%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.91", %%% date = "15 February 2024", %%% time = "11:12:37 MST", %%% filename = "borwein-jonathan-m.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "https://www.math.utah.edu/~beebe", %%% checksum = "31683 54544 240172 2460703", %%% 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 in %%% 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 1.91, the COMPLETE year coverage %%% looked like this: %%% %%% 1972 ( 1) 1990 ( 52) 2008 ( 47) %%% 1973 ( 0) 1991 ( 36) 2009 ( 65) %%% 1974 ( 1) 1992 ( 28) 2010 ( 71) %%% 1975 ( 0) 1993 ( 43) 2011 ( 100) %%% 1976 ( 4) 1994 ( 49) 2012 ( 125) %%% 1977 ( 5) 1995 ( 62) 2013 ( 136) %%% 1978 ( 4) 1996 ( 39) 2014 ( 119) %%% 1979 ( 10) 1997 ( 71) 2015 ( 100) %%% 1980 ( 7) 1998 ( 41) 2016 ( 113) %%% 1981 ( 10) 1999 ( 61) 2017 ( 37) %%% 1982 ( 8) 2000 ( 56) 2018 ( 33) %%% 1983 ( 11) 2001 ( 47) 2019 ( 2) %%% 1984 ( 19) 2002 ( 39) 2020 ( 33) %%% 1985 ( 9) 2003 ( 55) 2021 ( 14) %%% 1986 ( 23) 2004 ( 51) 2022 ( 2) %%% 1987 ( 27) 2005 ( 79) 2023 ( 0) %%% 1988 ( 32) 2006 ( 62) 2024 ( 1) %%% 1989 ( 25) 2007 ( 57) %%% 19xx ( 7) %%% %%% Article: 827 %%% Book: 57 %%% InCollection: 92 %%% InProceedings: 70 %%% MastersThesis: 1 %%% Misc: 187 %%% PhdThesis: 2 %%% Proceedings: 18 %%% TechReport: 138 %%% Unpublished: 740 %%% %%% Total entries: 2132 %%% %%% 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|https://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-COMPUT-SCI= "Journal of Computational Science"} @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"} @String{j-MATH-SCAND= "Mathematica Scandinavica"} @String{j-MATH-STUDENT= "The Mathematics Student"} @String{j-METHODS-APPL-ANAL= "Methods and Applications of Analysis"} @String{j-MICH-MATH-J= "Michigan Mathematical Journal"} @String{j-NAMS= "Notices of the American Mathematical Society"} @String{j-NEUROCOMPUTING= "Neurocomputing"} @String{j-NONLINEAR-ANAL= "Nonlinear Analysis, Theory, Methods and Applications"} @String{j-NUM-LIN-ALG-APPL= "Numerical Linear Algebra with Applications"} @String{j-NUM-MATH= "Numerische Mathematik"} @String{j-NUMER-ALGEBRA-CONTROL-OPTIM= "Numerical Algebra, Control and Optimization"} @String{j-NUMER-ALGORITHMS= "Numerical Algorithms"} @String{j-NUMER-FUNCT-ANAL-OPTIM= "Numerical Functional Analysis and Optimization"} @String{j-OPTIM-LETT= "Optimization Letters"} @String{j-OPTIM-METHODS-SOFTW= "Optimization Methods and Software"} @String{j-OPTIMIZATION= "Optimization"} @String{j-PAC-J-MATH= "Pacific Journal of Mathematics"} @String{j-POSITIVITY= "Positivity"} @String{j-PROC-AM-MATH-SOC= "Proceedings of the American Mathematical Society"} @String{j-PROC-EDINBURGH-MATH-SOC-2= "Proceedings of the Edinburgh Mathematical Society (2)"} @String{j-PROC-LONDON-MATH-SOC-3= "Proceedings of the London Mathematical Society. Third Series"} @String{j-RAMANUJAN-J= "The {Ramanujan} Journal"} @String{j-ROCKY-MOUNTAIN-J-MATH= "Rocky Mountain Journal of Mathematics"} @String{j-SCI-AMER= "Scientific American"} @String{j-SCI-CHINA-MATH= "Science China. Mathematics"} @String{j-SCIENCE= "Science"} @String{j-SERDICA-MATH-J= "Serdica. Mathematical Journal. Serdika. Matematichesko Spisanie"} @String{j-SET-VALUED-ANAL= "Set-Valued Analysis"} @String{j-SET-VALUED-VAR-ANAL= "Set-Valued and Variational Analysis"} @String{j-SIAM-J-CONTROL-OPTIM= "SIAM Journal on Control and Optimization"} @String{j-SIAM-J-NUMER-ANAL= "SIAM Journal on Numerical Analysis"} @String{j-SIAM-J-OPT= "SIAM Journal on Optimization"} @String{j-SIAM-NEWS= "SIAM News"} @String{j-SIAM-REVIEW= "SIAM Review"} @String{j-SIGSAM= "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)"} @String{j-STUDIA-MATH= "Studia Mathematica"} @String{j-THEOR-COMP-SCI= "Theoretical Computer Science"} @String{j-TRANS-AM-MATH-SOC= "Transactions of the American Mathematical Society"} @String{j-TRANS-INFO-PROCESSING-SOC-JAPAN= "Transactions of the Information Processing Society of Japan"} @String{j-UTIL-MATH= "Utilitas Mathematica"} @String{j-Z-OPER-RES= "Zeitschrift f{\"u}r Operations Research. Mathematical Methods of Operations Research"} @String{j-ZOR-MATH-METHODS-OPER-RES= "ZOR --- Mathematical Methods of Operations Research"}

%%% ==================================================================== %%% Publisher abbreviations:

@String{pub-A-K-PETERS= "A. K. Peters, Ltd."} @String{pub-A-K-PETERS:adr= "Wellesley, MA, USA"} @String{pub-ACADEMIC= "Academic Press"} @String{pub-ACADEMIC:adr= "New York, NY, USA"} @String{pub-ACM= "ACM Press"} @String{pub-ACM:adr= "New York, NY 10036, USA"} @String{pub-AMS= "American Mathematical Society"} @String{pub-AMS:adr= "Providence, RI, USA"} @String{pub-CAMBRIDGE= "Cambridge University Press"} @String{pub-CAMBRIDGE:adr= "Cambridge, UK"} @String{pub-COLLINS= "Collins"} @String{pub-COLLINS:adr= "London, UK"} @String{pub-ELSEVIER= "Elsevier"} @String{pub-ELSEVIER:adr= "Amsterdam, The Netherlands"} @String{pub-HARPERCOLLINS= "HarperCollins"} @String{pub-HARPERCOLLINS:adr= "London, UK"} @String{pub-IEEE= "IEEE Computer Society Press"} @String{pub-IEEE:adr= "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-KLUWER= "Kluwer Academic Publishers Group"} @String{pub-KLUWER:adr= "Norwell, MA, USA, and Dordrecht, The Netherlands"} @String{pub-LITTLE-BROWN= "Little, Brown and Co."} @String{pub-LITTLE-BROWN:adr= "Boston, MA, USA"} @String{pub-LONGMAN= "Longman Scientific and Technical"} @String{pub-LONGMAN:adr= "Harlow, Essex, UK"} @String{pub-MATH-ASSOC-AMER= "Mathematical Association of America"} @String{pub-MATH-ASSOC-AMER:adr= "Washington, DC, USA"} @String{pub-NORTH-HOLLAND= "North-Hol{\-}land"} @String{pub-NORTH-HOLLAND:adr= "Amsterdam, The Netherlands"} @String{pub-PRINCETON= "Princeton University Press"} @String{pub-PRINCETON:adr= "Princeton, NJ, USA"} @String{pub-REIDEL= "D. Reidel"} @String{pub-REIDEL:adr= "Dordrecht, The Netherlands; Boston, MA, USA; Lancaster, UK; Tokyo, Japan"} @String{pub-SIAM= "Society for Industrial and Applied Mathematics"} @String{pub-SIAM:adr= "Philadelphia, PA, USA"} @String{pub-SV= "Spring{\-}er-Ver{\-}lag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-WADSWORTH= "Wadsworth"} @String{pub-WADSWORTH:adr= "Pacific Grove, CA, USA"} @String{pub-WILEY= "Wiley"} @String{pub-WILEY:adr= "New York, NY, USA"}

%%% ==================================================================== %%% 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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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/; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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/; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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", editor = "Anthony V. Fiacco and Kenneth O. Kortanek", booktitle = "{Semi-Infinite Programming and Applications: an International Symposium, Austin, Texas, September 8 -10, 1981}", title = "Semi-infinite programming duality: how special is it?", volume = "215", publisher = pub-SV, address = pub-SV:adr, bookpages = "xi + 322", pages = "10--36", year = "1983", DOI = "https://doi.org/10.1007/978-3-642-46477-5_2", ISBN = "0-387-12304-0 (paperback: New York), 3-540-12304-0 (paperback: Berlin)", ISBN-13 = "978-0-387-12304-2 (paperback: New York), 978-3-540-12304-0 (paperback: Berlin)", LCCN = "QA402.5 .S428 1983", MRclass = "49D39 (90C30)", MRnumber = "709266", MRreviewer = "Sven-{\.A}ke Gustafson", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Lecture Notes in Economics and Mathematical Systems", acknowledgement = ack-nhfb, aseries = "Lecture Notes in Econom. and Math. Systems", author-dates = "Jonathan Michael Borwein (20 May 1951--2 August 2016)", book-DOI = "https://doi.org/10.1007/978-3-642-46477-5", 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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://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 = "https://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 = "https://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/; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib; https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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", xxaddress = "Falls Church, VA", xxbooktitle = "{APICS Microprocessor Seminar proceedings, January 30, 31, February 1, 1984, Palm Springs, {CA}}", xxISBN = "0-935406-40-9", xxisbn-13 = "978-0-935406-40-5", xxLCCN = "TS157 .A64 1984", xxpublisher = "American Production and Inventory Control Society", } @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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://www.jstor.org/journals/00029890.htm", 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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://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 = "https://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; https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://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 = "https://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", title = "More {Ramanujan}-type series for $ 1 / \pi $", crossref = "Andrews:1988:RRP", pages = "359--374", year = "1988", MRclass = "11Y60", MRnumber = "938974", MRreviewer = "Duncan A. Buell", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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", 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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://www.jstor.org/journals/00029890.htm", 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)", LCCN = "QA5 B67 1989", MRclass = "00A20", MRnumber = "1210061", MRreviewer = "F. J. Papp", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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", editor = "Michael A. Th{\'e}ra and Jean-Bernard Baillon", booktitle = "Fixed point theory and applications: proceedings of the {International Conference on Fixed Point Theory and Applications, held at CIRM (Centre International de Rencontres Math{\'e}matiques) located in the campus of the University of Marseille-Luminy, June 5--9, 1989}", title = "Minimal {CUSCOS} and subgradients of {Lipschitz} functions", volume = "252", publisher = pub-LONGMAN, address = pub-LONGMAN:adr, pages = "57--81", year = "1991", ISBN = "0-582-08063-0 (Harlow), 0-470-21759-6 (New York)", ISBN-13 = "978-0-582-08063-8 (Harlow), 978-0-470-21759-7 (New York)", LCCN = "QA329.9 .F58 1991", MRclass = "46G05 (47H04 49J52)", MRnumber = "1122818", MRreviewer = "Doug Ward", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "https://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 = "https://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 = "https://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 = "https://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 = "https://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/", 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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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", } @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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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", title = "Differentiability properties of convex, of {Lipschitz}, and of semicontinuous mappings on {Banach} spaces", crossref = "Ioffe:1992:ONA", pages = "39--52", year = "1992", ISBN = "0-582-08065-7 (paperback), 0-470-21943-2", ISBN-13 = "978-0-582-08065-2 (paperback), 978-0-470-21943-0", ISSN = "0269-3674", ISSN-L = "0269-3674", LCCN = "QA402.5 .O6424 1991", MRclass = "49J50 (46B20 46G05 47H99)", MRnumber = "1184630", MRreviewer = "Julian Revalski", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Pitman research notes in mathematics series", URL = "", ZMnumber = "0745.00050", 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 differentiability properties of convex, {Lipschitz} and lsc functions", } @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", pages = "275--290", year = "1992", bibdate = "Mon Aug 15 14:57:23 2016", bibsource = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://www.jstor.org/journals/00029890.htm", 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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://www.jstor.org/journals/00029890.htm", 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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://www.jstor.org/journals/00029890.htm", 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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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/; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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/", 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 = "https://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 = "https://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; https://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; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://links.jstor.org/sici?sici=0002-9890(199612)103:10<911:1>2.0.CO%3B2-5&origin=MSN", acknowledgement = ack-nhfb, 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 = "https://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 = "https://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/", 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/; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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", } @InProceedings{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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib", note = "Reprint of \cite{Borwein:1989:RME}.", series = "CMS Conference Proceedings", URL = "http://docserver.carma.newcastle.edu.au/1587/; http://www.cecm.sfu.ca/organics/papers/borwein/index.html; https://web.archive.org/web/20170328083101/", 