%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.54", %%% date = "15 October 2018", %%% time = "19:01:53 MDT", %%% filename = "borwein-jonathan-m.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "http://www.math.utah.edu/~beebe", %%% checksum = "45091 46834 199771 2077969", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "arithmetic--geometric mean (AGM); Atlantic %%% Association for Research in the Mathematical %%% Sciences (AARMS); BBP %%% (Bailey--Borwein--Plouffe) algorithm; %%% bibliography; BibTeX; Borwein--Preiss smooth %%% variational principle in optimization theory; %%% Centre for Computer-assisted Research %%% Mathematics and its Applications (CARMA); %%% classical analysis; cubic theta function; %%% Douglas--Rachford algorithm; experimental %%% mathematics; financial mathematics; functional %%% analysis; high performance computing (HPC); %%% International Mathematical Union (IMU) %%% Executive's Committee on Electronic %%% Information and Communication (CEIC); Jonathan %%% Michael Borwein; mathematics by experiment; %%% number theory; Online Encyclopedia of Integer %%% Sequences (OEIS); operations research; %%% optimization theory and practice; $\pi$; PSLQ %%% algorithm; theory of computation", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a COMPLETE bibliography of works by, %%% and about, the late distinguished %%% Canadian/British mathematician Jonathan %%% Michael Borwein (20 May 1951--2 August 2016) %%% (ORCID Borwein, Jonathan/0000-0002-1263-0646). %%% %%% This bibliography is divided into four parts: %%% %%% 1: Academic works by Jonathan M. Borwein %%% 2: Blog publications by Jonathan M. Borwein %%% 3: Invited talks by Jonathan M. Borwein %%% 4: Publications about Jonathan M. Borwein and his works %%% %%% Jon Borwein was born in Scotland to a %%% mathematical family: his father David and his %%% younger brother Peter are themselves %%% distinguished mathematicians. His mother is %%% a physician and retired medical-school dean. %%% %%% Jon grew up in Canada, taking a B.A. (Honours %%% Mathematics) at the University of Western %%% Ontario (later branded Western University), %%% London, ON in 1972 (and the city in which he %%% died in 2016 while holding the post of %%% Distinguished Scholar in Residence), and an %%% M.Sc. in 1974 and a D.Phil. in 1974 from %%% Oxford University, where he was a Rhodes %%% Scholar at Jesus College. %%% %%% Jon Borwein later worked at Dalhousie %%% University, Halifax, NS, Canada (1974--1980, %%% 1982--1991, 2004--), Carnegie--Mellon %%% University, Pittsburgh, PA, USA (1980--1982), %%% the University of Waterloo, Waterloo, ON, %%% Canada (1991--1993), Simon Fraser University, %%% Burnaby, BC, Canada (1993--2003), the %%% University of Newcastle, Newcastle, NSW, %%% Australia (2009--2016), King Abdulaziz %%% University, Jeddah, Saudi Arabia %%% (2011--2013), and Chiang Mia University, %%% Thailand (2013--2016). %%% %%% Jon Borwein was President of the Canadian %%% Mathematical Society (2000--2002), Governer %%% at Large of the American Mathematical Society %%% (2004--2007), co-winner of the Chauvenet %%% Prize of the Mathematical Association of %%% America (1993) --- see entry Borwein:1989:RME %%% and the Web site %%% %%% http://www.maa.org/programs/maa-awards/writing-awards/chauvenet-prizes %%% %%% co-winner of the AMS 2017 Levi L. Conant %%% Prize --- see entries Bailey:2016:BBM and %%% Breen:2016:DBJ and the Web site %%% %%% http://www.ams.org/news?news_id=3232 %%% %%% and a fellow of the Royal Society of Canada %%% (1994), the American Association for the %%% Advancement of Science (2002), the Bulgarian %%% Academy of Sciences (2003), the Australian %%% Academy of Science (2010), the American %%% Mathematical Society (2014), and the Royal %%% Society of New South Wales (2015). %%% %%% Jon Borwein travelled, spoke, and wrote, %%% widely, and collaborated with many other %%% mathematicians, including his father David %%% and brother Peter, and David H. Bailey, with %%% whom he co-authored more than 80 papers and %%% five books, and co-wrote a blog on %%% mathematical and scientific issues before the %%% public, many of them reprinted in the %%% Huffington Post and in The Conversation. %%% %%% There is an encyclopedia article about him at %%% %%% https://en.wikipedia.org/wiki/Jonathan_Borwein %%% %%% plus personal Web sites at %%% %%% http://carma.newcastle.edu.au/jon/ %%% http://carma.newcastle.edu.au/jon/CV/CV.html %%% http://jonathanmborwein.com/ %%% http://jonborwein.com/ %%% %%% a mathematical genealogy at %%% %%% https://genealogy.math.ndsu.nodak.edu/id.php?id=23187 %%% %%% and obituaries at %%% %%% http://blogs.ams.org/beyondreviews/2016/08/03/jonathan-borwein/ %%% http://jonborwein.org/2016/08/he-left-this-world-a-better-place/ %%% https://cms.math.ca/MediaReleases/2016/borweinobituary %%% https://www.science.org.au/fellowship/fellows/professor-jonathan-borwein %%% %%% The increasingly-famous BBP formula (entry %%% Bailey:1997:RCV) is named after its authors: %%% David Bailey, Jon's brother Peter Borwein, %%% and Simon Plouffe. That astonishing formula %%% allows computation of digits of pi in any %%% number base that is an integral power of two, %%% the power being greater than zero, starting %%% from any prescribed digit, without knowing %%% any previous digits! BBP-like formulas have %%% since been found for several other %%% transcendental contants. David Bailey and %%% Jon Borwein have written and spoken %%% extensively about the importance of, and use %%% of, the BBP formula. %%% %%% Jon Borwein updated his curriculum vitae just %%% five hours before he died, so we have some %%% confidence that coverage of his works in this %%% bibliography is complete as far as he %%% recorded them. However, additional %%% publications are to be expected, and are %%% included here, such as from reprints, %%% articles in accepted and in press, or %%% submitted, and ones that he simply forgot, or %%% chose not, to record. %%% %%% At version 1.54, the COMPLETE year coverage %%% looked like this: %%% %%% 1972 ( 1) 1988 ( 31) 2004 ( 51) %%% 1973 ( 0) 1989 ( 25) 2005 ( 79) %%% 1974 ( 1) 1990 ( 52) 2006 ( 61) %%% 1975 ( 0) 1991 ( 36) 2007 ( 57) %%% 1976 ( 4) 1992 ( 27) 2008 ( 46) %%% 1977 ( 5) 1993 ( 40) 2009 ( 65) %%% 1978 ( 4) 1994 ( 37) 2010 ( 70) %%% 1979 ( 10) 1995 ( 47) 2011 ( 100) %%% 1980 ( 7) 1996 ( 31) 2012 ( 125) %%% 1981 ( 10) 1997 ( 63) 2013 ( 136) %%% 1982 ( 8) 1998 ( 33) 2014 ( 119) %%% 1983 ( 11) 1999 ( 50) 2015 ( 100) %%% 1984 ( 19) 2000 ( 48) 2016 ( 115) %%% 1985 ( 9) 2001 ( 42) 2017 ( 33) %%% 1986 ( 23) 2002 ( 37) 2018 ( 31) %%% 1987 ( 27) 2003 ( 53) %%% 19xx ( 7) %%% %%% Article: 803 %%% Book: 54 %%% InCollection: 88 %%% InProceedings: 47 %%% MastersThesis: 1 %%% Misc: 184 %%% PhdThesis: 2 %%% Proceedings: 14 %%% TechReport: 51 %%% Unpublished: 743 %%% %%% Total entries: 1987 %%% %%% As an indication of the breadth of Jon %%% Borwein's interests, his published articles %%% appear in at least 135 journals, with these %%% being the most commonly chosen (as recorded %%% at version 1.07): %%% %%% ======================================== %%% count | journal %%% ======================================== %%% 47 | The Conversation %%% 46 | j-AMER-MATH-MONTHLY %%% 37 | Huffington Post %%% 36 | ArXiv e-prints %%% 21 | j-PROC-AM-MATH-SOC %%% 18 | j-J-CONVEX-ANAL %%% 17 | j-J-MATH-ANAL-APPL %%% 16 | j-EXP-MATH %%% 14 | j-MATH-PROG %%% 13 | j-CAN-J-MATH %%% 13 | j-NONLINEAR-ANAL %%% 12 | j-CAN-MATH-BULL %%% 12 | j-TRANS-AM-MATH-SOC %%% 11 | j-J-OPT-THEORY-APPL %%% 11 | j-NAMS %%% 11 | j-RAMANUJAN-J %%% 10 | j-SIAM-J-OPT %%% 10 | j-SET-VALUED-ANAL %%% 8 | j-SIAM-REVIEW %%% 8 | ArXiv Mathematics e-prints %%% 8 | j-MATH-INTEL %%% 7 | j-SIAM-J-CONTROL-OPTIM %%% 7 | j-J-APPROX-THEORY %%% 7 | j-MATH-COMPUT %%% 6 | j-OPTIMIZATION %%% 6 | j-BULL-AUSTRAL-MATH-SOC %%% 6 | j-J-NONLINEAR-CONVEX-ANAL %%% 6 | j-AUSTRALIAN-MATH-SOC-GAZ %%% 5 | j-OPTIM-LETT %%% 4 | j-MATH-OP-RES %%% 4 | j-MAPLE-TECH-NEWS %%% 4 | j-J-FUNCT-ANAL %%% 4 | j-MATH-INEQUAL-APPL %%% 4 | j-SIAM-NEWS %%% 3 | j-PAC-J-MATH %%% 3 | j-J-COMPUT-APPL-MATH %%% 3 | ArXiv High Energy Physics --- Theory e-prints %%% 3 | j-ELECT-J-COMB %%% 3 | j-J-GLOBAL-OPT %%% 3 | j-SET-VALUED-VAR-ANAL %%% 3 | j-APPL-MATH-COMP %%% 3 | j-INTEGERS %%% 2 | j-J-LOND-MATH-SOC-2 %%% 2 | j-INT-J-MATH-MATH-SCI %%% 2 | j-MATH-PROG-STUDY %%% 2 | j-J-AUSTRAL-MATH-SOC-SER-A %%% 2 | j-BIT %%% 2 | j-PROC-EDINBURGH-MATH-SOC-2 %%% 2 | j-J-MATH-PHYS %%% 2 | j-J-AUSTRAL-MATH-SOC-SER-B %%% 2 | j-ISRAEL-J-MATH %%% 2 | j-IMA-J-NUMER-ANAL %%% 2 | j-J-PHYS-A %%% 2 | j-Z-OPER-RES %%% 2 | j-SCIENCE %%% 2 | j-AEQUATIONES-MATHEMATICAE %%% 2 | j-NUM-MATH %%% 2 | j-IEEE-TRANS-NUCL-SCI %%% 2 | j-SIGSAM %%% 2 | j-INT-J-NUMBER-THEORY %%% 2 | j-J-PHYS-A-MATH-THEOR %%% 2 | Rhodes Scholar Blog %%% 2 | j-J-AUSTRAL-MATH-SOC %%% 2 | j-ANZIAM-J %%% 2 | j-J-SYMBOLIC-COMP %%% 1 | in each of 70 other journals %%% ======================================== %%% %%% Besides at least 504 articles, 90 blogs, and %%% 708 invited talks on five continents, Jon %%% Borwein also authored or edited, or was the %%% subject of, 34 books (including new editions %%% and translations): %%% %%% ================================================================================================= %%% 1987 | Pi and the AGM: a Study in Analytic Number Theory and Computational Complexity %%% 1990 | A dictionary of real numbers %%% 1991 | The HarperCollins dictionary of mathematics %%% 1995 | Dizionario Collins della matematica %%% 1995 | Shu xue ci dian %%% 1997 | Pi, a source book %%% 1997 | The MathResource interactive math dictionary %%% 1998 | Pi and the AGM: A study in analytic number theory and computational complexity %%% 1999 | Dictionary of mathematics %%% 2000 | Convex Analysis and Nonlinear Optimization %%% 2000 | Pi: a source book %%% 2002 | Mathematics: Collins dictionary %%% 2002 | Multimedia tools for communicating mathematics %%% 2003 | Experimentation in mathematics: computational paths to discovery %%% 2004 | Mathematics by Experiment: Plausible Reasoning in the 21st Century %%% 2004 | Pi: a source book %%% 2005 | Techniques of Variational Analysis %%% 2006 | Convex analysis and nonlinear optimization %%% 2006 | Experiments in Mathematics %%% 2007 | Experimental Mathematics in Action %%% 2008 | Communicating Mathematics in the Digital Era %%% 2008 | Mathematics by Experiment %%% 2009 | The computer as crucible: an introduction to experimental mathematics %%% 2010 | Convex functions: constructions, characterizations and counterexamples %%% 2010 | Experimental and computational mathematics: selected writings %%% 2011 | An introduction to modern mathematical computing: with Maple %%% 2011 | Experimentelle Mathematik: Eine beispielorientierte Einfuhrung %%% 2012 | An introduction to modern mathematical computing: with Mathematicareg %%% 2012 | Exploratory experimentation in mathematics: selected works %%% 2013 | Computational and analytical mathematics: in honor of Jonathan Borwein's 60th Birthday %%% 2013 | Lattice Sums: Then and Now %%% 2014 | Neverending fractions: an introduction to continued fractions %%% 2016 | Pi: the next generation: a sourcebook on the recent history of Pi and its computation %%% 2016 | Tools and Mathematics %%% ================================================================================================= %%% %%% The tables given above have been produced %%% automatically, and reliably, from the output %%% of queries to an SQL database containing the %%% entries in this bibliography. %%% %%% A count of recorded page ranges of the form %%% mmm--nnn in parts 1--3 of this file finds %%% 7939 pages in 514 documents, an average of %%% 15.45 pages each. That is an impressive %%% production in the mathematical literature! %%% %%% Entries for this bibliography have been %%% derived from data in the BibNet Project and %%% TeX User Group bibliography archives, and %%% from the ACM Portal, American Physical %%% Society (APS), American Institute of Physics %%% (AIP), arxiv.org, Australian Mathematical %%% Society, Cambridge Journals, Canadian %%% Mathematical Society (CMS), Canadian %%% Association of Physicists, Elsevier %%% ScienceDirect, EuroPhysics, IEEE Xplore, %%% Institute of Physics (IOP), JSTOR, MathSciNet, %%% Nature, PubMed, Royal Society, Science, %%% Smithsonian Astrophysical Observatory, %%% SpringerLink, Web of Science, Wiley, and %%% zbMATH databases. Once those resources were %%% exhausted, the BibTeX entries produced from %%% them were matched entry by entry with Jon %%% Borwein's curriculum vitae in his file %%% CV.pdf, and all previously-missing ones were %%% converted to BibTeX form and added to this %%% file. %%% %%% Numerous errors and inconsistencies in those %%% sources have been corrected, and many %%% heuristic checks, and spelling corrections, %%% have been done. The companion file %%% borwein-jonathan-m.sok contains a private %%% spelling-exception dictionary for this file. %%% %%% Special thanks go to David H. Bailey of %%% the University of California, Davis, and %%% Karl Dilcher of Dalhousie University for %%% uncovering many previously unrecorded works %%% by Jonathan Borwein. %%% %%% TO DO: More work is still needed to locate %%% electronic addresses for some entries. Of %%% the 592 article entries containing Borwein in %%% the author field, 536 have either a DOI or a %%% URL value, and 164 have both DOI and URL %%% values, but 56 have neither. %%% %%% Of the 115 Borwein entries for InXxx blocks, %%% 61 have neither DOI nor URL values. %%% %%% Of the 37 Borwein entries for Book and %%% Proceedings blocks, 17 have neither DOI nor %%% URL values. %%% %%% Except for those publications in open-access %%% journals or technical reports, document %%% access via DOI or URL values may require an %%% institutional journal subscription, or online %%% payment. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ====================================================================

@Preamble{ "\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" # "\ifx \undefined \cdprime \def \cdprime {$''$} \fi" # "\ifx \undefined \cftilf \def \cftil #1{\ifmmode \setbox7 \hbox{$\accent5E#1$}\else \setbox7 \hbox{\accent5E#1}\penalty 10000 \relax \fi \raise 1\ht7 \hbox{\lower 1.15ex \hbox to 1\wd7{\hss \accent7E \hss}}\penalty 10000 \hskip-1\wd7 \penalty 10000 \box7} \fi" # "\ifx \undefined \circled \def \circled #1{(#1)}\fi" # "\ifx \undefined \cprime \def \cprime {$'$} \fi" # "\ifx \undefined \coloneq \def \coloneq {\colon=} \fi" # "\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}} \fi" # "\ifx \undefined \mathrm \def \mathrm #1{{\rm #1}} \fi" # "\ifx \undefined \refcno \def \refcno{Cno. } \fi" # "\ifx \undefined \reg \def \reg {\circled{R}}\fi" }

%%% ==================================================================== %%% Acknowledgement abbreviations:

@String{ack-nhfb= "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|http://www.math.utah.edu/~beebe/|"} @String{ack-njh= "Nick Higham, e-mail: \path|nick.higham@manchester.ac.uk|"}

%%% ==================================================================== %%% Institutional abbreviations:

@String{inst-CARMA= "Centre for Computer-assisted Research Mathematics and its Applications (CARMA), School of Mathematical and Physical Sciences, University of Newcastle"} @String{inst-CARMA:adr= "Callaghan, NSW 2308, Australia"} @String{inst-CECM= "Centre for Experimental and Constructive Mathematics (CECM) at Simon Fraser University (SFU)"} @String{inst-CECM:adr= "Burnaby, BC, Canada"}

%%% ==================================================================== %%% Journal abbreviations:

@String{j-ABSTR-APPL-ANAL= "Abstract and Applied Analysis"} @String{j-ACM-COMM-COMP-ALGEBRA= "ACM Communications in Computer Algebra"} @String{j-ACTA-ARITHMETICA= "Acta Arithmetica"} @String{j-ACTA-SCI-NATUR-UNIV-SUNYATSENI= "Acta Scientiarum Naturalium Universitatis Sunyatseni. Zhongshan Daxue Xuebao. Ziran Kexue Ban"} @String{j-ADV-NONLINEAR-ANAL= "Advances in Nonlinear Analysis"} @String{j-AEQUATIONES-MATHEMATICAE= "Aequationes Mathematicae"} @String{j-AM-SCI= "American Scientist"} @String{j-AMER-MATH-MONTHLY= "American Mathematical Monthly"} @String{j-ANZIAM-J= "The ANZIAM Journal"} @String{j-APPL-ANAL= "Applicable Analysis"} @String{j-APPL-MATH-COMP= "Applied Mathematics and Computation"} @String{j-APPL-MATH-LETT= "Applied Mathematics Letters"} @String{j-APPL-MATH-OPTIM= "Applied Mathematics and Optimization"} @String{j-AUSTRALIAN-MATH-SOC-GAZ= "Australian Mathematical Society Gazette"} @String{j-BIT= "BIT (Nordisk tidskrift for informationsbehandling)"} @String{j-BOUND-VALUE-PROBL= "Boundary Value Problems"} @String{j-BULL-AMS-N-S= "Bulletin of the American Mathematical Society (new series)"} @String{j-BULL-AUSTRAL-MATH-SOC= "Bulletin of the Australian Mathematical Society"} @String{j-BULL-CALCUTTA-MATH-SOC= "Bulletin of the Calcutta Mathematical Society"} @String{j-C-R-ACAD-BULGARE-SCI= "Comptes rendus de l'Acad{\'e}mie bulgare des sciences"} @String{j-C-R-ACAD-SCI-CANADA= "Comptes rendus de l'Acad{\'e}mie des sciences. Canada"} @String{j-CAN-J-MATH= "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques"} @String{j-CAN-MATH-BULL= "Canadian mathematical bulletin = Bulletin canadien de math{\'e}matiques"} @String{j-CMS-NOTES= "Canadian Mathematical Society Notes"} @String{j-COLLOQ-MATH= "Colloquium Mathematicum"} @String{j-COMMUN-CONTEMP-MATH= "Communications in Contemporary Mathematics"} @String{j-COMP-OPTIM-APPL= "Computational optimization and applications"} @String{j-COMP-PHYS-COMM= "Computer Physics Communications"} @String{j-COMPUT-SCI-ENG= "Computing in Science and Engineering"} @String{j-COMPUTING= "Computing: Archiv f{\"u}r informatik und numerik"} @String{j-CONST-APPROX= "Constructive Approximation"} @String{j-DISCRETE-MATH= "Discrete Mathematics"} @String{j-EDUC-STUD-MATH= "Educational Studies in Mathematics"} @String{j-ELECT-J-COMB= "Electronic Journal of Combinatorics"} @String{j-ELECTRON-TRANS-NUMER-ANAL= "Electronic Transactions on Numerical Analysis"} @String{j-ENTROPY= "Entropy"} @String{j-EUR-MATH-SOC-NEWSL= "European Mathematical Society. Newsletter"} @String{j-EXP-MATH= "Experimental Mathematics"} @String{j-FIB-QUART= "Fibonacci Quarterly"} @String{j-HOUSTON-J-MATH= "Houston Journal of Mathematics"} @String{j-IEEE-CONTROL-SYST-MAG= "IEEE Control Systems Magazine"} @String{j-IEEE-TRANS-MED-IMAG= "IEEE Transactions on Medical Imaging"} @String{j-IEEE-TRANS-NUCL-SCI= "IEEE Transactions on Nuclear Science"} @String{j-IMA-J-NUMER-ANAL= "IMA Journal of Numerical Analysis"} @String{j-INDAG-MATH= "Indagationes Mathematic{\ae}"} @String{j-INFO-SCI= "Information Sciences"} @String{j-INT-J-COMPUT-MATH= "International Journal of Computer Mathematics"} @String{j-INT-J-MATH-MATH-SCI= "International Journal of Mathematics and Mathematical Sciences"} @String{j-INT-J-NUMBER-THEORY= "International Journal of Number Theory"} @String{j-INTEGERS= "Integers"} @String{j-INTEGRAL-TRANSFORMS-SPEC-FUNCT= "Integral Transforms and Special Functions"} @String{j-INVERSE-PROBL-SCI-ENG= "Inverse Problems in Science and Engineering"} @String{j-ISRAEL-J-MATH= "Israel Journal of Mathematics"} @String{j-J-ALG= "Journal of Algorithms"} @String{j-J-APPL-MATH= "Journal of Applied Mathematics"} @String{j-J-APPROX-THEORY= "Journal of Approximation Theory"} @String{j-J-AUSTRAL-MATH-SOC= "Journal of the Australian Mathematical Society"} @String{j-J-AUSTRAL-MATH-SOC-SER-A= "Journal of the Australian Mathematical Society. Series A: Pure Mathematics and Statistics"} @String{j-J-AUSTRAL-MATH-SOC-SER-B= "Journal of the Australian Mathematical Society. Series B"} @String{j-J-AUSTRALIAN-MATH-SOC= "Journal of the Australian Mathematical Society"} @String{j-J-COMB-THEORY-A= "Journal of Combinatorial Theory (Series A)"} @String{j-J-COMP-MATH= "Journal of Computational Mathematics"} @String{j-J-COMPUT-APPL-MATH= "Journal of Computational and Applied Mathematics"} @String{j-J-COMPUT-FINANCE= "Journal of Computational Finance"} @String{j-J-CONVEX-ANAL= "Journal of Convex Analysis"} @String{j-J-FUNCT-ANAL= "Journal of Functional Analysis"} @String{j-J-GLOBAL-OPT= "Journal of Global Optimization"} @String{j-J-HUMANIST-MATH= "Journal of Humanistic Mathematics"} @String{j-J-INTEGER-SEQ= "Journal of Integer Sequences"} @String{j-J-INVESTMENT-MANAGE= "Journal of Investment Management"} @String{j-J-LOND-MATH-SOC-2= "Journal of the London Mathematical Society (series 2)"} @String{j-J-MATH-ANAL-APPL= "Journal of Mathematical Analysis and Applications"} @String{j-J-MATH-PHYS= "Journal of Mathematical Physics"} @String{j-J-NONLINEAR-CONVEX-ANAL= "Journal of Nonlinear and Convex Analysis"} @String{j-J-NUMBER-THEORY= "Journal of Number Theory"} @String{j-J-OPT-THEORY-APPL= "Journal of Optimization Theory and Applications"} @String{j-J-PHYS-A= "Journal of Physics A (Mathematical and General)"} @String{j-J-PHYS-A-MATH-THEOR= "Journal of Physics A: Mathematical and Theoretical"} @String{j-J-REINE-ANGEW-MATH= "{Journal f{\"u}r die reine und angewandte Mathematik}"} @String{j-J-SCI-COMPUT= "Journal of Scientific Computing"} @String{j-J-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 = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @PhdThesis{Borwein:1974:ORP, author = "Jonathan Michael Borwein", title = "Optimization with respect to partial orderings", type = "{D.Phil.} thesis", school = "Oxford University", address = "Oxford, UK", year = "1974", bibdate = "Wed Aug 10 10:59:56 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://search.proquest.com/pqdtglobal/docview/1767375969/", acknowledgement = ack-nhfb, advisor = "M. A. H. (Michael Alan Howarth) Dempster", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1976:FPD, author = "J. M. Borwein", title = "Fractional programming without differentiability", journal = j-MATH-PROG, volume = "11", number = "1", pages = "283--290", year = "1976", CODEN = "MHPGA4", DOI = "https://doi.org/10.1007/BF01580396", ISSN = "0025-5610 (print), 1436-4646 (electronic)", ISSN-L = "0025-5610", MRclass = "90C10 (65K05)", MRnumber = "0449664", MRreviewer = "Siegfried Schaible", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1671/; http://link.springer.com/article/10.1007/BF01580396", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming", journal-URL = "http://link.springer.com/journal/10107", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", xxnumber = "3", } @Article{Borwein:1976:NFJ, author = "J. M. Borwein", title = "A note on {Fritz John} sufficiency", journal = j-BULL-AUSTRAL-MATH-SOC, volume = "15", number = "2", pages = "293--296", month = oct, year = "1976", CODEN = "ALNBAB", DOI = "https://doi.org/10.1017/S0004972700022656", ISSN = "0004-9727 (print), 1755-1633 (electronic)", ISSN-L = "0004-9727", MRclass = "90C30", MRnumber = "0426851", MRreviewer = "R. N. Kaul", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1515/; http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=4812456", acknowledgement = ack-nhfb, fjournal = "Bulletin of the Australian Mathematical Society", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1976:TCC, author = "J. Borwein and R. O'Brien", title = "Tangent cones and convexity", journal = j-CAN-MATH-BULL, volume = "19", number = "3", pages = "257--261", year = "1976", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1976-040-x", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", MRclass = "46A99 (52A05)", MRnumber = "0454586", MRreviewer = "A. Gopfert", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1517/", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1976:VS, author = "J. Borwein and M. Edelstein and R. O'Brien", title = "Visibility and Starshape", journal = j-J-LOND-MATH-SOC-2, volume = "S2-14", number = "2", pages = "313--318", month = nov, year = "1976", CODEN = "JLMSAK", DOI = "https://doi.org/10.1112/jlms/s2-14.2.313", ISSN = "0024-6107 (print), 1469-7750 (electronic)", ISSN-L = "0024-6107", MRclass = "46B05", MRnumber = "0428010", MRreviewer = "Bor-Luh Lin", bibdate = "Fri Aug 12 16:38:27 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1670/; http://jlms.oxfordjournals.org/content/s2-14/2/313.full.pdf+html", acknowledgement = ack-nhfb, ajournal = "J. Lond. Math. Soc. (2)", fjournal = "Journal of the London Mathematical Society (series 2)", journal-URL = "http://jlms.oxfordjournals.org/content/by/year", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1977:MCO, author = "J. Borwein", title = "Multivalued convexity and optimization: a unified approach to inequality and equality constraints", journal = j-MATH-PROG, volume = "13", number = "2", pages = "183--199", year = "1977", CODEN = "MHPGA4", DOI = "https://doi.org/10.1007/BF01584336", ISSN = "0025-5610 (print), 1436-4646 (electronic)", ISSN-L = "0025-5610", MRclass = "52A40 (90C25)", MRnumber = "0451166", MRreviewer = "J. Stoer", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1669/; http://link.springer.com/article/10.1007/BF01584336", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming", journal-URL = "http://link.springer.com/journal/10107", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1977:PEH, author = "J. Borwein", title = "A proof of the equivalence of {Helly}'s and {Krasnoselski}'s theorems", journal = j-CAN-MATH-BULL, volume = "20", number = "1", pages = "35--37", month = mar, year = "1977", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1977-007-4", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", MRclass = "52A35", MRnumber = "0478014", MRreviewer = "John D. Baildon", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://cms.math.ca/cmb/v20/; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/canmathbull.bib", URL = "http://docserver.carma.newcastle.edu.au/1518/", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1977:PEP, author = "J. Borwein", title = "Proper Efficient Points for Maximizations with Respect to Cones", journal = j-SIAM-J-CONTROL-OPTIM, volume = "15", number = "1", pages = "57--63", month = jan, year = "1977", CODEN = "SJCODC", DOI = "https://doi.org/10.1137/0315004", ISSN = "0363-0129 (print), 1095-7138 (electronic)", ISSN-L = "0363-0129", MRclass = "90C30 (65K05 49B99)", MRnumber = "0434441", MRreviewer = "M. Rossler", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICON/15/1; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/siamjcontroloptim.bib", URL = "http://docserver.carma.newcastle.edu.au/1667/", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Control and Optimization", journal-URL = "http://epubs.siam.org/sicon", journalabr = "SIAM J Control Optim", onlinedate = "January 1977", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1977:SRV, author = "J. Borwein and M. Edelstein and R. O'Brien", title = "Some remarks on visibility and starshape", journal = j-J-LOND-MATH-SOC-2, volume = "S2-15", number = "2", pages = "342--344", month = apr, year = "1977", CODEN = "JLMSAK", DOI = "https://doi.org/10.1112/jlms/s2-15.2.342", ISSN = "0024-6107 (print), 1469-7750 (electronic)", ISSN-L = "0024-6107", MRclass = "46A99", MRnumber = "0442642", MRreviewer = "Bor-Luh Lin", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1666/; http://jlms.oxfordjournals.org/content/s2-15/2/342.full.pdf+html", acknowledgement = ack-nhfb, ajournal = "J. Lond. Math. Soc. (2)", fjournal = "Journal of the London Mathematical Society (series 2)", journal-URL = "http://jlms.oxfordjournals.org/content/by/year", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Misc{Borwein:1977:WLP, author = "J. M. Borwein", title = "The {William Lowell Putnam} Competition. {A} Brief History", howpublished = "Unpublished notes.", pages = "9", day = "26", month = jan, year = "1977", bibdate = "Mon Nov 07 06:59:36 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "In December 1921 William Lowell Putnam, a magna cum laude Mathematics graduate of the Harvard class of 1882, wrote in the Harvard Graduate Magazine on ``A Suggestion For Increasing The Undergraduate Interest In Studies''. He noted that all prizes for scholarship were individual and suggested that ``a Harvard man prefers for example to be a member of a tennis team to play against Yale \ldots{} rather than to be champion of Harvard'' and that the same principle of team work and team competition ``which has inspired young men to undertake and undergo so much for the sake of athletic victories might accomplish some result in academic fields''. These sentiments, and others which seem even more dated, would probably have had no effect were it not that Putnam's wife was a Lowell, was extremely rich and was the sister of then President Abbott Lowell of Harvard. Putnam's mother was also a Lowell while his father was a Unitarian with all the right connections and memberships who founded the English Speaking Union among other organizations and wrote prodigiously on many learned topics", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1978:CCC, author = "J. M. Borwein and R. C. O'Brien", title = "Cancellation characterizes convexity", journal = "Nanta Mathematica", volume = "11", number = "1", pages = "100--102", year = "1978", CODEN = "NAMAB2", ISSN = "0077-2739", MRclass = "52A20", MRnumber = "510842", MRreviewer = "John D. Baildon", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1659/", acknowledgement = ack-nhfb, ajournal = "Nanta Math.", fjournal = "Nanyang University. Nanta Mathematica", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1978:SEF, author = "J. M. Borwein", title = "On strongly exposing functionals", journal = j-PROC-AM-MATH-SOC, volume = "69", number = "1", pages = "46--48", year = "1978", CODEN = "PAMYAR", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "46B99 (52A05)", MRnumber = "0493272", MRreviewer = "Ka Sing Lau", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1665/; http://www.jstor.org/stable/2043185", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1978:TCS, author = "J. M. Borwein", title = "Tangent cones, starshape and convexity", journal = j-INT-J-MATH-MATH-SCI, volume = "1", number = "4", pages = "459--477", year = "1978", DOI = "https://doi.org/10.1155/S0161171278000460", ISSN = "0161-1712 (print), 1687-0425 (electronic)", ISSN-L = "0161-1712", MRclass = "52A30 (90C30)", MRnumber = "517949", MRreviewer = "Gerald Beer", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1663/", acknowledgement = ack-nhfb, fjournal = "International Journal of Mathematics and Mathematical Sciences", journal-URL = "https://www.hindawi.com/journals/ijmms/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1978:WTC, author = "J. Borwein", title = "Weak Tangent Cones and Optimization in a {Banach} Space", journal = j-SIAM-J-CONTROL-OPTIM, volume = "16", number = "3", pages = "512--522", month = may, year = "1978", CODEN = "SJCODC", DOI = "https://doi.org/10.1137/0316034", ISSN = "0363-0129 (print), 1095-7138 (electronic)", ISSN-L = "0363-0129", MRclass = "65K05 (90C99)", MRnumber = "0478612", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICON/16/3; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/siamjcontroloptim.bib", URL = "http://docserver.carma.newcastle.edu.au/1664/", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Control and Optimization", journal-URL = "http://epubs.siam.org/sicon", journalabr = "SIAM J Control Optim", onlinedate = "May 1978", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Unpublished{Borwein:1979:CD, author = "J. M. Borwein", title = "On convex decompositions", year = "1979", bibdate = "Fri Aug 12 16:51:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Accepted for publication in \booktitle{Nanta Mathematica}, but the journal ceased publication in 1979 before the paper appeared.", URL = "http://docserver.carma.newcastle.edu.au/1672/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1979:COA, author = "J. M. Borwein and H. Wolkowicz", title = "Characterizations of Optimality for the Abstract Convex Program", type = "Research Report", number = "19", institution = "Department of Mathematics, Dalhousie University", address = "Halifax, NS, Canada", pages = "54", month = jul, year = "1979", bibdate = "Tue Nov 08 15:45:14 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib", abstract = "This paper presents characterizations of optimality for the convex program $$ (p) \mu = \inf \{ p(x) \colon g(x) \in - S, x \in \Omega \} $$ when $S$ is an arbitrary convex cone in a finite dimensional space, $ \Omega $ is a convex set and $p$ and $g$ are respectively convex and S-convex(on $ \Omega $). These characterizations, which include a Lagrange multiplier and do not presume any a priori constraint qualification, subsume those presently in the literature.", acknowledgement = ack-nhfb, keywords = "abstract programming; cone of positive semi-definite matrices; convexity; duality principles; facial reduction; Lagrange multipliers; Slater's condition; subgradients; symmetric matrices", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1979:COC, author = "J. M. Borwein and H. Wolkowicz", title = "Characterizations of optimality without constraint qualification for the abstract convex program", type = "Research Report", number = "14", institution = "Department of Mathematics, Dalhousie University", address = "Halifax, NS, Canada", pages = "59", month = jun, year = "1979", bibdate = "Tue Nov 08 15:45:14 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1979:DTS, author = "J. M. Borwein", title = "Direct theorems in semi-infinite convex programming", type = "Report", number = "11", institution = "Department of Mathematics, Dalhousie University", address = "Halifax, NS, Canada", pages = "33", month = apr, year = "1979", bibdate = "Tue Nov 08 15:45:14 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "Recently Ben-Tal, Ben-Israel and Rossinger [1] have proven a ``direct theorem'' for the existence of finite subprograms for infinitely constrained programming problems with finitely many variables. They did this via a Helly-type theorem for open convex sets due to Klee [10], [7]. The proof of Klee's theorem [10] is somewhat difficult to follow and, in addition, requires the use of the notion of an ``open-closed'' family of sets. One of the purposes of this paper is to provide an entirely self-contained proof of an extension of the result in [1].", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1979:LLC, author = "J. M. Borwein", title = "The Limiting Lagrangean as a Consequence of {Helly's Theorem}", type = "Report", number = "7", institution = "Department of Mathematics, Dalhousie University", address = "Halifax, NS, Canada", month = mar, year = "1979", bibdate = "Tue Nov 08 15:34:18 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "The perturbational Lagrangean equation established by Jeroslow in convex semi-infinite programming is derived from Helly's Theorem and some prior results on one dimensional perturbations of convex programs.", acknowledgement = ack-nhfb, keywords = "Affine Minorants; convex semi-infinite programming; Helly's Theorem; limiting Lagrangeans; Recession Directions", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1979:MAF, author = "J. M. Borwein", title = "A multivalued approach to the {Farkas} lemma", journal = j-MATH-PROG-STUDY, volume = "10", pages = "42--47", year = "1979", CODEN = "MPSTDF", DOI = "https://doi.org/10.1007/BFb0120842", ISSN = "0303-3929", ISSN-L = "0303-3929", MRclass = "90C99", MRnumber = "527056", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Point-to-set maps and mathematical programming.", URL = "http://docserver.carma.newcastle.edu.au/1660/; http://link.springer.com/chapter/10.1007/BFb0120842", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming Study", journal-URL = "https://link.springer.com/bookseries/8439", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1979:MFP, author = "J. M. Borwein", booktitle = "{Third Symposium on Operations Research (Univ. Mannheim, Mannheim, 1978), Section I}", title = "The minimum of a family of programs", volume = "31", publisher = "Hain", pages = "99--111", year = "1979", MRclass = "90C25", MRnumber = "541191", MRreviewer = "Jacques Dubois", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Operations Res. Verfahren", acknowledgement = ack-nhfb, addresss = "K{\"o}nigstein im Taunus, West Germany", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1979:MLP, author = "Jonathan M. Borwein", title = "Monochrome lines in the plane", journal = j-MATH-MAG, volume = "52", number = "1", pages = "41--45", year = "1979", CODEN = "MAMGA8", DOI = "https://doi.org/10.2307/2689976", ISSN = "0025-570X (print), 1930-0980 (electronic)", ISSN-L = "0025-570X", MRclass = "54B20 (57N05)", MRnumber = "524202", MRreviewer = "H. W. Lambert", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1662/", acknowledgement = ack-nhfb, fjournal = "Mathematics Magazine", journal-URL = "http://www.maa.org/pubs/mathmag.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1979:TVS, author = "J. M. Borwein", title = "Two variants of {Sylvester}'s theorem", journal = "Atlantic Mathematics Bulletin", volume = "3", number = "??", pages = "11--13", month = "????", year = "1979", DOI = "", ISSN = "0705-9078", ISSN-L = "0705-9078", bibdate = "Fri Aug 12 16:08:43 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1658/", acknowledgement = ack-nhfb, ajournal = "Atlantic Math. Bull.", fjournal = "Atlantic Mathematics Bulletin", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1979:WLS, author = "J. M. Borwein", title = "Weak local supportability and applications to approximation", journal = j-PAC-J-MATH, volume = "82", number = "2", pages = "323--338", year = "1979", CODEN = "PJMAAI", ISSN = "0030-8730 (print), 1945-5844 (electronic)", ISSN-L = "0030-8730", MRclass = "46B99 (41A25 49A27 58C20 90C30)", MRnumber = "551692", MRreviewer = "Ka Sing Lau", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://projecteuclid.org/euclid.pjm/1102784876", acknowledgement = ack-nhfb, fjournal = "Pacific Journal of Mathematics", journal-URL = "http://msp.org/pjm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1980:GPE, author = "J. M. Borwein", title = "The geometry of {Pareto} efficiency over cones", journal = j-OPTIMIZATION, volume = "11", number = "2", pages = "235--248", year = "1980", CODEN = "OPTZDQ", DOI = "https://doi.org/10.1080/02331938008842650", ISSN = "0323-3898", ISSN-L = "0233-1934", MRclass = "90C31 (58E17 90C25 90C30)", MRnumber = "640689", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/02331938008842650", acknowledgement = ack-nhfb, fjournal = "Mathematische Operationsforschung und Statistik Series Optimization", journal-URL = "http://www.tandfonline.com/loi/gopt20", onlinedate = "5 July 2007", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1980:HMC, author = "J. Borwein and L. Keener", title = "The {Hausdorff} metric and {{\v{C}}eby{\v{s}}ev} centres", journal = j-J-APPROX-THEORY, volume = "28", number = "4", pages = "366--376", year = "1980", CODEN = "JAXTAZ", DOI = "https://doi.org/10.1016/0021-9045(80)90071-4", ISSN = "0021-9045 (print), 1096-0430 (electronic)", ISSN-L = "0021-9045", MRclass = "41A65 (46B20)", MRnumber = "589992", MRreviewer = "S. Cobza{\c{s}}", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1652/; http://www.sciencedirect.com/science/article/pii/0021904580900714", acknowledgement = ack-nhfb, fjournal = "Journal of Approximation Theory", journal-URL = "http://www.sciencedirect.com/science/journal/00219045", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1980:LM, author = "J. M. Borwein", title = "Lexicographic multipliers", journal = j-J-MATH-ANAL-APPL, volume = "78", number = "1", pages = "309--327", year = "1980", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(80)90228-0", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "90C25 (58C20)", MRnumber = "595782", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1653/; http://www.sciencedirect.com/science/article/pii/0022247X80902280", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1980:LMT, author = "J. M. Borwein", title = "A {Lagrange} Multiplier Theorem and a Sandwich Theorem for Convex Relations", type = "Research Report", number = "80-1", institution = "Department of Mathematics, Dalhousie University", address = "Halifax, NS, Canada", pages = "26", day = "15", month = jan, year = "1980", bibdate = "Tue Nov 08 15:45:14 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "We formulate and prove various separation principles for convex relations taking values in an order complete vector space. These principles subsume the standard ones", acknowledgement = ack-nhfb, keywords = "convex relations; Fenchel's theorem; Lagrange multipliers; order complete spaces; separation", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1980:NPD, author = "J. M. Borwein", title = "A note on perfect duality and limiting {Lagrangeans}", journal = j-MATH-PROG, volume = "18", number = "1", pages = "330--337", year = "1980", CODEN = "MHPGA4", DOI = "https://doi.org/10.1007/BF01588327", ISSN = "0025-5610 (print), 1436-4646 (electronic)", ISSN-L = "0025-5610", MRclass = "90C25", MRnumber = "571994", MRreviewer = "N. N. Astaf{\cprime}ev", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1654/; http://link.springer.com/article/10.1007/BF01588327", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming", journal-URL = "http://link.springer.com/journal/10107", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", xxnumber = "3", } @Article{Borwein:1980:SDT, author = "J. M. Borwein", title = "A strong duality theorem for the minimum of a family of convex programs", journal = j-J-OPT-THEORY-APPL, volume = "31", number = "4", pages = "453--472", year = "1980", CODEN = "JOTABN", DOI = "https://doi.org/10.1007/BF00934472", ISSN = "0022-3239 (print), 1573-2878 (electronic)", ISSN-L = "0022-3239", MRclass = "90C25 (46G99 90C30)", MRnumber = "600199", MRreviewer = "Tadashi Nakamura", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1657/; http://link.springer.com/article/10.1007/BF00934472", acknowledgement = ack-nhfb, fjournal = "Journal of Optimization Theory and Applications", journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Tijs:1980:SGC, author = "S. H. Tijs and J. M. Borwein", title = "Some Generalizations of {Carath{\'e}odory}'s Theorem via Barycentres, with Application to Mathematical Programming", journal = j-CAN-MATH-BULL, volume = "23", number = "3", pages = "339--346", month = sep, year = "1980", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1980-048-x", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", MRclass = "90C05 (46G99 58C20)", MRnumber = "593393", MRreviewer = "M. Brannigan", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://cms.math.ca/cmb/v23/; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/canmathbull.bib", URL = "http://docserver.carma.newcastle.edu.au/1656/", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:1981:CCP, author = "J. M. Borwein and H. Wolkowicz", title = "Cone-convex programming, stability and affine constraints", crossref = "Schaible:1981:CCP", pages = "379--397", year = "1981", bibdate = "Mon Mar 6 22:00:29 MST 1995", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib", note = "Invited paper.