%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "1.81",
%%% date = "01 September 2022",
%%% time = "18:02:15 MDT",
%%% 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 = "58623 53312 232396 2390580",
%%% 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)
%%% (ORCID Borwein, Jonathan/0000-0002-1263-0646).
%%%
%%% 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 accepted and in press, or submitted,
%%% and ones that he simply forgot, or chose not,
%%% to record.
%%%
%%% At version 1.81, the COMPLETE year coverage
%%% looked like this:
%%%
%%% 1972 ( 1) 1989 ( 25) 2006 ( 62)
%%% 1973 ( 0) 1990 ( 52) 2007 ( 57)
%%% 1974 ( 1) 1991 ( 36) 2008 ( 47)
%%% 1975 ( 0) 1992 ( 28) 2009 ( 65)
%%% 1976 ( 4) 1993 ( 43) 2010 ( 70)
%%% 1977 ( 5) 1994 ( 49) 2011 ( 100)
%%% 1978 ( 4) 1995 ( 62) 2012 ( 125)
%%% 1979 ( 10) 1996 ( 39) 2013 ( 136)
%%% 1980 ( 7) 1997 ( 71) 2014 ( 119)
%%% 1981 ( 10) 1998 ( 41) 2015 ( 100)
%%% 1982 ( 8) 1999 ( 61) 2016 ( 113)
%%% 1983 ( 11) 2000 ( 56) 2017 ( 37)
%%% 1984 ( 19) 2001 ( 47) 2018 ( 33)
%%% 1985 ( 9) 2002 ( 39) 2019 ( 2)
%%% 1986 ( 23) 2003 ( 53) 2020 ( 33)
%%% 1987 ( 27) 2004 ( 51) 2021 ( 14)
%%% 1988 ( 31) 2005 ( 79) 2022 ( 1)
%%% 19xx ( 7)
%%%
%%% Article: 825
%%% Book: 56
%%% InCollection: 89
%%% InProceedings: 74
%%% MastersThesis: 1
%%% Misc: 187
%%% PhdThesis: 2
%%% Proceedings: 15
%%% TechReport: 137
%%% Unpublished: 740
%%%
%%% Total entries: 2126
%%%
%%% 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 V5A 1S6, 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-APPL-NUM-MATH = "Applied Numerical Mathematics: Transactions
of IMACS"}
@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-COLLOQ-MATH = "Colloquium Mathematicum"}
@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-INTEGRAL-TRANSFORMS-SPEC-FUNCT = "Integral Transforms and Special
Functions"}
@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-AUSTRALIAN-MATH-SOC = "Journal of the Australian Mathematical Society"}
@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-SUPERCOMPUTING = "The Journal of Supercomputing"}
@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-COMP-SIM = "Mathematics and Computers in Simulation"}
@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"}
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Mathematical Methods of Operations Research"}
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%%% ====================================================================
%%% Series abbreviations:
@String{ser-LNCS = "Lecture Notes in Computer Science"}
%%% ====================================================================
%%% 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Not found in Proquest or in Oxford Solo catalog.",
}
@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",
pages = "200",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Found in Proquest, but not available for viewing.
Oxford Solo catalog identifies physical location as
Radcliffe Science Library.",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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)",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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)",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
ISSN-L = "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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Mathematical Programming Study",
journal-URL = "https://link.springer.com/bookseries/8439",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Mathematische Operationsforschung und Statistik Series
Optimization",
journal-URL = "http://www.tandfonline.com/loi/gopt20",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
}
@InProceedings{Borwein:1981:CCP,
author = "J. M. Borwein and H. Wolkowicz",
title = "Cone-convex programming, stability and affine
constraints",
crossref = "Schaible:1981:CCP",
pages = "379--397",
year = "1981",
bibdate = "Mon Mar 6 22:00:29 MST 1995",
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 = "Invited paper.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxpages = "379--392",
xxtitle = "Cone-convex programming, stability and affine
constraint functions",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Mathematical Programming Study",
journal-URL = "https://link.springer.com/bookseries/8439",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Mathematische Operationsforschung und Statistik Series
Optimization",
journal-URL = "http://www.tandfonline.com/loi/gopt20",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Mathematische Operationsforschung und Statistik Series
Optimization",
journal-URL = "http://www.tandfonline.com/loi/gopt20",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis",
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^\infty $ 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)",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
ISSN-L = "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;
http://www.math.utah.edu/pub/tex/bib/anziamj.bib",
URL = "http://docserver.carma.newcastle.edu.au/1607/;
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=3973752;
https://www.cambridge.org/core/journals/anziam-journal/article/generic-differentiability-of-orderbounded-convex-oparators/EBC10922AB270DAAF5784308C7E3157A",
acknowledgement = ack-nhfb,
ajournal = "J. Austral Math. Soc. Ser. B",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of the Australian Mathematical Society. Series
B, Applied Mathematics",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
onlinedate = "17 February 2009",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis",
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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://docserver.carma.newcastle.edu.au/1596/1/barzilai-borwein-ocr.pdf;
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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].
Received 24 September 1986 and in revised form 14 April
1987.",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = pub-COLLINS,
address = pub-COLLINS:adr,
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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;
https://web.archive.org/web/20170328083101/http://docserver.carma.newcastle.edu.au/1587/1/P40.pdf",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
pagecount = "11",
remark = "The title in the PDF file is ``A Survey of Convex
Functions and Sequential Convergence'', with co-author
Jon D. Vanderwerff: is that a completely different
paper?",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxseries = "Pitman Res. Notes Math. Ser.",
}
@InCollection{Borwein:1991:RP,
author = "Jonathan M. 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/;
https://web.archive.org/web/20170227063951/http://docserver.carma.newcastle.edu.au/1379/1/RAMA125f.pdf",
abstract = "This contribution highlights the progress made
regarding Ramanujan's work on Pi since the centennial
of his birth in 1987.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxauthor = "Jonathan M. Borwein and Peter B. Borwein",
}
@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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
volume = "244",
publisher = "Longman",
address = "Essex, UK",
bookpages = "315",
pages = "39--52",
year = "1992",
DOI = "",
ISBN = "0-582-08065-7 (paperback), 0-582-08065-7,
0-470-21943-2",
ISBN-13 = "978-0-582-08065-2 (paperback), 978-0-582-08065-2,
978-0-470-21943-0",
ISSN = "0269-3674",
ISSN-L = "0269-3674",
LCCN = "QA402.5 .O6424 1991",
bibdate = "Mon Aug 15 14:55:03 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
series = "Pitman research notes in mathematics series",
URL = "",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Proceedings of a Binational Workshop on Optimization
and Nonlinear Analysis, held at Technion City, Haifa,
21--27 March 1990, organized by the Institute of
Advanced Studies in Mathematics at the Technion and
sponsored by the U.S.--Israel Binational Science
Foundation and the Technion--Israel Institute of
Technology.",
}
@InCollection{Borwein:1992:SEC,
author = "J. M. Borwein and A. {Ben Tal} and M. Teboulle",
title = "Spectral estimation via convex programming",
crossref = "Phillips:1992:SMS",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "275--290",
year = "1992",
bibdate = "Mon Aug 15 14:57:23 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
month = oct,
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",
URL = "http://www.ams.org/journals/notices/199210/199210FullIssue.pdf",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Bailey:1993:EEE,
author = "David H. Bailey and Jonathan M. Borwein and Roland
Girgensohn",
title = "Experimental evaluation of {Euler} sums",
type = "Technical Report",
number = "RNR-93-014",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
pages = "24",
day = "20",
month = oct,
year = "1993",
bibdate = "Thu Sep 01 13:58:44 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/60",
abstract = "In response to a letter from Goldbach, Euler
considered sums of the form\par
$$ \sum_{k = 1}^\infty \big (1 + \frac {1}{2^m} +
\cdots + \frac {1}{k^m} \big) (k + 1)^{-n} $$ \par
for positive integers $m$ and $n$. Euler was able to
give explicit values for certain of these sums in terms
of the Riemann zeta function. In a recent companion
paper, Euler's results were extended to a significantly
larger class of sums of this type, including sums with
alternating signs.\par
This research was facilitated by numerical computations
using an algorithm that can determine, with high
confidence, whether or not a particular numerical value
can be expressed as a rational linear combination of
several given constants. The present paper presents the
numerical techniques used in these computations and
lists many of the experimental results that have been
obtained.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "Bauschke, Heinz/0000-0002-4155-9930; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "math/9302212",
keywords = "Mathematics - Functional Analysis, 46B",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1993:FAS,
author = "Jon Borwein and Jon Vanderwerff",
title = "Further arguments for slice convergence in
nonreflexive spaces",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
pages = "18",
day = "6",
month = nov,
year = "1993",
MRclass = "52A41 (40A30, 46A55, 46B20)",
bibdate = "Thu Sep 01 14:11:31 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/62",
abstract = "It is shown that no notion of set convergence at least
as strong as Wijsman convergence but not as strong as
slice convergence can be preserved in superspaces. We
also show that such intermediate notions of convergence
do not always admit representations analogous to those
given by Attouch and Beer for slice convergence, and
provide a valid reformulation. Some connections between
bornologies and the relationships between certain gap
convergences for nonconvex sets are also observed.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
pages = "13",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
pages = "13",
day = "15",
month = dec,
year = "1993",
MRclass = "46A17, 46G05, 58C20 (46B20)",
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/",
abstract = "We study the relationships between Gateaux, Weak
Hadamard and Fr{\'e}chet differentiability and their
bornologies for Lipschitz and for convex functions.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.a",
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;
https://www.science.org/doi/10.1126/science.259.5103.1928.a",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
xxDOI = "https://doi.org/10.1126/science.259.5103.1928",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
}
@TechReport{Borwein:1993:WSC,
author = "Jonathan Borwein and Simon Fitzpatrick",
title = "Weak sequential compactness and bornological limit
derivatives",
type = "Report",
institution = "Department of Mathematics and Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 1S6, Canada",
pages = "10",
day = "7",
month = sep,
year = "1993",
bibdate = "Thu Sep 01 13:54:08 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/58/2/93_001-Borwein-Borwein-Girgensohn.pdf",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:1994:EEEb,
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
Jonathan/0000-0002-1263-0646",
}
@TechReport{Bauschke:1994:MCP,
author = "H. H. Bauschke and J. M. Borwein and A. S. Lewis",
title = "On the method of cyclic projections for convex sets in
{Hilbert} space",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "51",
day = "10",
month = feb,
year = "1994",
MRclass = "47H09, 4OM45, 65-02, 65J05, 90C25 (26B25, 41A65,
46C99, 46N10, 47N10, 52A05, 52A41, 65F10, 65KO05,
90C90, 92C55)",
bibdate = "Thu Sep 01 14:51:27 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/77",
abstract = "The method of cyclic projections 1s a powerful tool
for solving convex feasibility problems in Hilbert
space. Although in many applications, in particular in
the field of image reconstruction (electron microscopy,
computed tomography), the convex constraint sets do not
necessarily intersect, the method of cyclic projections
