 49N15",
MRnumber = "3575643",
MRreviewer = "Ern{\"o} Robert Csetnek",
bibdate = "Fri Aug 12 07:40:19 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special issue of JOTA on Nondifferentiable
Optimization and Nonsmooth Analysis, dedicated to
Vladimir Demyanov.",
URL = "http://link.springer.com/article/10.1007/s10957-015-0756-2",
abstract = "We discuss Lagrange multiplier rules from a
variational perspective. This allows us to highlight
many of the issues involved and also to illustrate how
broadly an abstract version can be applied.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
onlinedate = "27 May 2015",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000389232900001",
xxpages = "1--30",
}
@Article{Borwein:2016:VCP,
author = "Jonathan M. Borwein",
title = "A very complicated proof of the minimax theorem",
journal = "Minimax Theory and its Applications",
volume = "1",
number = "1",
pages = "21--27",
month = "????",
year = "2016",
ISSN = "2199-1413 (print), 2199-1421 (electronic)",
MRclass = "91B50 (49N15 49N45 90C25)",
MRnumber = "3477894",
MRreviewer = "Sirous Moradi",
bibdate = "Fri Aug 12 07:35:14 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1499/;
http://www.heldermann.de/MTA/MTA01/MTA011/mta01002.htm",
abstract = "The justly celebrated von Neumann minimax theorem has
many proofs. Here I reproduce the most complex one I am
aware of. This provides a fine didactic example for
many courses in convex analysis or functional
analysis.",
acknowledgement = ack-nhfb,
fjournal = "Minimax Theory and Applications",
journal-URL = "http://www.heldermann.de/MTA/mtacover.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000408632400003",
}
@Book{Monaghan:2016:TMI,
author = "John Monaghan and Luc Trouche and Jonathan M.
Borwein",
title = "Tools and Mathematics: Instruments for Learning",
volume = "110",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxi + 483",
year = "2016",
DOI = "https://doi.org/10.1007/978-3-319-02396-0",
ISBN = "3-319-02395-0, 3-319-02396-9 (e-book)",
ISBN-13 = "978-3-319-02395-3, 978-3-319-02396-0 (e-book)",
ISSN = "0924-4921 (print), 2214-983X (electronic)",
ISSN-L = "0924-4921",
LCCN = "QA11.2 .M65 2016",
bibdate = "Fri Sep 30 09:15:30 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Mathematics Education Library",
URL = "http://docserver.carma.newcastle.edu.au/1717/;
http://sfx.ethz.ch/sfx_locater?sid=ALEPH:EBI01\%26genre=book\%26isbn=9783319023960;
http://swbplus.bsz-bw.de/bsz470387262cov.htm",
abstract = "This book is an exploration of tools and mathematics
and issues in mathematics education related to tool
use. The book has four parts. The first part sets the
scene with a reflection on doing a mathematical task
with different tools, a mathematician's account of tool
use in his work and historical considerations of tool
use. The second part opens with a broad review of
technology and intellectual trends, circa 1970, and
continues with three case studies of approaches in
mathematics education and the place of tools in these
approaches. The third part considers issues related to
mathematics instructions: curriculum, assessment and
policy; the calculator debate; mathematics in the real
world; and teachers' use of technology. The final part
looks to the future and digital tools: task design; the
importance of artefacts in gameplay; and new forms of
activity via connectivity.",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "Mathematics; Study and teaching; Education;
Education.; Study and teaching.",
tableofcontents = "Foreword \\
Preface \\
Contents \\
About the Authors \\
Part I: Setting the Scene \\
Chapter 1: Introduction to the Book \\
1.1 Introduction \\
1.2 The Purpose and Scope of This Book \\
1.3 What Is a Tool? \\
1.3.1 John's Attempt to Address This Question \\
1.3.2 Luc's Attempt to Address This Question \\
1.4 The Structure of the Book \\
References \\
Chapter 2: Doing Mathematics with Tools: One Task, Four
Tools \\
2.1 Introduction \\