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", xxpages = "379--392", xxtitle = "Cone-convex programming, stability and affine constraint functions", } @Article{Borwein:1981:COA, author = "Jon M. Borwein and Henry Wolkowicz", title = "Characterization of optimality for the abstract convex program with finite dimensional range", journal = j-J-AUSTRAL-MATH-SOC-SER-A, volume = "30", number = "4", pages = "390--411", month = apr, year = "1981", CODEN = "JAMADS", DOI = "https://doi.org/10.1017/S1446788700017882", ISSN = "0263-6115 (print), 2396-8192 (electronic)", ISSN-L = "0263-6115", MRclass = "90C48", MRnumber = "621556 (83i:90156)", MRreviewer = "R. L. Graves", bibdate = "Wed Aug 31 15:25:43 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib", URL = "http://docserver.carma.newcastle.edu.au/1649/; http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=4896312", acknowledgement = ack-nhfb, fjournal = "Journal of the Australian Mathematical Society. Series A", journal-URL = "http://journals.cambridge.org/action/displayBackIssues?jid=JAZ", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", received = "21 March 1980", } @InCollection{Borwein:1981:CRO, author = "J. M. Borwein", booktitle = "Generalized Convexity in Optimization and Economics", title = "Convex relations in optimization and analysis", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "335--377", year = "1981", ISBN = "", ISBN-13 = "", LCCN = "", bibdate = "Mon Aug 15 15:17:45 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1981:DTS, author = "J. M. Borwein", title = "Direct theorems in semi-infinite convex programming", journal = j-MATH-PROG, volume = "21", number = "1", pages = "301--318", year = "1981", CODEN = "MHPGA4", DOI = "https://doi.org/10.1007/BF01584251", ISSN = "0025-5610 (print), 1436-4646 (electronic)", ISSN-L = "0025-5610", MRclass = "90C25 (49D39 90C30)", MRnumber = "632637", MRreviewer = "{\c{S}}tefan {\c{T}}igan", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://link.springer.com/article/10.1007/BF01584251", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming", journal-URL = "http://link.springer.com/journal/10107", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", xxnumber = "3", } @Article{Borwein:1981:FRC, author = "Jon M. Borwein and Henry Wolkowicz", title = "Facial reduction for a cone-convex programming problem", journal = j-J-AUSTRAL-MATH-SOC-SER-A, volume = "30", number = "3", pages = "369--380", month = feb, year = "1981", CODEN = "JAMADS", DOI = "https://doi.org/10.1017/S1446788700017250", ISSN = "0263-6115 (print), 2396-8192 (electronic)", ISSN-L = "0263-6115", MRclass = "90C25; 90C48", MRnumber = "83b:90121 (614086)", MRreviewer = "B. T. Polyak", bibdate = "Wed Aug 31 16:29:21 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib", URL = "http://docserver.carma.newcastle.edu.au/1650/; http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=5441184", ZMnumber = "0464.90086", acknowledgement = ack-nhfb, fjournal = "Journal of the Australian Mathematical Society. Series A", journal-URL = "http://journals.cambridge.org/action/displayBackIssues?jid=JAZ", onlinedate = "28 July 1980", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", received = "21 March 1980", } @Article{Borwein:1981:LLC, author = "J. M. Borwein", title = "The limiting {Lagrangian} as a consequence of {Helly}'s theorem", journal = j-J-OPT-THEORY-APPL, volume = "33", number = "4", pages = "497--513", year = "1981", CODEN = "JOTABN", DOI = "https://doi.org/10.1007/BF00935755", ISSN = "0022-3239 (print), 1573-2878 (electronic)", ISSN-L = "0022-3239", MRclass = "90C25", MRnumber = "616567", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1647/; http://link.springer.com/article/10.1007/BF00935755", acknowledgement = ack-nhfb, fjournal = "Journal of Optimization Theory and Applications", journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1981:LMT, author = "J. M. Borwein", title = "A {Lagrange} multiplier theorem and a sandwich theorem for convex relations", journal = j-MATH-SCAND, volume = "48", number = "2", pages = "189--204", year = "1981", CODEN = "MTSCAN", ISSN = "0025-5521 (print), 1903-1807 (electronic)", ISSN-L = "0025-5521", MRclass = "49A50 (26A51 46A22 90C25); 49J45 (Optimal control problems involving semicontinuity and convergence; relaxation); 58C06 (Set-valued and function-space valued mappings on manifolds); 49J27 (Optimal control problems in abstract spaces (existence)); 46A30 (Open mapping and closed graph theorems; completeness); 46A40 (Ordered topological linear spaces, vector lattices)", MRnumber = "631335", MRreviewer = "Michel Th{\'e}ra", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1646/; http://www.mscand.dk/article/view/11911/9927", ZMnumber = "0468.49007", acknowledgement = ack-nhfb, fjournal = "Mathematica Scandinavica", journal-URL = "http://www.mscand.dk/issue/archive", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1981:RAC, author = "Jon Borwein and Henry Wolkowicz", title = "Regularizing the abstract convex program", journal = j-J-MATH-ANAL-APPL, volume = "83", number = "2", pages = "495--530", year = "1981", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(81)90138-4", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "90C48 (90C25)", MRnumber = "641348", MRreviewer = "S. Zlobec", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib", URL = "http://docserver.carma.newcastle.edu.au/1645/; http://www.sciencedirect.com/science/article/pii/0022247X81901384", abstract = "Characterizations of optimality for the abstract convex program $ \mu = i n f \{ p(x) \colon g(x) \in - S, x \in \Omega \} (P) $ where $S$ is an arbitrary convex cone in a finite dimensional space, $ \Omega $ is a convex set, and $p$ and $g$ are respectively convex and $S$-convex (on $ \Omega $), were given in [10]. These characterizations hold without any constraint qualification. They use the ``minimal cone'' $ S^f$ of $ (P)$ and the cone of directions of constancy $ D_g = (S^f)$. In the faithfully convex case these cones can be used to regularize $ (P)$, i.e., transform $ (P)$ into an equivalent program $ (P_r)$ for which Slater's condition holds. We present an algorithm that finds both $ S^$ f and $ D_g = (S^f)$. The main step of the algorithm consists in solving a particular complementarity problem. We also present a characterization of optimality for $ (P)$ in terms of the cone of directions of constancy of a convex functional $ D_{\phi g}^ = $ rather than $ D_g^ = (S^f)$.", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1981:SRP, author = "J. Borwein", title = "Some remarks on a paper of {{\c{S}. Cobza{\c{s}} on antiproximal sets: ``Antiproximinal sets in some Banach spaces'' [Math. Balkanica {\bf 4} (1974), 79--82; MR {\bf 51} \#13553]}}", journal = j-BULL-CALCUTTA-MATH-SOC, volume = "73", number = "1", pages = "5--8", year = "1981", CODEN = "BCMSA5", ISSN = "0008-0659", ISSN-L = "0008-0659", MRclass = "46B20", MRnumber = "669750", MRreviewer = "M. M. Day", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1648/", acknowledgement = ack-nhfb, fjournal = "Bulletin of the Calcutta Mathematical Society", journal-URL = "http://bulletin.calmathsoc.org/database.php", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1982:CDP, author = "J. M. Borwein", title = "Continuity and differentiability properties of convex operators", journal = j-PROC-LONDON-MATH-SOC-3, volume = "44", number = "3", pages = "420--444", year = "1982", CODEN = "PLMTAL", DOI = "https://doi.org/10.1112/plms/s3-44.3.420", ISSN = "0024-6115 (print), 1460-244x (electronic)", ISSN-L = "0024-6115", MRclass = "58C20 (46G99 47H99 49A51 52A07)", MRnumber = "656244", MRreviewer = "Jean-Paul Penot", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1640/", acknowledgement = ack-nhfb, fjournal = "Proceedings of the London Mathematical Society. Third Series", journal-URL = "http://londmathsoc.onlinelibrary.wiley.com/hub/journal/10.1112/(ISSN)1460-244X/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1982:COCa, author = "J. M. Borwein and H. Wolkowicz", title = "Characterizations of optimality without constraint qualification for the abstract convex program", journal = j-MATH-PROG-STUDY, volume = "19", pages = "77--100", year = "1982", CODEN = "MPSTDF", ISSN = "0303-3929", ISSN-L = "0303-3929", MRclass = "90C25", MRnumber = "669726", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib", note = "Optimality and stability in mathematical programming.", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming Study", journal-URL = "https://link.springer.com/bookseries/8439", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:1982:COCb, author = "J. M. Borwein and H. Wolkowicz", booktitle = "{Optimality and Stability in Mathematical Programming}", title = "Characterizations of optimality without constraint qualification for the abstract convex program", publisher = pub-SV, address = pub-SV:adr, pages = "??--??", year = "1982", DOI = "https://doi.org/10.1007/BFb0120983", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib", URL = "http://link.springer.com/chapter/10.1007/BFb0120983", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1982:HBE, author = "Jonathan M. Borwein", title = "On the {Hahn--Banach} extension property", journal = j-PROC-AM-MATH-SOC, volume = "86", number = "1", pages = "42--46", year = "1982", CODEN = "PAMYAR", DOI = "https://doi.org/10.2307/2044393", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "46A40 (06F20)", MRnumber = "663863", MRreviewer = "M. M. Day", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1982:NES, author = "J. M. Borwein", title = "A note on the existence of subgradients", journal = j-MATH-PROG, volume = "24", number = "2", pages = "225--228", year = "1982", CODEN = "MHPGA4", DOI = "https://doi.org/10.1007/BF01585105", ISSN = "0025-5610 (print), 1436-4646 (electronic)", ISSN-L = "0025-5610", MRclass = "49A50 (90C25)", MRnumber = "674632", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1641/; http://link.springer.com/article/10.1007/BF01585105", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming", journal-URL = "http://link.springer.com/journal/10107", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", xxnumber = "1", } @Article{Borwein:1982:NSC, author = "J. M. Borwein", title = "Necessary and sufficient conditions for quadratic minimality", journal = j-NUMER-FUNCT-ANAL-OPTIM, volume = "5", number = "2", pages = "127--140", year = "1982", CODEN = "NFADOL", DOI = "https://doi.org/10.1080/01630568208816135", ISSN = "0163-0563 (print), 1532-2467 (electronic)", ISSN-L = "0163-0563", MRclass = "90C20", MRnumber = "704109", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1639/", acknowledgement = ack-nhfb, fjournal = "Numerical Functional Analysis and Optimization. An International Journal", journal-URL = "http://www.tandfonline.com/loi/lnfa20", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1982:NSM, author = "J. M. Borwein", title = "A note on {$ \varepsilon $}-subgradients and maximal monotonicity", journal = j-PAC-J-MATH, volume = "103", number = "2", pages = "307--314", year = "1982", CODEN = "PJMAAI", ISSN = "0030-8730 (print), 1945-5844 (electronic)", ISSN-L = "0030-8730", MRclass = "90C25 (49A50 58C20)", MRnumber = "705231", MRreviewer = "J. E. Spingarn", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://projecteuclid.org/euclid.pjm/1102723964", acknowledgement = ack-nhfb, fjournal = "Pacific Journal of Mathematics", journal-URL = "http://msp.org/pjm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1982:SSI, author = "J. M. Borwein and G. P. H. Styan and H. Wolkowicz", title = "Solutions: Some Inequalities Involving Statistical Expressions ({L. V. Foster})", journal = j-SIAM-REVIEW, volume = "24", number = "3", pages = "340--342", month = "????", year = "1982", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1024072", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Sat Mar 29 09:53:30 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/24/3; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "July 1982", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1983:APD, author = "J. M. Borwein", title = "Adjoint process duality", journal = j-MATH-OP-RES, volume = "8", number = "3", pages = "403--434", year = "1983", CODEN = "MOREDQ", DOI = "https://doi.org/10.1287/moor.8.3.403", ISSN = "0364-765x (print), 1526-5471 (electronic)", ISSN-L = "0364-765X", MRclass = "90C25", MRnumber = "716121", MRreviewer = "J. E. Spingarn", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "See letter \cite{Zalinescu:1986:LEJ}.", URL = "http://docserver.carma.newcastle.edu.au/1633/", acknowledgement = ack-nhfb, fjournal = "Mathematics of Operations Research", journal-URL = "http://pubsonline.informs.org/loi/moor", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1983:CCP, author = "J. M. Borwein", title = "Completeness and the contraction principle", journal = j-PROC-AM-MATH-SOC, volume = "87", number = "2", pages = "246--250", year = "1983", CODEN = "PAMYAR", DOI = "https://doi.org/10.2307/2043697", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "54H25 (54E40)", MRnumber = "681829", MRreviewer = "L. Janos", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1637/", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1983:EPE, author = "Jonathan M. Borwein", title = "On the existence of {Pareto} efficient points", journal = j-MATH-OP-RES, volume = "8", number = "1", pages = "64--73", month = feb, year = "1983", CODEN = "MOREDQ", DOI = "https://doi.org/10.1287/moor.8.1.64", ISSN = "0364-765x (print), 1526-5471 (electronic)", ISSN-L = "0364-765X", MRclass = "90C25 (46N05 52A05)", MRnumber = "703826", MRreviewer = "Autorreferat", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1636/; http://www.jstor.org/stable/3689411", acknowledgement = ack-nhfb, fjournal = "Mathematics of Operations Research", journal-URL = "http://pubsonline.informs.org/loi/moor", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1983:FDS, author = "J. M. Borwein and K. O. Kortanek", title = "{Fenchel}-duality and separably-infinite programs", journal = j-OPTIMIZATION, volume = "14", number = "1", pages = "37--48.", year = "1983", CODEN = "OPTZDQ", DOI = "https://doi.org/10.1080/02331938308842831", ISSN = "0323-3898", ISSN-L = "0233-1934", MRclass = "90C25 (90C05)", MRnumber = "694801", MRreviewer = "W. F. Tyndall", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "Mathematische Operationsforschung und Statistik Series Optimization", journal-URL = "http://www.tandfonline.com/loi/gopt20", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1983:HSS, author = "J. M. Borwein", booktitle = "Semi-infinite Programming", title = "How special is semi-infinite programming?", publisher = pub-SV, address = pub-SV:adr, pages = "139--172", year = "1983", bibdate = "Mon Aug 15 15:11:40 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1983:NFL, author = "J. M. Borwein", title = "A note on the {Farkas} lemma", journal = j-UTIL-MATH, volume = "24", pages = "235--241", year = "1983", CODEN = "UTMADA", ISSN = "0315-3681", MRclass = "90C05 (90C30)", MRnumber = "724772", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1631/", acknowledgement = ack-nhfb, fjournal = "Utilitas Mathematica. A Canadian Journal of Applied Mathematics, Computer Science, and Statistics", journal-URL = "http://bkocay.cs.umanitoba.ca/utilitas/index.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1983:NMB, author = "Jonathan Borwein and Brailey Sims", title = "Nonexpansive mappings on {Banach} lattices", journal = j-C-R-ACAD-SCI-CANADA, volume = "5", number = "1", pages = "21--26", year = "1983", ISSN = "0706-1994", MRclass = "46A40 (46B20 47H09)", MRnumber = "690312", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1635/", acknowledgement = ack-nhfb, fjournal = "La Soci{\'e}t{\'e} Royale du Canada. L'Academie des Sciences. Comptes Rendus Math{\'e}matiques. (Mathematical Reports)", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1983:PSA, author = "J. Borwein and Gabor J. Szekely and Andras Zempleni and Michael Barr and Edmund Butler and Allen J. Schwenk and Thomas Q. Sibley", title = "Problems and Solutions: Advanced Problems: 6430-6435", journal = j-AMER-MATH-MONTHLY, volume = "90", number = "6", pages = "402--403", year = "1983", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2975584", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1540218", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1983:SIP, author = "Jonathan M. Borwein", booktitle = "Semi-infinite programming and applications ({Austin}, {Tex}., 1981)", title = "Semi-infinite programming duality: how special is it?", volume = "215", publisher = pub-SV, address = pub-SV:adr, pages = "10--36", year = "1983", MRclass = "49D39 (90C30)", MRnumber = "709266", MRreviewer = "Sven-{\.A}ke Gustafson", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Lecture Notes in Econom. and Math. Systems", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1983:VRC, author = "J. M. Borwein and P. B. Borwein", title = "A very rapidly convergent product expansion for $ \pi $", journal = j-BIT, volume = "23", number = "4", pages = "538--540", month = dec, year = "1983", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/BF01933626", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", MRclass = "65B99", MRnumber = "721199, 85h:65011", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=23&issue=4; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/bit.bib", URL = "http://docserver.carma.newcastle.edu.au/1634/; http://link.springer.com/article/10.1007/BF01933626; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=23&issue=4&spage=538", acknowledgement = ack-nhfb, fjournal = "BIT (Nordisk tidskrift for informationsbehandling)", journal-URL = "http://link.springer.com/journal/10543", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1984:AGM, author = "J. M. Borwein and P. B. Borwein", title = "The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions", journal = j-SIAM-REVIEW, volume = "26", number = "3", pages = "351--366", month = jul, year = "1984", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1026073", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "65D20 (26A09)", MRnumber = "750454; 86d:65029", MRreviewer = "S. Conde", bibdate = "Tue Mar 14 07:52:56 2017", bibsource = "Compendex database; ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; http://epubs.siam.org/toc/siread/26/3; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; http://www.math.utah.edu/pub/tex/bib/agm.bib; http://www.math.utah.edu/pub/tex/bib/elefunt.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "http://www.jstor.org/stable/2031275", abstract = "We produce a self contained account of the relationship between the Gaussian arithmetic--geometric mean iteration and the fast computation of elementary functions. A particularly pleasant algorithm for pi is one of the by-products.", acknowledgement = ack-nhfb # " and " # ack-nj, affiliationaddress = "Dalhousie Univ, Halifax, NS, Can", classification = "723; 921", fjournal = "SIAM Review. A Publication of the Society for Industrial and Applied Mathematics", journal-URL = "http://epubs.siam.org/sirev", journalabr = "SIAM Rev", keywords = "AGM (Arithmetic--Geometric Mean); arithmetic--geometric mean; calculation of pi; computational methods; elliptic functions; Iterative Methods; mathematical techniques; numerical mathematics", onlinedate = "July 1984", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1984:ANV, author = "J. M. Borwein and D. T. Yost", title = "Absolute norms on vector lattices", journal = j-PROC-EDINBURGH-MATH-SOC-2, volume = "27", number = "2", pages = "215--222", month = jun, year = "1984", CODEN = "PEMSA3", DOI = "https://doi.org/10.1017/S0013091500022318", ISSN = "0013-0915 (print), 1464-3839 (electronic)", ISSN-L = "0013-0915", MRclass = "46A40 (46B30 90C48)", MRnumber = "760617", MRreviewer = "I. Namioka", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1624/; http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=3076132", acknowledgement = ack-nhfb, fjournal = "Proceedings of the Edinburgh Mathematical Society. Series II", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PEM", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1984:CCO, author = "J. M. Borwein and J.-P. Penot and M. Th{\'e}ra", title = "Conjugate convex operators", journal = j-J-MATH-ANAL-APPL, volume = "102", number = "2", pages = "399--414", year = "1984", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(84)90180-X", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "90C48 (46G99 49A50)", MRnumber = "755971", MRreviewer = "Christian Malivert", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1620/; http://www.sciencedirect.com/science/article/pii/0022247X8490180X", abstract = "Convex mappings from a locally convex space X into F. = F \cup {+\infty } are considered, where F is an ordered topological vector space and + \infty an arbitrary greatest element adjoined to F. In view of applications to the polarity theory of convex operators, the possibility is investigated of representing a convex mapping taking values in F. as a supremum of continuous affine mappings.", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1984:CHO, author = "J. M. Borwein and P. B. Borwein", title = "Cubic and higher order algorithms for $ \pi $", journal = j-CAN-MATH-BULL, volume = "27", number = "4", pages = "436--443", month = dec, year = "1984", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1984-067-7", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", MRclass = "11Y16 (33A25 65D20)", MRnumber = "763041", MRreviewer = "L. C. Eggan", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://cms.math.ca/cmb/v27/; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/canmathbull.bib; http://www.math.utah.edu/pub/tex/bib/pi.bib", URL = "http://docserver.carma.newcastle.edu.au/1622/", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1984:DLM, author = "J. M. Borwein and H. M. Str{\'o}jwas", title = "Directionally {Lipschitzian} mappings on {Baire} spaces", journal = j-CAN-J-MATH, volume = "36", number = "1", pages = "95--130", year = "1984", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1984-008-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "49A52 (26A27 58C20 90C30 90C48)", MRnumber = "733710", MRreviewer = "Jean-Paul Penot", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1627/", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics. Journal Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:1984:EAO, author = "J. M. Borwein and P. B. Borwein", title = "Explicit algebraic $n$ th order approximations to pi", crossref = "Singh:1984:ATS", volume = "136", pages = "247--256", year = "1984", DOI = "https://doi.org/10.1007/978-94-009-6466-2_12", MRclass = "65D20", MRnumber = "786845", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/pi.bib", URL = "http://link.springer.com/chapter/10.1007/978-94-009-6466-2_12", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:1984:EEH, author = "J. M. Borwein", editor = "????", booktitle = "APICS Proceedings", title = "On the existence of eigenvalues for {Hermitian} matrices", publisher = "????", address = "????", pages = "1--5", year = "1984", DOI = "", ISBN = "", ISBN-13 = "", LCCN = "", bibdate = "Mon Aug 15 15:10:50 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Unpublished{Borwein:1984:EIA, author = "J. M. Borwein and P. B. Borwein", title = "Elliptic integrals and approximations to $ \pi $", month = jan, year = "1984", bibdate = "Mon Nov 07 17:37:11 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Typescript, with 84-01 added by hand on cover page.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1984:GLC, author = "J. M. Borwein", title = "Generalized linear complementarity problems treated without fixed-point theory", journal = j-J-OPT-THEORY-APPL, volume = "43", number = "3", pages = "343--356", year = "1984", CODEN = "JOTABN", DOI = "https://doi.org/10.1007/BF00934459", ISSN = "0022-3239 (print), 1573-2878 (electronic)", ISSN-L = "0022-3239", MRclass = "90C33 (90C25)", MRnumber = "750013", MRreviewer = "Ikuyo Kaneko", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://link.springer.com/article/10.1007/BF00934459", acknowledgement = ack-nhfb, fjournal = "Journal of Optimization Theory and Applications", journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1984:HMM, author = "J. M. Borwein and B. Richmond", title = "How many matrices have roots?", journal = j-CAN-J-MATH, volume = "36", number = "2", pages = "286--299", year = "1984", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1984-018-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "15A23", MRnumber = "749985", MRreviewer = "J. L. Brenner", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1628/", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics. Journal Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1984:ICE, author = "J. M. Borwein", title = "An integral characterization of {Euclidean} space", journal = j-BULL-AUSTRAL-MATH-SOC, volume = "29", number = "3", pages = "357--364", year = "1984", CODEN = "ALNBAB", DOI = "https://doi.org/10.1017/S0004972700021602", ISSN = "0004-9727 (print), 1755-1633 (electronic)", ISSN-L = "0004-9727", MRclass = "46C10", MRnumber = "748728", MRreviewer = "M. M. Day", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1623/", acknowledgement = ack-nhfb, fjournal = "Bulletin of the Australian Mathematical Society", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1984:NMB, author = "Jon M. Borwein and Brailey Sims", title = "Nonexpansive mappings on {Banach} lattices and related topics", journal = j-HOUSTON-J-MATH, volume = "10", number = "3", pages = "339--356", year = "1984", CODEN = "HJMADZ", ISSN = "0362-1588", MRclass = "47H10 (46A40 46B20)", MRnumber = "763236", MRreviewer = "Gregory B. Passty", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "https://www.math.uh.edu/~hjm/restricted/archive/v010n3/0339BORWEIN.pdf", acknowledgement = ack-nhfb, fjournal = "Houston Journal of Mathematics", journal-URL = "https://www.math.uh.edu/~hjm/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1984:RCC, author = "J. M. Borwein and P. B. Borwein", title = "Reduced Complexity Calculation of Log", number = "DALTR 84-01", institution = "Department of Mathematics, Dalhousie University", address = "Halifax, NS, Canada", pages = "17", month = jan, year = "1984", bibdate = "Mon Nov 07 17:37:11 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "Various reduced complexity methods for high precision computation of the logarithm are investigated.", acknowledgement = ack-nhfb, keywords = "analytic complexity; arithmetic--geometric mean; binary splitting; bit complexity; elliptic integrals; Fast Fourier Transform; logarithms; operational complexity; theta functions", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Typescript, with 84-01 added by hand on cover page.", } @Article{Borwein:1984:SCO, author = "J. M. Borwein", title = "Subgradients of convex operators", journal = j-OPTIMIZATION, volume = "15", number = "2", pages = "179--191", year = "1984", CODEN = "OPTZDQ", DOI = "https://doi.org/10.1080/02331938408842921", ISSN = "0323-3898", ISSN-L = "0233-1934", MRclass = "90C25 (65K05)", MRnumber = "741284", MRreviewer = "C. A. Botsaris", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "Mathematische Operationsforschung und Statistik Series Optimization", journal-URL = "http://www.tandfonline.com/loi/gopt20", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1984:SCS, author = "J. M. Borwein and D. W. Tingley", title = "On Supportless Convex Sets", type = "Report", number = "DALTR 84-04", institution = "Department of Mathematics, Dalhousie University", address = "Halifax, NS, Canada", pages = "13", year = "1984", bibdate = "Tue Nov 08 15:45:14 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "We give some general constructions of supportless convex subsets of normed spaces and pose a number of open questions.", acknowledgement = ack-nhfb, keywords = "Bishop-Phelps Theorem; convex sets; support points", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1984:SRP, author = "J. M. Borwein", title = "Stability and Regular Points of Inequality Systems", type = "Report", number = "DALTR 84-02", institution = "Department of Mathematics, Dalhousie University and Carnegie-Mellon University", address = "Halifax, NS, Canada and Pittsburgh, PA, USA", pages = "67", year = "1984", bibdate = "Tue Nov 08 15:45:14 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "We undertake a general study of regular points of Lipschitz and strictly differentiable mappings with applications to tangent cone analysis, inversion theorems, perturbed optimization problems and higher order conditions.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1984:TCS, author = "J. M. Borwein and P. B. Borwein", title = "A tangent cone separation principle", type = "Report", number = "DALTR 84-03", institution = "Department of Mathematics, Dalhousie University", address = "Halifax, NS, Canada", month = jan, year = "1984", bibdate = "Mon Nov 07 17:37:11 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Typescript, with DALTR added by hand on cover page before typewritten 84-03.", } @Article{Borwein:1984:TKN, author = "J. M. Borwein and J. W. Nieuwenhuis", title = "Two kinds of normality in vector optimization", journal = j-MATH-PROG, volume = "28", number = "2", pages = "185--191", year = "1984", CODEN = "MHPGA4", DOI = "https://doi.org/10.1007/BF02612358", ISSN = "0025-5610 (print), 1436-4646 (electronic)", ISSN-L = "0025-5610", MRclass = "90C31", MRnumber = "733210", MRreviewer = "M. Ma{\v{n}}as", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1626/; http://link.springer.com/article/10.1007/BF02612358", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming", journal-URL = "http://link.springer.com/journal/10107", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1985:ATG, author = "Jonathan M. Borwein", booktitle = "Infinite programming ({Cambridge}, 1984)", title = "Alternative theorems for general complementarity problems", volume = "259", publisher = pub-SV, address = pub-SV:adr, pages = "194--203", year = "1985", DOI = "https://doi.org/10.1007/978-3-642-46564-2_15", MRclass = "90C33 (52A40)", MRnumber = "824573", MRreviewer = "J. Parida", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Lecture Notes in Econom. and Math. Systems", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1985:CLS, author = "David Borwein and Jonathan M. Borwein and Keith F. Taylor", title = "Convergence of lattice sums and {Madelung}'s constant", journal = j-J-MATH-PHYS, volume = "26", number = "11", pages = "2999--3009", month = nov, year = "1985", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.526675", ISSN = "0022-2488", ISSN-L = "0022-2488", MRclass = "82A67 (82A60)", MRnumber = "808518", MRreviewer = "Pierre Moussa", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/1985JMP....26.2999B; http://docserver.carma.newcastle.edu.au/1618/", abstract = "The lattice sums involved in the definition of Madelung's constant of an NaCl-type crystal lattice in two or three dimensions are investigated. The fundamental mathematical questions of convergence and uniqueness of the sum of these, not absolutely convergent, series are considered. It is shown that some of the simplest direct sum methods converge and some do not converge. In particular, the very common method of expressing Madelung's constant by a series obtained from expanding spheres does not converge. The concept of analytic continuation of a complex function to provide a basis for an unambiguous mathematical definition of Madelung's constant is introduced. By these means, the simple intuitive direct sum methods and the powerful integral transformation methods, which are based on theta function identities and the Mellin transform, are brought together. A brief analysis of a hexagonal lattice is also given.", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1985:PSA, author = "Jon Borwein and Anatole Beck", title = "Problems and Solutions: Advanced Problems: 6491--6492", journal = j-AMER-MATH-MONTHLY, volume = "92", number = "3", pages = "217--217", month = mar, year = "1985", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2322884", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1540608", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.jstor.org/journals/00029890.htm; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib", note = "See also \cite{Beck:1987:PSS,Borwein:1986:PSS}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1985:PSS, author = "J. Borwein", title = "Problems and Solutions: Solutions of Advanced Problems: 6430", journal = j-AMER-MATH-MONTHLY, volume = "92", number = "2", pages = "148--149", month = feb, year = "1985", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2322656", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1540590", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.jstor.org/journals/00029890.htm; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib", note = "See also \cite{Borwein:1983:PSA}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1985:SCS, author = "J. M. Borwein and D. W. Tingley", title = "On supportless convex sets", journal = j-PROC-AM-MATH-SOC, volume = "94", number = "3", pages = "471--476", year = "1985", CODEN = "PAMYAR", DOI = "https://doi.org/10.2307/2045238", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "46B20 (46A55 52A07)", MRnumber = "787897", MRreviewer = "N. T. Peck", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1619/", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1985:SMI, author = "Jon Borwein", title = "Some modular identities of {Ramanujan} useful in approximating $ \pi $", journal = j-PROC-AM-MATH-SOC, volume = "95", number = "3", pages = "365--371", month = nov, year = "1985", CODEN = "PAMYAR", DOI = "https://doi.org/10.2307/2045804", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "11F03 (11J72 41A25)", MRnumber = "806072", MRreviewer = "Bruce C. Berndt", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1616/; http://www.jstor.org/stable/2045804", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1985:TA, author = "J. M. Borwein and H. M. Str{\'o}jwas", title = "Tangential approximations", journal = j-NONLINEAR-ANAL, volume = "9", number = "12", pages = "1347--1366", year = "1985", CODEN = "NOANDD", DOI = "https://doi.org/10.1016/0362-546X(85)90095-1", ISSN = "0362-546x (print), 1873-5215 (electronic)", ISSN-L = "0362-546X", MRclass = "90C48 (46A55 90C25)", MRnumber = "820646", MRreviewer = "Christian Malivert", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1617/; http://www.sciencedirect.com/science/article/pii/0362546X85900951", acknowledgement = ack-nhfb, fjournal = "Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods", journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis", keywords = "epi-Lipschitzian (compactly epi-Lipschitzian; Tangent cones; tangentially regular) set at a point; unsupportable space", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Honor:1985:DTR, author = "R. B. Honor", title = "Density and transitivity results on $ l^\infty $ and $ l^1 $", journal = j-J-LOND-MATH-SOC-2, volume = "S2-32", number = "3", pages = "521--527", month = dec, year = "1985", CODEN = "JLMSAK", DOI = "https://doi.org/10.1112/jlms/s2-32.3.521", ISSN = "0024-6107 (print), 1469-7750 (electronic)", ISSN-L = "0024-6107", bibdate = "Fri Aug 12 15:21:25 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "The `author' is an acronym for the family names of seven people: Heydar Radjavi, Jon Borwein, Don Hadwin, Richard O'Brien, Eric Nordgren, Mehmet Orhon, and Peter Rose.", URL = "http://jlms.oxfordjournals.org/content/s2-32/3/521.full.pdf+html", acknowledgement = ack-nhfb, ajournal = "J. Lond. Math. Soc. (2)", fjournal = "Journal of the London Mathematical Society (series 2)", journal-URL = "http://jlms.oxfordjournals.org/content/by/year", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Adler:1986:PSS, author = "Irving Adler and A. A. Jagers and J. M. Borwein", title = "Problems and Solutions: Solutions of Elementary Problems: {E2997}", journal = j-AMER-MATH-MONTHLY, volume = "93", number = "4", pages = "304--304", month = apr, year = "1986", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2323694", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1540849", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.jstor.org/journals/00029890.htm; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib", note = "See also \cite{Asic:1983:PSE}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1986:ECI, author = "J. M. Borwein and P. B. Borwein", title = "An explicit cubic iteration for $ \pi $", journal = j-BIT, volume = "26", number = "1", pages = "123--126", month = mar, year = "1986", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/BF01939368", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", MRclass = "11Y60 (65D20)", MRnumber = "833837, 87e:11144", MRreviewer = "Duncan A. Buell", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=1; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/bit.bib", URL = "http://docserver.carma.newcastle.edu.au/1609/; http://link.springer.com/article/10.1007/BF01939368; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=1&spage=123", acknowledgement = ack-nhfb, fjournal = "BIT (Nordisk tidskrift for informationsbehandling)", journal-URL = "http://link.springer.com/journal/10543", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1986:FMT, author = "J. M. Borwein and D. Zhuang", title = "On {Fan}'s minimax theorem", journal = j-MATH-PROG, volume = "34", number = "2", pages = "232--234", year = "1986", CODEN = "MHPGA4", DOI = "https://doi.org/10.1007/BF01580587", ISSN = "0025-5610 (print), 1436-4646 (electronic)", ISSN-L = "0025-5610", MRclass = "90C30 (90C48)", MRnumber = "838482", MRreviewer = "Marco Gaviano", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1608/; http://link.springer.com/article/10.1007/BF01580587", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming", journal-URL = "http://link.springer.com/journal/10107", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1986:GDO, author = "Jonathan M. Borwein", title = "Generic differentiability of order-bounded convex operators", journal = j-J-AUSTRAL-MATH-SOC-SER-B, volume = "28", number = "1", pages = "22--29", month = jul, year = "1986", CODEN = "JAMMDU", DOI = "https://doi.org/10.1017/S0334270000005166", ISSN = "0334-2700", MRclass = "90C25 (46G05 90C48)", MRnumber = "846780", MRreviewer = "Christian Malivert", bibdate = "Fri Sep 30 10:52:51 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1607/; http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=3973752", acknowledgement = ack-nhfb, fjournal = "Australian Mathematical Society. Journal. Series B. Applied Mathematics", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1986:LOC, author = "J. M. Borwein and M. A. H. Dempster", title = "The Linear Order Complementarity Problem", type = "Report", number = "DALTR 86-3", institution = "Department of Mathematics, Statistics \& Computing Science, Dalhousie University and Balliol College, Oxford University", address = "Halifax, NS, Canada and Oxford, England OX1 3BJ", pages = "47", month = jul, year = "1986", bibdate = "Tue Nov 08 15:45:14 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "The classical complementarity problem in Euclidean space can be viewed alternatively as a variational inequality or as a lattice orthogonality problem. Generalizations of the former have been extensively studied, but infinite dimensional analogues of the latter have been largely ignored. Moreover, as we show, many well known results about the classical complementarity problem are more appropriately viewed order-theoretically. This is particularly true of least element solutions, which are central to the present study of order complementarity in vector lattices.", acknowledgement = ack-nhfb, keywords = "(P) operators; (Z) operators; Banach lattices; complementarity problems; Least elements; order complementarity", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Revision of August 1985 original.", } @Article{Borwein:1986:MQC, author = "J. M. Borwein and P. B. Borwein", title = "More quadratically converging algorithms for $ \pi $", journal = j-MATH-COMPUT, volume = "46", number = "173", pages = "247--253", month = jan, year = "1986", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2008229", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65D20", MRnumber = "815846, 87e:65014", MRreviewer = "M. M. Chawla", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib; JSTOR database", URL = "http://docserver.carma.newcastle.edu.au/1614/", acknowledgement = ack-nhfb, classcodes = "B0290F (Interpolation and function approximation); B0290Z (Other numerical methods); C4130 (Interpolation and function approximation); C4190 (Other numerical methods)", corpsource = "Dalhousie Univ., Halifax, NS, Canada", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "arithmetic--geometric mean iteration; complete elliptic; convergence of numerical methods; Gauss--Legendre iteration; geometry; integrals; iterative; Legendre formula; methods; pi evaluation; quadratically converging algorithms", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", treatment = "T Theoretical or Mathematical", } @Article{Borwein:1986:NAS, author = "David Borwein and Jonathan M. Borwein", title = "A Note on Alternating Series in Several Dimensions", journal = j-AMER-MATH-MONTHLY, volume = "93", number = "7", pages = "531--539", month = aug # "\slash " # sep, year = "1986", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2323026", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "40B05 (40A05)", MRnumber = "856292, 87j:40008", MRreviewer = "F. M{\'o}ricz", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.jstor.org/journals/00029890.htm; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib", URL = "http://docserver.carma.newcastle.edu.au/1610/", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1986:NDC, author = "J. M. Borwein", title = "Norm duality for convex processes and applications", journal = j-J-OPT-THEORY-APPL, volume = "48", number = "1", pages = "53--64", year = "1986", CODEN = "JOTABN", DOI = "https://doi.org/10.1007/BF00938589", ISSN = "0022-3239 (print), 1573-2878 (electronic)", ISSN-L = "0022-3239", MRclass = "90C25 (46N05)", MRnumber = "825384", MRreviewer = "Lionel Thibault", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Fourth symposium on nonlinear programming with data perturbations.", URL = "http://docserver.carma.newcastle.edu.au/1613/; http://link.springer.com/article/10.1007/BF00938589", acknowledgement = ack-nhfb, fjournal = "Journal of Optimization Theory and Applications", journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1986:PAB, author = "J. M. Borwein and H. M. Str{\'o}jwas", title = "Proximal analysis and boundaries of closed sets in {Banach} space. {I}. {Theory}", journal = j-CAN-J-MATH, volume = "38", number = "2", pages = "431--452", year = "1986", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1986-022-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "90C48 (46B10 49A50 58C20)", MRnumber = "833578", MRreviewer = "Bruce D. Craven", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1611/", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics. Journal Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1986:PMO, author = "J. M. Borwein", title = "Partially monotone operators and the generic differentiability of convex-concave and biconvex mappings", journal = j-ISRAEL-J-MATH, volume = "54", number = "1", pages = "42--50", year = "1986", CODEN = "ISJMAP", DOI = "https://doi.org/10.1007/BF02764875", ISSN = "0021-2172 (print), 1565-8511 (electronic)", ISSN-L = "0021-2172", MRclass = "90C48 (47H05 49A51 58C20)", MRnumber = "852468", MRreviewer = "Jean-Paul Penot", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1605/; http://link.springer.com/article/10.1007/BF02764875", acknowledgement = ack-nhfb, fjournal = "Israel Journal of Mathematics", journal-URL = "http://link.springer.com/journal/11856", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1986:PSS, author = "Jon Borwein and William A. Newcomb", title = "Problems and Solutions: Solutions of Advanced Problems: 6491", journal = j-AMER-MATH-MONTHLY, volume = "93", number = "10", pages = "822--823", year = "1986", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2322952", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1541009", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1986:SCQ, author = "J. M. Borwein and H. Wolkowicz", title = "A simple constraint qualification in infinite-dimensional programming", journal = j-MATH-PROG, volume = "35", number = "1", pages = "83--96", year = "1986", CODEN = "MHPGA4", DOI = "https://doi.org/10.1007/BF01589443", ISSN = "0025-5610 (print), 1436-4646 (electronic)", ISSN-L = "0025-5610", MRclass = "90C48", MRnumber = "842636", MRreviewer = "W. W. Breckner", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib", URL = "http://docserver.carma.newcastle.edu.au/1606/; http://link.springer.com/article/10.1007/BF01589443", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming", journal-URL = "http://link.springer.com/journal/10107", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1986:SRP, author = "J. M. Borwein", title = "Stability and regular points of inequality systems", journal = j-J-OPT-THEORY-APPL, volume = "48", number = "1", pages = "9--52", year = "1986", CODEN = "JOTABN", DOI = "https://doi.org/10.1007/BF00938588", ISSN = "0022-3239 (print), 1573-2878 (electronic)", ISSN-L = "0022-3239", MRclass = "58C20 (46N05 90C30 90C48)", MRnumber = "825383", MRreviewer = "Lionel Thibault", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Fourth symposium on nonlinear programming with data perturbations.", URL = "http://docserver.carma.newcastle.edu.au/1612/; http://link.springer.com/article/10.1007/BF00938588", acknowledgement = ack-nhfb, fjournal = "Journal of Optimization Theory and Applications", journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1987:ACO, author = "J. M. Borwein", title = "Automatic continuity and openness of convex relations", journal = j-PROC-AM-MATH-SOC, volume = "99", number = "1", pages = "49--55", month = jan, year = "1987", CODEN = "PAMYAR", DOI = "https://doi.org/10.2307/2046269", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "46A55 (47H99)", MRnumber = "866428", MRreviewer = "Robert T. Vescan", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1604/; http://www.jstor.org/stable/2046269", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:1987:CCM, author = "J. M. Borwein", booktitle = "{Recent Advances and Historical Development of Vector Optimization}", title = "Convex Cones, Minimality Notions, and Consequences", publisher = pub-SV, address = pub-SV:adr, pages = "??