is still employed. Results on the behaviour of the
algorithm for this general case are improved, unified,
and reviewed. The analysis relies on key concepts from
convex analysis and the theory of nonexpansive
mappings. The notion of the angle of a tuple of
subspaces is introduced. New linear convergence results
follow for the case when the constraint sets are closed
subspaces whose orthogonal complements have a closed
sum; this holds, in particular, for hyperplanes or in
Euclidean space.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "angle; computerized tomography; convex feasibility
problem; convex polyhedron; convex set; Fej{\'e}r
monotone sequence; Hilbert space; image reconstruction;
Kaczmarz s method; method of cyclic projections;
nearest point mapping; nonexpansive map",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1994:BSA,
author = "J. M. Borwein and J. D. Vanderwerff",
title = "{Banach} spaces that admit support sets",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
pages = "6",
day = "10",
month = jul,
year = "1994",
bibdate = "Thu Sep 01 15:46:06 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/87",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1994:CCS,
author = "Jonathan Borwein and Simon Fitzpatrick",
title = "Characterization of {Clarke} subgradients among
one-dimensional multifunctions",
type = "Report",
institution = "Department of Mathematics, Simon Fraser University",
address = "Burnaby, BC V5A 1S6, Canada",
pages = "14",
day = "2",
month = feb,
year = "1994",
bibdate = "Thu Sep 01 09:17:17 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:1995:CCS}.",
URL = "http://docserver.carma.newcastle.edu.au/23/",
abstract = "We introduce the notions of an robustly lower
semicontinuous and an robustly upper semicontinuous
function of a real variable. The Clarke subgradients of
locally Lipschitz functions on an open interval $I$ are
shown to be exactly those multifunctions on $I$ of the
form $ [\alpha (x), \beta (x)]$ where $ \alpha $ is
robustly lower semicontinuous and $ \beta $ is robustly
upper semicontinuous on $I$. The approximate and
symmetric subgradients of locally Lipschitz functions
on $I$ are also characterized.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1994:CFS,
author = "Jon Borwein and Jon Vanderwerff",
title = "Convex Functions on ``Sequentially Reflexive''
{Banach} Spaces",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
pages = "11",
day = "14",
month = sep,
year = "1994",
bibdate = "Wed Aug 31 09:48:34 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/115/2/95_050-Borwein-Vanderwerff.pdf",
abstract = "There is a sizeable class of results precisely
relating boundedness, convergence and differentiability
properties of continuous convex functions on Banach
spaces to whether or not the space contains an
isomorphic copy of $ \ell_1 $. In this note, we provide
constructions showing that the main such results do not
extend to natural broader classes of functions.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:CMI,
author = "Jonathan Borwein",
title = "A convergent mean iteration: a proof that {$ 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "The Michigan Mathematical Journal",
journal-URL = "https://projecteuclid.org/all/euclid.mmj",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxtitle = "{Mosco}, {Wijsman} and slice convergence in
nonreflexive {Banach} spaces",
}
@Article{Borwein:1994:ECFc,
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1994:EEEa,
author = "David Borwein and Jonathan M. Borwein and Roland
Girgensohn",
title = "Explicit evaluation of {Euler} sums",
type = "Report",
institution = "Department of Mathematics and Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 1S6, Canada",
pages = "21",
day = "18",
month = mar,
year = "1994",
MRclass = "40A25, 40B05 (11M99, 33E99)",
bibdate = "Thu Sep 01 11:00:10 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/58",
abstract = "In response to a letter from Goldbach, Euler
considered sums of the form\par
$$ \sigma_h(s, t) = \sum_{n = 1}^\infty \big (1 +
\frac {1}{2^s} + \cdots + \frac {1}{(n - 1)^s} \big)
n^{-t}, $$ \par
where $s$ and $t$ are positive integers.\par
As Euler discovered by a process of extrapolation (from
$ s + t \leq 13$), $ \sigma_h(s, t)$ can be evaluated
in terms of Riemann $ \zeta $-functions when $ s + t$
is odd. We provide a rigorous proof of Euler's
discovery and then give analogous evaluations with
proofs for corresponding alternating sums. Relatedly we
give a formula for the series\par $$ \sum_{n =
1}^\infty \big (1 + \frac {1}{2} + \cdots + \frac
{1}{n} \big)^2 (n + 1)^{-m} $$ \par
This evaluation involves $ \zeta $-functions and $
\sigma_h(2, m)$.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "beta function; generating functions; harmonic numbers;
polylogarithms; psi function; Riemann zeta function",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
}
@TechReport{Borwein:1994:FEDa,
author = "Jonathan M. Borwein and Roland Girgensohn",
title = "Functional equations and distribution functions",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
pages = "10",
day = "15",
month = jul,
year = "1994",
bibdate = "Thu Sep 01 15:54:10 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Dedicated to Professor J{\'a}nos Acz{\'e}l's on the
occasion of his 70th birthday.",
URL = "http://docserver.carma.newcastle.edu.au/90",
abstract = "Wee consider the functional equation\par
$$ f(t) = \frac {1}{b} \sum_{\nu = 0}^{b - 1} f \big
(\frac {t - \beta_nu}{a} \big) \mbox {for all $ t \in
\mathbb{R}$ }, \qquad (F) $$ \par
where $ 0 < a < 1 $ , $ b \in \mathbb {N} \backslash \{
1 \} $ and $ - 1 = \beta_0 \leq \beta_1 \leq \beta_2
\leq \cdots \leq \beta_{p - 1} = 1 $ are given
parameters, $ f \color \mathbb {R} \to \mathbb {R} $ is
the unknown. We show that there is a unique bounded
function $f$ which solves (F) and satisfies $ f(t) = 0$
for $ t < - 1 / (1 - a)$, $ f(t) = 1$ for $ t > 1 / (1
- a)$. This solution can be interpreted as the
distribution function of a certain random series. It 1s
known to be either singular or absolutely continuous,
but the problem for which parameters it 1s absolutely
continuous 1s largely open. We collect some previously
established partial answers and generalize them. We
also point out an interesting connection to the
so-called Schilling equation.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:FEDb,
author = "Jonathan M. Borwein and Roland Girgensohn",
title = "Functional equations and distribution functions",
journal = "Results in Mathematics. Resultate der Mathematik",
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 J{\'a}nos Acz{\'e}l's 70th birthday.",
URL = "http://docserver.carma.newcastle.edu.au/90/",
acknowledgement = ack-nhfb,
ajournal = "Results Math.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Results in Mathematics. Resultate der Mathematik",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1994:MER,
author = "J. M. Borwein and A. S. Lewis and D. Noll",
title = "Maximum entropy reconstruction using derivative
information. {Part 1}: {Fisher} information and convex
duality",
type = "Report",
institution = "Department of Combinatorics and Optimization
University of Waterloo",
address = "Waterloo, ON N2L 3G1, Canada",
pages = "31",
day = "14",
month = dec,
year = "1994",
bibdate = "Thu Sep 01 15:39:54 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/82",
abstract = "Maximum entropy spectral density estimation is a
technique for reconstructing an unknown density
function from some known measurements by maximizing a
given measure of entropy of the estimate. Here we
present a variety of new entropy measures which attempt
to control derivative values of the densities. Our
models apply among others to the inference problem
based on the averaged Fisher information measure. The
duality theory we develop resembles models used in
convex optimal control problems. We present a variety
of examples, including relaxed moment matching with
Fisher information and best interpolation on a strip.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "duality; Fisher information; generalized solutions;
Maximum Entropy method; optimal control; Partially
finite convex programming; Spectral Density
estimation",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1994:MES,
author = "J. M. Borwein and A. S. Lewis and M. N. Limber and D.
Noll",
title = "Maximum Entropy Spectral Analysis Using Derivative
Information Part 2: Computational Results",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "19",
day = "10",
month = jan,
year = "1994",
bibdate = "Thu Sep 01 14:47:08 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/71",
abstract = "Maximum entropy density estimation, a technique for
reconstructing an unknown density function on the basis
of certain measurements, has applications in various
areas of applied physical sciences and engineering.
Here we present concrete results for the maximum
entropy inversion program based on a new class of
information measures which are designed to control
derivative values of the unknown densities.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "Convex duality; Fisher information; Optimal Control;
Primal dual program; Runge--Kutta methods; Spectral
density estimation",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1994:SEC,
author = "Jonathan M. Borwein",
title = "A survey of examples of convex functions and
classifications of normed spaces",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
pages = "13",
day = "1",
month = dec,
year = "1994",
MRclass = "46B20, 46N10 (46B10)",
bibdate = "Thu Sep 01 16:26:49 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Revised 22 January 1995. Published in
\cite{Borwein:1995:SEC}.",
URL = "http://docserver.carma.newcastle.edu.au/92;
http://docserver.carma.newcastle.edu.au/93",
abstract = "This paper represents a slightly extended version of
the eponymous talk given at the VII Colloque
Franco-Allemand d'Optimisation. My aim is to illustrate
the tight connection between the sequential properties
of a Banach space and the corresponding properties of
the convex functions and sets which may or may not be
defined on that space.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "classical Banach spaces; convex functions;
differentiability; Haar-null sets.; nearest points;
sequential properties",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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:1994:UCMa,
author = "J. M. Borwein and W. Huang",
title = "Uniform convergence for moment problems with
{Fermi--Dirac} type entropies",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
pages = "11",
day = "7",
month = jan,
year = "1994",
MRclass = "49M39, 41A10, 44A60",
bibdate = "Thu Sep 01 14:42:30 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/70/",
abstract = "We consider the best entropic estimation to a unknown
density $ \bar {x} $, given some of its algebraic or
trigonometric moments. A uniform convergence theorem is
established in this paper for such problems using
Fermi--Dirac type entropic objectives",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "best approximation; Fenchel duality; Fermi--Dirac
entropy; linear constrained optimization; moment
problems; uniform convergence",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1994:UCMb,
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Which journal is this??",
}
@TechReport{Borwein:1994:VAN,
author = "Jonathan M. Borwein and Qiji J. Zhu",
title = "Variational analysis in nonreflexive spaces and
applications to control problems with {$ L^1 $}
perturbations",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
pages = "40",
day = "2",
month = may,
year = "1994",
bibdate = "Thu Sep 01 14:58:07 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/78",
abstract = "We provide a refined sensitivity analysis for finite
and infinite horizon control problems where in both
cases the perturbation space is $ L^1 $. Our underlying
technique relies on a recent sequential description of
both the generalized gradient of Clarke and of the
approximate $G$-subdifferential of functions defined on
a smooth Banach space. We also show that the proximal
limit formula for the generalized gradient and its $
L^p$ analogue are direct consequences of these
sequential formulas. Related characterizations of
Lipschitzness of a function on a smooth space are
given.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646",
}
@TechReport{Bauschke:1995:CLM,
author = "Heinz H. Bauschke and Jonathan M. Borwein",
title = "Continuous linear monotone mappings in {Banach}
space",
type = "CECM Research Report",
number = "95:049",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "48",
day = "29",
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/;
https://web.archive.org/web/20110313015539/http://docserver.carma.newcastle.edu.au/114/2/95_049%2DBauschke%2DBorwein.pdf",
abstract = "The concept of a monotone operator --- which covers
both linear positive semi-definite operators and
subdifferentials of convex functions --- has turned out
to be very powerful in various branches of mathematics.