2.2 Bisecting an Angle with a Straight Edge and a
Compass \\
2.3 Bisecting an Angle with a Protractor \\
2.4 Bisecting an Angle with a Dynamic Geometry System
\\
2.5 Bisecting an Angle with a Book \\
Chapter 3: The Life of Modern Homo Habilis
Mathematicus: Experimental Computation and Visual
Theorems \\
3.1 Introduction \\
3.1.1 Who I Am and How I Got That Way \\
3.1.2 What Follows \\
3.1.3 Some Early Conclusions \\
3.2 Visual Theorems and Experimental Mathematics \\
3.2.1 Visual Theorems \\
3.2.2 On Picture-Writing \\
3.2.2.1 Proofs Without Words \\
3.3 Experimental Mathematics \\
3.3.1 Experimental Mathodology \\
3.3.2 When Science Becomes Technology \\
3.3.2.1 Minimal Configurations \\
3.3.3 Mathematical Discovery (or Invention) \\
3.3.4 Digital Assistance \\
3.3.5 The Twentieth Century's Top Ten Algorithms \\
3.3.6 Secure Knowledge Without Proof \\
3.3.7 Is `Free' Software Better? \\
3.4 A Dozen or So Accessible Examples \\
3.5 Simulation in Pure Mathematics \\
3.5.1 Monte Carlo Simulation of pi \\
3.5.2 Finding a Region of Convergence \\
3.6 Case Studies I: Dynamic Geometry \\
3.6.1 Case Study Ia: Iterative Reflections \\
3.6.2 Case Study Ib: Protein Conformation \\
3.7 Case Studies II: Numerical Analysis \\
3.7.1 Case Study IIa: Trefethen's 100 Digit Challenge
\\
3.7.2 Case Study IIb: Algorithms for Polylogarithms \\
3.8 Case Studies III: Randomish Walks \\
3.8.1 Case Study IIIa: Short Walks \\
3.8.1.1 The Three-Step Walk3.8.1.2 The Four-Step Walk
\\
3.8.2 Case Study IIIb: Number Walks \\
3.8.3 Case Study IIIc: Normality of Stoneham Numbers
\\
3.9 Conclusion \\
References \\
Chapter 4: Tools, Human Development and Mathematics \\
4.1 Introduction \\
4.2 Tool Use and Phylogenesis \\
4.3 Ancient Greece \\
4.3.1 Discussion of This Proof \\
4.3.2 Tools \\
4.3.3 Oral and Written Mathematics \\
Communities of Practice \\
4.4 Ancient Indian Square Roots \\
4.5 Abaci \\
4.6 Tools for Calculation in Europe Circa 1600 \\
4.7 Discussion: Insights on Tool Use Over Time \\
References \\
Chapter 5: The Development of Mathematics Practices in
the Mesopotamian Scribal Schools \\
5.1 Introduction \\
5.2 A Critical Moment \\
5.3 The Computation Practices and Their Support in
Scribal Schools \\
5.4 Evidencing Computing Artefacts Complementing the
Usage of Tablets and Memory \\
5.5 Analysing the Algorithm for Calculating a
Reciprocal, a Way for Entering the Spirit of
Mesopotomian Computation \\
\\
5.6 Conclusion and Discussion \\
References \\
Chapter 6: Discussions of Part I Chapters \\
6.1 Introduction \\
6.2 Interactions with John and Jon Follow-Up \\
6.2.1 Writing and Mathematics, a Dual Invention?",
}
@Article{AragonArtacho:2017:AMO,
author = "Francisco Javier {Arag{\'o}n Artacho} and Rene Henrion
and Marco Antonio Lopez-Cerda and Claudia Sagastizabal
and Jonathan M. Borwein",
title = "Advances in Monotone Operators Theory and Optimization
(Part 2) Preface",
journal = j-SET-VALUED-VAR-ANAL,
volume = "25",
number = "4, 2",
pages = "637--638",
month = dec,
year = "2017",
DOI = "https://doi.org/10.1007/s11228-017-0466-z",
ISSN = "1877-0533 (print), 1877-0541 (electronic)",
ISSN-L = "1877-0533",
bibdate = "Tue Feb 6 07:32:24 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "Set-Valued and Variational Analysis",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000418588300001",
}
@Article{AragonArtacho:2017:SIA,
author = "Francisco Javier {Arag{\'o}n Artacho} and Rene Henrion
and Marco Antonio Lopez-Cerda and Claudia Sagastizabal
and Jonathan M. Borwein",
title = "Special Issue: Advances in Monotone Operators Theory
and Optimization Preface",
journal = j-SET-VALUED-VAR-ANAL,
volume = "25",
number = "3 (SI)",
pages = "463--465",
month = sep,
year = "2017",
DOI = "https://doi.org/10.1007/s11228-017-0441-8",
ISSN = "1877-0533 (print), 1877-0541 (electronic)",
ISSN-L = "1877-0533",
bibdate = "Tue Feb 6 07:34:04 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
fjournal = "Set-Valued and Variational Analysis",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