--??", year = "1987", DOI = "https://doi.org/10.1007/978-3-642-46618-2_3", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://link.springer.com/chapter/10.1007/978-3-642-46618-2_3", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1987:CMN, author = "J. M. Borwein", booktitle = "Recent Advances and Historic Development of Vector Optimization", title = "Cones, minimality notions and consequences", publisher = pub-SV, address = pub-SV:adr, pages = "62--85", year = "1987", bibdate = "Mon Aug 15 15:09:27 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1987:DRF, author = "J. M. Borwein and S. P. Fitzpatrick and J. R. Giles", title = "The differentiability of real functions on normed linear space using generalized subgradients", journal = j-J-MATH-ANAL-APPL, volume = "128", number = "2", pages = "512--534", year = "1987", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(87)90203-4", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "58C20 (26E15 46G05 49A52 90C48)", MRnumber = "917385", MRreviewer = "W. W. Breckner", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1598/; http://www.sciencedirect.com/science/article/pii/0022247X87902034", abstract = "The modification of the Clarke generalized subdifferential due to Michel and Penot is a useful tool in determining differentiability properties for certain classes of real functions on a normed linear space. The G{\^a}teaux differentiability of any real function can be deduced from the G{\^a}teaux differentiability of the norm if the function has a directional derivative which attains a constant related to its generalized directional derivative. For any distance function on a space with uniformly G{\^a}teaux differentiable norm, the Clarke and Michel-Penot generalized subdifferentials at points off the set reduce to the same object and this generates a continuity characterization for G{\^a}teaux differentiability. However, on a Banach space with rotund dual, the Fr{\'e}chet differentiability of a distance function implies that it is a convex function. A mean value theorem for the modified generalized subdifferential has implications for G{\^a}teaux differentiability.", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1987:EIE, author = "J. M. Borwein and I. J. Zucker", title = "Elliptic Integral Evaluation of the Gamma Function at Values with Small Rational Denominators", type = "Report", institution = "Department of Mathematics, Statistics and Computing Science, Dalhousie University and Department of Physics, King's College", address = "Halifax, NS B3H 3J5, Canada and London WC2, UK", pages = "13", day = "2", month = sep, year = "1987", bibdate = "Fri Nov 11 06:50:29 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "We produce simplified evaluations of certain complete elliptic integrals in terms of Gamma and Beta functions. We also provide explicit quadratically convergent recursions for quantities including $ \Gamma (n / 4) $ and $ \Gamma (n / 6) $.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1987:ELL, author = "Jonathan Michael Borwein", title = "Epi-{Lipschitz}-like sets in {Banach} space: theorems and examples", journal = j-NONLINEAR-ANAL, volume = "11", number = "10", pages = "1207--1217", year = "1987", CODEN = "NOANDD", DOI = "https://doi.org/10.1016/0362-546X(87)90008-3", ISSN = "0362-546x (print), 1873-5215 (electronic)", ISSN-L = "0362-546X", MRclass = "90C48 (46G99 58C20 90C25)", MRnumber = "913679", MRreviewer = "J. E. Spingarn", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1599/; http://www.sciencedirect.com/science/article/pii/0362546X87900083", acknowledgement = ack-nhfb, fjournal = "Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods", journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis", keywords = "differential inclusions; epi-Lipschitz-like sets; Lipschitz-like functions; locally compact subgradients; non-support points; Nonsmooth analysis; normal cones", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1987:ERT, author = "J. M. Borwein and P. B. Borwein", title = "Explicit {Ramanujan}-type approximations to pi of high order", journal = "Proceedings of the Indian Academy of Sciences --- Mathematical Sciences", volume = "97", number = "1--3", pages = "53--59", year = "1987", DOI = "https://doi.org/10.1007/BF02837813", ISSN = "0253-4142 (print), 0973-7685 (electronic)", ISSN-L = "0253-4142", MRclass = "11Y60", MRnumber = "983604", MRreviewer = "D. H. Lehmer", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Centennial issue.", URL = "http://link.springer.com/article/10.1007/BF02837813", acknowledgement = ack-nhfb, ajournal = "Proc. Indian Acad. Sci. Math. Sci.", fjournal = "Indian Academy of Sciences. Proceedings. Mathematical Sciences", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", xxyear = "1988", } @TechReport{Borwein:1987:ESE, author = "D. Borwein and J. M. Borwein and R. Shail and I. J. Zucker", title = "Energy of Static Electron Lattices", type = "Report", institution = "University of Western Ontario and Department of Mathematics, Statistics and Computing Science, Dalhousie University and University of Surrey and University of Surrey", address = "London, ON N6A 3K7, Canada and Halifax, NS B3H 3J5, Canada and Guildford, UK GU2 5XH and Guildford, UK GU2 5XH", pages = "20", day = "11", month = sep, year = "1987", bibdate = "Fri Nov 11 06:54:37 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "A new approach to evaluating the static lattice energy of any given Wigner lattice is proposed. The method is much simpler than the traditional one and the results are much faster to evaluate. The new approach is applied to two-dimensional triangular lattices where it is shown that the triangular lattice is more stable than the square lattice. Three dimensional hexagonal lattices are also investigated. In addition, we have placed many of our considerations on a rigorous mathematical footing.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Date recorded in ambiguous form 11/9/87; entry Borwein:1988:CCJ has 31/12/88, suggesting that the first number is the day.", } @Article{Borwein:1987:PAB, author = "J. M. Borwein and H. M. Str{\'o}jwas", title = "Proximal analysis and boundaries of closed sets in {Banach} space. {II}. {Applications}", journal = j-CAN-J-MATH, volume = "39", number = "2", pages = "428--472", year = "1987", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1987-019-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "46B20 (41A65 90C48)", MRnumber = "899844", MRreviewer = "Bruce D. Craven", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1600/", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics. Journal Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Book{Borwein:1987:PAS, author = "Jonathan M. Borwein and Peter B. Borwein", title = "Pi and the {AGM}: a Study in Analytic Number Theory and Computational Complexity", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xv + 414", year = "1987", ISBN = "0-471-83138-7, 0-471-31515-X (paperback)", ISBN-13 = "978-0-471-83138-9, 978-0-471-31515-5 (paperback)", LCCN = "QA241 .B774 1987", MRclass = "11Y60 (68Q30)", MRnumber = "877728", MRreviewer = "H. London", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; z3950.loc.gov:7090/Voyager", series = "Canadian Mathematical Society series of monographs and advanced texts = Monographies et {\'e}tudes de la Soci{\'e}t{\'e} math{\'e}matique du Canada", abstract = "Critical Acclaim for Pi and the AGM: ``Fortunately we have the Borwein's beautiful book \ldots{} explores in the first five chapters the glorious world so dear to Ramanujan \ldots{} would be a marvelous text book for a graduate course.'' --- Bulletin of the American Mathematical Society \\ ``What am I to say about this quilt of a book? One is reminded of Debussy who, on being asked by his harmony teacher to explain what rules he was following as he improvised at the piano, replied, ``Mon plaisir.'' The authors are cultured mathematicians. They have selected what has amused and intrigued them in the hope that it will do the same for us. Frankly, I cannot think of a more provocative and generous recipe for writing a book \ldots{} (it) is cleanly, even beautifully written, and attractively printed and composed. The book is unique. I cannot think of any other book in print which contains more than a smidgen of the material these authors have included. --- SIAM Review \\ ``If this subject begins to sound more interesting than it did in the last newspaper article on 130 million digits of Pi, I have partly succeeded. To succeed completely I will have gotten you interested enough to read the delightful and important book by the Borweins.'' --- American Mathematical Monthly \\ ``The authors are to be commended for their careful presentation of much of the content of Ramanujan's famous paper, 'Modular Equations and Approximations to Pi'. This material has not heretofore appeared in book form. However, more importantly, Ramanujan provided no proofs for many of the claims that he made, and so the authors provided many of the missing details \ldots{} The Borweins, indeed have helped us find the right roads.'' --- Mathematics of Computation", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Chinese edition 1995.", subject = "Number theory; Computational complexity; Elliptic functions; Pi", tableofcontents = "Complete Elliptic Integrals and the Arithmetic-Geometric Mean Iteration \\ Theta Functions and the Arithmetic-Geometric Mean Iteration \\ Jacobi's Triple-Product and Some Number Theoretic Applications \\ Higher Order Transformations \\ Modular Equations and Algebraic Approximations to $\pi$ \\ The Complexity of Algebraic Functions \\ Algorithms for the Elementary Functions \\ General Means and Iterations \\ Some Additional Applications \\ Other Approaches to the Elementary Functions \\ Pi \\ Bibliography \\ Symbol List \\ Index", } @Article{Borwein:1987:PNF, author = "J. M. Borwein and J. R. Giles", title = "The proximal normal formula in {Banach} space", journal = j-TRANS-AM-MATH-SOC, volume = "302", number = "1", pages = "371--381", year = "1987", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/2000915", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "49A52 (46B20 46G05)", MRnumber = "887515", MRreviewer = "Gianfranco Bottaro", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1602/", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1987:RRA, author = "J. M. Borwein and P. B. Borwein", title = "{Ramanujan}'s rational and algebraic series for {$ 1 / \pi $}", journal = "J. Indian Math. Soc. (N.S.)", volume = "51", pages = "147--160 (1988)", year = "1987", CODEN = "JIMTA2", ISSN = "0019-5839", ISSN-L = "0019-5839", MRclass = "11Y60 (33A30)", MRnumber = "988313", MRreviewer = "Herman J. J. te Riele", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Ramanujan Centennial issue.", acknowledgement = ack-nhfb, fjournal = "The Journal of the Indian Mathematical Society. New Series", journal-URL = "http://www.indianmathsociety.org.in/jims.htm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1987:SVPa, author = "Jonathan M. Borwein and David Preiss", title = "A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions", journal = j-TRANS-AM-MATH-SOC, volume = "303", number = "2", pages = "517--527", month = oct, year = "1987", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/2000681", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "49A27 (46B20 46G05 49A51 49A52 58C20 90C25 90C48)", MRnumber = "902782", MRreviewer = "B. Mordukhovich", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1597/; http://www.jstor.org/stable/2000681", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "According to \cite{Thera:2016:HSH}, this paper is the first published {\em smooth variational principle}.", } @Article{Borwein:1987:UPW, author = "J. M. Borwein and P. B. Borwein", title = "Unsolved Problems: The Way of All Means", journal = j-AMER-MATH-MONTHLY, volume = "94", number = "6", pages = "519--522", month = jun # "\slash " # jul, year = "1987", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2322842", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1541118", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.jstor.org/journals/00029890.htm; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib", URL = "http://www.jstor.org/stable/2322842", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Schoenberg:1987:APS, author = "I. J. Schoenberg and Peter B. Borwein", title = "Advanced Problems and Solutions: Solutions: 6501", journal = j-AMER-MATH-MONTHLY, volume = "94", number = "4", pages = "390--390", month = apr, year = "1987", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2323115", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.jstor.org/journals/00029890.htm; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib", note = "See also \cite{Schoenberg:1985:PSA}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Ward:1987:NCF, author = "D. E. Ward and J. M. Borwein", title = "Nonsmooth Calculus in Finite Dimensions", journal = j-SIAM-J-CONTROL-OPTIM, volume = "25", number = "5", pages = "1312--1340", month = sep, year = "1987", CODEN = "SJCODC", DOI = "https://doi.org/10.1137/0325072", ISSN = "0363-0129 (print), 1095-7138 (electronic)", ISSN-L = "0363-0129", MRclass = "58C20 (46G05 49A52 90C48)", MRnumber = "905047, 88m:58011", MRreviewer = "A. B. N{\'e}meth", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICON/25/5; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/siamjcontroloptim.bib", URL = "http://docserver.carma.newcastle.edu.au/1601/", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Control and Optimization", journal-URL = "http://epubs.siam.org/sicon", journalabr = "SIAM J Control Optim", onlinedate = "September 1987", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Barzilai:1988:TPS, author = "Jonathan Barzilai and Jonathan M. Borwein", title = "Two-Point Step Size Gradient Methods", journal = j-IMA-J-NUMER-ANAL, volume = "8", number = "1", pages = "141--148", year = "1988", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/8.1.141", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65K05", MRnumber = "967848, 90h:65113", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; http://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib; MathSciNet database", acknowledgement = ack-nhfb, fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "According to \cite{Thera:2016:HSH}, Google Scholar says that this paper has been cited more than 1300 times [checked: 1378 times as of 02 January 2017].", } @Article{Ben-Tal:1988:DAM, author = "A. Ben-Tal and J. M. Borwein and M. Teboulle", title = "A dual approach to multidimensional {$ L_p $} spectral estimation problems", journal = j-SIAM-J-CONTROL-OPTIM, volume = "26", number = "4", pages = "985--996", year = "1988", CODEN = "SJCODE", DOI = "https://doi.org/10.1137/0326053", ISSN = "0363-0129 (print), 1095-7138 (electronic)", ISSN-L = "0363-0129", MRclass = "49A55 (42A05 49D29 90C25 94A11)", MRnumber = "948654", MRreviewer = "Krzysztof C. Kiwiel", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Control and Optimization", journal-URL = "http://epubs.siam.org/sicon", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Book{Borowski:1988:DM, author = "E. J. (Ephraim J.) Borowski and Jonathan M. Borwein", title = "Dictionary of mathematics", publisher = pub-COLLINS, address = pub-COLLINS:adr, pages = "xi + 659", year = "1988", ISBN = "0-00-434347-6 (paperback)", ISBN-13 = "978-0-00-434347-1 (paperback)", LCCN = "QA5", bibdate = "Mon Oct 23 07:36:34 MDT 2017", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "With contributions by J. F. Bowers.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", subject = "Mathematics; Dictionaries", } @TechReport{Borwein:1988:CCJ, author = "J. M. Borwein and P. B. Borwein", title = "A Cubic Counterpart of {Jacobi}'s Identity and the {AGM}", type = "Report", institution = "Department of Mathematics, Statistics and Computing Science, Dalhousie University", address = "Halifax, NS B3H 3J5, Canada", pages = "20", day = "31", month = dec, year = "1988", bibdate = "Fri Nov 11 07:03:04 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "We produce cubic analogues of Jacobi's celebrated theta function identity and of the arithmetic--geometric mean iteration of Gauss and Legendre. The iteration in question is $ a_{n + 1} = (a_n + 2 b_n) / 3 $ and $ b_{n + 1} = \sqrt [3]{b_n((a_n^2 + a_n b_n + b_n^2) / 3)} $. The limit of this iteration is identified in terms of the hypergeometric function $_2 F_1 (1 / 3, 2 / 3; 1; \cdot)$ which supports a particularly simple cubic transformation.", acknowledgement = ack-nhfb, keywords = "$\pi$; arithmetic--geometric mean (AGM); cubic transformations; generalised elliptic functions; hypergeometric functions; mean iterations; theta functions", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1988:CFF, author = "J. M. Borwein and P. B. Borwein", title = "On the Complexity of Familiar Functions and Numbers", journal = j-SIAM-REVIEW, volume = "30", number = "4", pages = "589--601", month = dec, year = "1988", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1030134", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "68Q25 (03D15 11Y16)", MRnumber = "967961, 89k:68061", MRreviewer = "Klaus W. Wagner", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "ACM Computing Archive CD-ROM database (1991); Compendex database; http://epubs.siam.org/toc/siread/30/4; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/elefunt.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "http://docserver.carma.newcastle.edu.au/1593/; http://www.jstor.org/stable/2030559", abstract = "This paper examines low-complexity approximations to familiar functions and numbers. The intent is to suggest that it is possible to base a taxonomy of such functions and numbers on their computational complexity. A central theme is that traditional methods of approximation are often very far from optimal, while good or optimal methods are often very far from obvious. For most functions, provably optimal methods are not known; however the gap between what is known and what is possible is often small. A considerable number of open problems are posed and a number of related examples are presented.", acknowledgement = ack-nhfb, affiliationaddress = "Halifax, NS, Can", bibno = "58008", catcode = "G.1.2; F.2.1; F.1.3", classification = "921", CRclass = "G.1.2 Approximation; G.1.2 Elementary function approximation; F.2.1 Numerical Algorithms and Problems; F.1.3 Complexity Classes", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation; Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems; Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Complexity Classes", fjournal = "SIAM Review. A Publication of the Society for Industrial and Applied Mathematics", genterm = "algorithms; theory; performance", guideno = "1988-13907", journal-URL = "http://epubs.siam.org/sirev", journalabbrev = "SIAM Rev.", journalabr = "SIAM Rev", jrldate = "Dec. 1988", keywords = "Algebraic Approximation; Approximation Theory; Computation of Digits; Familiar Functions; Low Complexity Approximation; Mathematical Techniques; Rational Approximation; Reduced Complexity Approximation", onlinedate = "December 1988", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT DEVICES", } @Article{Borwein:1988:ESE, author = "D. Borwein and J. M. Borwein and R. Shail and I. J. Zucker", title = "Energy of static electron lattices", journal = j-J-PHYS-A, volume = "21", number = "7", pages = "1519--1531", month = apr, year = "1988", CODEN = "JPHAC5", DOI = "https://doi.org/10.1088/0305-4470/21/7/015", ISSN = "0305-4470 (print), 1361-6447 (electronic)", ISSN-L = "0305-4470", MRclass = "82A65 (81H99)", MRnumber = "951042", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/1988JPhA...21.1519B; http://docserver.carma.newcastle.edu.au/1592/; http://stacks.iop.org/0305-4470/21/1519; http://stacks.iop.org/0305-4470/21/i=7/a=015", acknowledgement = ack-nhfb, fjournal = "Journal of Physics. A. Mathematical and General", journal-URL = "http://iopscience.iop.org/1751-8121", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1988:MRT, author = "J. M. Borwein and P. B. Borwein", booktitle = "{Ramanujan} revisited ({Urbana-Champaign, Ill.}, 1987)", title = "More {Ramanujan}-type series for {$ 1 / \pi $}", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "359--374", year = "1988", MRclass = "11Y60", MRnumber = "938974", MRreviewer = "Duncan A. Buell", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1988:RP, author = "Jonathan M. Borwein and Peter B. Borwein", title = "{Ramanujan} and {Pi}", journal = j-SCI-AMER, volume = "258", number = "2", pages = "112--117", month = feb, year = "1988", CODEN = "SCAMAC", DOI = "https://doi.org/10.1038/scientificamerican0288-112", ISSN = "0036-8733 (print), 1946-7087 (electronic)", ISSN-L = "0036-8733", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/sciam1980.bib", note = "Japanese edition (April 1988), Russian edition (April 1988), German edition (May 1988). Reprinted in \cite{Borwein:1991:RP,Borwein:1996:SRZ,Borwein:2001:RP,Bailey:2016:PNG}.", URL = "http://docserver.carma.newcastle.edu.au/1379/; http://www.nature.com/scientificamerican/journal/v258/n2/pdf/scientificamerican0288-112.pdf", acknowledgement = ack-nhfb, fjournal = "Scientific American", journal-URL = "http://www.nature.com/scientificamerican", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", xxnewdata = "1998.01.30", } @Article{Borwein:1988:VNS, author = "J. M. Borwein and D. M. Zhuang", title = "Verifiable necessary and sufficient conditions for openness and regularity of set-valued and single-valued maps", journal = j-J-MATH-ANAL-APPL, volume = "134", number = "2", pages = "441--459", year = "1988", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(88)90034-0", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "90C48 (54C60 58C20 90C25)", MRnumber = "961349", MRreviewer = "Jean-Paul Penot", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1594/; http://www.sciencedirect.com/science/article/pii/0022247X88900340", abstract = "We provide several equivalences to the regularity of closed set-valued maps around a point in general metric settings. In particular, an easy to verify approximate openness notion is shown equivalent to regularity. A simple specialization of our theorem strengthens Frankowska's novel ``open mapping principle.''", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Deutsch:1988:PSSa, author = "Emeric Deutsch and Jonathan M. Borwein and Paul Cull and G. Behrendt", title = "Problems and Solutions: Solutions of Elementary Problems: {E3159}", journal = j-AMER-MATH-MONTHLY, volume = "95", number = "6", pages = "557--558", month = jun # "\slash " # jul, year = "1988", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2322769", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1541335", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.jstor.org/journals/00029890.htm; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib", note = "See also \cite{Deutsch:1986:PSE}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1989:ACL, author = "D. Borwein and J. M. Borwein and R. Shail", title = "Analysis of certain lattice sums", journal = j-J-MATH-ANAL-APPL, volume = "143", number = "1", pages = "126--137", year = "1989", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(89)90032-2", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "82A67 (11M99)", MRnumber = "1019453", MRreviewer = "A. K. Rajagopal", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1589/; http://www.sciencedirect.com/science/article/pii/0022247X89900322", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1989:ARM, author = "J. M. Borwein and P. B. Borwein", title = "Approximating $ \pi $ with {Ramanujan}'s modular equations", journal = j-ROCKY-MOUNTAIN-J-MATH, volume = "19", number = "1", pages = "93--102", year = "1989", CODEN = "RMJMAE", DOI = "https://doi.org/10.1216/RMJ-1989-19-1-93", ISSN = "0035-7596 (print), 1945-3795 (electronic)", ISSN-L = "0035-7596", MRclass = "11Y35 (11F11 33E05)", MRnumber = "1016163", MRreviewer = "Bruce C. Berndt", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Constructive Function Theory---86 Conference (Edmonton, AB, 1986).", acknowledgement = ack-nhfb, fjournal = "The Rocky Mountain Journal of Mathematics", journal-URL = "http://projecteuclid.org/euclid.rmjm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1989:ENP, author = "Jonathan M. Borwein and Simon Fitzpatrick", title = "Existence of nearest points in {Banach} spaces", journal = j-CAN-J-MATH, volume = "41", number = "4", pages = "702--720", year = "1989", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1989-032-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "46B20", MRnumber = "1012624", MRreviewer = "Mari{\'a}n Fabian", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1582/", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics. Journal Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1989:HC, author = "J. M. Borwein and H. M. Str{\'o}jwas", title = "The hypertangent cone", journal = j-NONLINEAR-ANAL, volume = "13", number = "2", pages = "125--144", year = "1989", CODEN = "NOANDD", DOI = "https://doi.org/10.1016/0362-546X(89)90039-4", ISSN = "0362-546x (print), 1873-5215 (electronic)", ISSN-L = "0362-546X", MRclass = "90C30 (47H99 49A52)", MRnumber = "979036", MRreviewer = "D{\cftil{o}} V{\u{a}}n Lu{\cprime}u", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1588/; http://www.sciencedirect.com/science/article/pii/0362546X89900394", acknowledgement = ack-nhfb, fjournal = "Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods", journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis", keywords = "directional derivatives and subgradients; directionally Lipschitzian functions; Discrete tangent cone formulas; epi-Lipschitzian sets; inversion theorems; mean value theorems", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1989:LBM, author = "Jon Borwein and Simon Fitzpatrick", title = "Local boundedness of monotone operators under minimal hypotheses", journal = j-BULL-AUSTRAL-MATH-SOC, volume = "39", number = "3", pages = "439--441", year = "1989", CODEN = "ALNBAB", DOI = "https://doi.org/10.1017/S000497270000335X", ISSN = "0004-9727 (print), 1755-1633 (electronic)", ISSN-L = "0004-9727", MRclass = "47H05", MRnumber = "995141", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1590/", acknowledgement = ack-nhfb, fjournal = "Bulletin of the Australian Mathematical Society", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1989:LOC, author = "J. M. Borwein and M. A. H. Dempster", title = "The linear order complementarity problem", journal = j-MATH-OP-RES, volume = "14", number = "3", pages = "534--558", year = "1989", CODEN = "MOREDQ", DOI = "https://doi.org/10.1287/moor.14.3.534", ISSN = "0364-765x (print), 1526-5471 (electronic)", ISSN-L = "0364-765X", MRclass = "90C33 (47H99 90C48)", MRnumber = "1008428", MRreviewer = "Morgan A. Hanson", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1585/", acknowledgement = ack-nhfb, fjournal = "Mathematics of Operations Research", journal-URL = "http://pubsonline.informs.org/loi/moor", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1989:MCK, author = "Jonathan M. Borwein and Simon Fitzpatrick", title = "{Mosco} convergence and the {Kadec} property", journal = j-PROC-AM-MATH-SOC, volume = "106", number = "3", pages = "843--851", year = "1989", CODEN = "PAMYAR", DOI = "https://doi.org/10.2307/2047444", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "46B20 (52A05 54C60)", MRnumber = "969313", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1584/", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1989:MI, author = "J. M. Borwein and P. B. Borwein", title = "On the Mean Iteration $ (a, b) \leftarrow \big (\frac {a + 3b}{4}, \frac {\sqrt {ab} + b}{2} \big) $", journal = j-MATH-COMPUT, volume = "53", number = "187", pages = "311--326", month = jul, year = "1989", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2008364", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "30D05 (33A25)", MRnumber = "968148, 90a:30075", MRreviewer = "Carl C. Cowen", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib; JSTOR database", URL = "http://docserver.carma.newcastle.edu.au/1586/", acknowledgement = ack-nhfb, classcodes = "C4130 (Interpolation and function approximation)", corpsource = "Dept. of Math. Stat. and Comput. Sci., Dalhousie Univ., Halifax, NS, Canada", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "computation; convergence of numerical methods; converging process; iterative methods; iterative process; limit; mean iteration; nontrivial identifications; quadratically; symbolic; uniformizing parameters", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", treatment = "T Theoretical or Mathematical", } @Article{Borwein:1989:PEN, author = "J. M. Borwein and P. B. Borwein and K. Dilcher", title = "Pi, {Euler} numbers, and asymptotic expansions", journal = j-AMER-MATH-MONTHLY, volume = "96", number = "8", pages = "681--687", year = "1989", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2324715", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "40A25 (11Y60 65B15)", MRnumber = "1019148", MRreviewer = "Bruce C. Berndt", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1583/", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1989:RME, author = "J. M. Borwein and P. B. Borwein and D. H. Bailey", title = "{Ramanujan}, modular equations, and approximations to pi, or {How} to compute one billion digits of pi", journal = j-AMER-MATH-MONTHLY, volume = "96", number = "3", pages = "201--219", month = mar, year = "1989", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2325206", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "11Y60 (01A60 11F03 33A25)", MRnumber = "991866", MRreviewer = "Herman J. J. te Riele", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Reprinted in \cite{Bailey:1997:RME}.", URL = "http://docserver.carma.newcastle.edu.au/1587/; http://www.jstor.org/stable/2325206", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Beer:1990:MCR, author = "Gerald Beer and Jonathan M. Borwein", title = "{Mosco} convergence and reflexivity", journal = j-PROC-AM-MATH-SOC, volume = "109", number = "2", pages = "427--436", year = "1990", CODEN = "PAMYAR", DOI = "https://doi.org/10.2307/2048005", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "46B10 (46B20 49J45 54B20 90C25)", MRnumber = "1012924", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1581/", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1990:BRG, author = "Jonathan Borwein", title = "Book Review: {{\booktitle{Generalized Concavity}} (Mordecai Avriel, Walter E. Diewert, Siegfried Schaible, and Israel Zang)}", journal = j-SIAM-REVIEW, volume = "32", number = "4", pages = "689--690", month = dec, year = "1990", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1032140", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://epubs.siam.org/toc/siread/32/4; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "December 1990", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Book{Borwein:1990:DRN, author = "Jonathan Borwein and Peter B. Borwein", title = "A dictionary of real numbers", publisher = pub-WADSWORTH, address = pub-WADSWORTH:adr, pages = "viii + 424", year = "1990", DOI = "https://doi.org/10.1007/978-1-4615-8510-7", ISBN = "0-534-12840-8", ISBN-13 = "978-0-534-12840-1", LCCN = "QA47.B625 1990", MRclass = "11-00 (11Y60 11Y70)", MRnumber = "1030542, 91g:11001", MRreviewer = "Jeffrey O. Shallit", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/maple-extract.bib", abstract = "This dictionary was designed for researchers who have encountered various numbers computationally and want to know if these numbers have simple form. The book is structured as a reverse handbook of special function values. It lists over 100,000 eight digit real numbers in the interval (1,0) that arise as the first eight digits of special values of familiar functions.", acknowledgement = ack-nhfb, keywords = "Maple", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", reviewer = "Jeffrey O. Shallit", } @Article{Borwein:1990:RCM, author = "J. M. Borwein and P. B. Borwein", booktitle = "Computational methods and function theory ({Valpara}{\'\i}so, 1989)", title = "A remarkable cubic mean iteration", journal = j-LECT-NOTES-MATH, volume = "1435", pages = "27--31", year = "1990", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/BFb0087894", ISBN = "3-540-52768-0 (print), 3-540-47139-1 (e-book)", ISBN-13 = "978-3-540-52768-8 (print), 978-3-540-47139-4 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", MRclass = "33C05", MRnumber = "1071759 (92b:33003)", MRreviewer = "W. H. J. Fuchs", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/lnm1990.bib", URL = "http://link.springer.com/chapter/10.1007/BFb0087894/", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/BFb0087892", book-URL = "http://www.springerlink.com/content/978-3-540-47139-4", fjournal = "Lecture Notes in Mathematics", journal-URL = "http://link.springer.com/bookseries/304", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:1990:SDPa, author = "J. M. Borwein", editor = "Gustave Choquet and others", booktitle = "S{\'e}minaire d'initiation {\`a} l'analyze", title = "A survey of differentiability properties of convex, {Lipschitz} and lsc functions", publisher = "Publ. Math. Univ. Pierre et Marie Curie", address = "Paris, France", pages = "??--??", year = "1990", DOI = "", ISBN = "", ISBN-13 = "", LCCN = "", bibdate = "Mon Aug 15 15:02:04 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "https://carma.newcastle.edu.au/jon/Preprints/Books/CUP/CUPold/convsurvey.pdf", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", pagecount = "11", } @TechReport{Borwein:1990:SSH, author = "J. M. Borwein and P. B. Borwein", title = "Strange Series and High Precision Fraud", type = "Preliminary Report", institution = "Department of Mathematics, Statistics and Computing Science, Dalhousie University", address = "Halifax, NS B3H 3J5, Canada", pages = "28", day = "4", month = sep, year = "1990", MRclass = "11A99, 11A55 (primary), 65B10 (secondary)", bibdate = "Fri Nov 11 07:05:53 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "We present a variety of series some of which have simple evaluations. Others appear to have simple evaluations when computed to several hundred or even several million digit precision, but are in fact frauds. Many of these examples are based on series whose terms involve digit sums and the integer part function.", acknowledgement = ack-nhfb, keywords = "approximation; continued fractions; digit series; generating functions; high precision estimates; integer parts; irrationality; Mahler's series; modular transformations; transcendence", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Date recorded in ambiguous form 4/9/90; entry Borwein:1988:CCJ has 31/12/88, suggesting that the first number is the day.", } @Article{Knuth:1990:PSSa, author = "D. E. Knuth and Jungmin Woo and Hans Kappus and J. M. Borwein and P. B. Borwein", title = "Problems and Solutions: Solutions of Elementary Problems: {E3335}", journal = j-AMER-MATH-MONTHLY, volume = "97", number = "10", pages = "927", year = "1990", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1541809", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "2-8&origin=MSN; http://links.jstor.org/sici?sici=0002-9890(199012)97:10<927:E>2.0.CO", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Knuth:1990:PSSb, author = "D. E. Knuth and Jungmin Woo and Hans Kappus and J. M. Borwein and P. B. Borwein", title = "Problems and Solutions: Solutions of Elementary Problems: {E3335}", journal = j-AMER-MATH-MONTHLY, volume = "97", number = "10", pages = "927", year = "1990", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1541809", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "2-8&origin=MSN; http://links.jstor.org/sici?sici=0002-9890(199012)97:10<927:E>2.0.CO", acknowledgement = ack-nhfb, fjournal = "The American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Knuth:1990:PSSc, author = "D. E. Knuth and Jungmin Woo and Hans Kappus and J. M. Borwein and P. B. Borwein", title = "Problems and Solutions: Solutions of Elementary Problems: {E3335}", journal = j-AMER-MATH-MONTHLY, volume = "97", number = "10", pages = "927--927", month = dec, year = "1990", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2324339", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.jstor.org/journals/00029890.htm; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib", note = "See also \cite{Rudin:1989:PSE}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Book{Borowski:1991:HDM, author = "E. J. Borowski and J. M. Borwein", title = "The {HarperCollins} dictionary of mathematics", publisher = "HarperPerennial", address = "New York, NY, USA", pages = "xii + 659", year = "1991", ISBN = "0-06-461019-5, 0-00-434347-6 (paperback)", ISBN-13 = "978-0-06-461019-3, 978-0-00-434347-1 (paperback)", MRclass = "00A20", MRnumber = "1210061", MRreviewer = "F. J. Papp", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "With the assistance of J. F. Bowers, A. Robertson and M. McQuillan, Revised reprint of the 1988 original \cite{Borowski:1988:DM}.", URL = "http://docserver.carma.newcastle.edu.au/1738/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Translations: Chinese (1995), Indonesian (Erlanga Penerbit, 1995), Italian (Gremese Editore) 1995, Arabic (Academia International) 1991", } @Article{Borwein:1991:CBE, author = "Jonathan M. Borwein and Adrian S. Lewis", title = "Convergence of best entropy estimates", journal = j-SIAM-J-OPT, volume = "1", number = "2", pages = "191--205", year = "1991", CODEN = "SJOPE8", DOI = "https://doi.org/10.1137/0801014", ISSN = "1052-6234 (print), 1095-7189 (electronic)", ISSN-L = "1052-6234", MRclass = "41A46 (28A20 28D20)", MRnumber = "1098426", MRreviewer = "Tiberiu Constantinescu", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1576/", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Optimization", journal-URL = "http://epubs.siam.org/siopt", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1991:CCJ, author = "J. M. Borwein and P. B. Borwein", title = "A cubic counterpart of {Jacobi}'s identity and the {AGM}", journal = j-TRANS-AM-MATH-SOC, volume = "323", number = "2", pages = "691--701", month = feb, year = "1991", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/2001551", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "33C75 (11F11 11Y60 33C05)", MRnumber = "1010408", MRreviewer = "Bruce C. Berndt", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1578/; http://www.jstor.org/stable/2001551", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1991:CMP, author = "Jonathan M. Borwein and Adrian S. Lewis", title = "On the convergence of moment problems", journal = j-TRANS-AM-MATH-SOC, volume = "325", number = "1", pages = "249--271", month = may, year = "1991", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/2001670", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "44A60 (90C90)", MRnumber = "1008695", MRreviewer = "Tiberiu Constantinescu", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1579/; http://www.jstor.org/stable/2001670", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1991:DPC, author = "Jonathan M. Borwein", booktitle = "S{\'e}minaire d'Initiation {\`a} l'Analyse", title = "Differentiability properties of convex, of {Lipschitz}, and of semicontinuous mappings on {Banach} spaces", volume = "104(19)", publisher = "Universit{\'e} de Paris VI", address = "Paris, France", pages = "1--11", year = "1991", MRclass = "46G05 (26E15 46B20 46N10 49J50 58C20)", MRnumber = "1217320", MRreviewer = "Saheb Dayal", bibdate = "Fri Oct 13 14:59:36 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Publ. Math. Univ. Pierre et Marie Curie", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1991:DRE, author = "Jonathan M. Borwein and Adrian S. Lewis", title = "Duality relationships for entropy-like minimization problems", journal = j-SIAM-J-CONTROL-OPTIM, volume = "29", number = "2", pages = "325--338", year = "1991", CODEN = "SJCODE", DOI = "https://doi.org/10.1137/0329017", ISSN = "0363-0129 (print), 1095-7138 (electronic)", ISSN-L = "0363-0129", MRclass = "49N15 (90C29 90C48)", MRnumber = "1092730", MRreviewer = "C. P. Ortlieb", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1577/", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Control and Optimization", journal-URL = "http://epubs.siam.org/sicon", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1991:FPI, author = "David Borwein and Jonathan Borwein", title = "Fixed point iterations for real functions", journal = j-J-MATH-ANAL-APPL, volume = "157", number = "1", pages = "112--126", year = "1991", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(91)90139-Q", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "65H05 (39B12)", MRnumber = "1109446", MRreviewer = "Joe Thrash", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.sciencedirect.com/science/article/pii/0022247X9190139Q", abstract = "We give proofs of general results on the computation of fixed points of a continuous function or a Lipschitz function on the real line. We also show how completely these results can fail to hold in spaces of more than one dimension.", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1991:MCS, author = "J. M. Borwein", booktitle = "Fixed point theory and applications ({Marseille}, 1989)", title = "Minimal {CUSCOS} and subgradients of {Lipschitz} functions", volume = "252", publisher = pub-LONGMAN, address = pub-LONGMAN:adr, pages = "57--81", year = "1991", MRclass = "46G05 (47H04 49J52)", MRnumber = "1122818", MRreviewer = "Doug Ward", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Pitman Res. Notes Math. Ser.