- Over the last few decades, several new notions of
monotonicity have been introduced: Gossez' maximal
monotone of type (D), Simons' monotone of type (WD) and
of type (NI), Fitzpatrick and Phelps' locally maximal
monotone. While these monotonicities are automatic for
maximal monotone operators in reflexive Banach spaces
and for subdifferentials of convex functions, their
precise relationship is largely unknown. In view of the
origin of the theory of monotone operators, it is very
natural to investigate linear monotone (i.e. positive
semi-definite) operators. Here, it 1s shown --- within
the beautiful framework of Convex Analysis --- that for
continuous linear monotone operators, {\em all these
notions coincide and are equivalent to the monotonicity
of the conjugate operator}. The latter condition is
analyzed and illustrated by several examples. Some
nonlinear results on regularizations conclude the
paper.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
Jonathan/0000-0002-1263-0646",
xxtitle = "Continuous Linear Monotone Operators on {Banach}
Space",
}
@TechReport{Bauschke:1995:LFM,
author = "Heinz H. Bauschke and Jonathan M. Borwein",
title = "{Legendre} functions and the method of random
{Bregman} projections",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "48",
day = "2",
month = mar,
year = "1995",
MRclass = "49M45 (47TH17, 52A41, 65F10, 65K05, 90C25)",
bibdate = "Thu Sep 01 16:43:37 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Bauschke:1997:LFM}.",
URL = "http://docserver.carma.newcastle.edu.au/96",
abstract = "The convex feasibility problem, that is, finding a
point in the intersection of finitely many closed
convex sets in Euclidean space, arises in various areas
of mathematics and physical sciences. It can be solved
by the classical method of cyclic orthogonal
projections, where, by projecting cyclically onto the
sets, a sequence is generated that converges to a point
in the intersection. In 1967, Bregman extended this
method to non-orthogonal projections based on a new
notion of distance, now days called ``Bregman
distance''. The Bregman distance is induced by a convex
function. If this function is a so-called ``zone
consistent Bregman function'', then Bregman's method
works; however, deciding on this can be difficult. In
this paper, Bregman's method is studied within the
powerful framework of Convex Analysis. New insights are
obtained and the rich class of ``Bregman\slash Legendre
functions'' is introduced. Bregman's method still
works, if the underlying function is Bregman\slash
Legendre or more generally if it is Legendre but some
constraint qualification holds additionally. The key
advantage 1s the broad applicability and verifiability
of these concepts. The results presented here are
complementary to recent work by Censor and Reich on the
method of random Bregman projections (where the sets
are projected onto infinitely often --- not necessarily
cyclically). Special attention 1s given to examples,
some of which connect to Pythagorean means and to
Convex Analysis on the Hermitian or symmetric
matrices.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "Bregman function; Bregman projection; convex
feasibility problem; convex function; convex set;
essentially smooth function; essentially strictly
convex function; Hermitian matrix; Legendre function;
projection",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Bauschke:1995:PAS,
author = "Heinz H. Bauschke and Jonathan M. Borwein",
title = "On Projection Algorithms for Solving Convex
Feasibility Problems",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "99",
day = "28",
month = apr,
year = "1995",
bibdate = "Wed Aug 31 08:57:40 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Bauschke:1996:PAS}",
URL = "http://docserver.carma.newcastle.edu.au/100/2/95_034-Bauschke-Borwein.pdf",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Undated, but stored in 1995-labeled directory, and PDF
produced Fri Apr 28 14:11:01 1995.",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
pages = "9",
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/",
abstract = "If $E$ is a separable super-reflexive Banach space
then every closed convex subset of $E$ with empty
interior is a Haar null set.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of Functional Analysis",
journal-URL = "http://www.sciencedirect.com/science/journal/00221236",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1995:CML,
author = "David Borwein and Jonathan M. Borwein and Christopher
Pinner",
title = "Convergence of {Madelung}-Like Lattice Sums",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "46",
month = jun,
year = "1995",
bibdate = "Wed Aug 31 09:30:55 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/104/2/95_040-Borwein-Borwein-Pinner.pdf",
abstract = "We make a general study of the convergence properties
of lattice sums, involving potentials, of the form
occurring in Mathematical Chemistry and Physics. Many
specific examples are studied in detail. The prototype
is Madelung's constant for NaCl: $$ \sum_{- \infty }^{+
\infty } \frac {( - 1)^{n + m + p}}{\sqrt {n^2 + m^2 +
p^2}} = - 1.74756459 \cdots $$ resuming that one
appropriately interprets the summation process.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1995:DDF,
author = "J. M. Borwein and Xianfu Wang",
title = "Distinct Differentiable Functions May Share the Same
{Clarke} Subdifferential at all points",
type = "Report",
institution = inst-CARMA,
address = inst-CARMA:adr,
pages = "10",
day = "29",
month = jun,
year = "1995",
bibdate = "Wed Aug 31 06:33:16 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:1997:DDF}.",
URL = "https://docserver.carma.newcastle.edu.au/112/2/95_047-Borwein-Wang.pdf",
abstract = "We construct, using Zahorski's Theorem, two everywhere
differentiable real-valued Lipschitz functions
differing by more than a constant but sharing the same
Clarke subdifferential and the same approximate
subdifferential.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Revised 8 September 1995.",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
}
@TechReport{Borwein:1995:EUC,
author = "Jonathan M. Borwein and Jon D. Vanderwerff",
title = "Epigraphical and uniform convergence of convex
functions",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
pages = "19",
day = "17",
month = mar,
year = "1995",
MRclass = "46A55, 46B20, 52A41",
bibdate = "Thu Sep 01 16:32:28 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/94/",
abstract = "We examine when a sequence of lsc convex functions on
a Banach space con- verges uniformly on bounded sets
(resp. compact sets) provided it converges Attouch-Wets
(resp. Painlev{\'e}--Kuratowski). We also obtain
related results for pointwise convergence and uniform
convergence on weakly compact sets. Some known results
concerning the convergence of sequences of linear
functionals are shown to also hold for lsc convex
functions. For example, a sequence of lsc convex
functions converges uniformly on bounded sets to a
continuous affine function provided that the
convergence is uniform on weakly compact sets and the
space does not contain an isomorphic copy of $ \ell_1
$.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "Attouch-Wets convergence; Epi-convergence; lsc convex
function; Mosco convergence.; Painlev{\'e}--Kuratowski
convergence; pointwise convergence; uniform
convergence",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Applicable Analysis. An International Journal",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1995:GCP,
author = "D. Borwein and J. M. Borwein and P. B. Borwein and R.
Girgensohn",
title = "{Giuga}'s conjecture on primality",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
pages = "16",
day = "9",
month = jun,
year = "1995",
MRclass = "11A41, 11Y11 (11Y50)",
bibdate = "Thu Sep 01 15:48:11 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:1996:GCP}.",
URL = "http://docserver.carma.newcastle.edu.au/88",
abstract = "G. Giuga conjectured that if an integer $n$ satisfies
$ \sum_{k = 1}^{n - 1} k^{n - 1} \equiv - 1 \bmod n$,
then $n$ must be a prime. We survey what is known about
this interesting and now fairly old conjecture. Giuga
proved that $n$ is a counterexample to his conjecture
if and only if each prime divisor $p$ of $n$ satisfies
$ (p - 1) | (n / p - 1)$ and $ p | (n / p - 1)$. Using
this characterization, he proved computationally that
any counterexample has at least 1,000 digits; equipped
with more computing power, E. Bedocchi later raised
this bound to 1,700 digits. By improving on their
method, we determine that any counterexample has at
least 13,800 digits. We also give some new results on
the second of the above conditions. This leads, in our
opinion, to some interesting questions about what we
call Giuga numbers and Giuga sequences.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "Carmichael numbers; Computational number theory;
Primality",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1995:IIS,
author = "David Borwein and Jonathan M. Borwein",
title = "On an intriguing integral and some series related to
{$ \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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1995:LFP,
author = "Jonathan M. Borwein and Warren B. Moors and Xianfu
Wang",
title = "{Lipschitz} functions with prescribed derivatives and
subderivatives",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
pages = "16",
day = "25",
month = jul,
year = "1995",
MRclass = "49J52 (46N10, 58C20)",
bibdate = "Thu Sep 01 16:15:30 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/92",
abstract = "In general it is difficult to construct Lipschitz
functions which are not directly built up from either
convex or distance functions. One impediment to such
constructions is that outside of the real line it 1s
difficult to find anti-derivatives. The main result of
this paper provides, under suitable circumstances, a
technique for constructing such anti-derivatives. More
precisely, we show that if $ f_1, f_2, \ldots, f_n $
are continuously differentiable real-valued locally
Lipschitz functions defined on a non-empty open subset
$A$ of a separable Banach space $X$, then there exists
a real-valued locally Lipschitz function $g$ defined on
$A$ such that at each point $ x \in A$ the Clarke
subgradient of $g$ at $x$ equals $ \mathrm {co} \{
\nabla f_1 (x), \nabla f_2 (x), \ldots {}, \nabla
f_n(x) \} $.\par
This same construction also shows that for any finite
family $ \{ T_1, T_2, \ldots {}, T_n \} $ of maximal
cyclically monotone mappings from $A$ into non-empty
subsets of $ X^\star $, there exists a real-valued
locally Lipschitz function $g$ defined on $A$ such that
at each point $ x \in A$ the Clarke subgradient of $g$
at $x$ equals $ \mathrm {co} \{ T_1 (x), T_2 (x),
\ldots {}, T_n(x) \} $. Moreover, we show that $g$ is
convex if and only if $ T_1 = T_2 = \cdots = T_n$.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "Clarke subgradient; differentiability; Haar-null set;
Lipschitz functions; maximal cyclically monotone
operator; minimal cusco",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1995: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",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
month = sep,
year = "1995",
MRclass = "49J52 (49J40, 49J50, 58C20)",
bibdate = "Wed Aug 31 09:53:05 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/116/2/95_051-Borwein-Treiman-Zhu.pdf",
abstract = "We consider nonsmooth constrained optimization
problems with semicontinuous and continuous data in
Banach space and derive necessary conditions without
constraint qualification in terms of smooth
subderivatives and normal cones. These results, in
different versions, are set in reflexive and smooth
Banach spaces.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "Constrained optimization problems; multipliers;
nonsmooth analysis; normals and fuzzy calculus.;
subderivatives",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1995:PAS,
author = "Jonathan M. Borwein and Alexander Ioffe",
title = "Proximal Analysis in Smooth Spaces",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
pages = "30",
day = "21",
month = feb,
year = "1995",
bibdate = "Thu Sep 01 14:05:31 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/61",
abstract = "We provide a highly-refined sequential description of
the generalized gradients of Clarke and approximate
$G$-subdifferential of a lower semicontinuous
extended-real-valued function defined on a Banach space
with a $ \beta $-smooth equivalent renorm. In the case
of a Fr{\'e}chet differentiable renorm we give a
corresponding result for the corresponding singular
objects.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "$G$ subdifferentials; Clarke subdifferentials;
distance functions; Lipschitz functions; lower semi
continuous functions; normals; smooth renorms;
sub-derivatives; tangent cones; variational
principles",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1995:SAD,
author = "J. M. Borwein and W. Sun",
title = "The stability analysis of dynamic {SPECT} systems",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "14",
year = "1995",
MRclass = "68U10, 41A30, 65F35",
bibdate = "Thu Sep 01 17:55:00 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/99",
abstract = "SPECT (Single Photon Emission Computed Tomography)
techniques have been applied to a wide range of medical
studies. The stability of a SPECT model depends
strongly upon the data collected. We show that a SPECT
model is full rank and well-conditioned (stable) if the
projection data are large enough. Condition number
estimates for a linear model are given. Numerical
results for a class of linear models confirm our
theoretical analysis.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "least squares; medical imaging; SPECT model;
stability",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Undated and no date in PDF file metadata, but
directory numbering suggests 1995. Newest entry [1] in
References list is dated 1994. Reference [7] is
published in \cite{Limber:1995:DRF}.",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
xxtitle = "A survey of examples of convex functions and the
classification of {Banach} spaces",
}
@TechReport{Borwein:1995:SRR,
author = "J. M. Borwein and E. Wong",
title = "A survey of results relating to {Giuga}'s conjecture
on primality",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "21",
day = "8",
month = may,
year = "1995",
bibdate = "Wed Aug 31 08:44:19 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:1997:SRR}.",
abstract = "This article is an expanded version of the talk given
by the first author at the 25th Anniversary Conference
of the Centre de R{\'e}cherches Math{\'e}matiques.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1995:SRSa,
author = "Jonathan M. Borwein and Jon D. Vanderwerff",
title = "A survey on renorming and set convergence",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
pages = "19",
day = "25",
month = mar,
year = "1995",
MRclass = "46A55, 46B20, 52A41",
bibdate = "Thu Sep 01 16:51:41 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:1995:SRSb}.",
URL = "http://docserver.carma.newcastle.edu.au/97",
abstract = "This article presents a survey of some recent results
relating set convergence and renorming. We focus most
of our attention on norms having various Kadec--Klee
properties and their interplay with certain forms of
set convergence including Wijsman and slice
convergence.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "convex analysis; Kadec--Klee norms; Lipschitz
regularizations; Mosco convergence; set convergence;
slice convergence; Wijsman convergence",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1995:SRSb,
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
}
@TechReport{Borwein:1995:VSV,
author = "Jonathan M. Borwein and Qiji J. Zhu",
title = "Viscosity solutions and viscosity subderivatives in
smooth {Banach} spaces with applications to metric
regularity",
type = "Report",
institution = "Department of Mathematics \& Statistics, Simon Fraser
University",
address = "Burnaby, BC V5A 156, Canada",
pages = "40",
day = "18",
month = mar,
year = "1995",
MRclass = "49J52 (49L25, 49J40, 49J50, 58C20)",
bibdate = "Thu Sep 01 15:35:07 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/80",
abstract = "In Gateaux or bornologically differentiable spaces
there are two natural generalizations of the concept of
a Fr{\'e}chet subderivative: In this paper we study the
viscosity subderivative (which is the more robust of
the two) and establish refined fuzzy sum rules for it
in a smooth Banach space. These rules are applied to
obtain comparison results for viscosity solutions of
Hamilton--Jacobi equations in $ \beta $-smooth spaces.