ORCID-numbers = "Aragon Artacho, Francisco
Javier/0000-0002-2445-8011",
researcherid-numbers = "Aragon Artacho, Francisco Javier/C-2531-2012",
unique-id = "ISI:000410259100001",
}
@Misc{Bailey:2017:CAA,
author = "David H. Bailey and Jonathan M. Borwein and Andrew
Mattingly and Glenn Wightwick",
title = "Computation and analysis of arbitrary digits of {Pi}
and other mathematical constants",
howpublished = "Slides for Levi Conant Prize lecture at Worcester
Polytechnic Institute, Worcester, MA 01609-2280 USA.",
pages = "38",
day = "15",
month = sep,
year = "2017",
bibdate = "Wed Sep 13 14:57:54 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbtalks/dhb-conant.pdf",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2017:CDA,
author = "David H. Bailey and Jonathan M. Borwein and Jason S.
Kimberley and Watson Ladd",
title = "Computer Discovery and Analysis of Large {Poisson}
Polynomials",
journal = j-EXP-MATH,
volume = "26",
number = "3",
pages = "349--363",
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2016.1180565",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11Y16 (11C08)",
MRnumber = "3642112",
MRreviewer = "{\'I}sabel Pirsic",
bibdate = "Tue Jun 6 09:17:18 MDT 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib;
http://www.tandfonline.com/toc/uexm20/26/3",
URL = "http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1180565",
abstract = "In two earlier studies of lattice sums arising from
the Poisson equation of mathematical physics, it was
established that the lattice sum $ (1 / \pi) \sum {m, n
{\rm odd}} \cos (m \pi x) \cos (n \pi y) / (m^2 + n^2)
= \log A $, where $A$ is an algebraic number, and
explicit minimal polynomials associated with $A$ were
computed for a few specific rational arguments $x$ and
$y$. Based on these results, one of us (Kimberley)
conjectured a number-theoretic formula for the degree
of $A$ in the case $ x = y = 1 / s$ for some integer
$s$. These earlier studies were hampered by the
enormous cost and complexity of the requisite
computations. In this study, we address the Poisson
polynomial problem with significantly more capable
computational tools. As a result of this improved
capability, we have confirmed that Kimberley's formula
holds for all integers $s$ up to 52 (except for $ s =
41, 43, 47, 49, 51$, which are still too costly to
test), and also for $ s = 60$ and $ s = 64$. As far as
we are aware, these computations, which employed up to
64,000-digit precision, producing polynomials with
degrees up to 512 and integer coefficients up to $
10^{229}$, constitute the largest successful integer
relation computations performed to date. By examining
the computed results, we found connections to a
sequence of polynomials defined in a 2010 paper by
Savin and Quarfoot. These investigations subsequently
led to a proof, given in the Appendix, of Kimberley's
formula and the fact that when $s$ is even, the
polynomial is palindromic (i.e., coefficient $ a_k =
a_{m - k}$, where $m$ is the degree).",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
keywords = "experimental mathematics; MPFR; multiprecision
computation; parallel computing; Poisson equation; PSLQ
algorithm",
onlinedate = "24 Aug 2016",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000400342000010",
}
@InCollection{Bailey:2017:CMV,
author = "David H. Bailey and Jonathan M. Borwein",
booktitle = "Space, Time, and Frontiers of Human Understanding",
title = "A computational mathematics view of space, time and
complexity",
crossref = "Wuppuluri:2017:STL",
pages = "403--416",
year = "2017",
bibdate = "Sat Jan 21 18:28:46 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1696/",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Bailey:2017:ERM,
author = "David H. Bailey and Jonathan M. Borwein and Amir
Salehipour and Marcos {Lopez de Prado}",
title = "Evaluation and ranking of market forecasters",
type = "Preprint",
institution = "Department of Computer Science, University of