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1991:MCU, author = "Jonathan Borwein and Simon Fitzpatrick and Petar Kenderov", title = "Minimal convex uscos and monotone operators on small sets", journal = j-CAN-J-MATH, volume = "43", number = "3", pages = "461--476", year = "1991", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1991-028-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "46G05 (47H05 54C99)", MRnumber = "1118004", MRreviewer = "Doug Ward", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1573/", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics. Journal Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1991:NR, author = "Jonathan M. Borwein and G. de Barra", title = "Nested radicals", journal = j-AMER-MATH-MONTHLY, volume = "98", number = "8", pages = "735--739", year = "1991", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2324426", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "11A99 (11Y55 39A10 40A05)", MRnumber = "1130684", MRreviewer = "Heinrich Rolletschek", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1580/", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1991:PCF, author = "Jonathan M. Borwein and Adrian S. Lewis", editor = "J-B. Baillon and M. Th{\'e}ra", booktitle = "Fixed point theory and applications ({Marseille}, 1989)", title = "Practical conditions for {Fenchel} duality in infinite dimensions", volume = "252", publisher = pub-LONGMAN, address = pub-LONGMAN:adr, pages = "83--89", year = "1991", MRclass = "49N15 (46G99 90C45 90C48)", MRnumber = "1122819", MRreviewer = "Blagun Kalchev", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Pitman Lecture Notes in Mathematics", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", xxseries = "Pitman Res. Notes Math. Ser.", } @InCollection{Borwein:1991:RP, author = "Jonathan M. Borwein and Peter B. Borwein", title = "{Ramanujan} and {Pi}", crossref = "Ferris:1991:WTP", pages = "647--659", year = "1991", bibdate = "Fri Aug 12 15:11:12 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1379/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1991:SEC, author = "J. M. Borwein and D. M. Zhuang", title = "Super efficiency in convex vector optimization", journal = j-Z-OPER-RES, volume = "35", number = "3", pages = "175--184", year = "1991", CODEN = "ZMMRFZ", DOI = "https://doi.org/10.1007/BF01415905", ISSN = "0340-9422", MRclass = "90C29", MRnumber = "1114290", MRreviewer = "Emil Iwanow", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://link.springer.com/article/10.1007/BF01415905", acknowledgement = ack-nhfb, ajournal = "Z. Oper. Res.", fjournal = "Zeitschrift f{\"u}r Operations Research. Mathematical Methods of Operations Research", journal-URL = "http://link.springer.com/journal/186", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1991:SGB, author = "J. M. Borwein and P. B. Borwein", title = "A singular genius: [book review] {{\booktitle{The Man Who Knew Infinity. A Life of the Indian Genius Ramanujan}}. Robert Kanigel, Scribner, New York, 1991. x + 438 pp. + plates, \$27.95}", journal = j-SCIENCE, volume = "253", number = "5017", pages = "334--335", day = "19", month = jul, year = "1991", CODEN = "SCIEAS", DOI = "https://doi.org/10.1126/science.253.5017.334", ISSN = "0036-8075 (print), 1095-9203 (electronic)", ISSN-L = "0036-8075", bibdate = "Wed Aug 10 18:35:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.jstor.org/stable/2879085; http://www.ncbi.nlm.nih.gov/pubmed/17794700", acknowledgement = ack-nhfb, fjournal = "Science (New York, NY)", journal-URL = "http://www.sciencemag.org/archive/", onlinedate = "19 July 1991", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", publisherinfo = "17794700 ER", } @Article{Borwein:1992:ASW, author = "Jonathan Borwein and Shi Tuo Lou", title = "Asymptotics of a sequence of {Witt} vectors", journal = j-J-APPROX-THEORY, volume = "69", number = "3", pages = "326--337", year = "1992", CODEN = "JAXTAZ", DOI = "https://doi.org/10.1016/0021-9045(92)90006-A", ISSN = "0021-9045 (print), 1096-0430 (electronic)", ISSN-L = "0021-9045", MRclass = "05A16 (05E05 05E10 13K05)", MRnumber = "1164995", MRreviewer = "Jiang Zeng", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1565/; http://www.sciencedirect.com/science/article/pii/002190459290006A", abstract = "We provide asymptotic and order information about the Witt vectors and integers dn appearing in \prod n\le 111 + dn(tnn|)=(1-t)et.", acknowledgement = ack-nhfb, fjournal = "Journal of Approximation Theory", journal-URL = "http://www.sciencedirect.com/science/journal/00219045", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1992:BRS, author = "Jonathan Borwein", title = "Book Review: {{\booktitle{Set-valued analysis}}, J-P. Aubin and H. Frankowska}", journal = j-BULL-AMS-N-S, volume = "26", number = "1", pages = "157--160", year = "1992", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0273-0979-1992-00246-X", ISSN = "0273-0979 (print), 1088-9485 (electronic)", ISSN-L = "0273-0979", MRnumber = "1567970", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Society. Bulletin. New Series", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1992:DMF, author = "Jonathan M. Borwein and Adrian S. Lewis", title = "Decomposition of multivariate functions", journal = j-CAN-J-MATH, volume = "44", number = "3", pages = "463--482", year = "1992", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1992-030-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "54C05 (05C38 08A45 22C05 26B40 28A20)", MRnumber = "1176365", MRreviewer = "Douglass L. Grant", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1569/", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics. Journal Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1992:DPC, author = "J. Borwein", booktitle = "Optimization and nonlinear analysis ({Haifa}, 1990)", title = "Differentiability properties of convex, of {Lipschitz}, and of semicontinuous mappings on {Banach} spaces", volume = "244", publisher = pub-LONGMAN, address = pub-LONGMAN:adr, pages = "39--52", year = "1992", MRclass = "49J50 (46B20 46G05 47H99)", MRnumber = "1184630", MRreviewer = "Julian Revalski", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Pitman Res. Notes Math. Ser.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1992:FEG, author = "J. M. Borwein and I. J. Zucker", title = "Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind", journal = j-IMA-J-NUMER-ANAL, volume = "12", number = "4", pages = "519--526", year = "1992", CODEN = "IJNADN", DOI = "https://doi.org/10.1093/imanum/12.4.519", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65D20", MRnumber = "1186733", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/elefunt.bib", acknowledgement = ack-nhfb, fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1992:KMI, author = "Jonathan Borwein and Simeon Reich and Itai Shafrir", title = "{Krasnosel'ski--Mann} iterations in normed spaces", journal = j-CAN-MATH-BULL, volume = "35", number = "1", pages = "21--28", year = "1992", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1992-003-0", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", MRclass = "47H09 (47H10 47H17)", MRnumber = "1157459", MRreviewer = "Gregory B. Passty", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1992:MHP, author = "Jonathan M. Borwein and Mark A. Limber", title = "{Maple} as a High Precision Calculator", journal = j-MAPLE-TECH-NEWS, volume = "0", number = "8", pages = "39--44", month = "Fall", year = "1992", ISSN = "1061-5733", ISSN-L = "1061-5733", bibdate = "Fri May 09 22:33:19 1997", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/maple-tech.bib", URL = "http://www.can.nl/Systems_and_Packages/Per_Purpose/General/Maple/mtn/mtn8.html", acknowledgement = ack-nhfb, fjournal = "Maple technical newsletter", journal-URL = "http://web.mit.edu/maple/www/plibrary/mtn.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1992:PFCa, author = "Jonathan M. Borwein and Adrian S. Lewis", title = "Partially finite convex programming. {I}. {Quasi} relative interiors and duality theory", journal = j-MATH-PROG, volume = "57", number = "1--3", pages = "15--48", year = "1992", CODEN = "MHPGA4", DOI = "https://doi.org/10.1007/BF01581072", ISSN = "0025-5610 (print), 1436-4646 (electronic)", ISSN-L = "0025-5610", MRclass = "90C48 (49J15 65K05 90C25)", MRnumber = "1167406", MRreviewer = "M. Teboulle", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1571/; http://link.springer.com/article/10.1007/BF01581072", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming", journal-URL = "http://link.springer.com/journal/10107", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1992:PFCb, author = "Jonathan M. Borwein and Adrian S. Lewis", title = "Partially finite convex programming, {Part II}: Explicit lattice models", journal = j-MATH-PROG, volume = "57", number = "1--3", pages = "49--83", year = "1992", CODEN = "MHPGA4", DOI = "https://doi.org/10.1007/BF01581073", ISSN = "0025-5610 (print), 1436-4646 (electronic)", ISSN-L = "0025-5610", MRclass = "90C48 (49N15 65K05 90C25)", MRnumber = "1167407", MRreviewer = "M. Teboulle", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1572/; http://link.springer.com/article/10.1007/BF01581073", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming", journal-URL = "http://link.springer.com/journal/10107", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:1992:SDP, author = "J. M. Borwein", editor = "A. Ioffe and M. Marcus and S. Reich", booktitle = "Optimization and Nonlinear Analysis: Proceedings of the {Technion} Special Semester on Nonlinear Analysis ({Spring 1990})", title = "A survey of differentiability properties of convex, {Lipschitz} and lsc functions", publisher = "Longman", address = "Essex, UK", pages = "39--52", year = "1992", DOI = "", ISBN = "", ISBN-13 = "", LCCN = "", bibdate = "Mon Aug 15 14:55:03 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1992:SEC, author = "J. M. Borwein and A. {Ben Tal} and M. Teboulle", booktitle = "Systems and Management Science by extremal methods: research honoring {Abraham Charnes} at age 70", title = "Spectral estimation via convex programming", publisher = pub-KLUWER, address = pub-KLUWER:adr, pages = "275--290", year = "1992", DOI = "", ISBN = "", ISBN-13 = "", LCCN = "", bibdate = "Mon Aug 15 14:57:23 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1992:SOC, author = "Jonathan Borwein and Peter B. Borwein", title = "Some Observations on Computer Aided Analysis", journal = j-NAMS, volume = "39", number = "8", pages = "825--829", year = "1992", CODEN = "AMNOAN", ISSN = "0002-9920 (print), 1088-9477 (electronic)", ISSN-L = "0002-9920", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, fjournal = "Notices of the American Mathematical Society", journal-URL = "http://www.ams.org/notices/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "No journal online archives before 1995.", } @Article{Borwein:1992:SSH, author = "J. M. Borwein and P. B. Borwein", title = "Strange Series and High Precision Fraud", journal = j-AMER-MATH-MONTHLY, volume = "99", number = "7", pages = "622--640", month = aug # "\slash " # sep, year = "1992", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2324993", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "40-01 (40A05 40A25)", MRnumber = "1176589, 93f:40001", MRreviewer = "John A. Fridy", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.jstor.org/journals/00029890.htm; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1992:STS, author = "J. M. Borwein and M. Th{\'e}ra", title = "Sandwich theorems for semicontinuous operators", journal = j-CAN-MATH-BULL, volume = "35", number = "4", pages = "463--474", year = "1992", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1992-061-7", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", MRclass = "54C08 (46A99 54C60 54C65 54F05)", MRnumber = "1191505", MRreviewer = "P. Maritz", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Cook:1992:PSS, author = "Matthew Cook and Walther Janous and Marcin E. Kuczma and David Borwein", title = "Problems and Solutions: Solutions of Elementary Problems: {E3388}", journal = j-AMER-MATH-MONTHLY, volume = "99", number = "1", pages = "69--70", month = jan, year = "1992", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2324561", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.jstor.org/journals/00029890.htm; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib", note = "See also \cite{Sturm:1990:PSE}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bauschke:1993:CNA, author = "H. H. Bauschke and J. M. Borwein", title = "On the convergence of {von Neumann}'s alternating projection algorithm for two sets", journal = j-SET-VALUED-ANAL, volume = "1", number = "2", pages = "185--212", year = "1993", CODEN = "SVANEG", DOI = "https://doi.org/10.1007/BF01027691", ISSN = "0927-6947 (print), 1572-932X (electronic)", ISSN-L = "0927-6947", MRclass = "65J05 (41A65 47H17 65K10)", MRnumber = "1239403", MRreviewer = "F. Deutsch", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1555/; http://link.springer.com/article/10.1007/BF01027691", acknowledgement = ack-nhfb, fjournal = "Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications", journal-URL = "http://link.springer.com/journal/11228", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Beer:1993:MSC, author = "Gerald Beer and Jonathan M. Borwein", title = "{Mosco} and Slice Convergence of Level Sets and Graphs of Linear Functionals", journal = j-J-MATH-ANAL-APPL, volume = "175", number = "1", pages = "53--67", year = "1993", CODEN = "JMANAK", DOI = "https://doi.org/10.1006/jmaa.1993.1151", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "46B99 (46N10 49J45 54A20)", MRnumber = "1216744", MRreviewer = "Constantin Z{\u{a}}linescu", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1562/; http://www.sciencedirect.com/science/article/pii/S0022247X83711510", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Unpublished{Borwein:1993:ASS, author = "J. M. Borwein", title = "{Asplund} spaces are sequentially reflexive", year = "1993", bibdate = "Fri Aug 12 14:17:01 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Accepted for publication in the Canadian Journal of Mathematics, but withdrawn and merged with another paper. Jon Borwein recorded that as publication number 121, but because the article numbers changed with each update of his CV, that number has long been incorrect.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Research Report CORR 91-14.", } @Article{Borwein:1993:CDS, author = "Jonathan M. Borwein and Adrian S. Lewis", title = "Convergence of decreasing sequences of convex sets in nonreflexive {Banach} spaces", journal = j-SET-VALUED-ANAL, volume = "1", number = "4", pages = "355--363", year = "1993", CODEN = "SVANEG", DOI = "https://doi.org/10.1007/BF01027825", ISSN = "0927-6947 (print), 1572-932x (electronic)", ISSN-L = "0927-6947", MRclass = "49J45 (46N10)", MRnumber = "1267202", MRreviewer = "Roberto Lucchetti", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1551/", acknowledgement = ack-nhfb, fjournal = "Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications", journal-URL = "http://link.springer.com/journal/11228", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Unpublished{Borwein:1993:CEU, author = "J. M. Borwein and R. K. Goodrich and M. A. Limber", title = "A comparison of entropies in the underdetermined moment problem", month = may, year = "1993", bibdate = "Tue Aug 16 10:06:18 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Preprint.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1993:CFH, author = "J. M. Borwein and M. Fabi{\'a}n", title = "On convex functions having points of {G{\^a}teaux} differentiability which are not points of {Fr}{\'e}chet differentiability", journal = j-CAN-J-MATH, volume = "45", number = "6", pages = "1121--1134", year = "1993", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1993-062-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "46B20 (46B03)", MRnumber = "1247537", MRreviewer = "Gilles Godefroy", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1552/", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics. Journal Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1993:CNT, author = "J. M. Borwein and P. B. Borwein", title = "Class number three {Ramanujan} type series for $ 1 / \pi $", journal = j-J-COMPUT-APPL-MATH, volume = "46", number = "1--2", pages = "281--290", day = "14", month = jun, year = "1993", CODEN = "JCAMDI", DOI = "https://doi.org/10.1016/0377-0427(93)90302-R", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", MRclass = "11Y60 (11R11)", MRnumber = "1222488", MRreviewer = "Andrew Granville", bibdate = "Sat Feb 25 12:20:57 MST 2017", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib", note = "Computational complex analysis.", URL = "http://docserver.carma.newcastle.edu.au/1560/; http://www.sciencedirect.com/science/article/pii/037704279390302R", abstract = "There is a class of remarkable series for $ 1 / \pi $ of the form $ \sqrt {-C^3} / \pi = \sum_{n = 0}^\infty \frac {A + n B}{C^{3 n}} \frac {(6n)!}{(3n)!(n!)^3} $ where $A$, $B$, $C$ are certain algebraic numbers. These were first examined by Ramanujan. These examples arise by computing singular invariants for j and the constants involved will have degree equal to the class number of the associated imaginary quadratic field. Our intention is compute all such class number three examples. The largest such example, with discriminant $ - 907$, adds $ 37$ additional digit accuracy per term. A class number four example with discriminant $ 1555$ gives $ 50$ digits per term.", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", keywords = "class number; pi; Ramanujan; series", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1993:DKK, author = "J. M. Borwein and J. Vanderwerff", title = "Dual {Kadec--Klee} norms and the relationships between {Wijsman}, slice and {Mosco} convergence", journal = "ArXiv Mathematics e-prints", month = feb, year = "1993", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/1993math......2212B", abstract = "In this paper, we completely settle several of the open questions regarding the relationships between the three most fundamental forms of set convergence. In particular, it is shown that Wijsman and slice convergence coincide precisely when the weak star and norm topologies agree on the dual sphere. Consequently, a weakly compactly generated Banach space admits a dense set of norms for which Wijsman and slice convergence coincide if and only if it is an Asplund space. We also show that Wijsman convergence implies Mosco convergence precisely when the weak star and Mackey topologies coincide on the dual sphere. A corollary of these results is that given a fixed norm on an Asplund space, Wijsman and slice convergence coincide if and only if Wijsman convergence implies Mosco convergence.", acknowledgement = ack-nhfb, eprint = "math/9302212", keywords = "Mathematics - Functional Analysis, 46B", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1993:FME, author = "Jonathan M. Borwein", title = "On the failure of maximum entropy reconstruction for {Fredholm} equations and other infinite systems", journal = j-MATH-PROG, volume = "61", number = "2, Ser. A", pages = "251--261", year = "1993", CODEN = "MHPGA4", DOI = "https://doi.org/10.1007/BF01582150", ISSN = "0025-5610 (print), 1436-4646 (electronic)", ISSN-L = "0025-5610", MRclass = "94A12 (45B05 47N99 90C48)", MRnumber = "1240460", MRreviewer = "Henry Wolkowicz", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1559/", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming", journal-URL = "http://link.springer.com/journal/10107", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1993:GFI, author = "J. M. Borwein and P. B. Borwein", title = "On the generating function of the integer part: $ [n \alpha + \gamma] $", journal = j-J-NUMBER-THEORY, volume = "43", number = "3", pages = "293--318", year = "1993", CODEN = "JNUTA9", DOI = "https://doi.org/10.1006/jnth.1993.1023", ISSN = "0022-314x (print), 1096-1658 (electronic)", ISSN-L = "0022-314X", MRclass = "11J70 (11J91)", MRnumber = "1212686", MRreviewer = "A. J. van der Poorten", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1564/; http://www.sciencedirect.com/science/article/pii/S0022314X83710231", abstract = "We show that [long displayed formula]. Here $ p_n $ and $ q_n $ are the numerators and denominators of the convergents of the continued fraction expansion of $ \alpha $ and $ t^n $ and $ s^n $ are particular algorithmically generated sequences of best approximates for the non-homogeneous Diophantine approximation problem of minimizing $ |n \alpha + \gamma - m| $. This generalizes results of B{\"o}hmer and Mahler, who considered the special case where $ \gamma = 0 $. This representation allows us to easily derive various transcendence results. For example, $ \sum^\infty_{n = 1} [n e + 12] / (2 n) $ is a Liouville number. Indeed the first series is Liouville for rational $z$, $ w \subset [ - 1, 1]$ with $ |z w| \neq 1$ provided $ \alpha $ has unbounded continued fraction expansion. A second application, which generalizes a theorem originally due to Lord Raleigh, is to give a new proof of a theorem of Fraenkel, namely $ [n \alpha + \gamma]^\infty_{n = 1}$ and $ [n \alpha \prime + \gamma \prime]^\infty_{n = 1}$ partition the non-negative integers if and only if $ 1 / \alpha + 1 / \alpha \prime = 1$ and $ \gamma / \alpha + \gamma \prime / \alpha \prime = 0$ (provided some sign and integer independence conditions are placed on $ \alpha $, $ \beta $, $ \gamma $, $ \gamma \prime $). The analysis which leads to the results is quite delicate and rests heavily on a functional equation for $G$. For this a natural generalization of the simple continued fraction to Kronecker's forms $ |n \alpha + \gamma - m|$ is required.", acknowledgement = ack-nhfb, fjournal = "Journal of Number Theory", journal-URL = "http://www.sciencedirect.com/science/journal/0022314X", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1993:GSO, author = "J. M. Borwein and M. Fabi{\'a}n", title = "On generic second-order {G{\^a}teaux} differentiability", journal = j-NONLINEAR-ANAL, volume = "20", number = "12", pages = "1373--1382", year = "1993", CODEN = "NOANDD", DOI = "https://doi.org/10.1016/0362-546X(93)90166-P", ISSN = "0362-546x (print), 1873-5215 (electronic)", ISSN-L = "0362-546X", MRclass = "46G05 (26E15 49J50 58C20)", MRnumber = "1225345", MRreviewer = "Marcin Studniarski", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1563/; http://www.sciencedirect.com/science/article/pii/0362546X9390166P", acknowledgement = ack-nhfb, fjournal = "Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods", journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis", keywords = "residual space; second-order difference quotient; Separable space; twice G{\^a}teaux differentiability", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Research Report CORR 91-18.", } @Article{Borwein:1993:HAA, author = "J. Borwein and P. Borwein and F. Garvan", title = "Hypergeometric analogues of the arithmetic--geometric mean iteration", journal = j-CONST-APPROX, volume = "9", number = "4", pages = "509--523", year = "1993", DOI = "https://doi.org/10.1007/BF01204654", ISSN = "0176-4276 (print), 1432-0940 (electronic)", ISSN-L = "0176-4276", MRclass = "33C05", MRnumber = "1237931", MRreviewer = "Bruce C. Berndt", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1556/; http://link.springer.com/article/10.1007/BF01204654", acknowledgement = ack-nhfb, fjournal = "Constructive Approximation. An International Journal for Approximations and Expansions", journal-URL = "http://link.springer.com/journal/365", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1993:ICM, author = "Jonathan M. Borwein and Peter B. Borwein", title = "Inequalities for Compound Mean Iterations with Logarithmic Asymptotes", journal = j-J-MATH-ANAL-APPL, volume = "177", number = "2", pages = "572--582", year = "1993", CODEN = "JMANAK", DOI = "https://doi.org/10.1006/jmaa.1993.1278", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "33B99", MRnumber = "1231502", MRreviewer = "P. Anandani", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1553/; http://www.sciencedirect.com/science/article/pii/S0022247X83712783", abstract = "We consider the compound means arising as limits from the arithmetic--geometric mean iteration and related iterations. Each of these iterations possesses a logarithmic asymptote. We show that these limit means satisfy very precise inequalities. These can be deduced in a quite uniform fashion from a `comparison lemma' for compound means.", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1993:LLFa, author = "J. M. Borwein and M. Fabian and J. Vanderwerff", title = "Locally {Lipschitz} Functions and Bornological Derivatives", journal = "ArXiv Mathematics e-prints", month = feb, year = "1993", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/1993math......2211B; http://docserver.carma.newcastle.edu.au/69/", abstract = "We study the relationships between G{\^a}teaux, weak Hadamard and Frechet differentiability and their bornologies for Lipschitz and for convex functions. In particular, Frechet and weak Hadamard differentiability coincide for all Lipschitz functions if and only if the space is reflexive (an earlier paper of the first two authors shows that these two notions of differentiability coincide for continuous convex functions if and only if the space does not contain a copy of $ \ell_1$). We also examine when G{\^a}teaux and weak Hadamard differentiability coincide for continuous convex functions. For instance, spaces with the Dunford--Pettis (Schur) property can be characterized by the coincidence of G{\^a}teaux and weak Hadamard (Frechet) differentiability for dual norms.", acknowledgement = ack-nhfb, eprint = "math/9302211", keywords = "Mathematics - Functional Analysis, 46B", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1993:LLFb, author = "Jonathan M. Borwein and Marian Fabian and Jon Vanderwerff", title = "Locally {Lipschitz} functions and bornological derivatives", type = "CECM Research Report", number = "93:012", institution = inst-CECM, address = inst-CECM:adr, month = nov, year = "1993", bibdate = "Tue Aug 16 10:06:43 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/69/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1993:MMB, author = "Jonathan M. Borwein and Peter B. Borwein", title = "Mathematical Malaises: Book Review: {{\booktitle{Pi in the sky: counting, thinking and being}}, John D. Barrow. Clarendon (Oxford University Press), New York, 1992. xii, 317 pp., illus. \$25}", journal = j-SCIENCE, volume = "259", number = "5103", pages = "1928--1930", day = "26", month = mar, year = "1993", CODEN = "SCIEAS", DOI = "https://doi.org/10.1126/science.259.5103.1928", ISSN = "0036-8075 (print), 1095-9203 (electronic)", ISSN-L = "0036-8075", bibdate = "Sat Sep 03 09:11:44 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.ncbi.nlm.nih.gov/pubmed/17836254", acknowledgement = ack-nhfb, fjournal = "Science (New York, N.Y.)", journal-URL = "http://www.sciencemag.org/archive/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", report-number = "Borwein, Jonathan/A-6082-2009", } @Article{Borwein:1993:PFP, author = "Jonathan M. Borwein and Adrian S. Lewis", title = "Partially-finite programming in {$ L_1 $} and the existence of maximum entropy estimates", journal = j-SIAM-J-OPT, volume = "3", number = "2", pages = "248--267", year = "1993", CODEN = "SJOPE8", DOI = "https://doi.org/10.1137/0803012", ISSN = "1052-6234 (print), 1095-7189 (electronic)", ISSN-L = "1052-6234", MRclass = "90C48 (49N15 65K05)", MRnumber = "1215444", MRreviewer = "M. Teboulle", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1558/", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Optimization", journal-URL = "http://epubs.siam.org/siopt", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1993:PSPa, author = "Jonathan M. Borwein", title = "Problems and Solutions: Problems: 10281", journal = j-AMER-MATH-MONTHLY, volume = "100", number = "1", pages = "76--77", month = jan, year = "1993", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2324828", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.jstor.org/journals/00029890.htm; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1993:PSPb, author = "David Borwein and Jonathan Borwein", title = "Problems and Solutions: Problems: 10335", journal = j-AMER-MATH-MONTHLY, volume = "100", number = "8", pages = "796--798", month = oct, year = "1993", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2324793", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.jstor.org/journals/00029890.htm; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:1993:SCR, author = "Jonathan M. Borwein and Adrian S. Lewis", editor = "A. Mohammad-Djafari and G. Demoments", booktitle = "Maximum entropy and {Bayesian} methods ({Paris}, 1992)", title = "A Survey of Convergence Results for Maximum Entropy Methods", volume = "53", publisher = pub-KLUWER, address = pub-KLUWER:adr, pages = "39--48", year = "1993", DOI = "https://doi.org/10.1007/978-94-017-2217-9_5", MRclass = "49J45 (41A30 42A10)", MRnumber = "1269789", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Fund. Theories Phys.", URL = "http://link.springer.com/chapter/10.1007/978-94-017-2217-9_5", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Research Report CORR 92-32.", } @Article{Borwein:1993:SEV, author = "J. M. Borwein and D. Zhuang", title = "Super efficiency in vector optimization", journal = j-TRANS-AM-MATH-SOC, volume = "338", number = "1", pages = "105--122", year = "1993", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/2154446", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "90C29 (52A41)", MRnumber = "1098432", MRreviewer = "Bernard Lemaire", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1993:WHS, author = "Jonathan M. Borwein and Simon Fitzpatrick", title = "A weak {Hadamard} smooth renorming of {$ L_1 (\Omega, \mu) $}", journal = j-CAN-MATH-BULL, volume = "36", number = "4", pages = "407--413", year = "1993", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1993-055-5", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", MRclass = "46B25 (46B03 46B20 46E30)", MRnumber = "1245313", MRreviewer = "W. A. J. Luxemburg", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://cms.math.ca/10.4153/CMB-1993-055-5; http://docserver.carma.newcastle.edu.au/1554/", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Byerly:1993:PSP, author = "Robert E. Byerly and Murray S. Klamkin and A. Liu and Stephen M. {Gagola, Jr.} and L. E. Mattics and Raphael M. Robinson and M. Al-Ahmar and Donald E. Knuth and Jonathan M. Borwein", title = "Problems and Solutions: Problems: 10274--10281", journal = j-AMER-MATH-MONTHLY, volume = "100", number = "1", pages = "75--77", year = "1993", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2324823", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1542259", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Hirschhorn:1993:CAJ, author = "Michael Hirschhorn and Frank Garvan and Jon Borwein", title = "Cubic analogues of the {Jacobian} theta function {$ \theta (z, q) $}", journal = j-CAN-J-MATH, volume = "45", number = "4", pages = "673--694", month = "????", year = "1993", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1993-038-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "33D10 (11F27)", MRnumber = "1227653", MRreviewer = "Bruce C. Berndt", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://cms.math.ca/cjm/v45/; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/canjmath1990.bib", URL = "http://docserver.carma.newcastle.edu.au/1557/", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Richter:1993:PSP, author = "R. Bruce Richter and Josef Siran and Carl Pomerance and Kiran S. Kedlaya and Michael Golomb and John Sarli and David Borwein and Jonathan Borwein and Ignacy I. Kotlarski and Horst Alzer", title = "Problems and Solutions: Problems: 10330--10337", journal = j-AMER-MATH-MONTHLY, volume = "100", number = "8", pages = "796--798", year = "1993", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2324792", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1542408", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bailey:1994:EEE, author = "David H. Bailey and Jonathan M. Borwein and Roland Girgensohn", title = "Experimental evaluation of {Euler} sums", journal = j-EXP-MATH, volume = "3", number = "1", pages = "17--30", year = "1994", CODEN = "????", DOI = "https://doi.org/10.1080/10586458.1994.10504573", ISSN = "1058-6458 (print), 1944-950X (electronic)", ISSN-L = "1058-6458", MRclass = "11Y60", MRnumber = "1302815", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://projecteuclid.org/euclid.em; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/expmath.bib", URL = "http://docserver.carma.newcastle.edu.au/60/; http://projecteuclid.org/euclid.em/1062621000", acknowledgement = ack-nhfb, fjournal = "Experimental Mathematics", journal-URL = "http://www.tandfonline.com/loi/uexm20", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bauschke:1994:DAP, author = "H. H. Bauschke and J. M. Borwein", title = "{Dykstra}'s alternating projection algorithm for two sets", journal = j-J-APPROX-THEORY, volume = "79", number = "3", pages = "418--443", year = "1994", CODEN = "JAXTAZ", DOI = "https://doi.org/10.1006/jath.1994.1136", ISSN = "0021-9045 (print), 1096-0430 (electronic)", ISSN-L = "0021-9045", MRclass = "41A65 (46N10 47N10)", MRnumber = "1305442", MRreviewer = "F. Deutsch", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1543/; http://www.sciencedirect.com/science/article/pii/S0021904584711361", abstract = "We analyze Dykstra's algorithm for two arbitrary closed convex sets in a Hilbert space. Our technique also applies to von Neumann's algorithm. Various convergence results follow. An example allows one to compare qualitative and quantitative behaviour of the two algorithms. We discuss the case of finitely many sets.", acknowledgement = ack-nhfb, 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", } @Article{Borwein:1994:CMI, author = "Jonathan Borwein", title = "A convergent mean iteration: a proof that {$ x_n \coloneq M(x_{n - 1}, x_{n - 2}, \cdots, x_{n - k}) $} converges", journal = j-AEQUATIONES-MATHEMATICAE, volume = "47", number = "1", pages = "115--118", year = "1994", CODEN = "AEMABN", DOI = "https://doi.org/10.1007/BF01838145", ISSN = "0001-9054 (print), 1420-8903 (electronic)", ISSN-L = "0001-9054", MRclass = "39B12", MRnumber = "1251136", MRreviewer = "Shigeru Haruki", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1541/", acknowledgement = ack-nhfb, fjournal = "Aequationes Mathematicae", journal-URL = "http://link.springer.com/journal/10", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1994:DKK, author = "Jon Borwein and Jon Vanderwerff", title = "Dual {Kadec--Klee} norms and the relationships between {Wijsman}, slice, and {Mosco} convergence", journal = j-MICH-MATH-J, volume = "41", number = "2", pages = "371--387", year = "1994", CODEN = "MIMJA5", DOI = "https://doi.org/10.1307/mmj/1029005003", ISSN = "0026-2285 (print), 1945-2365 (electronic)", ISSN-L = "0026-2285", MRclass = "46B10 (46B20 46N10 49J45 54B20)", MRnumber = "1278442", MRreviewer = "Simon Fitzpatrick", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "The Michigan Mathematical Journal", 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:ECFa, author = "Jon Borwein and Simon Fitzpatrick and Jon Vanderwerff", title = "Examples of convex functions and classifications of normed spaces", journal = j-J-CONVEX-ANAL, volume = "1", number = "1", pages = "61--73", year = "1994", ISSN = "0944-6532 (print), 2363-6394 (electronic)", MRclass = "46B20 (26B25 46B10 46N10 52A41)", MRnumber = "1326942", MRreviewer = "Roland Durier", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/64/; http://www.heldermann-verlag.de/jca/jca01/jca01004.pdf", acknowledgement = ack-nhfb, fjournal = "Journal of Convex Analysis", journal-URL = "http://www.heldermann.de/JCA/jcacon.htm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1994:EML, author = "Jonathan M. Borwein and Adrian S. Lewis and Mark A. Limber", title = "Entropy Minimization with Lattice Bounds", journal = j-J-APPROX-THEORY, volume = "79", number = "1", pages = "1--16", year = "1994", CODEN = "JAXTAZ", DOI = "https://doi.org/10.1006/jath.1994.1110", ISSN = "0021-9045 (print), 1096-0430 (electronic)", ISSN-L = "0021-9045", MRclass = "41A46 (41A29 90C48)", MRnumber = "1294317", MRreviewer = "Dominikus Noll", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1545/; http://www.sciencedirect.com/science/article/pii/S0021904584711105", abstract = "We characterize solutions to the problem of minimizing a convex integral objective function subject to a finite number of linear constraints and requiring that the feasible functions lie in a strip $ [\alpha, \beta] $ where $ \alpha $ and $ \beta $ are extended real valued measurable functions. We use the duality theory of J. M. Borwein and A. S. Lewis (Math. Programming, Series \{B57\} (1992), 15-48, 49-84) to show that the solutions are of the usual form, but truncated where they leave the strip.", acknowledgement = ack-nhfb, fjournal = "Journal of Approximation Theory", journal-URL = "http://www.sciencedirect.com/science/journal/00219045", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1994:EMPa, author = "Jonathan M. Borwein and Adrian S. Lewis and Roger D. Nussbaum", title = "Entropy Minimization, {$ D A D $} Problems, and Doubly Stochastic Kernels", journal = j-J-FUNCT-ANAL, volume = "123", number = "2", pages = "264--307", year = "1994", CODEN = "JFUAAW", DOI = "https://doi.org/10.1006/jfan.1994.1089", ISSN = "0022-1236 (print), 1096-0783 (electronic)", ISSN-L = "0022-1236", MRclass = "47N10 (47B99 47H15 49N15 90C30)", MRnumber = "1283029", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1546/; http://www.sciencedirect.com/science/article/pii/S0022123684710895", abstract = "The classical $ D A D $ problem asks, for a square matrix $A$ with nonnegative entries, when it is possible to find positive diagonal matrices $ D_1$ and $ D_2$ with $ D_1 A D_2$ doubly stochastic. We consider various continuous and measurable generalizations of this problem. Through a fusion of variational and fixed point techniques we obtain strong analogues of the classical results. Our extensions appear inaccessible by either technique separately.", acknowledgement = ack-nhfb, fjournal = "Journal of Functional Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/00221236", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1994:FAS, author = "Jon Borwein and Jon Vanderwerff", title = "Further arguments for slice convergence in nonreflexive spaces", journal = j-SET-VALUED-ANAL, volume = "2", number = "4", pages = "529--544", year = "1994", CODEN = "SVANEG", DOI = "https://doi.org/10.1007/BF01033070", ISSN = "0927-6947 (print), 1572-932x (electronic)", ISSN-L = "0927-6947", MRclass = "49J45 (46N10 54B20)", MRnumber = "1308483", MRreviewer = "Gerald Beer", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/62/", acknowledgement = ack-nhfb, fjournal = "Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications", journal-URL = "http://link.springer.com/journal/11228", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1994:FED, author = "Jonathan M. Borwein and Roland Girgensohn", title = "Functional equations and distribution functions", journal = "Results Math.", volume = "26", number = "3--4", pages = "229--237", year = "1994", DOI = "https://doi.org/10.1007/BF03323043", ISSN = "0378-6218", ISSN-L = "0378-6218", MRclass = "39B22 (39B62 60E05 62E15)", MRnumber = "1300602", MRreviewer = "K. Lajk{\'o}", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "For Janos Aczel's 70th birthday.", URL = "http://docserver.carma.newcastle.edu.au/90/", acknowledgement = ack-nhfb, fjournal = "Results in Mathematics. Resultate der Mathematik", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1994:NRS, author = "Jonathan M. Borwein and Mari{\'a}n Fabi{\'a}n", title = "A note on regularity of sets and of distance functions in {Banach} space", journal = j-J-MATH-ANAL-APPL, volume = "182", number = "2", pages = "566--570", year = "1994", CODEN = "JMANAK", DOI = "https://doi.org/10.1006/jmaa.1994.1104", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "49J52", MRnumber = "1269478", MRreviewer = "Doug Ward", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022247X84711048", abstract = "We show that in every infinite dimensional Banach space there is a compact set C and x in C such that C is regular at x (in the sense of nonsmooth analysis) but such that the associated distance function dC is not regular at x and neither is -dC.", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1994:SCM, author = "J. M. Borwein and P. B. Borwein and F. G. Garvan", title = "Some cubic modular identities of {Ramanujan}", journal = j-TRANS-AM-MATH-SOC, volume = "343", number = "1", pages = "35--47", month = may, year = "1994", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/2154520", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "11B65 (11F27 33D10)", MRnumber = "1243610", MRreviewer = "George E. Andrews", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1547/; http://www.jstor.org/stable/2154520", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1994:SOD, author = "Jonathan M. Borwein and Dominikus Noll", title = "Second order differentiability of convex functions in {Banach} spaces", journal = j-TRANS-AM-MATH-SOC, volume = "342", number = "1", pages = "43--81", month = mar, year = "1994", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/2154684", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "46G05 (26E15)", MRnumber = "1145959", MRreviewer = "Lud{\v{e}}k Zaj{\'{\i}}{\v{c}}ek", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1549/; http://www.jstor.org/stable/2154684", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1994:SRO, author = "Jonathan M. Borwein and Adrian S. Lewis", title = "Strong rotundity and optimization", journal = j-SIAM-J-OPT, volume = "4", number = "1", pages = "146--158", year = "1994", CODEN = "SJOPE8", DOI = "https://doi.org/10.1137/0804008", ISSN = "1052-6234 (print), 1095-7189 (electronic)", ISSN-L = "1052-6234", MRclass = "49K27 (90C48)", MRnumber = "1260412", MRreviewer = "T. Zolezzi", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1550/", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Optimization", journal-URL = "http://epubs.siam.org/siopt", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1994:STE, author = "David Borwein and Jonathan M. Borwein", title = "On Some Trigonometric and Exponential Lattice Sums", journal = j-J-MATH-ANAL-APPL, volume = "188", number = "1", pages = "209--218", year = "1994", CODEN = "JMANAK", DOI = "https://doi.org/10.1006/jmaa.1994.1422", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "11L03 (11L07)", MRnumber = "1301727", MRreviewer = "Gunter Dufner", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1542/; http://www.sciencedirect.com/science/article/pii/S0022247X84714223", abstract = "Certain two-dimensional trigonometric lattice series, the ordinary convergence of which involves unresolved questions of a deep and delicate number-theoretic nature, are shown to be summable by a special Abelian method and their Abelian sums are obtained. This is done by first evaluating an absolutely convergent exponential lattice series and then analytically extending its sum.", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1994:UCM, author = "J. M. Borwein and W. Huang", title = "Uniform convergence for moment problems with {Fermi--Dirac} type entropies", journal = j-ZOR-MATH-METHODS-OPER-RES, volume = "40", number = "3", pages = "239--252", year = "1994", CODEN = "ZMRREP", DOI = "https://doi.org/10.1007/BF01432968", ISSN = "0340-9422", MRclass = "90C45 (44A60)", MRnumber = "1316390", MRreviewer = "Dominikus Noll", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/70/; http://link.springer.com/article/10.1007/BF01432968", acknowledgement = ack-nhfb, fjournal = "Zeitschrift f{\"u}r Operations Research. Mathematical Methods of Operations Research", journal-URL = "http://link.springer.com/journal/186", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1994:UMP, author = "J. M. Borwein and M. A. Limber", title = "Underdetermined moment problems: a case for convex analysis", journal = "SIAG/OPT", volume = "??", number = "5", pages = "9--13", month = "Fall", year = "1994", DOI = "", bibdate = "Mon Aug 15 14:52:57 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Invited talk at 1994 SIAM Conference on Optimization.", URL = "", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Which journal is this??", } @InProceedings{Bailey:1995:FNI, author = "D. H. Bailey and J. M. Borwein and R. Girgensohn", editor = "????", booktitle = "{SIAM Conference on Parallel Computing, San Francisco, February 1995}", title = "Finding new identities with supercomputers", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "??--??", year = "1995", bibdate = "Mon Aug 15 14:48:40 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Bauschke:1995:CLM, author = "H. H. Bauschke and J. M. Borwein", title = "Continuous linear monotone mappings in {Banach} space", type = "CECM Research Report", number = "95:049", institution = inst-CECM, address = inst-CECM:adr, month = aug, year = "1995", bibdate = "Tue Aug 16 10:12:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/114/", acknowledgement = ack-nhfb, ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", } @Book{Borowski:1995:DCD, author = "Ephraim J. Borowski and Jonathan M. Borwein", title = "Dizionario {Collins} della matematica", publisher = "Gremese Editore", address = "Roma, Italy", pages = "423", year = "1995", ISBN = "88-7605-813-3", ISBN-13 = "978-88-7605-813-4", LCCN = "????", bibdate = "Tue Aug 16 09:08:42 MDT 2016", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Translation to Italian by Andrea Stracca of \cite{Borowski:1991:HDM}.", series = "Dizionari Gremese", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", subject = "Matematica - Enciclopedie e dizionari", } @Book{Borowski:1995:SXC, author = "Ephraim J. Borowski and Jonathan M. Borwein", title = "Shu xue ci dian", volume = "10", publisher = "Mao tou ying chu ban", address = "Taibei", pages = "879", year = "1995", ISBN = "957-0337-14-1", ISBN-13 = "978-957-0337-14-3", LCCN = "????", bibdate = "Tue Aug 16 09:05:36 MDT 2016", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Chinese edition of \cite{Borowski:1991:HDM}.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1995:ATB, author = "Jonathan M. Borwein and Roland Girgensohn", title = "Addition theorems and binary expansions", journal = j-CAN-J-MATH, volume = "47", number = "2", pages = "262--273", year = "1995", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1995-013-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "39B62 (11A63)", MRnumber = "1335077", MRreviewer = "W. Herget", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1537/", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics. Journal Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1995:CCH, author = "Jonathan M. Borwein and Simon Fitzpatrick", title = "Closed convex {Haar} null sets", type = "CECM Research Report", number = "95:052", institution = inst-CECM, address = inst-CECM:adr, month = aug, year = "1995", bibdate = "Tue Aug 16 10:13:27 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/117/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:1995:CCS, author = "J. M. Borwein and S. Fitzpatrick", booktitle = "Proceedings of the Optimization Miniconference II", title = "Characterization of {Clarke} subgradients among one-dimensional multifunctions", publisher = "University of Ballarat", address = "Ballarat, VI, Australia", pages = "5--12", year = "1995", bibdate = "Mon Aug 15 14:41:04 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/23/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1995:CLR, author = "Jonathan M. Borwein and Jon D. Vanderwerff", title = "Convergence of {Lipschitz} regularizations of convex functions", journal = j-J-FUNCT-ANAL, volume = "128", number = "1", pages = "139--162", year = "1995", CODEN = "JFUAAW", DOI = "https://doi.org/10.1006/jfan.1995.1026", ISSN = "0022-1236 (print), 1096-0783 (electronic)", ISSN-L = "0022-1236", MRclass = "49J45 (46N10 49J52)", MRnumber = "1317713", MRreviewer = "Lionel Thibault", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1540/; http://www.sciencedirect.com/science/article/pii/S0022123685710269", abstract = "For a sequence or net of convex functions on a Banach space, we study pointwise convergence of their Lipschitz regularizations and convergence of their epigraphs. The Lipschitz regularizations we will consider are the infimal convolutions of the functions with appropriate multiples of the norm. For a sequence of convex functions on a separable Banach space we show that both pointwise convergence of their Lipschitz regularizations and Wijsman convergence of their epigraphs are equivalent to variants of two conditions used by Attouch and Beer to characterize slice convergence. Results for nonseparable spaces are obtained by separable reduction arguments. As a by-product, slice convergence for an arbitrary net of convex functions can be deduced from the pointwise convergence of their regularizations precisely when the w* and the norm topologies agree on the dual sphere. This extends some known results and answers an open question.", acknowledgement = ack-nhfb, fjournal = "Journal of Functional Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/00221236", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1995:EEEa, author = "David Borwein and Jonathan M. Borwein and Roland Girgensohn", title = "Explicit evaluation of {Euler} sums", journal = j-PROC-EDINBURGH-MATH-SOC-2, volume = "38", number = "2", pages = "277--294", month = jun, year = "1995", CODEN = "PRMSA3", DOI = "https://doi.org/10.1017/S0013091500019088", ISSN = "0013-0915 (print), 1464-3839 (electronic)", ISSN-L = "0013-0915", MRclass = "11M06 (11Y60)", MRnumber = "1335874", MRreviewer = "Bruce C. Berndt", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/58/", acknowledgement = ack-nhfb, fjournal = "Proceedings of the Edinburgh Mathematical Society (2)", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PEM", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1995:FHMa, author = "J. M. Borwein and W. Z. Huang", title = "A fast heuristic method for polynomial moment problems with {Boltzmann--Shannon} entropy", journal = j-SIAM-J-OPT, volume = "5", number = "1", pages = "68--99", year = "1995", CODEN = "SJOPE8", DOI = "https://doi.org/10.1137/0805004", ISSN = "1052-6234 (print), 1095-7189 (electronic)", ISSN-L = "1052-6234", MRclass = "90C45 (44A60 65K05)", MRnumber = "1315705", MRreviewer = "Dominikus Noll", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1539/", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Optimization", journal-URL = "http://epubs.siam.org/siopt", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1995:FHMb, author = "J. M. Borwein and M. N. Limber and D. Noll", title = "Fast heuristic methods for function reconstruction using derivative information", journal = j-APPL-ANAL, volume = "58", number = "3--4", pages = "241--261", year = "1995", CODEN = "APANCC", DOI = "https://doi.org/10.1080/00036819508840375", ISSN = "0003-6811", ISSN-L = "0003-6811", MRclass = "65D15 (49N15 62G05)", MRnumber = "1383191", MRreviewer = "Zdzis{\l}aw W. Trzaska", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1536/", acknowledgement = ack-nhfb, fjournal = "Applicable Analysis. An International Journal", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1995:IIS, author = "David Borwein and Jonathan M. Borwein", title = "On an intriguing integral and some series related to {$ \zeta (4) $}", journal = j-PROC-AM-MATH-SOC, volume = "123", number = "4", pages = "1191--1198", year = "1995", CODEN = "PAMYAR", DOI = "https://doi.org/10.2307/2160718", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "11Y60 (11M06 11Y35 33B15 42A16)", MRnumber = "1231029", MRreviewer = "Henri Joris", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1538/", abstract = "An intriguing log-cosine integral is fully analyzed and shown to have value a rational multiple of $ \zeta (4) $, $ \zeta $ being the Riemann zeta function. From this we deduce by means of generating functions and Parseval's identity the sums of certain series previously established by a completely different method.", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1995:MCF, author = "Jonathan M. Borwein and Kenneth R. Davidson", booktitle = "{Canadian Mathematical Society}. 1945--1995", title = "Mathematics in {Canada}: the future of mathematics in {Canada} 50 years later", volume = "1", publisher = "Canadian Mathematical Society", address = "Ottawa, ON, Canada", pages = "231--268 (249--268 fran{\c{c}}iai)", year = "1995", MRclass = "01A80 (01A67)", MRnumber = "1661625", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Dual English--French text.", series = "CMS Publications", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Unpublished{Borwein:1995:MEMa, author = "J. M. Borwein and P. B. Borwein and R. Girgensohn and S. Parnes", title = "Mathematical Experimentation and Methodology", month = jan, year = "1995", bibdate = "Tue Aug 16 10:07:27 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Unpublished report.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1995:MER, author = "J. M. Borwein and A. S. Lewis and M. N. Limber and D. Noll", title = "Maximum entropy reconstruction using derivative information. {II}. {Computational} results", journal = j-NUM-MATH, volume = "69", number = "3", pages = "243--256", year = "1995", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/s002110050090", ISSN = "0029-599x (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65K10 (65U05)", MRnumber = "1312779", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/71/; http://link.springer.com/article/10.1007/s002110050090", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", xxtitle = "Maximum entropy spectral analysis using first order information. {Part 2}: {A} Numerical Algorithm for {Fisher} information duality", } @TechReport{Borwein:1995:MSE, author = "Jonathan M. Borwein and Peter B. Borwein and Roland Girgensohn and S. Parnes", title = "Making sense of experimental mathematics", type = "CECM preprint", number = "95:032", institution = inst-CECM, address = inst-CECM:adr, year = "1995", bibdate = "Thu Aug 11 09:31:33 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/98/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1995:SCB, author = "Jonathan Borwein and Simon Fitzpatrick", title = "{$ {\rm Weak}^\ast $} sequential compactness and bornological limit derivatives", journal = j-J-CONVEX-ANAL, volume = "2", number = "1--2", pages = "59--67", year = "1995", ISSN = "0944-6532 (print), 2363-6394 (electronic)", MRclass = "49J52 (46G05 47N10 49J40 58C20)", MRnumber = "1363360", MRreviewer = "Nikolay V. Zhivkov", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Dedicated to R. T. Rockafellar on his 60th birthday.", URL = "http://www.heldermann.de/JCA/jcacon.htmvol.2_no.1+2/j4_49.ps.gz", abstract = "In this note we give a self-contained account of the relationship between the sequential and topological constructions of bornological limit derivatives for locally Lipschitzian real-valued functions on Banach spaces.", acknowledgement = ack-nhfb, fjournal = "Journal of Convex Analysis", journal-URL = "http://www.heldermann.de/JCA/jcacon.htm", keywords = "Asplund space; bornological limit derivative; Clarke subgradient; Fr{\'e}chet derivative; Gateaux derivative; subderivative; weak Hadamard derivative; weak* sequential compactness.; weakly compactly generated", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", received = "6 June 1994; revised 15 November 1994", } @InProceedings{Borwein:1995:SEC, author = "Jonathan M. Borwein", editor = "Roland Durier and Chistian Michelot", booktitle = "Recent Developments in Optimization: Seventh {French--German} Conference on Optimization ({Dijon} 1994)", title = "A survey of examples of convex functions and classifications of normed spaces", volume = "429", publisher = pub-SV, address = pub-SV:adr, pages = "60--71", year = "1995", DOI = "https://doi.org/10.1007/978-3-642-46823-0_5", ISBN = "3-642-46823-3", ISBN-13 = "978-3-642-46823-0", LCCN = "QA402.5", MRclass = "46N10 (46B20 49J50)", MRnumber = "1358388", MRreviewer = "A. B. N{\'e}meth", bibdate = "Mon Aug 15 14:50:05 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Lecture Notes in Economic and Mathematical Systems", URL = "http://docserver.carma.newcastle.edu.au/93/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", xxtitle = "A survey of examples of convex functions and the classification of {Banach} spaces", } @Article{Borwein:1995:SRS, author = "Jonathan M. Borwein and Jon D. Vanderwerff", title = "A survey on renorming and set convergence", journal = "Topological Methods in Nonlinear Analysis", volume = "5", number = "2", pages = "211--228", year = "1995", ISSN = "1230-3429", ISSN-L = "1230-3429", MRclass = "46B20 (46G05 46N10 49J45 54B20)", MRnumber = "1374058", MRreviewer = "David Yost", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/97/; https://www.tmna.ncu.pl/static/files/v05n2-01.pdf", acknowledgement = ack-nhfb, ajournal = "Topol. Methods Nonlinear Anal.", fjournal = "Topological Methods in Nonlinear Analysis", journal-URL = "https://www.tmna.ncu.pl/static/archives/archives.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Limber:1995:DRF, author = "M. A. Limber and M. N. Limber and A. Celler and J. S. Barney and J. M. Borwein", title = "Direct reconstruction of functional parameters for dynamic {SPECT}", journal = j-IEEE-TRANS-NUCL-SCI, volume = "42", number = "4", pages = "1249--1256", month = aug, year = "1995", CODEN = "IRNSAM", DOI = "https://doi.org/10.1109/23.467872", ISSN = "0018-9499 (print), 1558-1578 (electronic)", ISSN-L = "0018-9499", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/1995ITNS...42.1249L; http://docserver.carma.newcastle.edu.au/1535/", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Nuclear Science", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bauschke:1996:PAS, author = "Heinz H. Bauschke and Jonathan M. Borwein", title = "On Projection Algorithms for Solving Convex Feasibility Problems", journal = j-SIAM-REVIEW, volume = "38", number = "3", pages = "367--426", month = sep, year = "1996", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/S0036144593251710", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "90C25 (47N10 49M45 65J10)", MRnumber = "1 409 591", MRreviewer = "F. Deutsch", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "Compendex database; http://epubs.siam.org/toc/siread/38/3; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib; http://www.siam.org/journals/sirev/sirev383.htm", URL = "http://docserver.carma.newcastle.edu.au/100/; http://epubs.siam.org/sam-bin/dbq/article/25171", abstract = "Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and flexible framework is investigated. Several crucial new concepts which allow a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence are brought out. Numerous examples are given.", acknowledgement = ack-nhfb, affiliation = "Simon Fraser Univ", affiliationaddress = "BC, Can", classification = "723.2; 723.5; 921.5; 921.6; B0250 (Combinatorial mathematics); B0260 (Optimisation techniques); B0290F (Interpolation and function approximation); B6140C (Optical information, image and video signal processing); C1160 (Combinatorial mathematics); C1180 (Optimisation techniques); C1250 (Pattern recognition); C4130 (Interpolation and function approximation)", corpsource = "Dept. of Math. and Stat., Simon Fraser Univ., Burnaby, BC, Canada", fjournal = "SIAM Review. A Publication of the Society for Industrial and Applied Mathematics", journal-URL = "http://epubs.siam.org/sirev", journalabr = "SIAM Rev", keywords = "Algorithms; Approximation theory; Classical mathematics; computerised tomography; Computerized tomography; computerized tomography; convergence of numerical methods; Convergence of numerical methods; convex feasibility; Convex feasibility problems; Convex inequalities; Convex programming; convex programming; Functions; Hilbert spaces; Image reconstruction; image reconstruction; image recovery; iterative method; Iterative methods; iterative methods; Linear convergence; linear convergence; linear inequality; Mathematical programming; Problem solving; Projection algorithms; projection algorithms; set theory; Subgradient algorithm; subgradient algorithm", onlinedate = "September 1996", ORCID-numbers = "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", } @Article{Borwein:1996:ASC, author = "D. Borwein and J. M. Borwein and Xianfu Wang", title = "Approximate subgradients and coderivatives in {$ {\bf R}^n $}", journal = j-SET-VALUED-ANAL, volume = "4", number = "4", pages = "375--398", year = "1996", CODEN = "SVANEG", DOI = "https://doi.org/10.1007/BF00436112", ISSN = "0927-6947 (print), 1572-932x (electronic)", ISSN-L = "0927-6947", MRclass = "49J52", MRnumber = "1422402", MRreviewer = "Doug Ward", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/152/; http://link.springer.com/article/10.1007/BF00436112", acknowledgement = ack-nhfb, fjournal = "Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications", journal-URL = "http://link.springer.com/journal/11228", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1996:BRE, author = "Jonathan M. Borwein and Rob M. Corless", title = "Book Review: {{\booktitle{The Encyclopedia of Integer Sequences}}, by N. J. A. Sloane and Simon Plouffe. Academic Press, San Diego, CA, 1995. \$44.95. xii + 587 pp., hardcover. ISBN 0-12-558630-2}", journal = j-SIAM-REVIEW, volume = "38", number = "2", pages = "333--337", month = jun, year = "1996", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1038058", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Wed Aug 31 09:45:28 2016", bibsource = "http://epubs.siam.org/toc/siread/38/2; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "http://www.jstor.org/stable/2132886", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "June 1996", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1996:BSAa, author = "J. M. Borwein and J. D. Vanderwerff", title = "{Banach} spaces that admit support sets", journal = j-PROC-AM-MATH-SOC, volume = "124", number = "3", pages = "751--755", year = "1996", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/S0002-9939-96-03122-X", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "46B20 (46B03)", MRnumber = "1301010", MRreviewer = "Catherine Finet", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/87/", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1996:BSAb, author = "J. M. Borwein and J. D. Vanderwerff", title = "{Banach} spaces that admit support sets", journal = j-PROC-AM-MATH-SOC, volume = "124", number = "3", pages = "751--756", month = mar, year = "1996", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/S0002-9939-96-03122-X", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", bibdate = "Fri Aug 12 12:16:08 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/87/; http://www.ams.org/journals/proc/1996-124-03/S0002-9939-96-03122-X/", abstract = "It is shown that the existence of a closed convex set all of whose points are properly supported in a Banach space is equivalent to the existence of a certain type of uncountable ordered one-sided biorthogonal system. Under the continuum hypothesis, we deduce that this notion is weaker than the existence of an uncountable biorthogonal system.", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1996:DAM, author = "Jonathan M. Borwein and Peter B. Borwein and Stephen Braham and Robert Corless and Loki J{\"o}rgenson", title = "Digitally Activated Mathematics for a Brave New {World Wide Web}", journal = "Education, Research and Perspectives", volume = "23", number = "2", pages = "28--47", month = dec, year = "1996", ISSN = "0311-2543 (print), 1446-0017 (electronic)", ISSN-L = "0311-2543", bibdate = "Fri Aug 12 12:03:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Special issue on multimedia technologies and education.", URL = "http://docserver.carma.newcastle.edu.au/1533/; http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:13132; https://search.informit.com.au/documentSummary%3Bdn=970909729%3Bres=IELAPA", acknowledgement = ack-nhfb, journal-URL = "http://www.erpjournal.net/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "The journal Web site has no online archives before year 2000.", } @Article{Borwein:1996:EFE, author = "Jonathan M. Borwein and David M. Bradley and David J. Broadhurst", title = "Evaluations of $k$-fold {Euler\slash Zagier} sums: a compendium of results for arbitrary $k$", journal = "ArXiv High Energy Physics --- Theory e-prints", month = nov, year = "1996", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/1996hep.th...11004B; http://arxiv.org/abs/hep-th/9611004", abstract = "Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theory. There are various conjectures related to these sums whose incompletion is a sign that both the mathematics and physics communities do not yet completely understand the field. Here, we assemble results for Euler/Zagier sums (also known as multidimensional zeta/harmonic sums) of arbitrary depth, including sign alternations. Many of our results were obtained empirically and are apparently new. By carefully compiling and examining a huge data base of high precision numerical evaluations, we can claim with some confidence that certain classes of results are exhaustive. While many proofs are lacking, we have sketched derivations of all results that have so far been proved.", acknowledgement = ack-nhfb, eprint = "hep-th/9611004", keywords = "High Energy Physics - Theory", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1996:ETE, author = "Jonathan M. Borwein and Roland Girgensohn", title = "Evaluation of triple {Euler} sums", journal = j-ELECT-J-COMB, volume = "3", number = "1", pages = "Research Paper 23", year = "1996", ISSN = "1077-8926 (print), 1097-1440 (electronic)", ISSN-L = "1077-8926", MRclass = "11M99 (11Y60)", MRnumber = "1401442", MRreviewer = "Bruce C. Berndt", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/118/; http://www.combinatorics.org/Volume_3/Abstracts/v3i1r23.html", acknowledgement = ack-nhfb, fjournal = "Electronic Journal of Combinatorics", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", pagecount = "27", } @Article{Borwein:1996:EUC, author = "Jonathan M. Borwein and Jon D. Vanderwerff", title = "Epigraphical and uniform convergence of convex functions", journal = j-TRANS-AM-MATH-SOC, volume = "348", number = "4", pages = "1617--1631", month = apr, year = "1996", CODEN = "TAMTAM", DOI = "https://doi.org/10.1090/S0002-9947-96-01581-4", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "49J45 (46A55 46B20 46N10 52A41)", MRnumber = "1344203", MRreviewer = "W. W. Breckner", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/94/; http://www.jstor.org/stable/2155155", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1996:GCP, author = "D. Borwein and J. M. Borwein and P. B. Borwein and R. Girgensohn", title = "{Giuga}'s conjecture on primality", journal = j-AMER-MATH-MONTHLY, volume = "103", number = "1", pages = "40--50", year = "1996", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2975213", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "11A25", MRnumber = "1369150", MRreviewer = "Andrew Granville", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/88/", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1996:MER, author = "J. M. Borwein and A. S. Lewis and D. Noll", title = "Maximum entropy reconstruction using derivative information. {I}. {Fisher} information and convex duality", journal = j-MATH-OP-RES, volume = "21", number = "2", pages = "442--468", year = "1996", CODEN = "MOREDQ", DOI = "https://doi.org/10.1287/moor.21.2.442", ISSN = "0364-765x (print), 1526-5471 (electronic)", ISSN-L = "0364-765X", MRclass = "90C48 (49N15)", MRnumber = "1397223", MRreviewer = "Vaithilingam Jeyakumar", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/82/", acknowledgement = ack-nhfb, fjournal = "Mathematics of Operations Research", journal-URL = "http://pubsonline.informs.org/loi/moor", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1996:MSE, author = "Jonathan Borwein and Peter B. Borwein and Roland Girgensohn and S. Parnes", title = "Making sense of experimental mathematics", journal = j-MATH-INTEL, volume = "18", number = "4", pages = "12--18", month = "Fall", year = "1996", CODEN = "MAINDC", DOI = "https://doi.org/10.1007/BF03026747", ISSN = "0343-6993 (print), 1866-7414 (electronic)", ISSN-L = "0343-6993", MRclass = "00A35", MRnumber = "1413248", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/98/", acknowledgement = ack-nhfb, fjournal = "The Mathematical Intelligencer", journal-URL = "http://link.springer.com/journal/283", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "This entry appears to be contained in \cite{Octavio:1996:IT}. Is it a separate paper??", } @Article{Borwein:1996:PAS, author = "Jonathan M. Borwein and Alexander Ioffe", title = "Proximal analysis in smooth spaces", journal = j-SET-VALUED-ANAL, volume = "4", number = "1", pages = "1--24", year = "1996", CODEN = "SVANEG", DOI = "https://doi.org/10.1007/BF00419371", ISSN = "0927-6947 (print), 1572-932x (electronic)", ISSN-L = "0927-6947", MRclass = "49J52 (46N10 58C20)", MRnumber = "1384247", MRreviewer = "Philip D. Loewen", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/61/", acknowledgement = ack-nhfb, fjournal = "Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications", journal-URL = "http://link.springer.com/journal/11228", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1996:PSR, author = "Jonathan M. Borwein", title = "Problems and Solutions: Revivals: 10281", journal = j-AMER-MATH-MONTHLY, volume = "103", number = "10", pages = "911--912", year = "1996", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1542929", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://links.jstor.org/sici?sici=0002-9890(199612)103:10<911:1>2.0.CO%3B2-5&origin=MSN", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1996:PSS, author = "Jonathan M. Borwein and Donald A. Darling and D. B. Tyler", title = "Problems and Solutions: Solutions: 10281", journal = j-AMER-MATH-MONTHLY, volume = "103", number = "2", pages = "181--183", year = "1996", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2975121", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1542802", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1996:SRZ, author = "Jonathan M. Borwein and Peter B. Borwein", title = "{Srinivasa Ramanujan und die Zahl Pi}. ({German}) [{Srinivasa Ramanujan} and the number $ \pi $]", crossref = "Faltings:1996:MM", pages = "60--68", year = "1996", bibdate = "Fri Aug 12 14:57:29 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Reprint of \cite{Borwein:1988:RP}.", URL = "http://docserver.carma.newcastle.edu.au/1379/", acknowledgement = ack-nhfb, language = "German", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", xxtitle = "{Ramanujan} and {Pi}", } @Article{Borwein:1996:SSA, author = "Jonathan Borwein and David Bradley", title = "Searching Symbolically for {Ap{\'e}ry}-like Formulae for Values of the {Riemann} Zeta Function", journal = j-SIGSAM, volume = "30", number = "2", pages = "2--7", month = jun, year = "1996", CODEN = "SIGSBZ", DOI = "https://doi.org/10.1145/235699.235700", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Wed Aug 10 12:08:56 2016", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", URL = "http://docserver.carma.newcastle.edu.au/170/; http://doi.acm.org/10.1145/235699.235700", acknowledgement = ack-nhfb, acmid = "235700", classcodes = "C7310 (Mathematics computing)", corpsource = "Centre for Exp. and Constructive Math., Simon Fraser Univ., Burnaby, BC, Canada", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "116", issue-date = "June 1996", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "algebra; Apery-like formulae; computer; formal proof; functions; Riemann Zeta function; special values; symbol manipulation; symbolic methods", numpages = "6", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", treatment = "T Theoretical or Mathematical", } @Article{Borwein:1996:VSV, author = "Jonathan M. Borwein and Qiji J. Zhu", title = "Viscosity solutions and viscosity subderivatives in smooth {Banach} spaces with applications to metric regularity", journal = j-SIAM-J-CONTROL-OPTIM, volume = "34", number = "5", pages = "1568--1591", year = "1996", CODEN = "SJCODE", DOI = "https://doi.org/10.1137/S0363012994268801", ISSN = "0363-0129 (print), 1095-7138 (electronic)", ISSN-L = "0363-0129", MRclass = "49L25 (49J52 49N10)", MRnumber = "1404847", MRreviewer = "Abderrahim Jourani", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/80/", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Control and Optimization", journal-URL = "http://epubs.siam.org/sicon", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Octavio:1996:IT, author = "Alfredo Octavio and Jonathan Borwein and Peter B. Borwein and Roland Girgensohn and S. Parnes", title = "The ``indexed'' theorem", journal = j-MATH-INTEL, volume = "18", number = "4", pages = "9--18", month = sep, year = "1996", CODEN = "MAINDC", DOI = "https://doi.org/10.1007/bf03026747", ISSN = "0343-6993 (print), 1866-7414 (electronic)", ISSN-L = "0343-6993", bibdate = "Thu Aug 11 09:28:04 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "The Mathematical Intelligencer", journal-URL = "http://link.springer.com/journal/283", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bailey:1997:KC, author = "David H. Bailey and Jonathan M. Borwein and Richard E. Crandall", title = "On the {Khintchine} constant", journal = j-MATH-COMPUT, volume = "66", number = "217", pages = "417--431", year = "1997", CODEN = "MCMPAF", DOI = "https://doi.org/10.1090/S0025-5718-97-00800-4", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "11Y60 (11K50 11Y65)", MRnumber = "1377659", MRreviewer = "T. Mets{\"a}nkyl{\"a}", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/1997MaCom..66..417B; http://docserver.carma.newcastle.edu.au/102/", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bailey:1997:QP, author = "D. H. Bailey and J. M. Borwein and P. B. Borwein and S. Plouffe", title = "The quest for pi", journal = j-MATH-INTEL, volume = "19", number = "1", pages = "50--57", year = "1997", CODEN = "MAINDC", DOI = "https://doi.org/10.1007/BF03024340", ISSN = "0343-6993 (print), 1866-7414 (electronic)", ISSN-L = "0343-6993", MRclass = "01A99", MRnumber = "1439159", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/164/", acknowledgement = ack-nhfb, fjournal = "The Mathematical Intelligencer", journal-URL = "http://link.springer.com/journal/283", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Bailey:1997:RME, author = "D. H. Bailey and J. M. Borwein and P. B. Borwein", title = "{Ramanujan}, modular equations, and approximations to pi or {How} to compute one billion digits of pi [{MR0991866} (90d:11143)]", crossref = "Borwein:1997:OMP", pages = "35--71", year = "1997", ISSN = "0731-1036", ISSN-L = "0731-1036", MRclass = "11Y60 (01A60 11F03 33E20)", MRnumber = "1483913", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/pi.bib", note = "Reprint of \cite{Borwein:1989:RME}.", series = "CMS Conference Proceedings", URL = "http://docserver.carma.newcastle.edu.au/1587/; http://www.cecm.sfu.ca/organics/papers/borwein/index.html", abstract = "The article underlying our contribution started life in 1986 when David Bailey and Jon and Peter B. Borwein began to write separate pieces on ``Pi and its computation'' for the MAA Monthly. With urging from Herb Wilf (the then editor) the authors joined forces and a joint paper issued forth that was published in 1989. Since 1989, while the computers have continued to improve and the computation of has continued unabated, the underlying mathematical and computational techniques being employed are still much as described in the printed piece.\par We opted to use this article as our contribution to Organic Mathematics for several reasons: it is reasonably accessible; it clearly allows for ``enhancement''; it was complete as a written piece and so allowed us to concentrate on the key issues underlying the larger project. Moreover, it tells a 3,000 year story touching many themes (from transcendence theory, to elliptic functions, and the Fast Fourier Transform) and involving many great thinkers (Archimedes, Newton, Gauss, Euler, Ramanujan, Von Neumann, Hilbert). In sum then we felt that the article provided an exellent test-bed to try out what would work in a multi-modal mathematical environment.\par A project like this presents several challenges for the mathematician as multi-media author. First, the technology is changing so quickly that tools uninvented when the project began are sure to be obsolete before it is finished. Second, it involves a super-highway to be sure but one running through terra incognita. At many levels one must balance the issues of form and function, speed and scope. The version presently before you looks little like the one of six months ago --- small changes to the interface can greatly enhance or reduce readability.\par The opportunities are great. Within this article, you will see the bust of Ramanujan. You can read quotes from many sources and see part of the original documents from Hermite, Shanks, von Neumann and others. You may use ``lattice basis reduction'' over the Web; plot and compute many fascinating functions. If you want to try more examples the opportunities will be there.\par On the down side, you may plunge off into secondary links and get lost coming back. You may find the plethora of hypertext links and options distracting, and the present limitations of using Maple over the Internet frustrating.\par Our hope is that this article and this collection will play some role in limning the possibilities and flagging the pot-holes of trying to use these new tools to engage, educate and excite students, users and producers of mathematics.", acknowledgement = ack-nhfb, book-URL = "http://www.cecm.sfu.ca/organics", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Bauschke:1997:CSC, author = "H. H. Bauschke and J. M. Borwein and A. S. Lewis", editor = "Yair Censor and Simeon Reich", booktitle = "Recent Developments in Optimization Theory and Nonlinear Analysis", title = "Convex sets and the cyclic projection algorithm", volume = "204", publisher = pub-AMS, address = pub-AMS:adr, pages = "1--38", year = "1997", bibdate = "Mon Aug 15 14:42:36 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Contemporary Mathematics", acknowledgement = ack-nhfb, ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bauschke:1997:LFM, author = "Heinz H. Bauschke and Jonathan M. Borwein", title = "{Legendre} functions and the method of random {Bregman} projections", journal = j-J-CONVEX-ANAL, volume = "4", number = "1", pages = "27--67", year = "1997", ISSN = "0944-6532 (print), 2363-6394 (electronic)", MRclass = "49M45 (65K10 90C25)", MRnumber = "1459881", MRreviewer = "Alfredo N. Iusem", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/96/; http://www.heldermann-verlag.de/jca/jca04/jca04002.pdf", acknowledgement = ack-nhfb, fjournal = "Journal of Convex Analysis", journal-URL = "http://www.heldermann.de/JCA/jcacon.htm", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Bauschke:1997:MCP, author = "Heinz H. Bauschke and Jonathan M. Borwein and Adrian S. Lewis", booktitle = "Recent developments in optimization theory and nonlinear analysis ({Jerusalem}, 1995)", title = "The method of cyclic projections for closed convex sets in {Hilbert} space", volume = "204", publisher = pub-AMS, address = pub-AMS:adr, pages = "1--38", year = "1997", DOI = "https://doi.org/10.1090/conm/204/02620", MRclass = "49M45 (47H99 47N10 65F10 90C25)", MRnumber = "1442992", MRreviewer = "Alfredo N. Iusem", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Contemp. Math.", acknowledgement = ack-nhfb, ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1997:ADE, author = "J. M. Borwein and F. G. Garvan", title = "Approximations to $ \pi $ via the {Dedekind} eta function", crossref = "Borwein:1997:OMP", pages = "89--115", year = "1997", MRclass = "11F20 (11Y60)", MRnumber = "1483915", MRreviewer = "Bruce C. Berndt", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "CMS Conf. Proc.", URL = "http://docserver.carma.newcastle.edu.au/158/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:1997:AGMa, author = "J. M. Borwein and P. B. Borwein", booktitle = "{Pi: A Source Book}", title = "The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions", publisher = pub-SV, address = pub-SV:adr, pages = "??--??", year = "1997", DOI = "https://doi.org/10.1007/978-1-4757-2736-4_56", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_56", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1997:AGMb, author = "Jonathan A. Borwein and Petr Lison{\v{e}}k and John A. Macdonald", title = "Arithmetic--Geometric Means Revisited", journal = j-MAPLE-TECH-NEWS, volume = "4", number = "1", pages = "20--27", month = "Winter", year = "1997", ISSN = "1061-5733", ISSN-L = "1061-5733", bibdate = "Wed Jul 23 09:11:50 1997", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/maple-tech.bib", note = "Special issue on Maple in the mathematical sciences.", URL = "http://docserver.carma.newcastle.edu.au/4/", acknowledgement = ack-nhfb, fjournal = "Maple technical newsletter", journal-URL = "http://web.mit.edu/maple/www/plibrary/mtn.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:1997:APD, author = "J. M. Borwein and F. Garvan", editor = "????", booktitle = "Organic Mathematics Proceedings, {12 April 1996}", title = "Approximating Pi with the {Dedekind} eta function", publisher = "????", address = "????", pages = "??--??", year = "1997", ISSN = "0731-1036", bibdate = "Mon Aug 15 14:37:48 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.cecm.sfu.ca/organics", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1997:CBS, author = "J. Borwein and M. Fabian and J. Vanderwerff", title = "Characterizations of {Banach} spaces via convex and other locally {Lipschitz} functions", journal = "Acta Math. Vietnam.", volume = "22", number = "1", pages = "53--69", year = "1997", ISSN = "0251-4184 (print), 2315-4144 (electronic)", ISSN-L = "0251-4184", MRclass = "46B20 (46G99 52A41)", MRnumber = "1479738", MRreviewer = "Warren B. Moors", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Special edition in honour of Huang Tuy's seventieth birthday.", URL = "http://docserver.carma.newcastle.edu.au/179/", acknowledgement = ack-nhfb, fjournal = "Acta Mathematica Vietnamica", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1997:CFB, author = "Jon Borwein and Jon Vanderwerff", title = "Convex functions on {Banach} spaces not containing {$ l_1 $}", journal = j-CAN-MATH-BULL, volume = "40", number = "1", pages = "10--18", year = "1997", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1997-002-1", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", MRclass = "46B20 (46A55 46G05 46N10 52A41)", MRnumber = "1443721", MRreviewer = "Li Xin Cheng", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1532/", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1997:DDF, author = "J. M. Borwein and Xianfu Wang", title = "Distinct differentiable functions may share the same {Clarke} subdifferential at all points", journal = j-PROC-AM-MATH-SOC, volume = "125", number = "3", pages = "807--813", year = "1997", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/S0002-9939-97-03654-X", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "49J52 (26A16 26A24 58C20)", MRnumber = "1363449", MRreviewer = "Doug Ward", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/112/", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1997:DEM, author = "Jonathan Borwein and Michael Monagan", title = "Differential Equations in {Maple}: a Short Tutorial", journal = j-MAPLE-TECH-NEWS, volume = "4", number = "1", pages = "55--58", month = "Winter", year = "1997", ISSN = "1061-5733", ISSN-L = "1061-5733", bibdate = "Wed Jul 23 09:11:50 1997", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/maple-tech.bib", acknowledgement = ack-nhfb, fjournal = "Maple technical newsletter", journal-URL = "http://web.mit.edu/maple/www/plibrary/mtn.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1997:EDA, author = "Jonathan Borwein and David Bradley", title = "Empirically determined {Ap{\'e}ry}-like formulae for {$ \zeta (4 n + 3) $}", journal = j-EXP-MATH, volume = "6", number = "3", pages = "181--194", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1080/10586458.1997.10504608", ISSN = "1058-6458 (print), 1944-950X (electronic)", ISSN-L = "1058-6458", MRclass = "11Y60 (11M06)", MRnumber = "1481588", MRreviewer = "F. Beukers", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://projecteuclid.org/euclid.em; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/expmath.bib", URL = "http://docserver.carma.newcastle.edu.au/163/; http://projecteuclid.org/euclid.em/1047920419", acknowledgement = ack-nhfb, fjournal = "Experimental Mathematics", journal-URL = "http://www.tandfonline.com/loi/uexm20", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1997:EFE, author = "Jonathan M. Borwein and David M. Bradley and David J. Broadhurst", title = "Evaluations of $k$-fold {Euler\slash Zagier} sums: a compendium of results for arbitrary $k$", journal = j-ELECT-J-COMB, volume = "4", number = "2", pages = "Research Paper 5", year = "1997", ISSN = "1077-8926 (print), 1097-1440 (electronic)", ISSN-L = "1077-8926", MRclass = "11M41 (11Y60)", MRnumber = "1444152", MRreviewer = "Pavel Guerzhoy", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "The Wilf Festschrift (Philadelphia, PA, 1996).", URL = "http://www.combinatorics.org/Volume_4/Abstracts/v4i2r5.html", acknowledgement = ack-nhfb, fjournal = "Electronic Journal of Combinatorics", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", pagecount = "21", } @Article{Borwein:1997:ESLa, author = "Jonathan M. Borwein and Warren B. Moors", title = "Essentially smooth {Lipschitz} functions", journal = j-J-FUNCT-ANAL, volume = "149", number = "2", pages = "305--351", year = "1997", CODEN = "JFUAAW", DOI = "https://doi.org/10.1006/jfan.1997.3101", ISSN = "0022-1236 (print), 1096-0783 (electronic)", ISSN-L = "0022-1236", MRclass = "58C20 (46G05 46N10 49J52)", MRnumber = "1472362", MRreviewer = "Mari{\'a}n Fabian", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/95/; http://www.sciencedirect.com/science/article/pii/S0022123697931013", abstract = "In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on separable Banach spaces. For example, we examine the relationship between integrability,D-representability, and strict differentiability. In addition to this, we show that on any separable Banach space there is a significant family of locally Lipschitz functions that are integrable,D-representable and possess desirable differentiability properties. We also present some striking applications of our results to distance functions.", acknowledgement = ack-nhfb, fjournal = "Journal of Functional Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/00221236", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1997:ESLb, author = "Jonathan M. Borwein and Warren B. Moors", editor = "F. Cucker and M. Shub", booktitle = "Foundations of computational mathematics ({Rio de Janeiro, 1997})", title = "Essentially smooth {Lipschitz} functions: compositions and chain rules", publisher = pub-SV, address = pub-SV:adr, pages = "16--22", year = "1997", MRclass = "49J52 (46N10 58C20)", MRnumber = "1661969", MRreviewer = "Mari{\'a}n Fabian", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:1997:LFM, author = "J. M. Borwein and W. B. Moors", editor = "B. M. Glover and D. Ralph", booktitle = "Proceedings of the Optimization Miniconference III, University of Melbourne, July 1996", title = "{Lipschitz} functions with minimal {Clarke} subdifferential mappings", publisher = "University of Ballarat", address = "Ballarat, VI, Australia", pages = "5--12", year = "1997", bibdate = "Mon Aug 15 14:41:04 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/178/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1997:LFP, author = "Jonathan M. Borwein and Warren B. Moors and Xianfu Wang", title = "{Lipschitz} functions with prescribed derivatives and subderivatives", journal = j-NONLINEAR-ANAL, volume = "29", number = "1", pages = "53--63", year = "1997", CODEN = "NOANDD", DOI = "https://doi.org/10.1016/S0362-546X(96)00050-8", ISSN = "0362-546x (print), 1873-5215 (electronic)", ISSN-L = "0362-546X", MRclass = "49J52 (46G05 47N10 58C05)", MRnumber = "1447569", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/92/; http://www.sciencedirect.com/science/article/pii/S0362546X96000508", acknowledgement = ack-nhfb, fjournal = "Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods", journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis", keywords = "Clarke subgradient; differentiability; Haar-null set; Lipschitz functions; maximal cyclically monotone operator; minimal cusco", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Book{Borwein:1997:MIM, editor = "Jonathan M. Borwein and Carolyn Watters and Ephraim J. Borowski", title = "{The MathResource interactive math dictionary: version 1.0. The math visualizing program Newton and Leibniz didn't have. [An essential tool for high school, college and university students, teachers, scientists, engineers, researchers and anyone else who uses or studies mathematics]}", publisher = "MathResources, Inc.", address = "Halifax, NS, Canada", pages = "????", year = "1997", ISBN = "3-540-14650-4", ISBN-13 = "978-3-540-14650-6", LCCN = "????", bibdate = "Tue Aug 16 09:10:33 MDT 2016", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/maple-extract.bib", URL = "http://www.mathresources.com", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "1997 Eddie Award for best post-secondary reference software, by Education Software Review. MathProbe Media \& Methods 1998 Awards Portfolio winner. LetsDoMath, 2000 Technology \& Learning Award Winner. Integrated with MapleSoft help files in Maple 9.5.", } @Article{Borwein:1997:NEW, author = "Jon Borwein and Michael Monagan", title = "A Note from the {Editors}: Winter 1997, Vol. 4, No. 1", journal = j-MAPLE-TECH-NEWS, volume = "4", number = "1", pages = "1--1", month = "Winter", year = "1997", ISSN = "1061-5733", ISSN-L = "1061-5733", bibdate = "Wed Jul 23 09:11:50 1997", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/maple-tech.bib", acknowledgement = ack-nhfb, fjournal = "Maple technical newsletter", journal-URL = "http://web.mit.edu/maple/www/plibrary/mtn.