A unified treatment of metric regularity in smooth
spaces completes the paper. This illustrates the
flexibility of viscosity subderivatives as a tool for
analysis.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "fuzzy sum rule; Hamilton--Jacobi equations; metric
regularity; smooth spaces; viscosity solutions;
Viscosity subderivative",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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{Bailey:1996:QP,
author = "David H. Bailey and Jonathan M. Borwein and Peter B.
Borwein and Simon Plouffe",
title = "The quest for pi",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "16",
day = "25",
month = jun,
year = "1996",
bibdate = "Wed Aug 31 15:23:45 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Bailey:1997:QP}",
URL = "http://docserver.carma.newcastle.edu.au/164/",
abstract = "This article gives a brief history of the analysis and
computation of the mathematical constant $ \pi =
3.141359 \ldots {} $, including a number of the
formulas that have been used to compute $ \pi $ through
the ages. Recent developments in this area are then
discussed in some detail, including the recent
computation of $ \pi $ to over six billion decimal
digits using high-order convergent algorithms, and a
newly discovered scheme that permits arbitrary
individual hexadecimal digits of $ \pi $ to be
computed.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Bauschke:1996: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",
type = "Report",
institution = "Department of Combinatorics \& Optimization,
University of Waterloo",
address = "Waterloo, Ontario N2L 3G1, Canada",
pages = "23",
day = "20",
month = nov,
year = "1996",
bibdate = "Wed Aug 31 15:38:23 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Bauschke:1999:MMD}.",
URL = "http://docserver.carma.newcastle.edu.au/180/",
abstract = "The concept of a monotone operator --- which covers
both linear positive semi-definite operators and
subdifferentials of convex functions 1s fundamental in
various branches of mathematics. Over the last few
decades, several stronger notions of monotonicity have
been introduced: Gossez's maximal monotonicity of dense
type, Fitzpatrick and Phelps's local maximal
monotonicity, and Simons's monotonicity of type (NI).
While these monotonicities are automatic for maximal
monotone operators in reflexive Banach spaces and for
subdifferentials of convex functions, their precise
relationship is largely unknown. Here, it 1s shown ---
within the beautiful framework of Convex Analysis ---
that for continuous linear monotone operators, all
these notions coincide and are equivalent to the
monotonicity of the conjugate operator. This condition
is further analyzed and illustrated by examples.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "Bauschke, Heinz/0000-0002-4155-9930; 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",
}
@TechReport{Borwein:1996:ADE,
author = "J. M. Borwein and F. G. Garvan",
title = "Approximations to $ \pi $ via the {Dedekind} eta
function",
type = "Report",
institution = "Department of Mathematics, Simon Fraser University",
address = "Burnaby, BC V5A 1S6, Canada",
pages = "28",
day = "27",
month = mar,
year = "1996",
bibdate = "Wed Aug 31 14:56:53 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/158/",
abstract = "Arguably the most efficient algorithm currently known
for the extended precision calculation of $ \pi $ 1s a
quartic iteration due to J. M. and P. B. Borwein. In
their paper, the Borwein's show how this iteration and
others are intimately connected to the work of
Ramanujan. This connection 1s shown utilizing their
alpha-function which is defined in terms of
theta-functions. They are able to find p-th order
iterations based on this function using modular
equations for the theta-functions. In this paper we
construct an infinite family of functions $ \alpha_p $.
Each $ \alpha_p $ gives rise to a $p$-th order
iteration. For $ p = 4$ we obtain a quartic iteration
due to the Borweins but not the one that comes from the
alpha-function. For $ p = 3$ we obtain a cubic
iteration due to the Borweins that does not come from
the alpha-function. For $ p = 7$ we find a septic
iteration that is analogous to the cubic iteration. For
$ p = 9$ we obtain a nonic (ninth order) iteration that
does not seem to come from iterating the cubic twice.
Our method depends on using the computer and a symbolic
algebra package to find and solve certain modular
equations.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1996:AGM,
author = "Jonathan A. Borwein and Petr Lison{\v{e}}k and John A.
Macdonald",
title = "Arithmetic--Geometric Means Revisited",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "8",
year = "1996",
bibdate = "Thu Sep 01 10:39:15 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/4/",
abstract = "We use Maple's {\tt gfun} library to study the limit
formulae for a two-term recurrence (iteration) $ A G_N
$, which in the case $ N = 2 $ specializes to the
well-known Arithmetic-Geometric Mean iteration of
Gauss. Our main aim 1s to independently rediscover and
prove the limit formulae for two classical cases ($ N =
2, 3$) in a completely automated manner and to open the
way for studying the remaining cases ($ N > 3$).",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1996:ASC,
author = "D. Borwein and J. M. Borwein and Xianfu Wang",
title = "Approximate subgradients and coderivatives in {$ {\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",
abstract = "We show that in two dimensions or higher the
Mordukhovich--Ioffe approximate subgradient and Clarke
subgradient may differ almost everywhere for
real-valued Lipschitz functions. Uncountably many
Fr{\'e}chet differentiable vector-valued Lipschitz
functions differing by more than constants can share
the same Mordukhovich--Ioffe coderivatives. Moreover,
the approximate Jacobian associated with the
Mordukhovich--Ioffe coderivative can be nonconvex
almost everywhere for Fr{\'e}chet differentiable
vector-valued Lipschitz functions. Finally we show that
for vector-valued Lipschitz functions the approximate
Jacobian associated with the Mordukhovich-Ioffe
coderivative can be almost everywhere disconnected.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1996:CRE,
author = "Jonathan M. Borwein and Warren B. Moors",
title = "A chain rule for essentially smooth {Lipschitz}
functions",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
day = "16",
month = jan,
year = "1996",
bibdate = "Wed Aug 31 14:42:53 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:1998:CRE}",
URL = "http://docserver.carma.newcastle.edu.au/151/",
abstract = "In this paper we introduce a new class of real-valued
locally Lipschitz functions, (that are similar in
nature and definition to Valadier's {\em saine\/}
functions) which we call {\em arc-wise essentially
smooth}, and we show that if $ g \colon R^n \to R $ is
arc-wise essentially smooth on $ R^n $ and each
function $ f_j \colon R^m \to R $, $ 1 \leq j \leq n $
is strictly differentiable almost everywhere in $ R^m
$, then $ g \circ f $ is strictly differentiable almost
everywhere in $ R^m $, where $ f \equiv (f_1 f_2,
\ldots, f_n) $. We also show that all the semi-smooth
and pseudo-regular functions are arc-wise essentially
smooth. Thus, we provide a large and robust lattice
algebra of Lipschitz functions whose generalized
derivatives are well-behaved.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.",
}
@TechReport{Borwein:1996:EFEa,
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 $k$",
number = "CECM-96-067, OUT-4102-63, hep-th/9611004",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "21",
day = "2",
month = sep,
year = "1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/161",
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\slash
Zagier sums (also known as multidimensional zeta\slash
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1996:EFEb,
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "hep-th/9611004",
keywords = "High Energy Physics - Theory",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Accepted 31 October 1996.",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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??",
}
@TechReport{Borwein:1996:NSE,
author = "Jonathan M. Borwein and Warren B. Moors",
title = "Null sets and essentially smooth {Lipschitz}
functions",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "22",
day = "4",
month = jun,
year = "1996",
bibdate = "Wed Aug 31 15:13:13 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:1998:NSE}.",
URL = "http://docserver.carma.newcastle.edu.au/162/",
abstract = "In this paper we extend the notion of a Lebesgue-null
set to a notion which is valid in any completely
metrizable Abelian topological group. We then use this
definition to introduce and study the class of
essentially smooth functions. These are, roughly
speaking, those Lipschitz functions which are smooth
(in each direction) almost everywhere.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Revised January 17th 1997.",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.
Borwein:1982:NSMbib",
URL = "http://links.jstor.org/sici?sici=0002-9890(199612)103:10<911:1>2.0.CO%3B2-5&origin=MSN",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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/;
https://web.archive.org/web/20170227063951/http://docserver.carma.newcastle.edu.au/1379/1/RAMA125f.pdf",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
abstract = "We discuss some aspects of the search for identities
using computer algebra and symbolic methods. To keep
the discussion as concrete as possible, we shall focus
on so-called Ap{\'e}ry-like formulae for special values
of the Riemann Zeta function. Many of these results are
apparently new, and much more work needs to be done
before they can be formally proved and properly
classified. A first step in this direction can be found
in [1].",
acknowledgement = ack-nhfb,
acmid = "235700",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "SIAM Journal on Control and Optimization",
journal-URL = "http://epubs.siam.org/sicon",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1996: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?",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "20",
day = "24",
month = apr,
year = "1996",
bibdate = "Wed Aug 31 14:53:22 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:1997:WOM}.",
URL = "http://docserver.carma.newcastle.edu.au/157/",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "No abstract in report",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646",
}
@Article{Bailey:1997:QP,
author = "David H. Bailey and Jonathan M. Borwein and Peter B.