California, Davis",
address = "Davis, CA 95616, USA",
pages = "22",
day = "1",
month = mar,
year = "2017",
bibdate = "Wed Mar 01 10:45:15 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/forecaster.pdf;
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2944853",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:2017:PBO,
author = "David H. Bailey and Jonathan M. Borwein and Marcos
{Lopez de Prado} and Qiji Jim Zhu",
title = "The Probability of Backtest Overfitting",
journal = j-J-COMPUT-FINANCE,
volume = "20",
number = "4",
pages = "39--69",
month = apr,
year = "2017",
DOI = "https://doi.org/10.21314/JCF.2016.322",
ISSN = "1460-1559 (print), 1755-2850 (electronic)",
ISSN-L = "1460-1559",
bibdate = "Mon Oct 09 17:33:29 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/1710/;
http://ssrn.com/abstract=2326253;
https://www.risk.net/journal-of-computational-finance/2471206/the-probability-of-backtest-overfitting",
abstract = "Many investment firms and portfolio managers rely on
backtests (ie, simulations of performance based on
historical market data) to select investment strategies
and allocate capital. Standard statistical techniques
designed to prevent regression overfitting, such as
hold-out, tend to be unreliable and inaccurate in the
context of investment backtests. We propose a general
framework to assess the probability of backtest
overfitting (PBO). We illustrate this framework with
specific generic, model-free and non-parametric
implementations in the context of investment
simulations; we call these implementations
combinatorially symmetric cross-validation (CSCV). We
show that CSCV produces reasonable estimates of PBO for
several useful examples.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Finance",
journal-URL = "https://www.risk.net/journal-of-computational-finance",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000398686500003",
}
@Article{Bailey:2017:RCS,
author = "David H. Bailey and Jonathan M. Borwein and Richard P.
Brent and Mohsen Reisi",
title = "Reproducibility in Computational Science: A Case
Study: Randomness of the Digits of Pi",
journal = j-EXP-MATH,
volume = "26",
number = "3",
pages = "298--305",
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2016.1163755",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11K16 (03D32 11K45 62F03 62F35 62P99)",
MRnumber = "3642107",
MRreviewer = "Samuel S. Wagstaff, Jr.",
bibdate = "Tue Jun 6 09:17:18 MDT 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib;
http://www.tandfonline.com/toc/uexm20/26/3",
note = "See reply \cite{Ganz:2017:RRC}.",
URL = "http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1163755",
abstract = "Mathematical research is undergoing a transformation
from a mostly theoretical enterprise to one that
involves a significant amount of experimentation.
Indeed, computational and experimental mathematics is
now a full-fledged discipline with mathematics, and the
larger field of computational science is now taking its
place as an experimental discipline on a par with
traditional experimental fields. In this new realm,
reproducibility comes to the forefront as an essential
part of the computational research enterprise, and
establishing procedures to ensure and facilitate
reproducibility is now a central focus of researchers
in the field. In this study, we describe our attempts
to reproduce the results of a recently published
article by Reinhard Ganz, who concluded that the
decimal expansion of pi is not statistically random,
based on an analysis of several trillion decimal digits
provided by Yee and Kondo. While we are able to
reproduce the specific findings of Ganz, additional
statistical analysis leads us to reject his overall
conclusion.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
onlinedate = "24 Aug 2016",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000400342000005",
}
@Article{Borwein:2017:CLA,
author = "Jonathan M. Borwein and Neil J. Calkin and Scott B.