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1997:OJP, author = "Jonathan Borwein and Richard Smith", title = "Online journal publication: two views from the electronic trenches", journal = "Canadian Journal of Communication", volume = "22", number = "??", pages = "135--152", month = "????", year = "1997", DOI = "", bibdate = "Mon Aug 15 14:35:28 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://edie.cprost.sfu.ca/~scom", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Scholarly Communication in the Next Millennium, March 1997. Excerpted in extenso in Active Voice, the national bi-monthly newsletter of the Editors' Association of Canada.", } @InProceedings{Borwein:1997:PEN, author = "J. M. Borwein and P. B. Borwein and K. Dilcher", booktitle = "Pi: A Source Book", title = "Pi, {Euler} Numbers, and Asymptotic Expansions", publisher = pub-SV, address = pub-SV:adr, pages = "??--??", year = "1997", DOI = "https://doi.org/10.1007/978-1-4757-2736-4_65", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1583/; http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_65", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1997:PSS, author = "David Borwein and Jonathan Borwein and Heinz-J{\"u}rgen Seiffert and Robert D. Brown and Pawel Szeptycki", title = "Problems and Solutions: Solutions: 10335", journal = j-AMER-MATH-MONTHLY, volume = "104", number = "1", pages = "72--74", year = "1997", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2974831", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1542940", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:1997:RME, author = "J. M. Borwein and P. B. Borwein and D. H. Bailey", booktitle = "Pi: A Source Book", title = "{Ramanujan}, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi", publisher = pub-SV, address = pub-SV:adr, pages = "??--??", year = "1997", DOI = "https://doi.org/10.1007/978-1-4757-2736-4_64", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1587/; http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_64", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1997:SAD, author = "J. M. Borwein and W. Sun", title = "The stability analysis of dynamic {SPECT} systems", journal = j-NUM-MATH, volume = "77", number = "3", pages = "283--298", year = "1997", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/s002110050287", ISSN = "0029-599x (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65R30 (44A12 65R20 92C55)", MRnumber = "1469673", MRreviewer = "Dominikus Noll", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/99/; http://link.springer.com/article/10.1007/s002110050287", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Unpublished{Borwein:1997:SAR, author = "Jonathan M. Borwein and Jay Treiman and Qiji Zhu", title = "Sensitivity analysis in reflexive {Banach} spaces", month = aug, year = "1997", bibdate = "Tue Aug 16 10:14:16 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Preprint.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1997:SRR, author = "J. M. Borwein and E. Wong", editor = "L. Vinet", booktitle = "Advances in mathematical sciences: {CRM}'s 25 years ({Montreal}, {PQ}, 1994)", title = "A survey of results relating to {Giuga}'s conjecture on primality", volume = "11", publisher = pub-AMS, address = pub-AMS:adr, pages = "13--27", year = "1997", MRclass = "11A51 (11Y11)", MRnumber = "1479668", MRreviewer = "Andrew Granville", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "CRM Proc. Lecture Notes", URL = "http://docserver.carma.newcastle.edu.au/101/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1997:VAN, author = "Jonathan M. Borwein and Qiji J. Zhu", title = "Variational analysis in nonreflexive spaces and applications to control problems with {$ L^1 $} perturbations", journal = j-NONLINEAR-ANAL, volume = "28", number = "5", pages = "889--915", year = "1997", CODEN = "NOANDD", DOI = "https://doi.org/10.1016/0362-546X(95)00186-Y", ISSN = "0362-546x (print), 1873-5215 (electronic)", ISSN-L = "0362-546X", MRclass = "49K40", MRnumber = "1422192", MRreviewer = "Vera Zeidan", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/78/; http://www.sciencedirect.com/science/article/pii/0362546X9500186Y", acknowledgement = ack-nhfb, fjournal = "Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods", journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis", keywords = "Weak-Hadamard sub-derivatives; Clarke-subdifferentials; control system; $G$-subdifferentials; H{\"o}lder sub-derivatives; infinite horizon problems; sensitivity analysis; smooth renorms; variational principles", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1997:WOM, author = "Jonathan M. Borwein and Peter B. Borwein and Robert M. Corless and Loki J{\"o}rgenson and Nathalie Sinclair", title = "What is organic mathematics?", crossref = "Borwein:1997:OMP", pages = "1--18", year = "1997", ISSN = "0731-1036", ISSN-L = "0731-1036", MRclass = "00A99 (00A30 01A99)", MRnumber = "1483911", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "CMS/AMS Conference Proceedings", URL = "http://docserver.carma.newcastle.edu.au/157/; http://www.cecm.sfu.ca/organics", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Galvin:1997:PSP, author = "Fred Galvin and Franz Rothe and Wen-Xiu Ma and Dan Sachelarie and Vlad Sachelarie and Yury J. Ionin and Robin R. Lewis and Joseph Rosenblatt and Jonathan M. Borwein and C. G. Pinner", title = "Problems and Solutions: Problems: 10599--10605", journal = j-AMER-MATH-MONTHLY, volume = "104", number = "6", pages = "566--567", year = "1997", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2975086", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1543038", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1998:BHS, author = "Jonathan M. Borwein", title = "{Brouwer--Heyting} sequences converge", journal = j-MATH-INTEL, volume = "20", number = "1", pages = "14--15", year = "1998", CODEN = "MAINDC", DOI = "https://doi.org/10.1007/BF03024393", ISSN = "0343-6993 (print), 1866-7414 (electronic)", ISSN-L = "0343-6993", MRclass = "11A63", MRnumber = "1601815", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "The Mathematical Intelligencer", journal-URL = "http://link.springer.com/journal/283", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1998:CAMa, author = "Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lison{\v{e}}k", title = "Combinatorial aspects of multiple zeta values", journal = "ArXiv Mathematics e-prints", month = dec, year = "1998", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/1998math.....12020B; http://docserver.carma.newcastle.edu.au/201/", abstract = "Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The fact that an integral representation of MZVs obeys a shuffle product rule allows the possibility of a combinatorial approach to them. Using this approach we prove a longstanding conjecture of Don Zagier about MZVs with certain repeated arguments. We also prove a similar cyclic sum identity. Finally, we present extensive computational evidence supporting an infinite family of conjectured MZV identities that simultaneously generalize the Zagier identity.", acknowledgement = ack-nhfb, eprint = "math/9812020", keywords = "Number Theory, Combinatorics, Numerical Analysis, 05A19, 11M99, 68R15 (Primary) 11Y99 (Secondary)", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1998:CAMb, author = "Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lison{\v{e}}k", title = "Combinatorial aspects of multiple zeta values", journal = j-ELECT-J-COMB, volume = "5", pages = "Research Paper 38", year = "1998", ISSN = "1077-8926 (print), 1097-1440 (electronic)", ISSN-L = "1077-8926", MRclass = "11M41 (05A19 11Y60)", MRnumber = "1637378", MRreviewer = "Jerzy Browkin", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/201/; http://www.combinatorics.org/Volume_5/Abstracts/v5i1r38.html", acknowledgement = ack-nhfb, fjournal = "Electronic Journal of Combinatorics", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", pagecount = "12", } @Article{Borwein:1998:CHP, author = "J. M. Borwein and R. Girgensohn and Xianfu Wang", title = "On the construction of {H}{\"o}lder and proximal subderivatives", journal = j-CAN-MATH-BULL, volume = "41", number = "4", pages = "497--507", year = "1998", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1998-065-9", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", MRclass = "49J52 (26A16 26A24)", MRnumber = "1658271", MRreviewer = "Lionel Thibault", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/186/", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1998:CML, author = "David Borwein and Jonathan M. Borwein and Christopher Pinner", title = "Convergence of {Madelung}-like lattice sums", journal = j-TRANS-AM-MATH-SOC, volume = "350", number = "8", pages = "3131--3167", month = aug, year = "1998", CODEN = "TAMTAM", DOI = "https://doi.org/10.1090/S0002-9947-98-01983-7", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "11P21 (11M41 11Z05 30B50 40A05)", MRnumber = "1433111", MRreviewer = "Hartmut Menzer", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/104/; http://www.jstor.org/stable/117772", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1998:CMV, author = "J. M. Borwein and Xianfu Wang", title = "The converse of the mean value theorem may fail generically", journal = j-AMER-MATH-MONTHLY, volume = "105", number = "9", pages = "847--848", month = nov, year = "1998", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2589216", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "26A24", MRnumber = "1650850", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1530/; http://www.jstor.org/stable/2589216", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1998:CRE, author = "Jonathan M. Borwein and Warren B. Moors", title = "A chain rule for essentially smooth {Lipschitz} functions", journal = j-SIAM-J-OPT, volume = "8", number = "2", pages = "300--308", year = "1998", CODEN = "SJOPE8", DOI = "https://doi.org/10.1137/S1052623496297838", ISSN = "1052-6234 (print), 1095-7189 (electronic)", ISSN-L = "1052-6234", MRclass = "49J52 (46N10 58C20)", MRnumber = "1618794", MRreviewer = "John R. Giles", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/151/", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Optimization", journal-URL = "http://epubs.siam.org/siopt", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1998:CSR, author = "Jonathan M. Borwein and David M. Bradley and Richard E. Crandall", title = "Computational Strategies for the {Riemann} Zeta Function", type = "Report", number = "CECM-98-118", institution = inst-CECM, address = inst-CECM:adr, pages = "68", day = "30", month = oct, year = "1998", bibdate = "Mon Oct 24 11:29:15 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib; http://www.math.utah.edu/pub/tex/bib/elefunt.bib", URL = "http://people.reed.edu/~crandall/papers/attach01.pdf", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1998:DRDa, author = "Jonathan M. Borwein and David J. Broadhurst", title = "Determinations of rational {Dedekind}-zeta invariants of hyperbolic manifolds and {Feynman} knots and links", journal = "ArXiv High Energy Physics --- Theory e-prints", month = nov, year = "1998", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/1998hep.th...11173B; http://arxiv.org/abs/hep-th/9811173; http://docserver.carma.newcastle.edu.au/213/", abstract = "We identify 998 closed hyperbolic 3-manifolds whose volumes are rationally related to Dedekind zeta values, with coprime integers $a$ and $b$ giving $ a / {\rm bvol}(M) = ( - D)^{3 / 2} / (2 \pi)^{2n - 4} (\zeta_K(2)) / (2 \zeta (2))$ for a manifold $M$ whose invariant trace field $K$ has a single complex place, discriminant $D$, degree $n$, and Dedekind zeta value $ \zeta_K(2)$. The largest numerator of the 998 invariants of Hodgson--Weeks manifolds is, astoundingly, $ a = 2^4 \times 23 \times 37 \times 691 = 9 \, 408 \, 656$; the largest denominator is merely $ b = 9$. We also study the rational invariant $ a / b$ for single-complex-place cusped manifolds, complementary to knots and links, both within and beyond the Hildebrand-Weeks census. Within the censi, we identify 152 distinct Dedekind zetas rationally related to volumes. Moreover, 91 census manifolds have volumes reducible to pairs of these zeta values. Motivated by studies of Feynman diagrams, we find a 10-component 24-crossing link in the case $ n = 2$ and $ D = - 20$. It is one of 5 alternating platonic links, the other 4 being quartic. For 8 of 10 quadratic fields distinguished by rational relations between Dedekind zeta values and volumes of Feynman orthoschemes, we find corresponding links. Feynman links with $ D = - 39$ and $ D = - 84$ are missing; we expect them to be as beautiful as the 8 drawn here. Dedekind-zeta invariants are obtained for knots from Feynman diagrams with up to 11 loops. We identify a sextic 18-crossing positive Feynman knot whose rational invariant, $ a / b = 26$, is 390 times that of the cubic 16-crossing non-alternating knot with maximal $ D_9$ symmetry. Our results are secure, numerically, yet appear very hard to prove by analysis.", acknowledgement = ack-nhfb, eprint = "hep-th/9811173", keywords = "High Energy Physics - Theory, Mathematics - Classical Analysis and ODEs, Mathematics - Geometric Topology, Mathematics - Number Theory", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:1998:DRDb, author = "Jonathan M. Borwein and David J. Broadhurst", title = "Determinations of rational {Dedekind}-zeta invariants of hyperbolic manifolds and {Feynman} knots and links", type = "CECM Preprint", number = "98:120", institution = inst-CECM, address = inst-CECM:adr, month = nov, year = "1998", bibdate = "Tue Aug 16 10:14:52 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "arXiv preprint hep-th/9811173.", URL = "http://docserver.carma.newcastle.edu.au/213/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1998:GYI, author = "Jonathan M. Borwein", title = "A generalization of {Young}'s {$ l^p $} inequality", journal = j-MATH-INEQUAL-APPL, volume = "1", number = "1", pages = "131--136", year = "1998", DOI = "https://doi.org/10.7153/mia-01-11", ISSN = "1331-4343 (print), 1848-9966 (electronic)", ISSN-L = "1331-4343", MRclass = "90C25 (26B25 52A41)", MRnumber = "1492917", MRreviewer = "G{\'e}rard Lebourg", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/189/", acknowledgement = ack-nhfb, ajournal = "Math. Inequal. Appl.", fjournal = "Mathematical Inequalities \& Applications", journal-URL = "http://mia.ele-math.com/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1998:LCE, author = "Jonathan M. Borwein and Qiji J. Zhu", title = "Limiting convex examples for nonconvex subdifferential calculus", journal = j-J-CONVEX-ANAL, volume = "5", number = "2", pages = "221--235", year = "1998", ISSN = "0944-6532 (print), 2363-6394 (electronic)", MRclass = "49J52 (26B05)", MRnumber = "1670340", MRreviewer = "Lionel Thibault", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/191/; http://www.heldermann-verlag.de/jca/jca05/j163.pdf", acknowledgement = ack-nhfb, fjournal = "Journal of Convex Analysis", journal-URL = "http://www.heldermann.de/JCA/jcacon.htm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1998:MPW, author = "Jonathan Borwein", title = "Mathematical Publication on the {Web}", journal = j-SIGSAM, volume = "32", number = "1", pages = "4--7", month = mar, year = "1998", CODEN = "SIGSBZ", DOI = "https://doi.org/10.1145/294833.294836", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Wed Aug 10 12:08:56 2016", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", URL = "http://docserver.carma.newcastle.edu.au/190/; http://doi.acm.org/10.1145/294833.294836", acknowledgement = ack-nhfb, acmid = "294836", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "123", issue-date = "March 1998", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", numpages = "4", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1998:NCC, author = "Jonathan M. Borwein and Jay S. Treiman and Qiji J. Zhu", title = "Necessary conditions for constrained optimization problems with semicontinuous and continuous data", journal = j-TRANS-AM-MATH-SOC, volume = "350", number = "6", pages = "2409--2429", year = "1998", CODEN = "TAMTAM", DOI = "https://doi.org/10.1090/S0002-9947-98-01984-9", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "90C48 (49J52)", MRnumber = "1433112", MRreviewer = "B. Mordukhovich", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/116/", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1998:NSE, author = "Jonathan M. Borwein and Warren B. Moors", title = "Null sets and essentially smooth {Lipschitz} functions", journal = j-SIAM-J-OPT, volume = "8", number = "2", pages = "309--323", year = "1998", CODEN = "SJOPE8", DOI = "https://doi.org/10.1137/S1052623496305213", ISSN = "1052-6234 (print), 1095-7189 (electronic)", ISSN-L = "1052-6234", MRclass = "49J52 (46N10 58C20)", MRnumber = "1618798", MRreviewer = "John R. Giles", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/162/", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Optimization", journal-URL = "http://epubs.siam.org/siopt", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1998:NSP, author = "Jonathan M. Borwein and Alejandro Jofr{\'e}", title = "A nonconvex separation property in {Banach} spaces", journal = j-Z-OPER-RES, volume = "48", number = "2", pages = "169--179", year = "1998", CODEN = "ZMMRFZ", DOI = "https://doi.org/10.1007/s001860050019", ISSN = "1432-2994 (print), 1432-5217 (electronic)", ISSN-L = "1432-2994", MRclass = "46B20 (46A22 46N10 49J53 90C48)", MRnumber = "1662819", MRreviewer = "S. Simons", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Set-valued optimization.", URL = "http://docserver.carma.newcastle.edu.au/197/", acknowledgement = ack-nhfb, ajournal = "ZOR---Math. Methods Oper. Res.", fjournal = "Zeitschrift f{\"u}r Operations Research. Mathematical Methods of Operations Research", journal-URL = "http://link.springer.com/journal/186", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", xxjournal = "Math. Methods Oper. Res.", } @Book{Borwein:1998:PAS, author = "Jonathan M. Borwein and Peter B. Borwein", title = "Pi and the {AGM}: A study in analytic number theory and computational complexity", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xvi + 414", year = "1998", ISBN = "0-471-83138-7, 0-471-31515-X (paperback)", ISBN-13 = "978-0-471-83138-9, 978-0-471-31515-5 (paperback)", MRclass = "11Y60 (11B65 68Q25)", MRnumber = "1641658", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Reprint of the 1987 original.", series = "Canadian Mathematical Society Series of Monographs and Advanced Texts, 4", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", shorttableofcontents = "1. Complete Elliptic Integrals and the Arithmetic--Geometric Mean Iteration \\ 2. Theta Functions and the Arithmetic--Geometric Mean Iteration \\ 3. Jacobi's Triple-Product and Some Number Theoretic Applications \\ 4. Higher Order Transformations \\ 5. Modular Equations and Algebraic Approximations to $ \pi $ \\ 6. The Complexity of Algebraic Functions \\ 7. Algorithms for the Elementary Functions \\ 8. General Means and Iterations \\ 9. Some Additional Applications \\ 10. Other Approaches to the Elementary Functions \\ 11. Pi", subject = "Number theory; Computational complexity; Elliptic functions; Pi; Nombres, Th{\'e}orie des; Complexit{\'e} de calcul (Informatique); Fonctions elliptiques; Computational complexity; Elliptic functions; Number theory; Pi; Algebraische Funktion; Arithmetisch-geometrisches Mittel; Berechnung; Geschichte; Pi (Zahl); Nombres, Th{\'e}orie des; Complexit{\'e} de calcul (informatique); Fonctions elliptiques; Pi (le nombre); Arithmetisch-geometrisches Mittel; Algebraische Funktion; Pi (Zahl); Berechnung; Geschichte; moyenne arithm{\'e}tique; moyenne g{\'e}om{\'e}trique; it{\'e}ration; fonction elliptique; complexit{\'e} calcul; th{\'e}orie nombre", tableofcontents = "1 Complete Elliptic Integrals and the Arithmetic-Geometric Mean Iteration / 1 \\ 1.1 The Arithmetic--Geometric Mean Iteration / 1 \\ 1.2 Gauss's Derivation of the Fundamental Limit Formula / 5 \\ 1.3 Basic Properties of Complete Elliptic Integrals / 7 \\ 1.4 Quadratic Transformations and Iterations and a Third Proof of the Fundamental Limit Formula / 11 \\ 1.5 Jacobi's Differential Equation and a Fourth Proof of the Fundamental Limit Theorem / 18 \\ 1.6 Legendre's Relation / 23 \\ 1.7 Elliptic Functions / 28 \\ 2 Theta Functions and the Arithmetic--Geometric Mean Iteration / 33 \\ 2.1 A Theta Series Solution to the AGM / 33 \\ 2.2 Poisson Summation / 36 \\ 2.3 Poisson Summation and the AGM / 40 \\ 2.4 The Derived Iteration and Some Convergence Results / 44 \\ 2.5 Two Algorithms for 7T / 46 \\ 2.6 General Theta Functions / 52 \\ 2.7 The Landen Transformation / 57 \\ 3 Jacobi's Triple-Product and Some Number Theoretic Applications / 62 \\ 3.1 Jacobi's Triple-Product Identity / 62 \\ 3.2 Some Further Theta Function Identities / 67 \\ 3.3 A Combinatorial Approach to the Triple-Product Identity / 76 \\ 3.4 Bressoud's ``Easy Proof'' of the Rogers--Ramanujan Identities / 78 \\ 3.5 Some Number Theoretic Applications / 81 \\ 3.6 The Mellin Transform and the Zeta Function / 87 \\ 3.7 Evaluation of Sums of Reciprocals of Fibonacci Sequences / 91 \\ 4 Higher Order Transformations / 102 \\ 4.1 A First Approach to Higher Order Transformations / 102 \\ 4.2 An Elementary Transcendental Approach to Higher Order Transformations / 109 \\ 4.3 Elliptic Modular Functions / 112 \\ 4.4 The Modular Equations for $\lambda$ and $j$ / 119 \\ 4.5 The Modular Equation in $u$--$v$ Form / 126 \\ 4.6 The Multiplier / 136 \\ 4.7 Cubic Modular Identities / 142 \\ 5 Modular Equations and Algebraic Approximations to $ \pi $ / 152 \\ 5.1 Singular Values of the Second Kind / 152 \\ 5.2 Calculation of $\alpha$ / 155 \\ 5.3 Further Formulae for $\alpha$ / 164 \\ 5.4 Recursive Approximation to $ \pi $ / 169 \\ 5.5 Generalized Elliptic Integrals and Rational and Algebraic Series for $ 1 / \pi $ and $ 1 / K $ / 177 \\ 5.6 Other Approximations / 191 \\ 6 The Complexity of Algebraic Functions / 200 \\ 6.1 Complexity Concerns / 200 \\ 6.2 The Fast Fourier Transform (FFT) / 204 \\ 6.3 Fast Multiplication / 209 \\ 6.4 Newton's Method and the Complexity of Algebraic Functions / 212 \\ 7 Algorithms for the Elementary Functions / 219 \\ 7.1 $ \pi $ and Log / 219 \\ 7.2 Theta Function Algorithms for Log / 224 \\ 7.3 The Complexity of Elementary and Elliptic Functions / 226 \\ 8 General Means and Iterations / 230 \\ 8.1 Abstract Means / 230 \\ 8.2 Equivalence of Means / 239 \\ 8.3 Compound Means / 243 \\ 8.4 Convergence Rates and Some Examples / 249 \\ 8.5 Carlson's Integrals and More Examples 256 / 281 \\ 8.6 Series Expansions of Certain Means / 263 \\ 8.7 Multidimensional Means and Iterations / 266 \\ 8.8 Algebraic Iterations and Functional Relations / 273 \\ 9 Some Additional Applications / 281 \\ 9.1 Sums of Two Squares / 281 \\ 9.2 (Chemical) Lattice Sums / 288 \\ 9.3 Odd-Dimensional Sums and Benson's Formula / 301 \\ 9.4 The Quintuple-Product Identity / 306 \\ 9.5 Quintic and Septic Multipliers and Iterations / 309 \\ 10 Other Approaches to the Elementary Functions / 316 \\ 10.1 Classical Approximations / 316 \\ 10.2 Reduced Complexity Methods / 326 \\ 11 Pi / 337 \\ 11.1 On the History of the Calculation of $ \pi $ / 337 \\ 11.2 On the Transcendence of $ \pi $ / 347 \\ 11.3 Irrationality Measures / 362 \\ Bibliography / 387 \\ Symbol List / 396 \\ Index / 405", } @Unpublished{Borwein:1998:TAP, author = "Jonathan Borwein", title = "Talking about Pi", day = "20", month = jan, year = "1998", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/pi.bib", note = "The original URL is no longer found, but the archive URL worked on 26-Apr-2011.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Marechal:1998:APR, author = "P. Marechal and D. Togane and A. Celler and J. M. Borwein", booktitle = "{1998 IEEE Nuclear Science Symposium. Conference Record. Toronto, ON, Canada, November 8--14, 1998}", title = "Assessment of the performance of reconstruction processes for computed tomography", volume = "2", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "1353--1357", year = "1998", DOI = "https://doi.org/10.1109/NSSMIC.1998.774404", ISSN = "1082-3654", ISSN-L = "1082-3654", bibdate = "Fri Aug 12 11:41:45 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1529/", abstract = "This paper deals with the assessment of the performance of reconstruction methods for computed tomography, including filtered backprojection and `entropy-like' methods. For each of these methods, the influence of errors in the measured data on the reconstructed image is analyzed. A small perturbation of the data vector induces a perturbation of the reconstructed object which can be computed by means of the sensitivity matrix. Using appropriate matrix computation techniques, an upper bound on the size of the reconstruction error is determined, as well as the pattern of noise in the sinogram that will result in the largest reconstruction error. Simulations will illustrate our analysis and demonstrate its utility in the interpretation of computed images and in the selection of reconstruction parameters", acknowledgement = ack-nhfb, keywords = "Attenuation; computed tomography; Computed tomography; computerised tomography; Convolution; data vector; entropy-like methods; filtered backprojection; Image analysis; image reconstruction; Image reconstruction; image reconstruction processes; Integral equations; interpolation; inverse problems; Inverse problems; iterative methods; Mathematics; matrix computation techniques; maximum entropy methods; medical image processing; pattern of noise; performance assessment; positron emission tomography; Radon transforms; Radon-type inverse problem; reconstruction error size; reconstruction parameters selection; regularization scheme; sensitivity analysis; sensitivity matrix; singular value decomposition; sinogram; small perturbation; Transforms; upper bound; X-ray scattering", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Bauschke:1999:COM, author = "Heinz H. Bauschke and Jonathan M. Borwein", editor = "J. Giles and B. Ninness", booktitle = "{Proceedings of the Centre for Mathematics and its Applications (Australian National University) National Symposium on Functional Analysis, Optimization and Applications, March 1998}", title = "Conical open mapping theorems and regularity", volume = "36", publisher = "????", address = "????", pages = "1--10", year = "1999", bibdate = "Mon Aug 15 14:33:16 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/208/", acknowledgement = ack-nhfb, ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bauschke:1999:EAD, author = "Heinz H. Bauschke and Dominikus Noll and Anna Celler and Jonathan M. Borwein", title = "An {EM} algorithm for dynamic {SPECT}", journal = j-IEEE-TRANS-MED-IMAG, volume = "18", number = "3", pages = "252--261", month = mar, year = "1999", CODEN = "ITMID4", DOI = "https://doi.org/10.1109/42.764899", ISSN = "0278-0062 (print), 1558-254x (electronic)", ISSN-L = "0278-0062", bibdate = "Wed Aug 10 12:08:56 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.ncbi.nlm.nih.gov/pubmed/10363703", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Medical Imaging", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=42", keywords = "Algorithms; arbitrary decaying activities; Cameras; compartmental modeling; Computed tomography; dynamic SPECT; EM algorithm; exponentials sum; Face detection; Head; Heuristic algorithms; Humans; Instruments; M step; medical diagnostic imaging; Models, Statistical; Nuclear medicine; nuclear medicine; numerical tests; Pharmaceuticals; physiological models; Positron emission tomography; Reproducibility of Results; single photon emission computed tomography; Single photon emission computed tomography; Tomography, Emission-Computed, Single-Photon; underlying probabilistic models", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bauschke:1999:MMD, author = "Heinz H. Bauschke and Jonathan M. Borwein", title = "Maximal monotonicity of dense type, local maximal monotonicity, and monotonicity of the conjugate are all the same for continuous linear operators", journal = j-PAC-J-MATH, volume = "189", number = "1", pages = "1--20", year = "1999", CODEN = "PJMAAI", DOI = "https://doi.org/10.2140/pjm.1999.189.1", ISSN = "0030-8730 (print), 1945-5844 (electronic)", ISSN-L = "0030-8730", MRclass = "47H05 (47B99 49J52)", MRnumber = "1687802", MRreviewer = "Pando Georgiev", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/180/", acknowledgement = ack-nhfb, fjournal = "Pacific Journal of Mathematics", journal-URL = "http://msp.org/pjm", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bauschke:1999:SCH, author = "Heinz H. Bauschke and Jonathan M. Borwein and Wu Li", title = "Strong conical hull intersection property, bounded linear regularity, {Jameson}'s property {$ (G) $}, and error bounds in convex optimization", journal = j-MATH-PROG, volume = "86", number = "1, Ser. A", pages = "135--160", year = "1999", CODEN = "MHPGA4", DOI = "https://doi.org/10.1007/s101070050083", ISSN = "0025-5610 (print), 1436-4646 (electronic)", ISSN-L = "0025-5610", MRclass = "90C46 (41A29 90C31)", MRnumber = "1712477", MRreviewer = "Charles K. Chui", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/195/", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming. A Publication of the Mathematical Programming Society", journal-URL = "http://link.springer.com/journal/10107", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Research Report 98:107.", } @Book{Borowski:1999:DMa, author = "E. J. (Ephraim J.) Borowski and Jonathan M. Borwein", title = "Dictionary of mathematics", publisher = "Unwin Hyman", address = "London, UK", pages = "660", year = "1999", ISBN = "0-261-67198-7", ISBN-13 = "978-0-261-67198-0", LCCN = "????", bibdate = "Tue Aug 16 09:03:32 MDT 2016", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", subject = "Mathematics; Dictionaries", } @Book{Borowski:1999:DMb, author = "E. J. (Ephraim J.) Borowski and Jonathan M. Borwein", title = "Dictionary of mathematics", publisher = pub-HARPERCOLLINS, address = pub-HARPERCOLLINS:adr, pages = "672", year = "1999", ISBN = "0-00-434347-6 (paperback)", ISBN-13 = "978-0-00-434347-1 (paperback)", LCCN = "????", bibdate = "Mon Oct 23 07:36:34 MDT 2017", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "This dictionary of mathematics contains over 9,000 definitions and 400 diagrams and covers subjects such as abstract analysis; number theory; topology; vectors; differential equations and more.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Originally published in \cite{Borowski:1988:DM}.", subject = "Mathematics; Dictionaries; Mathematics.", } @Article{Borwein:1999:ESB, author = "Jonathan M. Borwein and Boris S. Mordukhovich and Yongheng Shao", title = "On the Equivalence of Some Basic Principles in Variational Analysis", journal = j-J-MATH-ANAL-APPL, volume = "229", number = "1", pages = "228--257", year = "1999", CODEN = "JMANAK", DOI = "https://doi.org/10.1006/jmaa.1998.6157", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "49J52 (46N10)", MRnumber = "1664320", MRreviewer = "Abderrahim Jourani", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/192/; http://www.sciencedirect.com/science/article/pii/S0022247X98961571", abstract = "The primary goal of this paper is to study relationships between certain basic principles of variational analysis and its applications to nonsmooth calculus and optimization. Considering a broad class of Banach spaces admitting smooth renorms with respect to some bornology, we establish an equivalence between useful versions of a smooth variational principle for lower semicontinuous functions, an extremal principle for nonconvex sets, and an enhanced fuzzy sum rule formulated in terms of viscosity normals and subgradients with controlled ranks. Further refinements of the equivalence result are obtained in the case of a Fr{\'e}chet differentiable norm. Based on the new enhanced sum rule, we provide a simplified proof for the refined sequential description of approximate normals and subgradients in smooth spaces.", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", keywords = "fuzzy calculus; generalized differentiation; Nonsmooth analysis; smooth Banach spaces; variational and extremal principles; viscosity normals and subdifferentials", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1999:ETE, author = "Jonathan M. Borwein and Robert M. Corless", title = "Emerging tools for experimental mathematics", journal = j-AMER-MATH-MONTHLY, volume = "106", number = "10", pages = "889--909", year = "1999", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2589743", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "68W30 (00A05 11Yxx)", MRnumber = "1732501", MRreviewer = "Michael M. Dediu", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/203/; http://www.jstor.org/stable/2589743", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Research Report 98:110.", } @Article{Borwein:1999:GSB, author = "Jonathan M. Borwein and Warren B. Moors and Xianfu Wang", title = "Generalized subdifferentials: a {Baire} categorical approach", journal = "C. R. Math. Acad. Sci. Soc. R. Can.", volume = "21", number = "4", pages = "132--138", year = "1999", ISSN = "0706-1994", MRclass = "49J52 (46G05 58C20)", MRnumber = "1728265", MRreviewer = "Mari{\'a}n Fabian", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/234/", acknowledgement = ack-nhfb, fjournal = "Comptes Rendus Math{\'e}matiques de l'Acad{\'e}mie des Sciences. La Soci{\'e}t{\'e} Royale du Canada. Mathematical Reports of the Academy of Science. The Royal Society of Canada", journal-URL = "https://mr.math.ca/article/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 99:128. The journal web site has no online archives before volume 27 (2005).", } @InProceedings{Borwein:1999:ITD, author = "J. M. Borwein and T. Stanway", editor = "John Grant McGloughlin", booktitle = "{Canadian Mathematics Education Study Group (CMESG) Proceedings 1999 Annual Meeting}", title = "The impact of technology on the doing of mathematics", publisher = "Memorial University Press", address = "St. Johns, NL, Canada", pages = "3--6", year = "1999", bibdate = "Mon Aug 15 14:30:19 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/248/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:1999:MFA, author = "Jonathan M. Borwein and Qiji J. Zhu", editor = "F. H. Clarke and R. J. Stern", booktitle = "Nonlinear analysis, differential equations and control ({Montreal, QC, 1998})", title = "Multifunctional and functional analytic techniques in nonsmooth analysis", volume = "528", publisher = pub-KLUWER, address = pub-KLUWER:adr, pages = "61--157", year = "1999", MRclass = "49J52 (26A16 26E25 46N10)", MRnumber = "1695006", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "NATO Sci. Ser. C Math. Phys. Sci.", URL = "http://docserver.carma.newcastle.edu.au/49/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1999:PSS, author = "Jonathan M. Borwein and C. G. Pinner and David Bradley", title = "Problems and Solutions: Solutions: An Infinite Product: 10605", journal = j-AMER-MATH-MONTHLY, volume = "106", number = "2", pages = "173--174", year = "1999", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2589069", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1543419", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1999:PSVa, author = "Jonathan M. Borwein and Jay S. Treiman and Qiji J. Zhu", title = "Partially smooth variational principles and applications", journal = j-NONLINEAR-ANAL, volume = "35", number = "8", pages = "1031--1059", year = "1999", CODEN = "NOANDD", DOI = "https://doi.org/10.1016/S0362-546X(98)00113-8", ISSN = "0362-546x (print), 1873-5215 (electronic)", ISSN-L = "0362-546X", MRclass = "49J53 (46T20 47H99)", MRnumber = "1707806", MRreviewer = "B. Mordukhovich", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/182/; http://www.sciencedirect.com/science/article/pii/S0362546X98001138", acknowledgement = ack-nhfb, fjournal = "Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods", 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", } @Article{Borwein:1999:SRM, author = "Jonathan M. Borwein and Warren B. Moors and Yongheng Shao", title = "Subgradient representation of multifunctions", journal = j-J-AUSTRAL-MATH-SOC-SER-B, volume = "40", number = "3", pages = "301--313", month = jan, year = "1999", CODEN = "JAMMDU", DOI = "https://doi.org/10.1017/S0334270000010924", ISSN = "0334-2700", MRclass = "49J52 (47H04)", MRnumber = "1674589", MRreviewer = "Constantin Z{\u{a}}linescu", bibdate = "Fri Sep 30 10:53:26 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Volume in honour of B. Craven and B. Mond.", URL = "http://docserver.carma.newcastle.edu.au/184/; http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=3964380", acknowledgement = ack-nhfb, fjournal = "Australian Mathematical Society. Journal. Series B. Applied Mathematics", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:1999:SSC, author = "Jonathan M. Borwein and Qiji J. Zhu", title = "A survey of subdifferential calculus with applications", journal = j-NONLINEAR-ANAL, volume = "38", number = "6", pages = "687--773", year = "1999", CODEN = "NOANDD", DOI = "https://doi.org/10.1016/S0362-546X(98)00142-4", ISSN = "0362-546x (print), 1873-5215 (electronic)", ISSN-L = "0362-546X", MRclass = "49J52 (46G05 46N10 49-02 49J53 58C05)", MRnumber = "1710152", MRreviewer = "Philip D. Loewen", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "See addendum \cite{Borwein:2002:ASS}.", URL = "http://docserver.carma.newcastle.edu.au/199/; http://www.sciencedirect.com/science/article/pii/S0362546X98001424", acknowledgement = ack-nhfb, fjournal = "Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods", 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.", } @Article{Borwein:1999:SVM, author = "Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lison{\v{e}}k", title = "Special Values of Multiple Polylogarithms", journal = "ArXiv Mathematics e-prints", month = oct, year = "1999", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/1999math.....10045B; http://docserver.carma.newcastle.edu.au/200/", abstract = "Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, we have been forced to consider multidimensional extensions encompassing the classical polylogarithm, Euler sums, and the Riemann zeta function. Here, we provide a general framework within which previously isolated results can now be properly understood. Applying the theory developed herein, we prove several previously conjectured evaluations, including an intriguing conjecture of Don Zagier.", acknowledgement = ack-nhfb, eprint = "math/9910045", keywords = "Mathematics - Classical Analysis and ODEs, Mathematics - Combinatorics, 40B05, 33E20", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Marechal:1999:CSA, author = "P. Marechal and D. Togane and A. Celler and J. M. Borwein", title = "Computation and stability analysis for regularized tomographic reconstructions", journal = j-IEEE-TRANS-NUCL-SCI, volume = "46", pages = "2177--2184", month = dec, year = "1999", CODEN = "IRNSAM", DOI = "https://doi.org/10.1109/23.819301", ISSN = "0018-9499 (print), 1558-1578 (electronic)", ISSN-L = "0018-9499", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/1999ITNS...46.2177M", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Nuclear Science", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Borwein:19xx:ASW, author = "Jonathan Borwein and Lou Shitou", title = "Asymptotics of a Sequence of {Witt} Vectors", type = "Report", institution = "Department of Mathematics, Statistics and Computing Science, Dalhousie University", address = "Halifax, NS B3H 3J5, Canada", pages = "13", year = "19xx", bibdate = "Fri Nov 11 07:09:34 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "We provide asymptotic and order information about the Witt vectors and integers $ d_n $ appearing in $ \Prod_{n \geq 1} (1 / (1 + d_n t^n / n!)) = (1 - t) e^t $.