Borwein and Simon 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "The Mathematical Intelligencer",
journal-URL = "http://link.springer.com/journal/283",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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://docserver.carma.newcastle.edu.au/1587/1/P40.pdf;
http://www.cecm.sfu.ca/organics/papers/borwein/index.html;
https://web.archive.org/web/20170328083101/http://docserver.carma.newcastle.edu.au/1587/1/P40.pdf",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
book-URL = "http://www.cecm.sfu.ca/organics",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
Jonathan/0000-0002-1263-0646",
}
@TechReport{Bauschke:1997: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",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "30",
day = "26",
month = sep,
year = "1997",
bibdate = "Thu Sep 01 07:28:55 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/195",
abstract = "The strong conical hull intersection property and
bounded linear regularity are properties of a
collection of finitely many closed convex intersecting
sets in Euclidean space. These fundamental notions
occur in various branches of convex optimization
(constrained approximation, convex feasibility
problems, linear inequalities, for instance). It is
shown that the standard constraint qualification from
convex analysis implies bounded linear regularity,
which in turn yields the strong conical hull
intersection property. Jameson's duality for two cones,
which relates bounded linear regularity to property
(G), is re-derived and refined. For polyhedral cones, a
statement dual to Hoffman's error bound result is
obtained. A sharpening of a result on error bounds for
convex inequalities by Auslender and Crouzeix is
presented. Finally, for two subspaces, property (G) is
quantified by the angle between the subspaces.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Maple technical newsletter",
journal-URL = "http://web.mit.edu/maple/www/plibrary/mtn.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1997:AIR,
author = "Jonathan M. Borwein and Petr Lison{\v{e}}k",
title = "Applications of integer relation algorithms",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
day = "18",
month = nov,
year = "1997",
bibdate = "Thu Sep 01 07:39:40 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2000:AIR}.",
URL = "http://docserver.carma.newcastle.edu.au/198",
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 $ c a^T = 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Submitted to the Proceedings of the 9th International
Conference on Formal Power Series and Algebraic
Combinatorics (FPSAC'97), July 1997, Vienna, Austria,
to appear as a special issue of Discrete Mathematics.",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1997:CAM,
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",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "12",
day = "31",
month = jul,
year = "1997",
bibdate = "Thu Sep 01 07:55:12 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1997:CBS,
author = "Jon Borwein and Marian Fabian and Jon Vanderwerff",
title = "Characterizations of {Banach} spaces via convex and
other locally {Lipschitz} functions",
journal = "Acta Mathematica Vietnamica",
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/",
abstract = "Various properties of Banach spaces, including the
reflexivity and the Schur property of a space, are
characterized in terms of properties of corresponding
classes of locally Lipschitz functions on those
spaces.",
acknowledgement = ack-nhfb,
ajournal = "Acta Math. Vietnam.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
}
@TechReport{Borwein:1997:CHP,
author = "J. M. Borwein and R. Girgensohn and Xianfu Wang",
title = "On the construction of {H{\"o}lder} and proximal
subderivatives",
type = "Report",
institution = "Department of Mathematics, Simon Fraser University",
address = "Burnaby, BC V5A 1S6, Canada",
pages = "13",
day = "14",
month = mar,
year = "1997",
bibdate = "Thu Sep 01 06:39:15 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:1998:CHP}.",
URL = "http://docserver.carma.newcastle.edu.au/186/",
abstract = "We construct Lipschitz functions such that for all $ s
> 0 $ they are s-H{\o}lder, and so proximally,
subdifferentiable only on dyadic rationals and nowhere
else. As applications we construct Lipschitz functions
with prescribed Holder and approximate
subderivatives.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1997:GYI,
author = "Jonathan M. Borwein",
title = "A generalization of {Young}'s {$ l^p $} inequality",
type = "Report",
institution = "Department of Mathematics, Simon Fraser University",
address = "Burnaby, BC V5A 1S6, Canada",
pages = "6",
day = "24",
month = jun,
year = "1997",
bibdate = "Thu Sep 01 06:48:28 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/189/",
abstract = "We show that, for positive real numbers with $ a \geq
1 + \sum_i^N \alpha_i $, the function\par
$$ \frac {r^a / a}{| \Prod_{i = 1}^N x_i^{\alpha_i}}
$$ \par
has a convex conjugate of the same form and so, in
particular, obtain a clean proof that $f$ is convex.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Borwein:1997:LFM,
author = "Jonathan M. Borwein and Warren 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/",
abstract = "In this paper we characterise, in terms of the upper
Dini derivative, when the Clarke subdifferential
mapping of a real-valued locally Lipschitz function is
a minimal weak$^\star $ cusco. We then use this
characterisation to deduce some new results concerning
Lipschitz functions with minimal subdifferential
mappings.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis",
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",
ZMnumber = "0884.00004",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Maple technical newsletter",
journal-URL = "http://web.mit.edu/maple/www/plibrary/mtn.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1997:NSP,
author = "Jonathan M. Borwein and Alejandro Jofr{\'e}",
title = "A nonconvex separation property in {Banach} spaces",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "11",
day = "13",
month = nov,
year = "1997",
bibdate = "Thu Sep 01 07:36:57 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:1998:NSP}.",
URL = "http://docserver.carma.newcastle.edu.au/197",
abstract = "We establish, in infinite dimensional Banach space, a
nonconvex separation property for general closed sets
that is an extension of Hahn-Banach separation theorem.
We provide some consequences in optimization, in
particular the existence of singular multipliers and
show the relation of our principle with the extremal
principle of Mordukhovich.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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;
http://www.cecm.sfu.ca/organics/papers/borwein/index.html",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Unpublished{Borwein:1997:SDIa,
author = "Jonathan M. Borwein",
title = "Symbolically discovered identities for ZETA(4N+3) and
multidimensional polylogarithms",
day = "31",
month = jul,
year = "1997",
bibdate = "Tue Aug 16 10:19:46 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Penn State Number Theory Conference, July 31--Aug 3.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1997:SDIb,
author = "Jonathan M. Borwein and Warren B. Moors",
title = "Separable determination of integrability and
minimality of the {Clarke} subdifferential mapping",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "10",
day = "30",
month = sep,
year = "1997",
bibdate = "Thu Sep 01 07:33:19 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2000:SDI}.",
URL = "http://docserver.carma.newcastle.edu.au/196",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1997:SRM,
author = "Jonathan M. Borwein and Warren B. Moors and Yongheng
Shao",
title = "Subgradient representation of multifunctions",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "14",
day = "21",
month = feb,
year = "1997",
bibdate = "Wed Aug 31 15:45:10 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:1999:SRM}.",
URL = "http://docserver.carma.newcastle.edu.au/184/",
abstract = "We provide necessary and sufficient conditions for a
minimal upper semicontinuous multifunction defined on a
separable Banach space to be the subdifferential
mapping of a Lipschitz function.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Bauschke:1998:COM,
author = "Heinz H. Bauschke and Jonathan M. Borwein",
title = "Conical open mapping theorems and regularity",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "14",
day = "10",
month = nov,
year = "1998",
bibdate = "Thu Sep 01 08:35:40 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Bauschke:1999:COM}.",
URL = "http://docserver.carma.newcastle.edu.au/208/",
abstract = "Suppose $T$ is a continuous linear operator between
two Hilbert spaces $X$ and $Y$ and let $K$ be a closed
convex nonempty cone in $X$. We investigate the
possible existence of $ \delta > 0$ such that $ \delta
B_Y \cap T(K) \subseteq T(B_X \cap K)$, where $ B_X$, $
B_Y$ denote the closed unit balls in $X$ and $Y$
respectively. This property, which we call openness
relative to $K$, is a generalization of the classical
openness of linear operators. We relate relative
openness to Jameson's property (G), to the strong
conical hull intersection property, to bounded linear
regularity, and to metric regularity. Our results allow
a simple construction of two closed convex cones that
have the strong conical hull intersection property but
fail to be boundedly linearly regular.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Bauschke:1998:MRS,
author = "Heinz H. Bauschke and Jonathan M. Borwein and Paul
Tseng",
title = "Metric regularity, strong {CHIP}, and {CHIP} are
distinct properties",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "17",
day = "20",
month = jul,
year = "1998",
MRclass = "90C25 (46C05, 52A15, 52A20)",
bibdate = "Thu Sep 01 08:17:03 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/204",
abstract = "Metric 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 in 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.\par
We show that --- even for convex cones --- the converse
implications need not hold by constructing
counter-examples in $ \mathbb {R}^4 $.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Electronic Journal of Combinatorics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
pagecount = "12",
}
@TechReport{Borwein:1998: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",
type = "Report",
institution = "Department of Mathematics, Simon Fraser University",
address = "Burnaby, BC V5A 1S6, Canada",
pages = "14",
day = "10",
month = nov,
year = "1998",
bibdate = "Thu Sep 01 08:31:11 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2000:CDA}.",
URL = "http://docserver.carma.newcastle.edu.au/207/",
abstract = "The particular entropy method proposed by Hoch {\em 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "convex duality; Entropy optimization; nuclear magnetic
resonance; spectral analysis",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
note = "Published in \cite{Borwein:2000:CSR}.",
URL = "http://docserver.carma.newcastle.edu.au/211;
http://people.reed.edu/~crandall/papers/attach01.pdf",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August 2016);
Richard Eugene Crandall (29 December 1947--20 December
2012)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1998:DIS,
author = "J. M. Borwein and S. P. Fitzpatrick",
title = "Duality inequalities and sandwiched functions",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "15",
day = "8",
month = jul,
year = "1998",
MRclass = "49J52, 90C25 (26B25, 46N10, 47H10, 52A41)",
bibdate = "Thu Sep 01 08:12:48 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/204",
abstract = "We establish a mixed convex-Lipschitz mean value
inequality from which recent results of Clarke and
Ledyaev and of Lewis and Ralph follow naturally. We
also provide various refinements and extensions.
Finally, we answer affirmatively several open questions
on the existence of ``squeeze'' theorems for a finite
number of Lipschitz functions.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "CECM-98-120, OUT-4102-76, hep-th/9811173",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "53",
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/",
abstract = "We identify 998 closed hyperbolic 3-manifolds whose
volumes are rationally related to Dedekind zeta values,
with coprime integers $a$ and $b$ giving\par
$$ \frac {a}{b} \mathrm {vol}(\mathcal {M}) = \frac {(
- D)^{3 / 2}}{(2 \pi)^{2 n - 4}} \frac {\zeta_K(2)}{2
\zeta (2)} $$ \par
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_g$ symmetry. Our results are secure, numerically, yet
appear very hard to prove by analysis.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1998:ETE,
author = "Jonathan M. Borwein and Robert M. Corless",
title = "Emerging tools for experimental mathematics",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "28",
day = "27",
month = nov,
year = "1998",
bibdate = "Thu Sep 01 08:05:55 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:1999:ETE}.",
URL = "http://docserver.carma.newcastle.edu.au/203",
abstract = "Using mostly elementary examples, we discuss the use
of some recent and emerging tools for experimental
mathematics. The tools discussed include so-called
``inverse symbolic computation'', lattice reduction
algorithms such as ``LLL'', and ``PSLQ'', and Sloane
and Plouffe's integer sequence lookup program.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1998:LFM,
author = "Jonathan M. Borwein and Xianfu Wang",
title = "{Lipschitz} functions with maximal {Clarke}
subdifferentials are generic",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
day = "11",
month = sep,
year = "1998",
bibdate = "Thu Sep 01 08:26:34 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2000:LFM}.",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
}
@TechReport{Borwein:1998:R,
author = "Jonathan Borwein and Kwok-Kwong Stephen Choi",
title = "On the representations of $ x y + y z + z x $",
type = "Report",
institution = "Department of Mathematics, Simon Fraser University",
address = "Burnaby, BC V5A 1S6, Canada",
pages = "8",
year = "1998",
bibdate = "Thu Sep 01 08:48:35 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/212",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Undated, but PDF file metadata has
98:119-Borwein-Choi.dvi. No abstract",
}
@TechReport{Borwein:1998: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",
type = "CECM Research Report",
number = "98-106",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "45",
day = "14",
month = may,
year = "1998",
bibdate = "Thu Sep 01 07:48:47 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "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 a longstanding
conjecture of Don Zagier.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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/",
abstract = "Suppose $T$ is a continuous linear operator between
two Hilbert spaces $X$ and $Y$ and let $K$ be a closed
convex nonempty cone in $X$. We investigate the
possible existence of $ \delta > 0$ such that $ \delta
B_Y \cap T(K) \subseteq T(B_X \cap K)$, where $ B_X$, $
B_Y$ denote the closed unit balls in $X$ and $Y$
respectively. This property, which we call openness
relative to $K$, is a generalization of the classical
openness of linear operators. We relate relative
openness to Jameson's property (G), to the strong
conical hull intersection property, to bounded linear
regularity, and to metric regularity. Our results allow
a simple construction of two closed convex cones that
have the strong conical hull intersection property but
fail to be boundedly linearly regular.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
Jonathan/0000-0002-1263-0646",
remark = "Preprint PDF file of 14 pages is dated 10-Nov-1998.",
}
@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://docserver.carma.newcastle.edu.au/187;
http://www.ncbi.nlm.nih.gov/pubmed/10363703",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
Jonathan/0000-0002-1263-0646",
remark = "Preprint is 19 pages, and titled \booktitle{An EM
algorithm for dynamic SPECT tomography}.",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Pacific Journal of Mathematics",
journal-URL = "http://msp.org/pjm",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Mathematical Programming. A Publication of the
Mathematical Programming Society",
journal-URL = "http://link.springer.com/journal/10107",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = pub-HARPERCOLLINS,
address = pub-HARPERCOLLINS:adr,
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Originally published in \cite{Borowski:1988:DM}.",
subject = "Mathematics; Dictionaries; Mathematics.",
}
@TechReport{Borwein:1999:CEL,
author = "Jonathan Borwein and Yves Lucet and Boris
Mordukhovich",
title = "Compactly epi-{Lipschitzian} convex sets and functions
in normed spaces",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "20",
day = "9",
month = jun,
year = "1999",
bibdate = "Thu Sep 01 08:42:56 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2000:CEL}.",
URL = "http://docserver.carma.newcastle.edu.au/210/",
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.\par
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1999:CSFa,
author = "Jonathan M. Borwein and John Read and Adrian S. Lewis
and Qiji Zhu",
title = "Convex spectral functions of compact operators",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "27",
day = "10",
month = mar,
year = "1999",
bibdate = "Thu Sep 01 10:08:54 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2000:CSF}.",
abstract = "We consider functions on the space of compact
self-adjoint Hilbert space operators. Specifically, we
study those extended-real functions which depend only
on the operators' spectral sequences. Examples include
the norms of the Schatten $p$-spaces, the Calder{\'e}n
norms, the $k$'th largest eigenvalue, and some
infinite-dimensional self-concordant barriers. We show
how various convex and nonsmooth-analytic properties of
such functions follow from the corresponding properties
of the restrictions to the space of diagonal operators,
and we derive subdifferential and conjugacy formulas.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1999:CSFb,
author = "Jonathan M. Borwein and Adrian S. Lewis and Qiji J.