Lindstrom and Andrew Mattingly",
title = "Continued Logarithms and Associated Continued
Fractions",
journal = j-EXP-MATH,
volume = "26",
number = "4",
pages = "412--429",
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2016.1195307",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "40A15 (11A55 11J70 11Y65)",
MRnumber = "3684575",
bibdate = "Fri Aug 18 08:39:18 MDT 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/expmath.bib;
http://www.tandfonline.com/toc/uexm20/26/4",
URL = "http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1195307",
abstract = "We investigate some of the connections between
continued fractions and continued logarithms. We study
the binary continued logarithms as introduced by Bill
Gosper and explore two generalizations of the continued
logarithm to base b. We show convergence for them using
equivalent forms of their corresponding continued
fractions. Through numerical experimentation, we
discover that, for one such formulation, the exponent
terms have finite arithmetic means for almost all real
numbers. This set of means, which we call the
logarithmic Khintchine numbers, has a pleasing
relationship with the geometric means of the
corresponding continued fraction terms. While the
classical Khintchine's constant is believed not to be
related to any naturally occurring number, we find
surprisingly that the logarithmic Khintchine numbers
are elementary.",
acknowledgement = ack-nhfb,
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
onlinedate = "16 Sep 2016",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000407599500003",
}
@Article{Borwein:2017:CRA,
author = "Jonathan M. Borwein and Guoyin Li and Matthew K. Tam",
title = "Convergence Rate Analysis for Averaged Fixed Point
Iterations in Common Fixed Point Problems",
journal = j-SIAM-J-OPT,
volume = "27",
number = "1",
pages = "1--33",
month = jan,
year = "2017",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/15m1045223",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
MRclass = "41A25 (41A50 90C25 90C31)",
MRnumber = "3592082",
MRreviewer = "Heinz H. Bauschke",
bibdate = "Mon Jan 16 11:46:35 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
http://www.math.utah.edu/pub/tex/bib/siamjopt.bib",
abstract = "In this paper, we establish sublinear and linear
convergence of fixed point iterations generated by
averaged operators in a Hilbert space. Our results are
achieved under a bounded Holder regularity assumption
which generalizes the well-known notion of bounded
linear regularity. As an application of our results, we
provide a convergence rate analysis for many important
iterative methods in solving broad mathematical
problems such as convex feasibility problems and
variational inequality problems. These include
Krasnoselskii-Mann iterations, the cyclic projection
algorithm, forward-backward splitting and the
Douglas--Rachford feasibility algorithm along with some
variants. In the important case in which the underlying
sets are convex sets described by convex polynomials in
a finite dimensional space, we show that the Holder
regularity properties are automatically satisfied, from
which sublinear convergence follows.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
onlinedate = "5 January 2017",
ORCID-numbers = "Li, Guoyin/0000-0002-2099-7974",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000404178500001",
}
@Article{Borwein:2017:GCL,
author = "Jonathan M. Borwein and Kevin G. Hare and Jason G.
Lynch",
title = "Generalized continued logarithms and related continued
fractions",
journal = j-J-INTEGER-SEQ,
volume = "20",
number = "5",
pages = "Art. 17.5.7, 51",
year = "2017",
ISSN = "1530-7638",
MRclass = "11J70 (11K50)",
MRnumber = "3669604",
bibdate = "Fri Oct 13 15:06:06 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "We study continued logarithms, as introduced by Gosper
and studied by Borwein et al. After providing an
overview of the type I and type II generalizations of
binary continued logarithms introduced by Borwein et
al., we focus on a new generalization to an arbitrary
integer base b. We show that all of our so-called type
III continued logarithms converge and all rational
numbers have finite type III continued logarithms. As
with simple continued fractions, we show that the
continued logarithm terms, for almost every real
number, follow a specific distribution. We also
generalize Khinchin's constant from simple continued
fractions to continued logarithms, and show that these
logarithmic Khinchin constants have an elementary
closed form. Finally, we show that simple continued
fractions are the limiting case of our continued
logarithms, and briefly consider how we could