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Undated report. The second author also appears in journal databases with family name Lou, and personal name Shi-Tuo.", } @TechReport{Borwein:19xx:CFF, author = "J. M. Borwein and P. B. Borwein", title = "On the Complexity of Familiar Functions and Numbers", type = "Report", institution = "Department of Mathematics, Statistics and Computing Science, Dalhousie University", address = "Halifax, NS B3H 3J5, Canada", pages = "30", year = "19xx", MRclass = "6BC25, 41A30, 1OA30", bibdate = "Fri Nov 11 07:08:04 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "This paper examines low-complexity approximations to familiar functions and numbers. The intent is to suggest that a taxonomy of such functions and numbers based on their computational complexity is possible. A central theme is that traditional methods of approximation are often very far from optimal, while good or optimal methods are often very far from obvious For most functions provably optimal methods are not known, however the gap between what is known and what is possible is often small. A considerable number of open problems are posed and a number of related examples are presented.", acknowledgement = ack-nhfb, keywords = "$\pi$; algebraic approximation; computation of digits; Elementary functions; low complexity approximation; open problems; rational approximation; reduced complexity approximation", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Undated report", } @Unpublished{Borwein:19xx:EIG, author = "Jonathan M. Borwein", title = "Elliptic Integrals and the {Gauss--Salamin} formula for $ \pi $", pages = "16", year = "19xx", bibdate = "Mon Nov 07 07:04:34 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Unpublished hand-written lecture slides at Dalhousie University. The slides are undated, and the 10 references on the final slides include a reference to E. Salamin (1976) and to P. Backmann's 1977 book \booktitle{A History of Pi}.", abstract = "$ \pi $ was first used by W. Jones (1703) as \emph{pi} (short for periphery). Euler (1733) first popularized it as a replacement for $p$ or $c$.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Unpublished{Borwein:19xx:EMI, author = "Jonathan M. Borwein and Peter B. Borwein and Roland Girgensohn and S. Parnes", title = "Experimental mathematical investigation of decimal and continued fraction expansions of select constants", year = "19xx", bibdate = "Thu Aug 11 09:30:52 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Unpublished.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Cited in \cite{Octavio:1996:IT}.", } @TechReport{Borwein:19xx:MI, author = "J. M. Borwein and P. B. Borwein", title = "On the Mean Iteration $ (a, b) \leftarrow ((a + 3 b) / 4, (\sqrt {ab} + b) / 2) $", type = "Report", institution = "Department of Mathematics, Statistics and Computing Science, Dalhousie University", address = "Halifax, NS B3H 3J5, Canada", pages = "39", year = "19xx", bibdate = "Fri Nov 11 07:10:57 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "The iterative process $ a_{n + 1} = (a_n + 3 b_n) / 4 $, $ b_{n + 1} = (\sqrt {a_n b_n} + b_n) / 2 $ is studied in detail. The limit of this quadratically converging process is explicitly identified, as are the uniformizing parameters. The role of symbolic computation, in discovering these non-trivial identifications, is highlighted.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Undated report", } @TechReport{Borwein:19xx:PCT, author = "Jonathan M. Borwein and Peter B. Borwein", title = "Pi and its computation: a twenty-two hundred year quest continues: why it is now possible to calculate a billion digits of pi", type = "Report", institution = "Dalhousie University", address = "Halifax, NS, Canada", pages = "21", year = "19xx", bibdate = "Mon Nov 07 07:01:20 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Undated typeset manuscript intended for \booktitle{Scientific American}, but never published. The latest reference is to a 1987 book.", abstract = "Classical mathematics of Gauss, Ramanujan, and others combines the modern theory of algorithms to dramatically improve our understanding of this ancient problem.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "This paper must have been written between 1987 and 1997, and before the discovery of the BBP algorithm \cite{Bailey:1997:RCV}, because the last paragraph says: ``It is also reasonable to speculate that computing the $n$-th digit of $ \pi $ is not very much easier than computing all the first $n$ digits. We think it very probable that computing the $n$-th digit of $ \pi $ cannot be of a lower order than multiplication. As a consequence, we conjecture that no one will ever determine the $ 10^{1000}$-th decimal digit of $ \pi $.", } @TechReport{Borwein:19xx:WMS, author = "J. M. Borwein and B. Richmond", title = "When is a matrix a square?", type = "Research report", number = "5", institution = "Department of Mathematics, Dalhousie University and Department of Combinatorics and Optimization, University of Waterloo", address = "Halifax, NS, Canada and Waterloo, ON, Canada", pages = "22", year = "19xx", bibdate = "Mon Nov 07 17:45:04 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "Necessary and sufficient conditions for an arbitrary $ n \times n $ matrix to possess a $k$-th root are given in terms of the associated Jordan form. These characterizations are used to give asymptotic estimates for the relative frequency of nilpotent matrices possessing square roots. The estimates are entirely combinatorial in genesis.", acknowledgement = ack-nhfb, keywords = "asymptotic formulae; Jordan forms; partition functions; square roots", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "There are only 5 references on the last page, the most recent a book from 1976.", } @Article{Bauschke:2000:BLR, author = "Heinz H. Bauschke and Jonathan M. Borwein and Paul Tseng", title = "Bounded linear regularity, strong {CHIP}, and {CHIP} are distinct properties", journal = j-J-CONVEX-ANAL, volume = "7", number = "2", pages = "395--412", year = "2000", ISSN = "0944-6532 (print), 2363-6394 (electronic)", MRclass = "90C48 (41A65 49J53 52A15 52A20)", MRnumber = "1811687", MRreviewer = "Wu Li", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.heldermann.de/JCA/JCA07/JCA072/jca07020.htm", abstract = "Bounded linear regularity, the strong conical hull intersection property (strong CHIP), and the conical hull intersection property (CHIP) are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. It was shown recently that these properties are fundamental in several branches of convex optimization, including convex feasibility problems, error bounds, Fenchel duality, and constrained approximation. It was known that regularity implies strong CHIP. which ill turn implies CHIP; moreover, the three properties always hold for subspaces. The question whether or not converse implications are true for general convex sets was open.", acknowledgement = ack-nhfb, fjournal = "Journal of Convex Analysis", journal-URL = "http://www.heldermann.de/JCA/jcacon.htm", ORCID-numbers = "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", } @Book{Berggren:2000:PSB, author = "Lennart Berggren and Jonathan Borwein and Peter Borwein", title = "Pi: a source book", publisher = pub-SV, address = pub-SV:adr, edition = "Second", pages = "xx + 736", year = "2000", DOI = "https://doi.org/10.1007/978-1-4757-3240-5", ISBN = "0-387-98946-3 (hardcover)", ISBN-13 = "978-0-387-98946-4 (hardcover)", LCCN = "QA484 .P5 2000", MRclass = "11-00 (01A05 01A75 11-03)", MRnumber = "1746004", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/master.bib; http://www.math.utah.edu/pub/tex/bib/mathcw.bib; http://www.math.utah.edu/pub/tex/bib/pi.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", tableofcontents = "Preface \\ Acknowledgements \\ Introduction \\ The Rhind Mathematical Papyrus-Problem 50 \\ Engles / Quadrature of the Circle in Ancient Egypt \\ Archimedes / Measurement of a Circle \\ Phillips / Archimedes the Numerical Analyst \\ Lam \& Ang / Circle Measurements in Ancient China \\ The Banu Musa: The Measurement of Plane and Solid Figures \\ Madhava's / The Power Series for Arctan and Pi \\ Hope-Jones / Ludolph van Ceulen \\ Vi{\`e}te / Variorum de Revus Mathematicis Reponsorum Liber VII \\ Wallis / Computation of Pi by Successive Interpolations \\ Wallis / Arithmetica Infinitorum \\ Huygens / De Circuli Magnitudine Inventa \\ Gregory / Correspondence with John Collins \\ Jones / The First Use of Pi for the Circle Ratio \\ Newton / Of The Method of Fluxions and Infinite Series \\ Euler / Chapter 10 of Introduction to Analysis of the Infinite \\ Lambert / M{\'e}moire Sur Quelques Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s Transcendentes Circulaires et Logarithmiques \\ Lambert / Irrationality of Pi \\ Shanks / Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals \\ Hermite / Sur La Fonction Exponentielle", } @InProceedings{Borwein:2000:AGM, author = "J. M. Borwein and P. B. Borwein", booktitle = "Pi: A Source Book", title = "The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions", publisher = pub-SV, address = pub-SV:adr, pages = "??--??", year = "2000", DOI = "https://doi.org/10.1007/978-1-4757-3240-5_56", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_56", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2000:AIR, author = "Jonathan M. Borwein and Petr Lison{\v{e}}k", title = "Applications of integer relation algorithms", journal = j-DISCRETE-MATH, volume = "217", number = "1--3", pages = "65--82", year = "2000", CODEN = "DSMHA4", DOI = "https://doi.org/10.1016/S0012-365X(99)00256-3", ISSN = "0012-365x (print), 1872-681x (electronic)", ISSN-L = "0012-365X", MRclass = "65Y15 (68W99)", MRnumber = "1766260", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Formal power series and algebraic combinatorics (Vienna, 1997).", URL = "http://docserver.carma.newcastle.edu.au/198/; http://www.sciencedirect.com/science/article/pii/S0012365X99002563", abstract = "Let a be a vector of real numbers. By an integer relation for a we mean a non-zero integer vector c such that caT=0. We discuss the algorithms for finding such integer relations from the user's point of view, by presenting examples of their applications and by reviewing the available software implementations.", acknowledgement = ack-nhfb, fjournal = "Discrete Mathematics", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Research Report 97:104.", } @Book{Borwein:2000:CAN, author = "Jonathan M. Borwein and Adrian S. Lewis", title = "Convex Analysis and Nonlinear Optimization", publisher = pub-SV, address = pub-SV:adr, pages = "x + 273", year = "2000", DOI = "https://doi.org/10.1007/978-1-4757-9859-3", ISBN = "0-387-98940-4", ISBN-13 = "978-0-387-98940-2", MRclass = "49-01 (46N10 47N10 49-02 49J53 90-01)", MRnumber = "1757448", MRreviewer = "John R. Giles", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Theory and examples.", series = "CMS Books in Mathematics/Ouvrages de Math{\'e}matiques de la SMC, 3", abstract = "This book is a concise account of convex analysis, its applications and extensions, for a broad audience. Blurring as it does the distinctions between mathematical optimization and modern analysis, the elegant language of convexity and duality is indispensable both in computational optimization and for understanding variational properties of functions and multifunctions. Primarily aimed at first-year graduate students, the text consists of short, self-contained sections, each followed by an extensive set of exercises, many of which are guided. The book is thus appropriate either as a class text or for self-study.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", tableofcontents = "1: Background \\ 1.1: Euclidean Spaces \\ 1.2: Symmetric Matrices \\ 2: Inequality Constraints \\ 2.1: Optimality Conditions \\ 2.2: Theorems of the Alternative \\ 2.3: Max-functions \\ 3: Fenchel Duality \\ 3.1: Subgradients and Convex Functions \\ 3.2: The Value Function \\ 3.3: The Fenchel Conjugate \\ 4: Convex Analysis \\ 4.1: Continuity of Convex Functions \\ 4.2: Fenchel Biconjugation \\ 4.3: Lagrangian Duality \\ 5: Special Cases \\ 5.1: Polyhedral Convex Sets and Functions \\ 5.2: Functions of Eigenvalues \\ 5.3: Duality for Linear and Semidefinite Programming \\ 5.4: Convex Process Duality \\ 6: Nonsmooth Optimization \\ 6.1: Generalized Derivatives \\ 6.2: Regularity and Strict Differentiability \\ 6.3: Tangent Cones", } @Article{Borwein:2000:CBS, author = "Jonathan M. Borwein and David J. Broadhurst and Joel Kamnitzer", title = "Central Binomial Sums, Multiple {Clausen} Values and Zeta Values", journal = "ArXiv High Energy Physics --- Theory e-prints", month = apr, year = "2000", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2000hep.th....4153B; http://docserver.carma.newcastle.edu.au/243/", abstract = "We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Ap{\'e}ry sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio. In the non-alternating case, there is a strong connection to polylogarithms of the sixth root of unity, encountered in the 3-loop Feynman diagrams of \url{hep-th/9803091} and subsequently in \url{hep-ph/9910223}, \url{hep-ph/9910224}, \url{cond-mat/9911452} and \url{hep-th/0004010}.", acknowledgement = ack-nhfb, eprint = "hep-th/0004153", keywords = "High Energy Physics - Theory, Mathematics - Classical Analysis and ODEs", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2000:CDA, author = "Jonathan M. Borwein and Pierre Mar{\'e}chal and David Naugler", title = "A convex dual approach to the computation of {NMR} complex spectra", journal = "Math. Methods Oper. Res.", volume = "51", number = "1", pages = "91--102", year = "2000", DOI = "https://doi.org/10.1007/s001860050004", ISSN = "1432-2994 (print), 1432-5217 (electronic)", ISSN-L = "1432-2994", MRclass = "90C30", MRnumber = "1742398", MRreviewer = "Massimo Pappalardo", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/207/", abstract = "The particular entropy method proposed by Hoch et al. [7] for the computation of NMR complex spectra allows an elegant application of the concepts of duality theory. Correspondingly, duality theory casts new light on their choice of entropy. The purpose of this paper is to present the relevant theoretical developments together with some numerical illustrations.", acknowledgement = ack-nhfb, fjournal = "Mathematical Methods of Operations Research", ORCID-numbers = "Naugler, David/0000-0001-5485-0498; Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Research Report 98:114.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2000:CDA", } @Article{Borwein:2000:CEL, author = "Jonathan Borwein and Yves Lucet and Boris Mordukhovich", title = "Compactly epi-{Lipschitzian} convex sets and functions in normed spaces", journal = j-J-CONVEX-ANAL, volume = "7", number = "2", pages = "375--393", year = "2000", ISSN = "0944-6532 (print), 2363-6394 (electronic)", MRclass = "49J53 (46B20 46N10 90C48)", MRnumber = "1811686", MRreviewer = "Abderrahim Jourani", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/210/; http://www.heldermann.de/JCA/JCA07/JCA072/jca07019.htm", abstract = "We provide several characterizations of compact epi-Lipschitzness for closed convex sets in normed vector spaces. In particular, we show that a closed convex set is compactly epi-Lipschitzian if and only if it has nonempty relative interior, finite codimension, and spans a closed subspace. Next, we establish that all boundary points of compactly epi-Lipschitzian sets are proper support points. We provide the corresponding results for functions hy using inf-convolutions and the Legendre Fenchel transform. We also give an application to constrained optimization with compactly epi-Lipschitzian data via a generalized Slater condition involving relative interiors.", acknowledgement = ack-nhfb, fjournal = "Journal of Convex Analysis", journal-URL = "http://www.heldermann.de/JCA/jcacon.htm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 98:113.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2000:CEL", } @Article{Borwein:2000:CSF, author = "Jonathan M. Borwein and John Read and Adrian S. Lewis and Qiji Zhu", title = "Convex spectral functions of compact operators", journal = j-J-NONLINEAR-CONVEX-ANAL, volume = "1", number = "1", pages = "17--35", year = "2000", ISSN = "1345-4773 (print), 1880-5221 (electronic)", ISSN-L = "1345-4773", MRclass = "49N15 (47N10 49J52 90C25)", MRnumber = "1751726", MRreviewer = "Mihai Turinici", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.ybook.co.jp/online2/jncav1.html", acknowledgement = ack-nhfb, fjournal = "Journal of Nonlinear and Convex Analysis. An International Journal", journal-URL = "http://www.ybook.co.jp/jnca.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 99:130.", xxauthor = "Jon Borwein and Adrian Lewis and John Read and Qiji Zhu", } @Article{Borwein:2000:CSR, author = "Jonathan M. Borwein and David M. Bradley and Richard E. Crandall", title = "Computational strategies for the {Riemann} zeta function", journal = j-J-COMPUT-APPL-MATH, volume = "121", number = "1--2", pages = "247--296", month = sep, year = "2000", CODEN = "JCAMDI", DOI = "https://doi.org/10.1016/S0377-0427(00)00336-8", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", MRclass = "11M06 (11Y35 33F05)", MRnumber = "1780051", MRreviewer = "Cem Y. Y{\i}ld{\i}r{\i}m", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Numerical analysis in the 20th century, Vol. I, Approximation theory.", URL = "http://adsabs.harvard.edu/abs/2000JCoAM.121..247B; http://docserver.carma.newcastle.edu.au/211/; http://www.sciencedirect.com/science/article/pii/S0377042700003368", abstract = "We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the incidence of what we call ``value recycling''.", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 98:118.", } @Article{Borwein:2000:LFM, author = "Jonathan M. Borwein and Xianfu Wang", title = "{Lipschitz} functions with maximal {Clarke} subdifferentials are generic", journal = j-PROC-AM-MATH-SOC, volume = "128", number = "11", pages = "3221--3229", year = "2000", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/S0002-9939-00-05914-1", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "49J52 (26B25 58C20)", MRnumber = "1777577", MRreviewer = "Jean-No{\"e}l Corvellec", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/206/", abstract = "We show that on a separable Banach space most Lipschitz functions have maximal Clarke subdifferential mappings. In particular, the generic nonexpansive function has the dual unit ball as its Clarke subdifferential at every point. Diverse corollaries are given.", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2000:LFM", } @InProceedings{Borwein:2000:NCMa, author = "J. M. Borwein and T. Stanway", editor = "Bruce Cload and Tom Jenkyns", booktitle = "{Proceedings of the Conference on Technology in Mathematics Education at the Secondary and Tertiary Levels, June 2--4, 1999 at Brock University}", title = "Numerical and computational mathematics (at the undergraduate level)", publisher = "Brock University Press", address = "St. Catharines, ON, L2S 3A1 Canada", pages = "20--37", year = "2000", bibdate = "Mon Aug 15 14:24:05 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/246/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Also appeared in Cubo.", } @InProceedings{Borwein:2000:PEN, author = "J. M. Borwein and P. B. Borwein and K. Dilcher", booktitle = "Pi: A Source Book", title = "Pi, {Euler} Numbers, and Asymptotic Expansions", publisher = pub-SV, address = pub-SV:adr, pages = "??--??", year = "2000", DOI = "https://doi.org/10.1007/978-1-4757-3240-5_65", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1583/; http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_65", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2000:R, author = "Jonathan Borwein and Kwok-Kwong Stephen Choi", title = "On the representations of $ x y + y z + z x $", journal = j-EXP-MATH, volume = "9", number = "1", pages = "153--158", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1080/10586458.2000.10504642", ISSN = "1058-6458 (print), 1944-950X (electronic)", ISSN-L = "1058-6458", MRclass = "11D85", MRnumber = "1758806", MRreviewer = "Mao Hua Le", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://projecteuclid.org/euclid.em; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/expmath.bib", URL = "http://docserver.carma.newcastle.edu.au/212/; http://projecteuclid.org/euclid.em/1046889597", abstract = "We show that there are at most 19 integers that are not of the form $ x y + y z + x z $ with $ x, y, z \geq 1 $. Eighteen of them are small and easily found. The remaining possibility must be greater than $ 10^{11} $ and cannot occur if we assume the Generalized Riemann Hypothesis.", acknowledgement = ack-nhfb, fjournal = "Experimental Mathematics", journal-URL = "http://www.tandfonline.com/loi/uexm20", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 98:119.", } @InProceedings{Borwein:2000:RME, author = "J. M. Borwein and P. B. Borwein and D. H. Bailey", booktitle = "Pi: A Source Book", title = "{Ramanujan}, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi", publisher = pub-SV, address = pub-SV:adr, pages = "623--641", year = "2000", DOI = "https://doi.org/10.1007/978-1-4757-2736-4_64; https://doi.org/10.1007/978-1-4757-3240-5_64", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1587/; http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_64; http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_64", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2000:SDI, author = "Jonathan M. Borwein and Warren B. Moors", title = "Separable determination of integrability and minimality of the {Clarke} subdifferential mapping", journal = j-PROC-AM-MATH-SOC, volume = "128", number = "1", pages = "215--221", month = jan, year = "2000", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/S0002-9939-99-05001-7", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "49J52 (46N10 58C20)", MRnumber = "1622793", MRreviewer = "Lionel Thibault", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/196/; http://www.jstor.org/stable/119403", abstract = "In this paper we show that the study of integrability and D-representability of Lipschitz functions defined on arbitrary Banach spaces reduces to the study of these properties on separable Banach spaces.", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Research Report 97:102.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2000:SDI", } @Article{Borwein:2000:SM, author = "D. Borwein and J. M. Borwein and P. Mar{\'e}chal", title = "Surprise maximization", journal = j-AMER-MATH-MONTHLY, volume = "107", number = "6", pages = "517--527", month = jun # "\slash " # jul, year = "2000", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2589347", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "00A08 (03B48 90C90)", MRnumber = "1767060", MRreviewer = "S. Kutateladze", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/209/", abstract = "The Surprise Examination or Unexpected Hanging Paradox has long fascinated mathematicians and philosophers, as the number of publications devoted to it attests. For an exhaustive bibliography on the subject, see [1]. We examine and solve the optimization problems arising from an information theoretic avoidance of the Paradox. These problems provide a very satisfactory application of both the Kuhn-Tucker theory and of various classical inequalities and estimation techniques. We assume some elementary knowledge of optimization but recall the necessary convex analytic concepts in the course of the paper. Readers unfamiliar with this background may simply skip a couple of proofs and a few technical details.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 98:116.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2000:SM", } @Article{Theodorescu:2000:PSS, author = "Radu Theodorescu and Jonathan M. Borwein", title = "Problems and Solutions: Solutions: Moments of the {Poisson} Distribution: 10738", journal = j-AMER-MATH-MONTHLY, volume = "107", number = "7", pages = "659--659", month = aug # "\slash " # sep, year = "2000", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2589135", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1543703", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.jstor.org/stable/2589135", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Bailey:2001:EMR, author = "David H. Bailey and Jonathan M. Borwein", title = "Experimental mathematics: recent developments and future outlook", crossref = "Engquist:2001:MUB", pages = "51--66", year = "2001", MRclass = "00A99", MRnumber = "1852153", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/250/", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 99:143.", } @Article{Bauschke:2001:ESE, author = "Heinz H. Bauschke and Jonathan M. Borwein and Patrick L. Combettes", title = "Essential smoothness, essential strict convexity, and {Legendre} functions in {Banach} spaces", journal = j-COMMUN-CONTEMP-MATH, volume = "3", number = "4", pages = "615--647", year = "2001", DOI = "https://doi.org/10.1142/S0219199701000524", ISSN = "0219-1997 (print), 1793-6683 (electronic)", MRclass = "49J53 (46G05 46N10)", MRnumber = "1869107", MRreviewer = "S. Simons", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/232/", abstract = "The classical notions of essential smoothness, essential strict convexity, and Legendreness for convex functions axe extended from Euclidean to Banach spaces. A pertinent duality theory is developed and several useful characterizations are given. The proofs rely on new results on the more subtle behavior of subdifferentials and directional derivatives at boundary points of the domain. In weak Asplund spaces, a new formula allows the recovery of the subdifferential from nearby gradients. Finally, it is shown that every Legendre function on a reflexive Banach space is zone consistent, a fundamental property in the analysis of optimization algorithms based on Bregman distances. Numerous illustrating examples are provided.", acknowledgement = ack-nhfb, fjournal = "Communications in Contemporary Mathematics", journal-URL = "http://www.worldscientific.com/worldscinet/ccm", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 00:156.", researcherid-numbers = "Combettes, Patrick/A-2442-2011 Borwein, Jonathan/A-6082-2009 Bauschke, Heinz/D-5582-2009", unique-id = "Bauschke:2001:ESE", } @InProceedings{Bauschke:2001:JSC, author = "Heinz H. Bauschke and Jonathan M. Borwein", editor = "Dan Butnariu and Yair Censor and Simeon Reich", booktitle = "Inherently Parallel Algorithms in Feasibility and Optimization and their Applications ({Haifa}, 2000)", title = "Joint and separate convexity of the {Bregman} distance", volume = "8", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "23--36", year = "2001", DOI = "https://doi.org/10.1016/S1570-579X(01)80004-5", ISSN = "1570-579X (print), 2212-1145 (electronic)", ISSN-L = "1570-579X", MRclass = "90C48 (49J53 65J05 90C30)", MRnumber = "1853214", MRreviewer = "Simeon Reich", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Studies in Computational Mathematics", URL = "http://docserver.carma.newcastle.edu.au/227/; http://www.sciencedirect.com/science/article/pii/S1570579X01800045", abstract = "Algorithms involving Bregman projections for solving optimization problems have been receiving much attention lately. Several of these methods rely crucially on the joint convexity of the Bregman distance. In this note, we study joint and separate convexity of Bregman distances. To bring out the main ideas more clearly, we consider first functions defined on an open interval. Our main result states that the Bregman distance of a given function is jointly convex if and only if the reciprocal of its second derivative is concave. We observe that Bregman distances induced by the two most popular choices --- the energy and the Boltzmann--Shannon entropy --- are limiting cases in a profound sense. This result is generalized by weakening assumptions on differentiability and strict convexity. We then consider general, not necessarily separable, convex functions. The characterization of joint convexity has a natural and beautiful analog. Finally, we discuss spectral functions, where the situation is less clear. Throughout, we provide numerous examples to illustrate our results.", acknowledgement = ack-nhfb, keywords = ":Bregman distance; convex function; joint convexity; separate convexity", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2001:CBS, author = "Jonathan Michael Borwein and David J. Broadhurst and Joel Kamnitzer", title = "Central binomial sums, multiple {Clausen} values, and zeta values", journal = j-EXP-MATH, volume = "10", number = "1", pages = "25--34", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1080/10586458.2001.10504426", ISSN = "1058-6458 (print), 1944-950X (electronic)", ISSN-L = "1058-6458", MRclass = "11G55 (05A10 11M06 33B99)", MRnumber = "1821569", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://projecteuclid.org/euclid.em; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/expmath.bib", URL = "http://arxiv.org/abs/hep-th/0004153; http://docserver.carma.newcastle.edu.au/243/; http://projecteuclid.org/euclid.em/999188418", abstract = "We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apery sums). The study of nonalternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio.", acknowledgement = ack-nhfb, fjournal = "Experimental Mathematics", journal-URL = "http://www.tandfonline.com/loi/uexm20", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2001:CBS", } @Article{Borwein:2001:CFL, author = "Jonathan M. Borwein and Jon D. Vanderwerff", title = "Convex functions of {Legendre} type in general {Banach} spaces", journal = j-J-CONVEX-ANAL, volume = "8", number = "2", pages = "569--581", year = "2001", ISSN = "0944-6532 (print), 2363-6394 (electronic)", MRclass = "46G99 (46N10 49J50)", MRnumber = "1915959", MRreviewer = "A. B. N{\'e}meth", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/228/; http://www.heldermann.de/JCA/JCA08/JCA082/jca08030.htm", abstract = "Convex functions of Legendre type are constructed on arbitrary open convex sets in Banach spaces that satisfy appropriate rotundity and smoothness conditions. A simple direct proof of the existence of ``universal'' barriers on arbitrary open convex sets in R-n is given.", acknowledgement = ack-nhfb, fjournal = "Journal of Convex Analysis", journal-URL = "http://www.heldermann.de/JCA/jcacon.htm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 00:151.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2001:CFL", } @Article{Borwein:2001:CMCa, author = "Jonathan M. Borwein and Peter B. Borwein", title = "Challenges in Mathematical Computing", journal = j-COMPUT-SCI-ENG, volume = "3", number = "3", pages = "48--53", month = may # "\slash " # jun, year = "2001", CODEN = "CSENFA", DOI = "https://doi.org/10.1109/5992.919266", ISSN = "1521-9615 (print), 1558-366X (electronic)", ISSN-L = "1521-9615", bibdate = "Wed Aug 10 12:08:56 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/computscieng.bib", URL = "http://dlib.computer.org/cs/books/cs2001/pdf/c3048.pdf; http://docserver.carma.newcastle.edu.au/135/; http://www.computer.org/cse/cs1999c3048abs.htm", abstract = "Almost all interesting mathematical algorithmic questions relate to NP-hard questions. Such computation is prone to explode exponentially. The authors anticipate the greatest benefit will come from mathematical platforms that allow for computer-assisted insight generation, not from solutions of grand-challenge problems.", acknowledgement = ack-nhfb, fjournal = "Computing in Science and Engineering", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992", keywords = "Algebra; computational complexity; Computer architecture; Computer networks; computer-assisted insight generation; Databases; Encyclopedias; grand-challenge problems; HTML; Java; mathematical algorithmic questions; mathematical computing; mathematical platforms; Mathematics; mathematics computing; NP-hard questions; Packaging; Statistics; symbol manipulation", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2001:CMC", } @InCollection{Borwein:2001:CSF, author = "Jonathan M. Borwein and Adrian S. Lewis and Qiji J. Zhu", booktitle = "Optimization and related topics ({Ballarat}/{Melbourne}, 1999)", title = "Convex spectral functions of compact operators. {II}. {Lower} semicontinuity and rearrangement invariance", volume = "47", publisher = pub-KLUWER, address = pub-KLUWER:adr, pages = "179--196", year = "2001", DOI = "https://doi.org/10.1007/978-1-4757-6099-6_12", MRclass = "49N15 (47A10 47B10 90C25)", MRnumber = "1893622", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Appl. Optim.", URL = "http://docserver.carma.newcastle.edu.au/251/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2001:DIS, author = "J. M. Borwein and S. P. Fitzpatrick", title = "Duality inequalities and sandwiched functions", journal = j-NONLINEAR-ANAL, volume = "46", number = "3", pages = "365--380", year = "2001", CODEN = "NOANDD", DOI = "https://doi.org/10.1016/S0362-546X(00)00129-2", ISSN = "0362-546x (print), 1873-5215 (electronic)", ISSN-L = "0362-546X", MRclass = "49J53 (49N15 90C46)", MRnumber = "1851858", MRreviewer = "Roberto Lucchetti", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/204/; http://www.sciencedirect.com/science/article/pii/S0362546X00001292", acknowledgement = ack-nhfb, fjournal = "Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods", journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis", keywords = "Ekeland variational principle; Fenchel duality; Mean-value inequalities; Nonconvex separation; Sandwich theorem; Schauder fixed-point theorem", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Research Report 98:111.", } @Article{Borwein:2001:EM, author = "Jonathan M. Borwein", title = "Experimental Mathematics", journal = j-AUSTRALIAN-MATH-SOC-GAZ, volume = "28", number = "??", pages = "77--80", month = "????", year = "2001", DOI = "", ISSN = "0311-0729 (print), 1326-2297 (electronic)", ISSN-L = "0311-0729", bibdate = "Fri Aug 12 11:12:55 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1527/", acknowledgement = ack-nhfb, ajournal = "Aust. Math. Soc. Gaz.", fjournal = "Australian Mathematical Society Gazette", journal-URL = "http://www.austms.org.au/gazette", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2001:GSB, author = "Jonathan M. Borwein and Warren B. Moors and Xianfu Wang", title = "Generalized subdifferentials: a {Baire} categorical approach", journal = j-TRANS-AM-MATH-SOC, volume = "353", number = "10", pages = "3875--3893", year = "2001", CODEN = "TAMTAM", DOI = "https://doi.org/10.1090/S0002-9947-01-02820-3", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "49J52 (46G05 58C20)", MRnumber = "1837212", MRreviewer = "Mari{\'a}n Fabian", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/234/", abstract = "We use Baire categorical arguments to construct pathological locally Lipschitz functions. The origins of this approach can be traced back to Banach and Mazurkiewicz (1931) who independently used similar categorical arguments to show that ``almost every continuous real-valued function defined on [0,1] is nowhere differentiable''. As with the results of Banach and Mazurkiewicz, it appears that it is easier to show that almost every function possesses a certain property than to construct a single concrete example. Among the most striking results contained in this paper are: Almost every 1-Lipschitz function defined on a Banach space has a Clarke subdifferential mapping that is identically equal to the dual ball; if \{T-1; T-2,...,T-n\} is a family of maximal cyclically monotone operators defined on a Banach space X then there exists a real-valued locally Lipschitz function g such that partial derivative (0g)(x) =co \{T-1(x); T-2(x),...,T-n(x)\} for each x is an element of X; in a separable Banach space each non-empty weak* compact convex subset in the dual space is identically equal to the approximate subdifferential mapping of some Lipschitz function and for locally Lipschitz functions defined on separable spaces the notions of strong and weak integrability coincide.", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 99:127.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2001:GSB", } @Article{Borwein:2001:RCS, author = "D. Borwein and J. Borwein and G. Fee and R. Girgensohn", title = "Refined convexity and special cases of the {Blaschke--Santalo} inequality", journal = j-MATH-INEQUAL-APPL, volume = "4", number = "4", pages = "631--638", year = "2001", DOI = "https://doi.org/10.7153/mia-04-56", ISSN = "1331-4343 (print), 1848-9966 (electronic)", ISSN-L = "1331-4343", MRclass = "52A38 (26B25 52A40)", MRnumber = "1859668", MRreviewer = "Beifang Chen", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/222/", abstract = "We derive the l(p) version of the classical Blaschke-Santalo inequality for polar volumes as a consequence of more subtle convexity estimates for the volume of the p-ball in Euclidean space. We also give analogs for the (p, q) -substitution norm.", acknowledgement = ack-nhfb, ajournal = "Math. Inequal. Appl.", fjournal = "Mathematical Inequalities \& Applications", journal-URL = "http://mia.ele-math.com/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 00:146.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2001:RCS", } @Article{Borwein:2001:RGC, author = "J. M. Borwein and M. Fabian and I. Kortezov and P. D. Loewen", title = "The range of the gradient of a continuously differentiable bump", journal = j-J-NONLINEAR-CONVEX-ANAL, volume = "2", number = "1", pages = "1--19", year = "2001", ISSN = "1345-4773 (print), 1880-5221 (electronic)", ISSN-L = "1345-4773", MRclass = "58C20 (46G05 49J53)", MRnumber = "1828155", MRreviewer = "Mari{\'a}n Fabian", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Special issue for Professor Ky Fan.", URL = "http://docserver.carma.newcastle.edu.au/231/; http://www.ybook.co.jp/online2/opjnca/vol2/p1.html", acknowledgement = ack-nhfb, fjournal = "Journal of Nonlinear and Convex Analysis. An International Journal", journal-URL = "http://www.ybook.co.jp/jnca.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:2001:RP, author = "Jonathan M. Borwein and Peter B. Borwein", title = "{Ramanujan} and pi", crossref = "Berndt:2001:RES", pages = "187--199", year = "2001", MRclass = "11-03 (01A70)", MRnumber = "1862751", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Reprint of \cite{Borwein:1988:RP}.", series = "Hist. Math.", URL = "http://docserver.carma.newcastle.edu.au/1379/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2001:SGR, author = "Jonathan M. Borwein and Ivaylo Kortezov", title = "Some generic results on nonattaining functionals", journal = j-SET-VALUED-ANAL, volume = "9", number = "1--2", pages = "35--47", year = "2001", CODEN = "SVANEG", DOI = "https://doi.org/10.1023/A:1011246414064", ISSN = "0927-6947 (print), 1572-932x (electronic)", ISSN-L = "0927-6947", MRclass = "46N10 (49J53 54E52)", MRnumber = "1845933", MRreviewer = "Gargi Chakraborty", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Wellposedness in optimization and related topics (Gargnano, 1999).", URL = "http://docserver.carma.newcastle.edu.au/221/", abstract = "We prove that (a) in a reflexive space, for any linearly bounded but unbounded closed convex subset the nonsupport functionals are a dense G(delta) subset of the polar set, and (b) any non-semicoercive proper convex Isc [weak*-lsc] function in a [dual] Banach space has a generic [dense G(delta)] set of L-infinity-perturbations which do not attain their infimum. We also characterize the proper convex functions that have inf-nonattaining L-infinity-perturbations. This results also in a criterion for reflexivity.", acknowledgement = ack-nhfb, fjournal = "Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications", journal-URL = "http://link.springer.com/journal/11228", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2001:SGR", } @Article{Borwein:2001:SRP, author = "David Borwein and Jonathan M. Borwein", title = "Some remarkable properties of sinc and related integrals", journal = j-RAMANUJAN-J, volume = "5", number = "1", pages = "73--89", year = "2001", CODEN = "RAJOF9", DOI = "https://doi.org/10.1023/A:1011497229317", ISSN = "1382-4090 (print), 1572-9303 (electronic)", ISSN-L = "1382-4090", MRclass = "42A38 (26D15 40A05 41A55)", MRnumber = "1829810", MRreviewer = "Philip Heywood", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/249/", abstract = "Using Fourier transform techniques, we establish inequalities for integrals of the form [GRAPHICS] We then give quite striking closed form evaluations of such integrals and finish by discussing various extensions and applications.", acknowledgement = ack-nhfb, fjournal = "The {Ramanujan} Journal", journal-URL = "http://link.springer.com/journal/11139", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2001:SRP", } @Article{Borwein:2001:STC, author = "J. M. Borwein and X. Wang", title = "Subdifferentiability of typical continuous functions", journal = "Nonlinear Analysis Forum", volume = "6", number = "1", pages = "49--58", year = "2001", ISSN = "1226-7228", MRclass = "49J52 (26A24 46G05 46T20)", MRnumber = "1844467", MRreviewer = "Yan Gao", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Nonlinear analysis and its applications (St. John's, NF, 1999).", URL = "http://docserver.carma.newcastle.edu.au/241/; http://prof.ks.ac.kr/bslee/naf/table/vol-0601/v0601-05a.PDF", acknowledgement = ack-nhfb, ajournal = "Nonlinear Anal. Forum", fjournal = "Nonlinear Analysis Forum. An International Journal", journal-URL = "http://prof.ks.ac.kr/bslee/naf/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2001:SVM, author = "Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lison{\v{e}}k", title = "Special values of multiple polylogarithms", journal = j-TRANS-AM-MATH-SOC, volume = "353", number = "3", pages = "907--941", month = mar, year = "2001", CODEN = "TAMTAM", DOI = "https://doi.org/10.1090/S0002-9947-00-02616-7", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "33B30 (11G55 11Y60 33E20)", MRnumber = "1709772", MRreviewer = "P. D. F. Ion", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.jstor.org/stable/221840", abstract = "Historically, the polylogarithm has attracted specialists and nonspecialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, we have been forced to consider multidimensional extensions encompassing the classical polylogarithm, Euler sums, and the Riemann zeta function. Here, we provide a general framework within which previously isolated results can now be properly understood. Applying the theory developed herein, we prove several previously conjectured evaluations, including an intriguing conjecture of Don Zagier.", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2001:SVM", } @Article{Lindqvist:2001:PSS, author = "Peter Lindqvist and Jaak Peetre and Jonathan M. Borwein", title = "Problems and Solutions: Solutions: Generalized Trigonometric Functions: 10744", journal = j-AMER-MATH-MONTHLY, volume = "108", number = "5", pages = "473--474", year = "2001", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2695813", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRnumber = "1544137", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Book{Borowski:2002:MCD, author = "Ephraim J. Borowski and Jonathan M. Borwein", title = "Mathematics: {Collins} dictionary", publisher = pub-COLLINS, address = pub-COLLINS:adr, edition = "Second", pages = "633", year = "2002", ISBN = "0-00-710295-X", ISBN-13 = "978-0-00-710295-2", LCCN = "????", bibdate = "Tue Aug 16 09:04:49 MDT 2016", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", subject = "Mathematics; Dictionaries; Mathematik; W{\"o}rterbuch.; Mathematics.", } @Article{Borwein:2002:ANB, author = "J. M. Borwein and M. Jim{\'e}nez-Sevilla and J. P. Moreno", title = "Antiproximinal norms in {Banach} spaces", journal = j-J-APPROX-THEORY, volume = "114", number = "1", pages = "57--69", year = "2002", CODEN = "JAXTAZ", DOI = "https://doi.org/10.1006/jath.2001.3636", ISSN = "0021-9045 (print), 1096-0430 (electronic)", ISSN-L = "0021-9045", MRclass = "46B20 (41A65)", MRnumber = "1880294", MRreviewer = "Ioan {\c{S}}erb", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/233/; http://www.sciencedirect.com/science/article/pii/S0021904501936366", abstract = "We prove that every Banach space containing a complemented copy of $ c_0 $ has an antiproximinal body for a suitable norm. If, in addition, the space is separable, there is a pair of antiproximinal norms. In particular, in a separable polyhedral space $X$, the set of all (equivalent) norms on $X$ having an isomorphic antiproximinal norm is dense. In contrast, it is shown that there are no antiproximinal norms in Banach spaces with the convex point of continuity property (CPCP). Other questions related to the existence of antiproximinal bodies are also discussed.", acknowledgement = ack-nhfb, fjournal = "Journal of Approximation Theory", journal-URL = "http://www.sciencedirect.com/science/journal/00219045", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", received = "CECM Preprint 00:157.