Zhu",
title = "Convex spectral functions of compact operators, {Part
II}: {Lower} semicontinuity and rearrangement
invariance",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "18",
year = "1999",
MRclass = "49J52, 47B10",
bibdate = "Thu Sep 01 10:33:31 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/251/",
abstract = "It was shown in Part I of this work that the Gateaux
differentiability of a convex unitarily invariant
function is characterized by that of a similar induced
rearrangement invariant function on the corresponding
spectral space. A natural question is then whether this
is also the case for Fr{\'e}chet differentibility. In
this paper we show the answer is positive. Although the
result appears very natural, the proof turns out to be
quite technically involved.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "Convex spectral functions; differentiability;
rearrangement invariant functions",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.",
}
@TechReport{Borwein:1999:GSBa,
author = "Jonathan M. Borwein and Warren B. Moors and Xianfu
Wang",
title = "Generalized subdifferentials: a {Baire} categorical
approach",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "19",
day = "8",
month = mar,
year = "1999",
bibdate = "Thu Sep 01 10:00:12 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2001:GSB}.",
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,\ldots{},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),\ldots{},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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1999:GSBb,
author = "Jonathan M. Borwein and Warren B. Moors and Xianfu
Wang",
title = "Generalized subdifferentials: a {Baire} categorical
approach",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "6",
day = "15",
month = apr,
year = "1999",
MRclass = "49J52, 26A27",
bibdate = "Thu Sep 01 10:03:41 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:1999:GSBc}.",
abstract = "Dans ce compte rendu, nous decrivons comment utiliser
des arguments de type cat{\'e}gorie de Baire pour
construire certaines fonctions localement Lipschitz
pathologiques. Les origines de cette approche remontent
a Banach et Mazurkiewicz (1931) qui, de mani{\'e}re
ind{\'e}pendante, utilis{\'e}rent une approche
semblable pour mon- trer que ``presque toutes les
fonctions r{\'e}lles continues d{\'e}finies sur [0,1]
sont nulle part diff{\'e}rentiables''. Comme dans les
r{\'e}sultats de Banach et Mazurkiewicz, il s avere qu
il est plus facile de montrer que presque toutes les
fonctions possedent une certaine pro- pri{\'e}t{\'e}
que de construire un seul exemple concret. Apres une
description du cadre de base de la construction,
l'article continue en donnant de nombreuses
applications. Parmis les r{\'e}sultats les plus
surprenants, citons le suivant : ``Presque toutes les
fonctions 1-Lipschitz d{\'e}finies sur un espace de
Banach admettent une application
sous-dift{\'e}rentielle de Clarke qui est identiquement
{\'e}gale a la boule unit{\'e} dans l'espace dual.''",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "Baire category; Banach spaces; differentiability;
subdifferentials; upper semi continuous set valued
map.",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:1999:GSBc,
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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:ITDb,
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1999:MFAa,
author = "Jonathan M. Borwein and Qiji J. Zhu*",
title = "Multifunctional and functional analytic techniques in
nonsmooth analysis",
type = "Report",
institution = "Department of Mathematics, Simon Fraser University",
address = "Burnaby, BC V5A 1S6, Canada",
pages = "97",
day = "2",
month = nov,
year = "1999",
bibdate = "Thu Sep 01 10:44:29 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/49",
abstract = "These lectures center on the structure of real-valued
Lipschitz functions, and their generalized derivatives
on Banach spaces. We pay some attention to the role of
measure and category and will try to illustrate a
number of different techniques. These published notes
are much more detailed and comprehensive than the
lectures as given. Much of this development is based on
recent joint work with Warren Moors (Wellington) and
others.\par
The exposition will be organized around the following
interwoven themes.\par
$ \bullet $ Set-valued analysis. Minimal upper
semi-continuous multifunctions (`uscos and cuscos') and
related topological tools. Selections and
single-valuedness. Relations to
differentiability.\par
$ \bullet $ Measure and category as competing notions
of smallness: Haar null sets and generic sets in Banach
spaces. Other concepts of prevalence.\par
$ \bullet $ `Utility grade' renorming theory and its
application to the study of viscosity subderivatives
and (partially) smooth variational principles.
``Fuzzy'' calculus and some equivalent
reformulations.\par
$ \bullet $ The structure of Lipschitz functions.
Especially the calculus of essentially smooth Lipschitz
functions and the vector-lattice algebra they generate.
Chain rules, and questions of integrability and
representability.\par
$ \bullet $ Applications to and examples of distance
functions. Minimality of distance functions and
proximal normal formulae revisited. More general
perturbation functions.\par
$ \bullet $ Convex functions and related sequences in
Banach space. How properties of given Banach spaces are
reflected in the convex functions they support.
Conjugates and subdifferentials of eigenvalue
functions.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InCollection{Borwein:1999:MFAb,
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1999:NCMb,
author = "J. M. Borwein and T. Stanway",
title = "Numerical and computational mathematics (at the
undergraduate level)",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "22",
day = "31",
month = aug,
year = "1999",
bibdate = "Thu Sep 01 10:18:27 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2000:NCMa}.",
abstract = "We present an argument for including numerical and
computational methods in the undergraduate mathematics
curriculum. The argument is supported by presenting a
number of specific examples; some fairly elementary and
some less elementary. We conclude by inviting the
reader to reflect on the impact that experimental
mathematics might have on the undergraduate curriculum
and we offer a final example which serendipitously
presented itself during the late stages of preparing
this paper.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
abstract = "We discuss a smooth variational principle for
partially smooth viscosity subdifferentials and explore
its applications in nonsmooth analysis.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis",
keywords = "Fuzzy sum rules; Mean value inequalities and partially
smooth spaces; Smooth variational principle",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:1999:SM,
author = "D. Borwein and J. M. Borwein and P. Mar{\'e}chal",
title = "Surprise maximization",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "16",
day = "25",
month = jul,
year = "1999",
bibdate = "Thu Sep 01 08:38:24 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2000:SM}.",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
ISSN-L = "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;
http://www.math.utah.edu/pub/tex/bib/anziamj.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;
https://www.cambridge.org/core/journals/anziam-journal/article/subgradient-representation-of-multifunctions/A035439B7CEE8FBA04EAD6EB6888CDDB",
acknowledgement = ack-nhfb,
ajournal = "J. Austral Math. Soc. Ser. B",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of the Australian Mathematical Society. Series
B, Applied Mathematics",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
onlinedate = "17 February 2009",
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 = "Dedicated to Francis Clarke on the occasion of his
fiftieth birthday and the twenty-fifth birthday of the
Clarke generalized gradient. See addendum
\cite{Borwein:2002:ASS}.",
URL = "http://docserver.carma.newcastle.edu.au/199/;
http://www.sciencedirect.com/science/article/pii/S0362546X98001424",
abstract = "This survey is an account of the current status of
subdifferential research. It is intended to serve as an
entry point for researchers and graduate students in a
wide variety of pure and applied analysis areas who
might profitably use subdifferentials as tools.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis",
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.",
}
@TechReport{Borwein:1999:STC,
author = "J. M. Borwein and X. Wang",
title = "Subdifferentiability of typical continuous functions",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "10",
day = "13",
month = aug,
year = "1999",
bibdate = "Thu Sep 01 10:11:30 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2001:STC}.",
URL = "http://docserver.carma.newcastle.edu.au/241/",
abstract = "We prove a ``typical'' subdifferentiability principle
and apply it to a variety of complete metric spaces of
continuous functions on separable Banach spaces; so as
to obtain existence of functions with maximal
subdifferentials when ordered by inclusion. The
relationship between continuous functions with maximal
subdifferentials and nowhere monotone functions is
discussed.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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{Bailey:199x:KC,
author = "David H. Bailey and Jonathan M. Borwein and Richard E.
Crandall",
title = "On the {Khintchine} constant",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "19",
year = "199x",
bibdate = "Wed Aug 31 08:55:14 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Bailey:1997:KC}",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Undated.",
}
@TechReport{Borwein:199x:SCF,
author = "Jonathan M. Borwein and Jon D. Vanderwerff",
title = "A Survey of Convex Functions and Sequential
Convergence",
institution = "Faculty of Computer Science, Dalhousie University",
address = "Halifax, NS, B3H2W5 Canada",
pages = "1--10",
year = "199x",
bibdate = "Mon Aug 29 17:09:33 2022",
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",
abstract = "Study various properties of convex functions related
to sequential convergence.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
pagecount = "10",
remark = "Undated: same URL as \cite{Borwein:1990:SDPa}, but PDF
file matches the title in this entry.",
}
@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
$.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Undated report. The second author also appears in
journal databases with family name Lou, and personal
name Shi-Tuo.",
}
@TechReport{Borwein:19xx:CFF,
author = "J. M. Borwein and P. B. Borwein",
title = "On the Complexity of Familiar Functions and Numbers",
type = "Report",
institution = "Department of Mathematics, Statistics and Computing
Science, Dalhousie University",
address = "Halifax, NS B3H 3J5, Canada",
pages = "30",
year = "19xx",
MRclass = "6BC25, 41A30, 1OA30",
bibdate = "Fri Nov 11 07:08:04 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
abstract = "This paper examines low-complexity approximations to
familiar functions and numbers. The intent is to
suggest that a taxonomy of such functions and numbers
based on their computational complexity is possible. A
central theme is that traditional methods of
approximation are often very far from optimal, while
good or optimal methods are often very far from obvious
For most functions provably optimal methods are not
known, however the gap between what is known and what
is possible is often small. A considerable number of
open problems are posed and a number of related
examples are presented.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "$\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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; 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",
}
@TechReport{Bauschke:2000: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",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "32",
year = "2000",
MRclass = "52A41 (46G05, 46N10, 49J50, 90C25)",
bibdate = "Thu Sep 01 09:53:22 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Bauschke:2001:ESE}.",
abstract = "The classical notions of essential smoothness,
essential strict convexity, and Legendreness for convex
functions are 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "Bregman distance; Bregman projection; coercive;
cofinite function; convex function of Legendre type;
essentially smooth; essentially strictly convex;
Legendre function; Schur property; Schur space;
subdifferential; supercoercive; weak Asplund space;
zone consistent.",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Bauschke:2000:JSC,
author = "Heinz H. Bauschke and Jonathan M. Borwein",
title = "Joint and separate convexity of the {Bregman}
distance",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "17",
year = "2000",
bibdate = "Thu Sep 01 09:08:34 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/227/",
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.\par
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.\par
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = ",convex function; Bregman distance; joint convexity;
separate convexity",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@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/agm.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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
libnote = "Not yet in my library.",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "Pi (mathematical constant)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 $ c a^T = 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Discrete Mathematics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Research Report 97:104.",
}
@TechReport{Borwein:2000:ANB,
author = "J. M. Borwein and M. Jim{\'e}nez-Sevilla and J. P.