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 = "https://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 = "https://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 = "https://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 = "https://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", } @InProceedings{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 = "https://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", } @InCollection{Borwein:1997:AGMa, author = "J. M. Borwein and P. B. Borwein", title = "The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions", crossref = "Berggren:1997:PSB", pages = "537--552", year = "1997", DOI = "https://doi.org/10.1007/978-1-4757-2736-4_56", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib", note = "Reprint of \cite{Borwein:1984:AGM}.", 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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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.", } @InCollection{Borwein:1997:PEN, author = "J. M. Borwein and P. B. Borwein and K. Dilcher", title = "Pi, {Euler} Numbers, and Asymptotic Expansions", crossref = "Berggren:1997:PSB", pages = "642--648", year = "1997", DOI = "https://doi.org/10.1007/978-1-4757-2736-4_65", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "https://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 = "https://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:1997:RME, author = "J. M. Borwein and P. B. Borwein and D. H. Bailey", title = "{Ramanujan}, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi", crossref = "Berggren:1997:PSB", 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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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", } @InProceedings{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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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/; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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; https://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; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.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 = "https://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 = "https://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 $.", acknowledgement = ack-nhfb, author-dates = "Jonathan Michael Borwein (20 May 1951--2 August 2016)", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Undated report. The second author also appears in journal databases with family name Lou, and personal name Shi-Tuo.", } @TechReport{Borwein:19xx:CFF, author = "J. M. Borwein and P. B. Borwein", title = "On the Complexity of Familiar Functions and Numbers", type = "Report", institution = "Department of Mathematics, Statistics and Computing Science, Dalhousie University", address = "Halifax, NS B3H 3J5, Canada", pages = "30", year = "19xx", MRclass = "6BC25, 41A30, 1OA30", bibdate = "Fri Nov 11 07:08:04 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "This paper examines low-complexity approximations to familiar functions and numbers. The intent is to suggest that a taxonomy of such functions and numbers based on their computational complexity is possible. A central theme is that traditional methods of approximation are often very far from optimal, while good or optimal methods are often very far from obvious For most functions provably optimal methods are not known, however the gap between what is known and what is possible is often small. A considerable number of open problems are posed and a number of related examples are presented.", acknowledgement = ack-nhfb, author-dates = "Jonathan Michael Borwein (20 May 1951--2 August 2016)", keywords = "$\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 $", pages = "16", year = "19xx", bibdate = "Mon Nov 07 07:04:34 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Unpublished hand-written lecture slides at Dalhousie University. The slides are undated, and the 10 references on the final slides include a reference to E. Salamin (1976) and to P. Backmann's 1977 book \booktitle{A History of Pi}.", abstract = "$ \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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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", } @InCollection{Borwein:2000:AGM, author = "J. M. Borwein and P. B. Borwein", title = "The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions", crossref = "Berggren:2000:PSB", pages = "537--552", year = "2000", DOI = "https://doi.org/10.1007/978-1-4757-3240-5_56", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib", note = "Reprint of \cite{Borwein:1984:AGM}.", 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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib; https://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 = "https://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 = "https://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.", } @InCollection{Borwein:2000:PEN, author = "J. M. Borwein and P. B. Borwein and K. Dilcher", title = "Pi, {Euler} Numbers, and Asymptotic Expansions", crossref = "Berggren:2000:PSB", pages = "642--648", year = "2000", DOI = "https://doi.org/10.1007/978-1-4757-3240-5_65", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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", } @InCollection{Borwein:2000:RME, author = "J. M. Borwein and P. B. Borwein and D. H. Bailey", title = "{Ramanujan}, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi", crossref = "Berggren:2000:PSB", 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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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", remark = "The journal has archives only from volume 31 (2004) at \url{https://austms.org.au/publications/gazette/gazette-past-issues/}.", } @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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Section Special Theme ERCIMathematics.", URL = "https://www.ercim.eu/publication/Ercim_News/enw50/borwein.html", 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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "J. Lennart Berggren and Jonathan Borwein and Peter Borwein", title = "A Pamphlet on Pi serving as a Supplement for the Third Edition of {{\booktitle{Pi: A Source Book}}}", type = "CECM Preprint", number = "2003:210", institution = inst-CECM, address = inst-CECM:adr, pages = "65", day = "17", month = jul, year = "2003", bibdate = "Tue Aug 16 10:15:54 2016", bibsource = "https://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", tableofcontents = "List of Figures / i \\ 1 Pi and Its Friends / 1 \\ 1.1 A Recent History of Pi / 1 \\ 1.1.1 The ENIAC Integrator and Calculator / 5 \\ 1.2 Computing Individual Digits of Pi / 7 \\ 1.3 Does Pi Have a Non-Binary BBP Formula? / 13 \\ \\ 2 Normality of Numbers / 17 \\ 2.1 Normality: A Stubborn Question / 17 \\ 2.2 BBP Constants and Normality / 22 \\ 2.3 A Class of Provably Normal Constants / 26 \\ \\ 3 Historia Cyclometrica / 29 \\ 3.1 1 Kings, 2 Chronicles, and Maimonides / 29 \\ 3.2 Fran{\c{c}}ois Vi{\`e}te. Book VIII, Chapter XVIII. / 30 \\ 3.2.1 Ratio of Regular Polygons, Inscribed in a Circle, to the Circle / 30 \\ 3.2.2 Defense Against the New Cyclometry or anti-axe. / 33 \\ 3.3 Christian Huygens. Problem IV, Proposition XX. / 43 \\ 3.3.1 Determining the Magnitude of the Circle / 43 \\ \\ 4 Demotica Cyclometrica / 47 \\ 4.1 Irving Kaplansky's ``Song of Pi'' / 47 \\ 4.2 Ludolph van Ceulen's Tombstone / 47 \\ \\ Bibliography / 55 \\ Index / 59", } @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 = "https://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", } @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 = "https://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", } @InCollection{Borwein:2003:DB, author = "Jonathan M. Borwein", editor = "Alex C. Michalos", booktitle = "The best teacher {I} ever had: personal reports from highly productive scholars", title = "On {David Borwein}", crossref = "Michalos:2003:BTE", chapter = "14", pages = "??--??", year = "2003", bibdate = "Sat Aug 13 17:29:16 2016", bibsource = "https://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: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 = "https://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 = "https://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 = "https://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 = "https://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", } @TechReport{Borwein:2003:MEP, author = "Jonathan M. Borwein and David H. Bailey and Roland Girgensohn", title = "Mathematics by Experiment: Plausible Reasoning in the 21st Century and Experiments in Mathematics: Computational Paths to Discovery", type = "Report", institution = inst-CECM, address = inst-CECM:adr, pages = "iv + 67", day = "28", month = aug, year = "2003", bibdate = "Mon Sep 05 06:29:13 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.187.5170&rep=rep1&type=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{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 = "https://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 = "https://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/; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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.", } @InCollection{Borwein:2004:AGMa, author = "J. M. Borwein and P. B. Borwein", title = "The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions", crossref = "Berggren:2004:PSB", pages = "537--552", year = "2004", DOI = "https://doi.org/10.1007/978-1-4757-4217-6_56", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib", note = "Reprint of \cite{Borwein:1984:AGM}.", 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 = "https://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 = "https://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 = "https://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", pages = "27--34", year = "2004", MRclass = "11M41 (11E25)", MRnumber = "2076564", MRreviewer = "Don Redmond", bibdate = "Sat Aug 13 17:30:35 2016", bibsource = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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", } @InCollection{Borwein:2004:PEN, author = "J. M. Borwein and P. B. Borwein and K. Dilcher", title = "Pi, {Euler} Numbers, and Asymptotic Expansions", crossref = "Berggren:2004:PSB", pages = "642--648", year = "2004", DOI = "https://doi.org/10.1007/978-1-4757-4217-6_65", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Reprint of \cite{Borwein:1989:PEN}.", 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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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", } @InCollection{Borwein:2004:RME, author = "J. M. Borwein and P. B. Borwein and D. H. Bailey", title = "{Ramanujan}, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi", crossref = "Berggren:2004:PSB", pages = "623--641", year = "2004", DOI = "https://doi.org/10.1007/978-1-4757-4217-6_64", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "https://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 = "https://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 = "https://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 = "https://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 = "https://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:BRS, author = "Jonathan M. Borwein", title = "Book Review: {{\booktitle{The SIAM 100-Digit challenge: a study in high-accuracy numerical computing}}, Folkmar Bornemann, Dirk Laurie, Stan Wagon, and JSrg Waldvogel, SIAM, Philadelphia, PA, USA 2004, xil + 306 pp. softcover, ISBN 0-89871 561-X, US\$57.00}", 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 = "https://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: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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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/", 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 = "https://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 = "https://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 = "https://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: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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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) $, initiated by Koecher and pursued further by Borwein, Bradley, and others.", acknowledgement = ack-nhfb, author-dates = "Jonathan Michael Borwein (20 May 1951--2 August 2016)", fjournal = "Experimental Mathematics", journal-URL = "http://www.tandfonline.com/loi/uexm20", onlinedate = "30 Jan 2011", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Bailey:2006:EDA", } @TechReport{Bailey:2006:FGE, author = "David H. Bailey and Jonathan M. Borwein", title = "Finding General Explicit Formulas for {Ising} Integral Recursions", type = "Report", institution = "Lawrence Berkeley National Laboratory and Faculty of Computer Science, Dalhousie University", address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5, Canada", day = "2", month = oct, year = "2006", bibdate = "Fri Sep 30 08:18:51 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.davidhbailey.com/dhbpapers/ising-int.pdf", acknowledgement = ack-nhfb, author-dates = "Jonathan Michael Borwein (20 May 1951--2 August 2016)", keywords = "$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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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; https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://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 analys