generalize beyond continued logarithms.",
acknowledgement = ack-nhfb,
ajournal = "J. Integer Seq.",
article-number = "UNSP 17.5.7",
fjournal = "Journal of Integer Sequences",
journal-URL = "https://cs.uwaterloo.ca/journals/JIS/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000406528900003",
}
@Article{Borwein:2017:GEC,
author = "Jonathan M. Borwein",
title = "Generalisations, Examples, and Counter-examples in
Analysis and Optimisation: In honour of {Michel
Th{\'e}ra} at 70",
journal = j-SET-VALUED-VAR-ANAL,
volume = "25",
number = "3",
pages = "467--479",
month = sep,
year = "2017",
DOI = "https://doi.org/10.1007/s11228-016-0379-2",
ISSN = "1877-0533 (print), 1877-0541 (electronic)",
ISSN-L = "1877-0533",
MRclass = "47H09 (49J52 90C25)",
MRnumber = "3694873",
bibdate = "Sat Aug 13 09:46:09 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Special issue for Michel Th{\'e}ra at 70. 7th
International Seminar on Optimization and Variational
Analysis (OVA), Universidad Alicante, Alicante, Spain,
1--3 June 2016.",
URL = "http://docserver.carma.newcastle.edu.au/1688/;
http://link.springer.com/article/10.1007/s11228-016-0379-2",
abstract = "In this essay, I talk about the role of examples and
counter-examples and of generalisation in mathematical
research. I use geometric fixed point theory and
nonsmooth optimisation to illustrate my opinions and
conclude with a few recommendations.",
acknowledgement = ack-nhfb,
fjournal = "Set-Valued and Variational Analysis",
journal-URL = "http://link.springer.com/journal/11228",
onlinedate = "5 August 2016",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000410259100002",
}
@Article{Borwein:2018:DFE,
author = "Jonathan M. Borwein and Karl Dilcher",
title = "Derivatives and fast evaluation of the {Tornheim} zeta
function",
journal = j-RAMANUJAN-J,
volume = "45",
number = "2",
pages = "413--432",
month = feb,
year = "2018",
DOI = "https://doi.org/10.1007/s11139-017-9890-9",
ISSN = "1382-4090 (print), 1572-9303 (electronic)",
ISSN-L = "1382-4090",
MRclass = "11M41 (33B20 33B30)",
MRnumber = "3749750",
bibdate = "Tue Feb 6 07:16:48 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "We study analytic properties of the Tornheim zeta
function , which is also named after Mordell and
Witten. In particular, we evaluate the function () at
and, as our main result, find the derivative of this
function at . Our principal tool is an identity due to
Crandall that involves a free parameter and provides an
analytic continuation. Furthermore, we derive special
values of a permutation sum. Throughout this paper, we
show by way of examples that Crandall's identity can be
used for efficient and high-precision evaluations of
the Tornheim zeta function.",
acknowledgement = ack-nhfb,
fjournal = "The {Ramanujan} Journal",
fjournal = "Ramanujan Journal. An International Journal Devoted to
the Areas of Mathematics Influenced by Ramanujan",
journal-URL = "http://link.springer.com/journal/11139",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
unique-id = "ISI:000423339500008",
}
%%% ====================================================================
%%% Part 2 (of 4): Blog publications by Jonathan M. Borwein
%%%
%%% NB: The CV.pdf file supplies links to author pages, but not to
%%% individual articles; URL values have been adjusted to point to
%%% articles where possible. Also, article dates are often off by one,
%%% and some have been changed to match the article Web sites; however,
%%% that could instead be due to Australian time versus US time, with
%%% the Web site displaying times in EST.
%%%
%%% The blogs in The Conversation have all been supplied with URLs,
%%% except for entry Bailey:2014:WSP, whose title cannot be found at
%%% the publisher site.
%%%
%%% The blogs in The Huffington Post have all been supplied with URLs,
%%% except for entry Bailey:2012:CPG, whose title cannot be found at
%%% the publisher site.
%%%
%%% The Web sites
%%%
%%% http://www.huffingtonpost.com/jonathan-m-borwein/
%%% http://www.huffingtonpost.com/author/david-h-bailey
%%% https://theconversation.edu.au/profiles/jon-borwein-101
%%%
%%% may provide a collection of links to author publications.
%%%
%%% Bibliography entries, sorted by ascending year, month, day
%%% with ``bibsort --byday'' (the opposite of their order in
%%% CV.pdf):
@Article{Borwein:2011:IAP,
author = "Jonathan M. Borwein",
title = "The infinite appeal of Pi",
journal = "ABC Science",
volume = "??",
number = "??",
pages = "??",
day = "10",
month = mar,
year = "2011",
bibdate = "Tue Aug 16 07:13:56 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.abc.net.au/science/articles/2011/03/10/3158045.htm",
acknowledgement = ack-nhfb,
ORCID-numbers = "Borw