Moreno",
title = "Antiproximinal norms in {Banach} spaces",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "13",
month = oct,
year = "2000",
MRclass = "46B20",
bibdate = "Thu Sep 01 09:56:52 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/233/",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
}
@TechReport{Borwein:2000:CBC,
author = "J. M. Borwein and J. D. Vanderwerff",
title = "On the continuity of biconjugate convex functions",
type = "Report",
institution = "Department of Mathematics, Simon Fraser University",
address = "Burnaby, BC V5A 1S6, Canada",
pages = "10",
year = "2000",
bibdate = "Thu Sep 01 09:43:33 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2002:CBC}.",
URL = "http://docserver.carma.newcastle.edu.au/230/",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2000:CBSa,
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "hep-th/0004153",
keywords = "High Energy Physics - Theory, Mathematics - Classical
Analysis and ODEs",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:2000:CBSb,
author = "Jonathan Michael Borwein and David J. Broadhurst and
Joel Kamnitzer",
title = "Central binomial sums, multiple {Clausen} values, and
zeta values",
type = "Report",
institution = "Department of Mathematics, Simon Fraser University",
address = "Burnaby, BC V5A 1S6, Canada",
pages = "17",
day = "4",
month = nov,
year = "2000",
bibdate = "Thu Sep 01 10:15:29 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2001:CBS}.",
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.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.\par
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
}
@TechReport{Borwein:2000:CFL,
author = "Jonathan M. Borwein and Jon D. Vanderwerff",
title = "Convex functions of {Legendre} type in general
{Banach} spaces",
type = "Report",
institution = "Department of Mathematics, Simon Fraser University",
address = "Burnaby, BC V5A 1S6, Canada",
pages = "14",
year = "2000",
MRclass = "46B20,46G05,49J50,52A41",
bibdate = "Thu Sep 01 09:13:15 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2001:CFL}.",
URL = "http://docserver.carma.newcastle.edu.au/228/",
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
$ \mathbb {R}^n $ is given.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "$\beta$-differentiability; barrier function;
essentially smooth; Legendre function; strict
convexity",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Undated, but PDF metadata says
00:151-Borwein-Vanderwerff.dvi.",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 (2001h:11110)",
MRreviewer = "Cem Y. Y{\i}ld{\i}r{\i}m",
bibdate = "Mon Oct 24 11:41:28 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",
note = "Numerical analysis in the 20th century, Vol. I,
Approximation theory",
URL = "http://people.reed.edu/~crandall/papers/attach01.pdf",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 98:119.",
}
@TechReport{Borwein:2000:RCS,
author = "David Borwein and Jonathan Borwein and Greg Fee and
Roland Girgensohn",
title = "Refined Convexity and Special Cases of the
{Blaschke--Santalo} Inequality",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "8",
day = "3",
month = apr,
year = "2000",
bibdate = "Thu Sep 01 09:02:50 2022",
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 norms.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Modified 6 June 2000.",
}
@TechReport{Borwein:2000: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",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "21",
day = "12",
month = oct,
year = "2000",
MRclass = "46G05, 58C20",
bibdate = "Thu Sep 01 09:47:22 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2001:RGC}.",
URL = "http://docserver.carma.newcastle.edu.au/231/",
abstract = "For a continuously differentiable function with
bounded nonempty support, the range of the gradient
cannot be locally contained in a hyperplane. However,
iterative methods allow the construction of
continuously differentiable functions whose gradient
ranges have rather general topological features. For
example, the gradient range may fail to be simply
connected.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
title = "Experimental mathematics: recent developments and
future outlook",
crossref = "Engquist:2001:MUB",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Communications in Contemporary Mathematics",
journal-URL = "http://www.worldscientific.com/worldscinet/ccm",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = ":Bregman distance; convex function; joint convexity;
separate convexity",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:2001:AWMa,
author = "Jonathan M. Borwein",
title = "Aesthetics for the Working Mathematician",
type = "Report",
institution = "Simon Fraser University",
address = "Burnaby, BC V5A 1S6, Canada",
pages = "22",
day = "18",
month = apr,
year = "2001",
bibdate = "Tue Aug 16 10:19:46 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Public Lecture at Queen's University Symposium on
Beauty and the Mathematical Beast, April 18--19,
Kingston, ON, Canada.",
URL = "http://docserver.carma.newcastle.edu.au/150/",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "No abstract available.",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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
$ \mathbb {R}^n $ is given.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
}
@TechReport{Borwein:2001:CMCc,
author = "Jonathan M. Borwein and Peter B. Borwein",
title = "Challenges in Mathematical Computing",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "12",
day = "19",
month = feb,
year = "2001",
bibdate = "Wed Aug 31 12:21:01 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/135/2/01_160-Borwein-Borwein-ocr.pdf",
abstract = "Almost all interesting mathematical algorithmic
questions relate to NP-hard questions and such
computation is prone to explode exponentially. More
space, more speed and processors, and even say massive
parallelism will have an impact but it will be largely
at a ``micro not macro'' level. We anticipate the
greatest benefit accruing from mathematical platforms
that allow for highly computer assisted insight
generation (more ``aha''s per cycle), not from solution
of grand challenge problems.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis",
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,\ldots{},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),\ldots{},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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
}
@TechReport{Borwein:2001:LLC,
author = "J. M. Borwein and J. Vanderwerff and Xianfu Wang",
title = "Local {Lipschitz}-constant functions and maximal
subdifferentials",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "28",
year = "2001",
MRclass = "49J52 (54E52)",
bibdate = "Thu Sep 01 10:51:58 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2003:LLC}.",
URL = "http://docserver.carma.newcastle.edu.au/55/2/01_158-Borwein-Vanderwerff-Wang.pdf",
abstract = "It is shown that if k(x) is an upper semicontinuous
and quasi lower semicontinuous function on a Banach
space X, then k(z)Bx~ 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "approximate subdifferential; Baire category; Clarke
subdifferential; Lipschitz function; local
Lipschitz-constant function",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:2001:MVS,
author = "David Borwein and Jonathan M. Borwein and Bernard A.
{Mares, Jr.}",
title = "Multi-variable sinc integrals and volumes of
polyhedra",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "19",
day = "9",
month = feb,
year = "2001",
bibdate = "Thu Sep 01 10:57:31 2022",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@TechReport{Borwein:2001:NRI,
author = "J. Borwein and R. Goebel",
title = "Notions of relative interior in {Banach} spaces",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "17",
day = "10",
month = oct,
year = "2001",
MRclass = "49J53 (46B20 90C48)",
MRnumber = "1992991",
MRreviewer = "Constantin Z{\u{a}}linescu",
bibdate = "Wed Aug 31 12:30:27 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2003:NRI}.",
URL = "http://docserver.carma.newcastle.edu.au/138/",
abstract = "Extensions to a Banach space of the equivalent notions
of relatively absorbing, non-support, and relative
interior points of a convex set in $ \mathbb {R}^n $
are presented. The relations between these extensions
are studied, and their basic calculus rules are
developed. Several explicit examples and
counterexamples in general Banach spaces are given; and
the tools for development of further examples are
explained. Various implications for infinite
dimensional optimization are highlighted.",
acknowledgement = ack-nhfb,
ajournal = "J. Math. Sci. (NY)",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of Mathematical Sciences (New York)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Special issue on optimization and related topics, 1.
CECM Preprint 01:162.",
}
@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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = pub-COLLINS,
address = pub-COLLINS:adr,
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
}
@TechReport{Borwein:2002:DSSc,
author = "Jonathan Michael Borwein and Kwok-Kwong Stephen Choi",
title = "On {Dirichlet} series for sums of squares",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "29",
day = "5",
month = feb,
year = "2002",
bibdate = "Wed Aug 31 14:12:44 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Published in \cite{Borwein:2003:DSS}.",
URL = "http://docserver.carma.newcastle.edu.au/142/",
abstract = "In [14], Hardy and Wright recorded elegant closed
forms for the generating functions of the divisor
functions $ \sigma_k(n) $ and $ \sigma_k(n)^2 $ 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 \par
$$ \sum_{n = 1}^\infty \frac {(f_1 \ast g_1)(n) \cdot
(f_2 \ast g_2)(n)}{n^s} = f r a c{L_{f_1 f_2}(s) L_{g_1
g_2}(s) L_{f_1 g_2}(s)}{L_{f_1 f_2 g_1 g_2}(2s)} $$
\par
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 + \cdots
+ x_N^2 = n$ and $ r_{2, P}(n)^2$ 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}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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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://docserver.carma.newcastle.edu.au/140/;
http://www.ybook.co.jp/online2/jncav3.html",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
}
@TechReport{Borwein:2002: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}",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "19",
day = "7",
month = jan,
year = "2002",
bibdate = "Wed Aug 31 07:10:33 2022",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://docserver.carma.newcastle.edu.au/10/2/02_3A176-Borwein-Choksi-Marechal.pdf",
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
semi-continuous on its domain. Reference is given to a
web-site which exploits these ideas for the efficient
computation of the maximum entropy solution.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Nonlinear Analysis, Theory, Methods and Applications",
journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "SIAM Journal on Control and Optimization",
journal-URL = "http://epubs.siam.org/sicon",
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 $
\mathbb {R}^n$.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
URL = "http://docserver.carma.newcastle.edu.au/128/",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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)",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "Journal of Mathematical Sciences (New York)",
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,
ajournal = "J. Math. Sci. (NY)",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal de Th{\'e}orie des Nombres de Bordeaux",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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/123/1/;
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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/163/;
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.",
abstract-2 = "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 < 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. It should be emphasized that our
main results are shown equivalent but are still only
conjectures.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "math/0505270",
keywords = "Mathematics - Number Theory, Mathematics - Classical
Analysis and ODEs, 11M06 (Primary), 33C20 (Secondary)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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",
month = may,
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Canadian Mathematical Society Notes",
journal-URL = "https://cms.math.ca/notes",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Eberhard,
Andrew/0000-0003-2977-3456",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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/",
abstract = "We give closed forms, recursion formulas and
experimental results for the series $ \sum n^k / \binom
{2n}{n} $ and $ \sum 2^{-n} n^k / \binom {3n}{n} $ with
$ k \in \mathbb {Z} $.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "Approximation error; Computer errors; Computer
science; Concurrent computing; Error analysis;
International collaboration; Mathematics; System
testing",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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) $, initiated
by Koecher and pursued further by Borwein, Bradley, and
others.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
onlinedate = "30 Jan 2011",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
unique-id = "Bailey:2006:EDA",
}
@TechReport{Bailey:2006:FGE,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Finding General Explicit Formulas for {Ising} Integral
Recursions",
type = "Report",
institution = "Lawrence Berkeley National Laboratory and Faculty of
Computer Science, Dalhousie University",
address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5,
Canada",
day = "2",
month = oct,
year = "2006",
bibdate = "Fri Sep 30 08:18:51 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
URL = "http://www.davidhbailey.com/dhbpapers/ising-int.pdf",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "$K_0$ modified Bessel function; ARPREC multiprecision
software system",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of Physics A (Mathematical and General)",
journal-URL = "http://iopscience.iop.org/1751-8121",
onlinedate = "19 September 2006",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646",
remark = "See improvements in \cite{Dolgov:2020:PCI}.",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "14 + vi + 294 + viii + 363",
year = "2006",
ISBN = "1-56881-283-3, 1-56881-211-6, 1-56881-136-5",
ISBN-13 = "978-1-56881-283-0, 978-1-56881-211-3,
978-1-56881-136-9",
LCCN = "QA76.95 .E9 2006",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646",
tableofcontents = "Preface to the CD-ROM edition \\
Mathematics by experiment: plausible reasoning in the
21st century / Jonathan Borwein and David Bailey \\
Experimentation in mathematics: computational paths to
discovery / Jonathan Borwein, David Bailey, and Roland
Girgensohn",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
month = mar,
year = "2006",
DOI = "https://doi.org/10.1142/S1793042106000383",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
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;
http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "http://docserver.carma.newcastle.edu.au/301/;
https://www.worldscientific.com/doi/10.1142/S1793042106000383",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of Global Optimization",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "Bailey, David H./0000-0002-7574-8342; 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",
MRnumber = "2320374",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Nonlinear Analysis. Theory, Methods \& Applications.
An International Multidisciplinary Journal. Series A:
Theory and Methods",
journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis",
keywords = "Convex function; Cyclically monotone operator; Fenchel
conjugate; Fitzpatrick function; Maximal monotone
operator; Subdifferential operator; Sublinear
function",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 $.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "0706.1409",
keywords = "Computer Science - Symbolic Computation, Mathematics -
Classical Analysis and ODEs",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Salvy,
Bruno/0000-0002-4313-0679",
primaryclass = "cs.SC",
}
@Unpublished{Borwein:2007:REM,
author = "J. M. Borwein and Mason Macklem",
title = "Retro-enhancement of Mathematical Literature",
month = mar,
year = "2007",
bibdate = "Tue Aug 16 10:05:13 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Preprint.",
URL = "http://docserver.carma.newcastle.edu.au/339/",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Borwein:2007:VPE,
author = "David Borwein and Jonathan Borwein",
title = "{van der Pol} Expansions of {$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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eid = "205203",
eprint = "0801.0891",
fjournal = "Journal of Physics. A. Mathematical and Theoretical",
journal-URL = "http://iopscience.iop.org/1751-8121",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "Bessel moment integrals",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Eberhard,
Andrew/0000-0003-2977-3456",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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;
http://www.math.utah.edu/pub/tex/bib/elefunt.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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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;
http://www.math.utah.edu/pub/tex/bib/elefunt.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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Salvy,
Bruno/0000-0002-4313-0679",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "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",
month = jul # "--" # aug,
year = "2009",
CODEN = "????",
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,
ajournal = "WIREs",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "WIREs Computational Statistics",
journal-URL = "https://onlinelibrary.wiley.com/journal/19390068",
keywords = "experimental mathematics, numerical integration,
numerical analysis, computational statistics",
onlinedate = "13 July 2009",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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 = "",
ISBN = "0-470-97388-9 (hardcover)",
ISBN-13 = "978-0-470-97388-2 (hardcover)",
LCCN = "GE45.S73 E56 2012",
bibdate = "Fri Aug 12 09:29:41 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
note = "Six volumes (lix + 3150 pages).",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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) (2012?)",
xxisbn-13 = "978-0-470-97388-2 (second edition) (2012?)",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
journal-URL = "http://www.inderscience.com/jhome.php?jcode=ijcse",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
journal-URL = "http://www.fachgruppe-computeralgebra.de/rundbrief/",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Mathematical Programming",
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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. Borwein's is a sidebar on page 49, with the
title \booktitle{Some Reflections on John Ewing}.",
URL = "https://www.ams.org/journals/notices/200901/200901-full-issue.pdf",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of Convex Analysis",
journal-URL = "http://www.heldermann.de/JCA/jcacon.htm",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Eberhard,
Andrew/0000-0003-2977-3456",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1005.0414",
keywords = "Mathematical Physics, High Energy Physics -
Phenomenology, Mathematics - Classical Analysis and
ODEs, Mathematics - Number Theory",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646; Zudilin,
Wadim/0000-0001-9551-2903",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646; Zudilin,
Wadim/0000-0001-9551-2903",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
month = may,
year = "2010",
DOI = "https://doi.org/10.1142/S1793042110003058",
ISSN = "1793-0421 (print), 1793-7310 (electronic)",
ISSN-L = "1793-0421",
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;
http://www.math.utah.edu/pub/tex/bib/ijnt.bib",
URL = "http://docserver.carma.newcastle.edu.au/1218/;
https://www.worldscientific.com/doi/10.1142/S1793042110003058",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "International Journal of Number Theory (IJNT)",
journal-URL = "https://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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
book-URL = "http://math.sfsu.edu/fpsac/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Nuyens,
Dirk/0000-0002-4555-2314; Straub,
Armin/0000-0001-6802-6053",
}
@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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Optimization",
journal-URL = "http://www.tandfonline.com/loi/gopt20",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646; Calude, Cristian
Sorin/0000-0002-8711-6799",
}
@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 = nov,
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/;
https://www.ams.org/notices/201110/rtx111001410p.pdf",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646",
}
@TechReport{Bailey:2011:GMDa,
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "decimal arithmetic history",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1110.5706",
keywords = "Mathematics - Functional Analysis, 47A06 (Primary),
47H05, 47B65 (Secondary), 47N10, 90C25",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1108.1463",
keywords = "Mathematics - Functional Analysis, Primary 47A06,
47H05, Secondary 47B65, 47N1, 90C25",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1104.0750",
keywords = "Mathematics - Functional Analysis, Primary 47H05,
Secondary 46B10, 47N10, 90C25",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
Jonathan/0000-0002-1263-0646",
primaryclass = "math.FA",
}
@Article{Bauschke:2011:MML,
author = "Heinz H. Bauschke and Jonathan M. Borwein 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1103.6239",
keywords = "Mathematics - Functional Analysis, Primary 47A06,
47H05, Secondary 47B65, 47N10, 90C25",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1108.2578",
keywords = "Mathematics - Functional Analysis, Primary 47A06,
47H05, Secondary 47B65, 47N10, 90C25",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of Nonlinear and Convex Analysis",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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; Straub,
Armin/0000-0001-6802-6053; Zudilin,
Wadim/0000-0001-9551-2903",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1103.3893",
keywords = "Mathematics - Classical Analysis and ODEs,
Mathematical Physics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
Armin/0000-0001-6802-6053",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1103.3035",
keywords = "Mathematics - Classical Analysis and ODEs,
Mathematical Physics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
Armin/0000-0001-6802-6053",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Zudilin,
Wadim/0000-0001-9551-2903",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1110.3102",
keywords = "Mathematics - Functional Analysis, Mathematics -
Optimization and Control, Primary 47A06, 47H05,
Secondary 47B65, 47N10, 90C25",
ORCID-numbers = "Burachik, Regina/0000-0003-1332-6213; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Eberhard,
Andrew/0000-0003-2977-3456",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "The {Ramanujan} Journal",
journal-URL = "http://link.springer.com/journal/11139",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Nuyens,
Dirk/0000-0002-4555-2314; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1103.4298",
keywords = "Mathematics - Classical Analysis and ODEs, Computer
Science - Symbolic Computation, Mathematical Physics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
Armin/0000-0001-6802-6053",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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; Straub,
Armin/0000-0001-6802-6053",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eid = "073708",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
onlinedate = "Sep 2012",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1203.2392",
keywords = "Mathematics - Optimization and Control",
ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646; Calude, Cristian
Sorin/0000-0002-8711-6799",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
language = "Chinese",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "Elliptic integrals; Experimental mathematics;
High-precision computing; Numerical integration; Random
walks",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Barrio, Roberto/L-4983-2014",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646; Calude, Cristian
Sorin/0000-0002-8711-6799",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646; Calude, Cristian
Sorin/0000-0002-8711-6799",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "The {Ramanujan} Journal",
journal-URL = "http://link.springer.com/journal/11139",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "Bauschke, Heinz/0000-0002-4155-9930; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Set-Valued and Variational Analysis",
journal-URL = "http://link.springer.com/journal/11228",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
Jonathan/0000-0002-1263-0646;",
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Optimization Letters",
journal-URL = "http://link.springer.com/journal/11590",
ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
Jonathan/0000-0002-1263-0646;",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1211.4953",
keywords = "Mathematics - Functional Analysis, Mathematics -
Optimization and Control, 49J52, 48N15 (Primary) 90C25,
90C30, 90C46 (Secondary)",
ORCID-numbers = "Burachik, Regina/0000-0003-1332-6213; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Journal of the Australian Mathematical Society",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
Armin/0000-0001-6802-6053",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Integers",
journal-URL = "http://www.degruyter.com/view/j/integ",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
Armin/0000-0001-6802-6053",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Optimization",
journal-URL = "http://www.tandfonline.com/loi/gopt20",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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",
DOI = "https://doi.org/10.1090/noti805",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "1534--1537",
month = dec,
year = "2012",
CODEN = "AMNOAN",
DOI = "https://doi.org/10.1090/noti917",
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/;
http://www.ams.org/journals/notices/201211/rtx121101522p.pdf",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Section of longer article edited by Krishnaswami
Alladi, \booktitle{Srinivasa Ramanujan: Going strong at
125, Part I}, pages 1522--1537.",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
Armin/0000-0001-6802-6053",
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Optimization Letters",
journal-URL = "http://link.springer.com/journal/11590",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Howlett,
Phil/0000-0003-2382-8137",
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",
month = "????",
year = "2012",
CODEN = "????",
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;
http://www.math.utah.edu/pub/tex/bib/naco.bib",
URL = "http://aimsciences.org/article/doi/10.3934/naco.2012.2.233",
acknowledgement = ack-nhfb,
ajournal = "Numer. Algebra Control Optim.",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Numerical Algebra, Control and Optimization",
journal-URL = "http://aimsciences.org/journal/2155-3289",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Howlett,
Phil/0000-0003-2382-8137",
}
@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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1302.1978",
keywords = "Mathematics - Functional Analysis, Mathematics -
Optimization and Control, Primary 47N10, 90C25,
Secondary 47H05, 47A06, 47B65",
ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1308.4243",
keywords = "Mathematics - Optimization and Control",
ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
eprint = "1305.2657",
keywords = "Mathematics - Optimization and Control, Mathematics -
Combinatorics, 90C27, 90C59, 47N10",
ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Serdica. Mathematical Journal. Serdika. Matematichesko
Spisanie",
ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
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/s00283-012-9340-x;
http://www.davidhbailey.com/dhbpapers/tools-walk.pdf",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
Bailey, David H./0000-0002-7574-8342; 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",
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Boundary Value Problems",
journal-URL = "http://boundaryvalueproblems.springeropen.com/",
onlinedate = "13 May 2013",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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",
month = aug,
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;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
URL = "http://docserver.carma.newcastle.edu.au/1436/;
http://www.ams.org/notices/201307/rnoti-p844.pdf",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
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 = "Bailey, David H./0000-0002-7574-8342; 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,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; 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 =