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2002:ANB", } @Article{Borwein:2002:ASS, author = "Jonathan M. Borwein and Qiji J. Zhu", title = "Addendum: ``{A survey of subdifferential calculus with applications'' [Nonlinear Anal.\ {\bf 38} (1999), no.\ 6, Ser.\ A: Theory Methods, 687--773; (2000j:49024)]}", journal = j-NONLINEAR-ANAL, volume = "49", number = "2, Ser. A: Theory Methods", pages = "295--296", year = "2002", CODEN = "NOANDD", DOI = "https://doi.org/10.1016/S0362-546X(01)00099-2", ISSN = "0362-546x (print), 1873-5215 (electronic)", ISSN-L = "0362-546X", MRclass = "49J52 (46G05 46N10 49-02 49J53 58C05)", MRnumber = "1885123", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "See \cite{Borwein:1999:SSC}.", acknowledgement = ack-nhfb, fjournal = "Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods", journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2002:CBC, author = "J. M. Borwein and J. D. Vanderwerff", title = "On the continuity of biconjugate convex functions", journal = j-PROC-AM-MATH-SOC, volume = "130", number = "6", pages = "1797--1803", month = jun, year = "2002", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/S0002-9939-01-06249-9", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "46B20 (46N10 52A41)", MRnumber = "1887028", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/230/; http://www.jstor.org/stable/2699775", abstract = "We show that a Banach space is a Grothendieck space if and only if every continuous convex function on $X$ has a continuous biconjugate function on $ X**$, thus also answering a question raised by S. Simons. Related characterizations and examples are given.", acknowledgement = ack-nhfb, article-number = "UNSP S 0002-9939(01)06249-9", fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 00:154.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2002:CBC", } @Article{Borwein:2002:EMI, author = "J. M. Borwein", title = "Experimental Mathematics and Integer Relations", journal = "European Research Consortium for Informatics and Mathematics, ERCIM News", volume = "50", number = "??", pages = "30--31", month = jul, year = "2002", bibdate = "Sat Aug 13 17:35:58 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Section Special Theme ERCIMathematics.", acknowledgement = ack-nhfb, journal-URL = "http://ercim-news.ercim.eu/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "The journal web sites has no online content before volume 86, July 2011.", } @Article{Borwein:2002:FES, author = "J. M. Borwein and I. Kortezov and H. Wiersma", title = "A {$ C^1 $}-function that is even on a sphere and has no critical points in the ball", journal = j-J-NONLINEAR-CONVEX-ANAL, volume = "3", number = "1", pages = "1--16", year = "2002", ISSN = "1345-4773 (print), 1880-5221 (electronic)", ISSN-L = "1345-4773", MRclass = "49J53 (26B35 47J30)", MRnumber = "1895233", MRreviewer = "S. Simons", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.ybook.co.jp/online2/jncav3.html", acknowledgement = ack-nhfb, fjournal = "Journal of Nonlinear and Convex Analysis. An International Journal", journal-URL = "http://www.ybook.co.jp/jnca.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 01:164.", } @Article{Borwein:2002:MVS, author = "David Borwein and Jonathan M. Borwein and Bernard A. {Mares, Jr.}", title = "Multi-variable sinc integrals and volumes of polyhedra", journal = j-RAMANUJAN-J, volume = "6", number = "2", pages = "189--208", year = "2002", CODEN = "RAJOF9", DOI = "https://doi.org/10.1023/A:1015727317007", ISSN = "1382-4090 (print), 1572-9303 (electronic)", ISSN-L = "1382-4090", MRclass = "52A38 (42B10)", MRnumber = "1908197", MRreviewer = "Carla Peri", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/56/", abstract = "We investigate multi-variable integrals of products of sinc functions and show how they may be interpreted as volumes of symmetric convex polyhedra. We then derive an explicit formula for computing such sinc integrals and so equivalently volumes of polyhedra.", acknowledgement = ack-nhfb, fjournal = "The {Ramanujan} Journal", journal-URL = "http://link.springer.com/journal/11139", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 01:159.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2002:MVS", } @Article{Borwein:2002:RGL, author = "J. M. Borwein and M. Fabian and P. D. Loewen", title = "The range of the gradient of a {Lipschitz} {$ C^1 $}-smooth bump in infinite dimensions", journal = j-ISRAEL-J-MATH, volume = "132", number = "1", pages = "239--251", month = dec, year = "2002", CODEN = "ISJMAP", DOI = "https://doi.org/10.1007/BF02784514", ISSN = "0021-2172 (print), 1565-8511 (electronic)", ISSN-L = "0021-2172", MRclass = "58C05 (46B20 46G05)", MRnumber = "1952623", MRreviewer = "Li Xin Cheng", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/144/; http://link.springer.com/article/10.1007/BF02784514", abstract = "If a Banach space has a Lipschitz C-1-smooth bump function, then it admits other bumps of the same smoothness whose gradients exactly fill the dual unit ball and other reasonable figures. This strengthens a result of Azagra and Deville who were able to cover the dual unit ball.", acknowledgement = ack-nhfb, fjournal = "Israel Journal of Mathematics", journal-URL = "http://link.springer.com/journal/11856", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 01:169.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Fabian, Marian/D-5427-2014", unique-id = "Borwein:2002:RGL", } @Article{Borwein:2002:RNC, author = "Jon Borwein and John Giles and Jon Vanderwerff", title = "Rotund norms, {Clarke} subdifferentials and extensions of {Lipschitz} functions", journal = j-NONLINEAR-ANAL, volume = "48", number = "2", pages = "287--301", year = "2002", CODEN = "NOANDD", DOI = "https://doi.org/10.1016/S0362-546X(00)00187-5", ISSN = "0362-546x (print), 1873-5215 (electronic)", ISSN-L = "0362-546X", MRclass = "49J52 (46B20)", MRnumber = "1870757", MRreviewer = "Lionel Thibault", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/219/; http://www.sciencedirect.com/science/article/pii/S0362546X00001875", acknowledgement = ack-nhfb, fjournal = "Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods", journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis", keywords = "Baire category; Clarke subdifferentials; Extensions; Lipschitz functions; Rotund norms", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 98:126.", } @Article{Borwein:2002:SSC, author = "Jonathan M. Borwein and Qiji J. Zhu", title = "A survey of subdifferential calculus with applications: [Nonlinear Anal. TMA {\bf 38} (1999) 687--773]", journal = j-NONLINEAR-ANAL, volume = "49", number = "2", pages = "295--296", year = "2002", CODEN = "NOANDD", DOI = "https://doi.org/10.1016/S0362-546X(01)00099-2", ISSN = "0362-546x (print), 1873-5215 (electronic)", ISSN-L = "0362-546X", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/199/; http://www.sciencedirect.com/science/article/pii/S0362546X01000992", acknowledgement = ack-nhfb, fjournal = "Nonlinear Analysis, Theory, Methods and Applications", journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bauschke:2003:BMO, author = "Heinz H. Bauschke and Jonathan M. Borwein and Patrick L. Combettes", title = "{Bregman} monotone optimization algorithms", journal = j-SIAM-J-CONTROL-OPTIM, volume = "42", number = "2", pages = "596--636", year = "2003", CODEN = "SJCODC", DOI = "https://doi.org/10.1137/S0363012902407120", ISSN = "0363-0129 (print), 1095-7138 (electronic)", ISSN-L = "0363-0129", MRclass = "90C25 (47H05 47N10 90C48)", MRnumber = "1982285", MRreviewer = "Simeon Reich", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/127/", abstract = "A broad class of optimization algorithms based on Bregman distances in Banach spaces is unified around the notion of Bregman monotonicity. A systematic investigation of this notion leads to a simplified analysis of numerous algorithms and to the development of a new class of parallel block-iterative surrogate Bregman projection schemes. Another key contribution is the introduction of a class of operators that is shown to be intrinsically tied to the notion of Bregman monotonicity and to include the operators commonly found in Bregman optimization methods. Special emphasis is placed on the viability of the algorithms and the importance of Legendre functions in this regard. Various applications are discussed.", acknowledgement = ack-nhfb, article-number = "PII S0363012902407120", fjournal = "SIAM Journal on Control and Optimization", journal-URL = "http://epubs.siam.org/sicon", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 02:184.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Combettes, Patrick/A-2442-2011 Bauschke, Heinz/D-5582-2009", unique-id = "Bauschke:2003:BMO", } @Article{Benoist:2003:CQV, author = "Jo{\"e}l Benoist and Jonathan M. Borwein and Nicolae Popovici", title = "A characterization of quasiconvex vector-valued functions", journal = j-PROC-AM-MATH-SOC, volume = "131", number = "4", pages = "1109--1113", month = apr, year = "2003", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/S0002-9939-02-06761-8", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "26B25 (49J53 90C26)", MRnumber = "1948101", MRreviewer = "Laura Martein", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/145/; http://www.jstor.org/stable/1194189", abstract = "The aim of this paper is to characterize in terms of scalar quasiconvexity the vector-valued functions which are $K$-quasiconvex with respect to a closed convex cone $K$ in a Banach space. Our main result extends a well-known characterization of $K$-quasiconvexity by means of extreme directions of the polar cone of $K$, obtained by Dinh The Luc in the particular case when $K$ is a polyhedral cone generated by exactly $n$ linearly independent vectors in the Euclidean space $ R^n$.", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Popovici, Nicolae/0000-0002-1842-6005; Roohi, Mehdi/0000-0002-8444-042X; Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 01:170.", researcherid-numbers = "Popovici, Nicolae/G-6304-2010 Borwein, Jonathan/A-6082-2009", unique-id = "Benoist:2003:CQV", } @TechReport{Berggren:2003:PP, author = "Lennart Berggren and Jonathan Borwein and Peter Borwein", title = "A Pamphlet on Pi", type = "CECM Preprint", number = "2003:210", institution = inst-CECM, address = inst-CECM:adr, month = jun, year = "2003", bibdate = "Tue Aug 16 10:15:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/33/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2003:BGT, author = "J. M. Borwein and A. L. Dontchev", title = "On the {Bartle--Graves} theorem", journal = j-PROC-AM-MATH-SOC, volume = "131", number = "8", pages = "2553--2560", year = "2003", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/S0002-9939-03-07229-0", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "49J53 (47J20)", MRnumber = "1974655", MRreviewer = "Mari{\'a}n Fabian", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "The Bartle-Graves theorem extends the Banach open mapping principle to a family of linear and bounded mappings, thus showing that surjectivity of each member of the family is equivalent to the openness of the whole family. In this paper we place this theorem in the perspective of recent concepts and results, and present a general Bartle-Graves theorem for set-valued mappings. As applications, we obtain versions of this theorem for mappings defined by systems of inequalities, and for monotone variational inequalities.", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 02:185.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Dontchev, Assen/J-6833-2017", unique-id = "Borwein:2003:BGT", } @InCollection{Borwein:2003:BTE, author = "Jonathan M. Borwein", editor = "A. Michalos", booktitle = "Royal Society of Canada Volume", title = "The best teacher {I} ever had: personal reports from highly productive scholars", publisher = "Althouse Press", address = "????", pages = "??--??", year = "2003", bibdate = "Sat Aug 13 17:29:16 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2003:CEI, author = "Jonathan Borwein and Roland Girgensohn", title = "A class of exponential inequalities", journal = j-MATH-INEQUAL-APPL, volume = "6", number = "3", pages = "397--411", year = "2003", DOI = "https://doi.org/10.7153/mia-06-37", ISSN = "1331-4343 (print), 1848-9966 (electronic)", ISSN-L = "1331-4343", MRclass = "26D15", MRnumber = "1992480", MRreviewer = "Feng Qi", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/148/", abstract = "We prove that for reals $ x_i $ with $ \sum x_i \geq 0 $, the estimate $ \sum x_i e^{x_i} \geq (C_N / N) \sum x_i^2 $ holds, where $ C_N = \max \{ 2, e (1 - 1 / N) \} $. We also prove analogues for the $I$-norm and for Lebesgue-integrable functions.", acknowledgement = ack-nhfb, ajournal = "Math. Inequal. Appl.", fjournal = "Mathematical Inequalities \& Applications", journal-URL = "http://mia.ele-math.com/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 01:174.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2003:CEI", } @Article{Borwein:2003:DSS, author = "Jonathan Michael Borwein and Kwok-Kwong Stephen Choi", title = "On {Dirichlet} series for sums of squares", journal = j-RAMANUJAN-J, volume = "7", number = "1--3", pages = "95--127", year = "2003", CODEN = "RAJOF9", DOI = "https://doi.org/10.1023/A:1026230709945", ISSN = "1382-4090 (print), 1572-9303 (electronic)", ISSN-L = "1382-4090", MRclass = "11M41 (11E25)", MRnumber = "2035795", MRreviewer = "Don Redmond", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Rankin memorial issues.", URL = "http://docserver.carma.newcastle.edu.au/142/", abstract = "Hardy and Wright (\booktitle{An Introduction to the Theory of Numbers}, 5th edn., Oxford, 1979) recorded elegant closed forms for the generating functions of the divisor functions $ \sigma_k(n) $ and $ \sigma^2_k(n) $ in the terms of Riemann Zeta function $ \zeta (s) $ only. In this paper, we explore other arithmetical functions enjoying this remarkable property. In Theorem 2.1 below, we are able to generalize the above result and prove that if $ f_i $ and $ g_i $ are completely multiplicative, then we have [large equation] where $ L_f(s) := \sum_{n = 1}^\infty f(n) n^{-s} $ is the Dirichlet series corresponding to $f$. Let $ r_N(n)$ be the number of solutions of $ x_1^2 + \ldots {} + x_N^2 = n$ and $ r_{2, P}(n)$ be the number of solutions of $ x^2 + P y^2 = n$. One of the applications of Theorem 2.1 is to obtain closed forms, in terms of $ \zeta (s)$ and Dirichlet $L$-functions, for the generating functions of $ r_N(n)$, $ r_N^2 (n)$, $ r_{2, P}(n)$ and $ r_{2, P}(n)^2$ for certain $N$ and $P$. We also use these generating functions to obtain asymptotic estimates of the average values for each function for which we obtain a Dirichlet series.", acknowledgement = ack-nhfb, fjournal = "The {Ramanujan} Journal", journal-URL = "http://link.springer.com/journal/11139", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 01:167.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2003:DSS", } @Article{Borwein:2003:LFL, author = "J. M. Borwein and Xianfu Wang", title = "{Lipschitz} functions on the line with prescribed {H}{\"o}lder subdifferentials", journal = "Advanced Studies in Contemporary Mathematics (Kyungshang).", volume = "7", number = "2", pages = "93--117", year = "2003", ISSN = "1229-3067", ISSN-L = "1229-3067", MRclass = "49J52 (26A16 26A24 26A27)", MRnumber = "2005859", MRreviewer = "Mari{\'a}n Fabian", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1526/", acknowledgement = ack-nhfb, ajournal = "Adv. Stud. Contemp. Math. (Kyungshang)", fjournal = "Advanced Studies in Contemporary Mathematics (Kyungshang). Memoirs of the Jangjeon Mathematical Society", journal-URL = "http://www.jangjeon.or.kr/etc/Search.html?division=ASCM", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Article archive requires login access.", } @Article{Borwein:2003:LLC, author = "J. M. Borwein and J. Vanderwerff and Xianfu Wang", title = "Local {Lipschitz}-constant functions and maximal subdifferentials", journal = j-SET-VALUED-ANAL, volume = "11", number = "1", pages = "37--67", year = "2003", CODEN = "SVANEG", DOI = "https://doi.org/10.1023/A:1021975622768", ISSN = "0927-6947 (print), 1572-932X (electronic)", ISSN-L = "0927-6947", MRclass = "49J52 (54E40 54E52)", MRnumber = "1954034", MRreviewer = "John R. Giles", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://link.springer.com/article/10.1023/A%3A1021975622768", abstract = "It is shown that if $ k(x) $ is an upper semicontinuous and quasi lower semicontinuous function on a Banach space $X$, then $ k(x) B - X*$ is the Clarke subdifferential of some locally Lipschitz function on $X$. Related results for approximate subdifferentials are also given. Moreover, on smooth Banach spaces, for every locally Lipschitz function with minimal Clarke subdifferential, one can obtain a maximal Clarke subdifferential map via its `local Lipschitz-constant' function. Finally, some results concerning the characterization and calculus of local Lipschitz-constant functions are developed.", acknowledgement = ack-nhfb, fjournal = "Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications", journal-URL = "http://link.springer.com/journal/11228", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 01:158.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2003:LLC", } @InProceedings{Borwein:2003:MDM, author = "J. M. Borwein and T. Stanway", title = "Managing Digital Mathematical Discourse", crossref = "Asperti:2003:MKM", pages = "45--55", year = "2003", bibdate = "Sat Aug 13 17:26:56 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "In this paper, we propose that the present state of Mathematical Knowledge Management (MKM) derives from two main imperatives: the desire to organize and encapsulate mathematical knowledge after it is produced and the desire to encapsulate the act of production. While progress in digital network technology has facilitated a confluence of these efforts, their original separation imposes an approximate rubric on MKM which may be used to help define the challenges facing the field. We propose that one of the main challenges lies in the question of fixed versus flexible ontologies and the related question of ontology resolution between applications. Finally, we describe Emkara, an application which adopts a flexible metadata definition in the archiving and retrieval of digital mathematical exchanges, queries, and grey literature.", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2003:MDM", } @Article{Borwein:2003:NRI, author = "J. Borwein and R. Goebel", title = "Notions of relative interior in {Banach} spaces", journal = "J. Math. Sci. (NY)", volume = "115", number = "4", pages = "2542--2553", year = "2003", CODEN = "JMTSEW", DOI = "https://doi.org/10.1023/A:1022988116044", ISSN = "1072-3374 (print), 1573-8795 (electronic)", MRclass = "49J53 (46B20 90C48)", MRnumber = "1992991", MRreviewer = "Constantin Z{\u{a}}linescu", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Special issue on optimization and related topics, 1.", URL = "http://docserver.carma.newcastle.edu.au/138/; http://link.springer.com/article/10.1023/A%3A1022988116044", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Sciences (New York)", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 01:162.", } @Article{Borwein:2003:PDA, author = "J. Borwein and R. Choksi and P. Mar{\'e}chal", title = "Probability distributions of assets inferred from option prices via the principle of maximum entropy", journal = j-SIAM-J-OPT, volume = "14", number = "2", pages = "464--478", year = "2003", CODEN = "SJOPE8", DOI = "https://doi.org/10.1137/S1052623401400324", ISSN = "1052-6234 (print), 1095-7189 (electronic)", ISSN-L = "1052-6234", MRclass = "90C25 (91B28)", MRnumber = "2048161", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/10/", abstract = "This article revisits the maximum entropy algorithm in the context of recovering the probability distribution of an asset from the prices of finitely many associated European call options via partially finite convex-programming. We are able to provide an effective characterization of the constraint qualification under which the problem reduces to optimizing an explicit function in finitely many variables. We also prove that the value (or objective) function is lower semicontinuous on its domain. Reference is given to a website which exploits these ideas for the efficient computation of the maximum entropy solution (MES).", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Optimization", journal-URL = "http://epubs.siam.org/siopt", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 02:176.", researcherid-numbers = "Choksi, Rustum/A-9985-2009 Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2003:PDA", } @Article{Borwein:2003:SWG, author = "Jonathan Borwein and Simon Fitzpatrick and Roland Girgensohn", title = "Subdifferentials whose graphs are not norm {$ \times $} weak$^*$ closed", journal = j-CAN-MATH-BULL, volume = "46", number = "4", pages = "538--545", month = dec, year = "2003", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-2003-051-5", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", MRclass = "49J52 (46N10 47H05 90C48)", MRnumber = "2011392", MRreviewer = "John R. Giles", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://cms.math.ca/cmb/v46/; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/canmathbull.bib", URL = "http://cms.math.ca/10.4153/CMB-2003-051-5; http://docserver.carma.newcastle.edu.au/149/", abstract = "In this note we give examples of convex functions whose subdifferentials have unpleasant properties. Particularly, we exhibit a proper lower semicontinuous convex function on a separable Hilbert space such that the graph of its subdifferential is not dosed in the product of the norm and bounded weak topologies. We also exhibit a set whose sequential normal cone is not norm dosed.", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 01:175.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2003:SWG", } @Article{Kellar:2003:DCM, author = "Melanie Kellar and Bonnie MacKay and Rui Zhang and Carolyn Watters and David Kaufman and Jonathan Borwein", title = "Dynamic Composition of Math Lessons", journal = "Journal of Educational Technology \& Society", volume = "6", number = "4", pages = "100--111", month = "????", year = "2003", ISSN = "1176-3647 (print), 1436-4522 (electronic)", ISSN-L = "1176-3647", bibdate = "Tue Feb 06 09:20:39 2018", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1525/; http://ifets.ieee.org/periodical/6_4/10.pdf; http://www.jstor.org/stable/jeductechsoci.6.4.100", acknowledgement = ack-nhfb, journal-URL = "http://www.jstor.org/journal/jeductechsoci", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bailey:2004:BEA, author = "David H. Bailey and Jonathan M. Borwein and Richard E. Crandall and Carl Pomerance", title = "On the binary expansions of algebraic numbers", journal = "Journal de Th{\'e}orie des Nombres de {Bordeaux}", volume = "16", number = "3", pages = "487--518", year = "2004", ISSN = "1246-7405 (print), 2118-8572 (electronic)", ISSN-L = "1246-7405", MRclass = "11K16 (11J25 11J91)", MRnumber = "2144954", MRreviewer = "John H. Loxton", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/36/; http://jtnb.cedram.org/item?id=JTNB_2004__16_3_487_0", acknowledgement = ack-nhfb, ajournal = "J. Th{\'e}or. Nombres Bordeaux", fjournal = "Journal de Th{\'e}orie des Nombres de Bordeaux", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 2003:204.", } @Book{Berggren:2004:PSB, author = "Lennart Berggren and Jonathan Borwein and Peter Borwein", title = "Pi: a source book", publisher = pub-SV, address = pub-SV:adr, edition = "Third", pages = "xx + 797", year = "2004", DOI = "https://doi.org/10.1007/978-1-4757-4217-6", ISBN = "0-387-20571-3", ISBN-13 = "978-0-387-20571-7", MRclass = "11-00 (01A05 01A75 11-03)", MRnumber = "2065455", MRreviewer = "F. Beukers", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 2003:210.", tableofcontents = "Preface to the Third Edition / v \\ Preface to the Second Edition / vi \\ Preface / vii \\ Acknowledgments / x \\ Introduction / xvii \\ 1. The Rhind Mathematical Papyrus --- Problem 50 ($\approx$1650 B.C.) / A problem dealing with the area of a round field of given diameter / 1 \\ 2. Engels / Quadrature of the Circle in Ancient Egypt (1977) / A conjectural explanation of how the mathematicians of ancient Egypt approximated the area of a circle / 3 \\ 3. Archimedes / Measurement of a Circle --- (-250 B.C.) / The seminal work in which Archimedes presents the first true algorithm for $ \pi $ / 7 \\ 4. Phillips / Archimedes the Numerical --- Analyst (1981) / A summary of Archimedes' work on the computation of $ \pi $ using modem notation / 15 \\ 5. Lam and Ang / Circle Measurements in Ancient China (1986) / This paper discusses and contains a translation of Liu Hui's (3rd century) method for evaluating $ \pi $ and also examines values for $ \pi $ given by Zu Chongzhi (429--500) / 20 \\ 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane and Solid Figures (--850) / This extract gives an explicit statement and proof that the ratio of the circumference to the diameter is constant / 36 \\ 7. M{\=a}dhava / The Power Series for Arctan and Pi (-1400) / These theorems by a fifteenth century Indian mathematician give Gregory's series for arctan with remainder terms and Leibniz's series for $ \pi $ / 45 \\ 8. Hope-Jones / Ludolph (or Ludolff or Lucius) van Ceulen (1938) / Correspondence about van Ceulen's tombstone in reference to it containing some digits of $ \pi $ / 51 \\ 9. Vi{\`e}te / \booktitle{Variorum de Rebus Mathematicis Reponsorum Liber VII} (1593) / Two excerpts. One containing the first infinite expression of $ \pi $, obtained by relating the area of a regular $2n$-gon to that of a regular $n$-gon / 53 \\ 10. Wallis. Computation of $ \pi $ by Successive Interpolations (1655) / How Wallis derived the infinite product for $ \pi $ that bears his name / 68 \\ 11. Wallis / \booktitle{Arithmetica Infinitorum} (1655) / An excerpt including Prop. 189, 191 and an alternate form of the result that gives Wm. Brounker's continued fraction expression for $ 4 / \pi$ / ?? \\ 12. Huygens / \booktitle{De Circuli Magnitudine Inventa} (1654) / Huygens's demonstration of how to triple the number of correct decimals over those in Archimedes' estimate of $ \pi $ / 81 13. Gregory / Correspondence with John Collins (1671) / A letter to Collins in which he gives his series for arctangent, carried to the ninth power / 87 \\ 14. Roy / The Discovery of the Series Formula for $ \pi $ by Leibniz, Gregory, and Nilakantha (1990) / A discussion of the discovery of the series $ \pi / 4 = 1 - 1/3 + 1/5 - \cdots{} $ / 92 \\ 15. Jones / The First Use of $ \pi $ for the Circle Ratio (1706) / An excerpt from Jones' book, the \booktitle{Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics}, London, 1706 / 108 \\ 16. Newton / Of the Method of Fluxions and Infinite Series (1737) / An excerpt giving Newton's calculation of $ \pi $ to 16 decimal places / 110 \\ 17. Euler / Chapter 10 of \booktitle{Introduction to Analysis of the Infinite (On the Use of the Discovered Fractions to Sum Infinite Series)} (1748) / This includes many of Euler's infinite series for $ \pi $ and powers of $ \pi $ / 112 \\ 18. Lambert / \booktitle{M{\'e}moire Sur Quelques Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s Transcendentes Circulaires et Logarithmiques} (1761) / An excerpt from Lambert's original proof of the irrationality of $ \pi $ / 129 19. Lambert / Irrationality of $ \pi $ (1969) / A translation and Struik's discussion of Lambert's proof of the irrationality of $ \pi $ / 141 \\ 20. Shanks / Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals (1853) / Pages from Shanks's report of his monumental hand calculation of $ \pi $ / 147 \\ 21. Hermite / \booktitle{Sur La Fonction Exponentielle} (1873) / The first proof of the transcendence of $ e $ / 162 \\ 22. Lindemann / \booktitle{Ueber die Zahl $ \pi $} (1882) / The first proof of the transcendence of $ \pi $ / 194 23. Weierstrass / \booktitle{Zu Lindemann's Abhandlung ``{\"U}ber die Ludolphsche Zahl''} (1885) / Weierstrass' proof of the transcendence of $ \pi $ / 207 24. Hilbert / \booktitle{Ueber die Transzendenz der Zahlen $ e $ und $ \pi $} (1893) / Hilbert's short and elegant simplification of the transcendence proofs for $ e $ and $ \pi $ / 226 25. Goodwin / Quadrature of the Circle (1894) / The dubious origin of the attempted legislation of the value of $ \pi $ in Indiana / 230 \\ 26. Edington / House Bill No. 246, Indiana State Legislature, 1897 (1935) / A summary of the action taken by the Indiana State Legislature to fix the value of $ \pi $ (including a copy of the actual bill that was proposed) / 231 \\ 27. Singmaster / The Legal Values of Pi (1985) / A history of the attempt by Indiana to legislate the value of $ \pi $ / 236 \\ 28. Ramanujan / Squaring the Circle (1913) / A geometric approximation to $ \pi $ / 240 \\ 29. Ramanujan / Modular Equations and Approximations to $ \pi $ (1914) / Ramanujan's seminal paper on pi that includes a number of striking series and algebraic approximations / 241 \\ 30. Watson / The Marquis and the Land Agent: A Tale of the Eighteenth Century (1933) / A Presidential address to the Mathematical Association in which the author gives an account of ``some of the elementary work on arcs and ellipses and other curves which led up to the idea of inverting an elliptic integral, and so laying the foundations of elliptic functions and doubly periodic functions generally.'' / ?? \\ 31. Ballantine / The Best (?) Formula for Computing $ \pi $ to a Thousand Places (1939) / An early attempt to orchestrate the calculation of $ \pi $ more cleverly / 271 \\ 32. Birch / An Algorithm for Construction of Arctangent Relations (1946) / The object of this note is to express $ \pi / 4$ as a sum of arctan relations in powers of 10 / 274 \\ 33. Niven / A Simple Proof that $ \pi $ is Irrational (1947) / A very concise proof of the irrationality of $ \pi $ / 276 \\ 34. Reitwiesner / An ENIAC Determination of $ \pi $ and $ e $ to 2000 Decimal Places (1950) / One of the first computer-based computations / 277 \\ 35. Schepler / The Chronology of Pi (1950) / A fairly reliable outline of the history of $ \pi $ from 3000 B.C. to 1949 / 282 \\ 36. Mahler / On the Approximation of $ \pi $ (1953) / ``The aim of this paper is to determine an explicit lower bound free of unknown constants for the distance of $ \pi $ from a given rational or algebraic number.'' / 306 \\ 37. Wrench, Jr. / The Evolution of Extended Decimal Approximations to $ \pi $ (1960) / A history of the calculation of the digits of $ \pi $ to 1960 / 319 \\ 38. Shanks and Wrench, Jr. / Calculation of $ \pi $ to 100,000 Decimals (1962) / A landmark computation of $ \pi $ to more than 100,000 places / 326 39. Sweeny / On the Computation of Euler's Constant (1963) / The computation of Euler's constant to 3566 decimal places / 350 40. Baker / Approximations to the Logarithms of Certain Rational Numbers (1964) / The main purpose of this deep and fundamental paper is to ``deduce results concerning the accuracy with which the natural logarithms of certain rational numbers may be approximated by rational numbers, or, more generally, by algebraic numbers of bounded degree.'' / 359 \\ 41. Adams / Asymptotic Diophantine Approximations to e (1966) / An asymptotic estimate for the rational approximation to $ e $ which disproves the conjecture that $ e $ behaves like almost all numbers in this respect / 368 \\ 42. Mahler / Applications of Some Formulae by Hermite to the Approximations of Exponentials of Logarithms (1967) / An important extension of Hilbert's approach to the study of transcendence / 372 43. Eves / In Mathematical Circles; A Selection of Mathematical Stories and Anecdotes (excerpt) (1969) / A collection of mathematical stories and anecdotes about $ \pi $ / 456 \\ 44. Eves / Mathematical Circles Revisited; A Second Collection of Mathematical Stories and Anecdotes (excerpt) (1971) / A further collection of mathematical stories and anecdotes about $ \pi $ / 402 45. Todd / The Lemniscate Constants (1975) / A unifying account of some of the methods used for computing the lemniscate constants / 412 \\ 46. Salamin / Computation of $ \pi $ Using Arithmetic--Geometric Mean (1976) / The first quadratically converging algorithm for $ \pi $ based on Gauss's AGM and on Legendre's relation for elliptic integrals / 418 \\ 47. Brent / Fast Multiple-Precision Evaluation of Elementary Functions (1976) / ``This paper contains the `Gauss--Legendre' method and some different algorithms for $\log$ and $\exp$ (using Landen transformations).'' / 424 \\ 48. Beukers / A Note on the Irrationality of $ \zeta(2) $ and $ \zeta(3) $ (1979) / A short and elegant recasting of Apery's proof of the irrationality of $\zeta(3)$ (and $\zeta(2)$) / 434 \\ 49. van der Poorten / A Proof that Euler Missed \ldots{} Apery's Proof of the Irrationality of $\zeta (3)$ (1979) / An illuminating account of Apery's astonishing proof of the irrationality of $\zeta (3)$ / 439 \\ 50. Brent and McMillan / Some New Algorithms for High-Precision Computation of Euler's Constant (1980) / Several new algorithms for high-precision calculation of Euler's constant, including one which was used to compute 30,100 decimal places / 448 \\ 51. Apostol / A Proof that Euler Missed: Evaluating $\zeta(2)$ the Easy Way (1983) / This note shows that one of the double integrals considered by Beukers ([48] in the table of contents) can be used to establish directly that $\zeta(2) = \pi^2 / 6$ / 456 \\ 52. O'Shaughnessy / Putting God Back in Math (1983) / An article about the Institute of Pi Research, an organization that ``pokes fun at creationists by pointing out that even the Bible makes mistakes.'' / 458 \\ 53. Stern / A Remarkable Approximation to $ \pi $ (1985) / Justification of the value of $ \pi $ in the Bible through numerological interpretations / 460 \\ 54. Newman and Shanks / On a Sequence Arising in Series for $ \pi $ (1984) / More connections between $ \pi $ and modular equations / 462 \\ 55. Cox / The Arithmetic--Geometric Mean of Gauss (1984) / An extensive study of the complex analytic properties of the AGM / 481 \\ 56. Borwein and Borwein / The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions (1984) / The relationship between the AGM iteration and fast computation of elementary functions (one of the by-products is an algorithm for $ \pi $) / 537 57. Newman / A Simplified Version of the Fast Algorithms of Brent and Salamin (1984) / Elementary algorithms for evaluating $ e^x $ and $ \pi $ using the Gauss AGM without explicit elliptic function theory / 553 \\ 58. Wagon / Is Pi Normal? (1985) / A discussion of the conjecture that $ \pi $ has randomly distributed digits / 557 \\ 59. Keith / Circle Digits: A Self-Referential Story (1986) / A mnemonic for the first 402 decimal places of $ \pi $ / 560 \\ 60. Bailey / The Computation of $ \pi $ to 29,360,000 Decimal Digits Using Borwein's Quartically Convergent Algorithm (1988) / The algorithms used, both for $ \pi $ and for performing the required multiple-precision arithmetic / 562 \\ 61. Kanada / Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of $ \pi $ Calculation (1988) / Details of the computation and statistical tests of the first 200 million digits of $ \pi $ / 576 \\ 62. Borwein and Borwein / Ramanujan and Pi (1988) / This article documents Ramanujan's life, his ingenious approach to calculating $ \pi $, and how his approach is now incorporated into modern computer algorithms / 588 \\ 63. Chudnovsky and Chudnovsky / Approximations and Complex Multiplication According to Ramanujan (1988) / This excerpt describes ``Ramanujan's original quadratic period--quasiperiod relations for elliptic curves with complex multiplication and their applications to representations of fractions of $ \pi $ and other logarithms in terms of rapidly convergent nearly integral (hypergeometric) series.'' / 596 \\ 64. Borwein, Borwein and Bailey / Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi (1989) / An exposition of the computation of $ \pi $ using mathematics rooted in Ramanujan's work / 623 \\ 65. Borwein, Borwein and Dilcher / Pi, Euler Numbers, and Asymptotic Expansions (1989) / An explanation as to why the slowly convergent Gregory series for $ \pi $, truncated at 500,000 terms, gives $ \pi $ to 40 places with only the 6th, 17th, 18th, and 29th places being incorrect / 642 \\ 66. Beukers, Bezivin, and Robba / An Alternative Proof of the Lindemann--Weierstrass Theorem (1990) / The Lindemann--Weierstrass theorem as a by-product of a criterion for rationality of solutions of differential equations / 649 \\ 67. Webster / The Tale of Pi (1991) / Various anecdotes about $ \pi $ from the 14th annual IMO Lecture to the Royal Society / 654 \\ 68. Eco / An excerpt from Foucault's Pendulum (1993) / ``The unnumbered perfection of the circle itself.'' / 658 \\ 69. Keith / Pi Mnemonics and the Art of Constrained Writing (1996) / A mnemonic for $ \pi $ based on Edgar Allen Poe's poem ``The Raven.'' / 659 \\ 70. Bailey, Borwein, and Plouffe / On the Rapid Computation of Various Polylogarithmic Constants (1997) / A fast method for computing individual digits of $ \pi $ in base 2 / 663 \\ Appendix I --- On the Early History of Pi / 677 \\ Appendix II --- A Computational Chronology of Pi / 683 \\ Appendix III --- Selected Formulae for Pi / 686 \\ Appendix IV --- Translations of Viele and Huygens / 690 \\ Bibliography / 710 \\ Credits / 717 \\ A Pamphlet on Pi / 721 \\ Contents / 723 \\ 1. Pi and Its Friends / 725 \\ 2. Normality of Numbers / 741 \\ 3. Historia Cyclometrica / 753 \\ 4. Demotica Cyclometrica / 771 \\ References / 779 \\ Index / 783", } @InProceedings{Borwein:2004:AGMa, author = "J. M. Borwein and P. B. Borwein", booktitle = "Pi: A Source Book", title = "The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions", publisher = pub-SV, address = pub-SV:adr, pages = "??--??", year = "2004", DOI = "https://doi.org/10.1007/978-1-4757-4217-6_56", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_56", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2004:CCS, author = "Jonathan M. Borwein and Jon D. Vanderwerff", title = "Constructible convex sets", journal = j-SET-VALUED-ANAL, volume = "12", number = "1--2", pages = "61--77", month = mar # "\slash " # jun, year = "2004", CODEN = "SVANEG", DOI = "https://doi.org/10.1023/B:SVAN.0000023393.75251.05", ISSN = "0927-6947 (print), 1572-932x (electronic)", ISSN-L = "0927-6947", MRclass = "49J53 (46B20 46N10 90C25 90C48)", MRnumber = "2069352", MRreviewer = "Diethard Pallaschke", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/38/", abstract = "We investigate when closed convex sets can be written as countable intersections of closed half-spaces in Banach spaces. It is reasonable to consider this class to comprise the constructible convex sets since such sets are precisely those that can be defined by a countable number of linear inequalities, hence are accessible to techniques of semi-infinite convex programming. We also explore some model theoretic implications. Applications to set convergence are given as limiting examples.", acknowledgement = ack-nhfb, fjournal = "Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications", journal-URL = "http://link.springer.com/journal/11228", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 2003:202.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2004:CCS", } @Article{Borwein:2004:CMU, author = "J. Borwein and I. Kortezov", title = "Constructive minimal uscos", journal = j-C-R-ACAD-BULGARE-SCI, volume = "57", number = "12", pages = "9--12", year = "2004", CODEN = "DBANAD", ISSN = "1310-1331 (print), 2367-5535 (electronic)", ISSN-L = "1310-1331", MRclass = "49J53 (54C60)", MRnumber = "2117234", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/273/", acknowledgement = ack-nhfb, fjournal = "Dokladi na B\cdprime lgarskata Akademiya na Naukite. Comptes Rendus de l'Acad{\'e}mie Bulgare des Sciences", journal-URL = "http://www.proceedings.bas.bg/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CoLab Preprint 273. The journal web site only has an abstract for this paper.", xxtitle = "Constructive minimal cuscos", } @Article{Borwein:2004:DCM, author = "Jonathan M. Borwein and James V. Burke and Adrian S. Lewis", title = "Differentiability of cone-monotone functions on separable {Banach} space", journal = j-PROC-AM-MATH-SOC, volume = "132", number = "4", pages = "1067--1076", month = apr, year = "2004", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/S0002-9939-03-07149-1", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "49J50 (46G05 46N10)", MRnumber = "2045422", MRreviewer = "Jes{\'u}s A. Jaramillo", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1242/; http://www.jstor.org/stable/4097135", abstract = "Motivated by applications to (directionally) Lipschitz functions, we provide a general result on the almost everywhere Gateaux differentiability of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone with nonempty interior. This seemingly arduous restriction is useful, since it covers the case of directionally Lipschitz functions, and necessary. We show by way of example that most results fail more generally.", acknowledgement = ack-nhfb, article-number = "PII S0002-9939(03)07149-1", fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 02:183.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2004:DCM", } @InProceedings{Borwein:2004:DSS, author = "Jonathan Michael Borwein and Kwok-Kwong Stephen Choi", title = "{Dirichlet} series for squares of sums of squares: a summary", crossref = "Kisilevsky:2004:NTP", volume = "36", publisher = pub-AMS, address = pub-AMS:adr, pages = "27--34", year = "2004", MRclass = "11M41 (11E25)", MRnumber = "2076564", MRreviewer = "Don Redmond", bibdate = "Sat Aug 13 17:30:35 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "CRM Proc. Lecture Notes", ZMnumber = "1078.11055", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Book{Borwein:2004:EMCa, author = "Jonathan M. Borwein and David H. Bailey and Roland Girgensohn", title = "Experimentation in mathematics: computational paths to discovery", publisher = pub-A-K-PETERS, address = pub-A-K-PETERS:adr, pages = "x + 357", year = "2004", ISBN = "1-56881-136-5", ISBN-13 = "978-1-56881-136-9", LCCN = "QA12 .B67 2004", MRclass = "11-01 (11Yxx 40-01 42A16 42A38 68W30)", MRnumber = "2051473", MRreviewer = "F. Beukers", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/master.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", shorttableofcontents = "Sequences, series, products and integrals / 1 \\ Fourier series and integrals / 69 \\ Zeta functions and multizeta functions / 131 \\ Partitions and powers / 183 \\ Primes and polynomials / 225 \\ The power of constructive proofs II / 263 \\ Numerical techniques II / 299", tableofcontents = "", xxyear = "2003", } @Article{Borwein:2004:FEA, author = "Jonathan M. Borwein and David Borwein and William F. Galway", title = "Finding and excluding {$b$}-ary {Machin}-type individual digit formulae", journal = j-CAN-J-MATH, volume = "56", number = "5", pages = "897--925", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2004-041-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11Y60 (11A67 11G55 33B30)", MRnumber = "2085627", MRreviewer = "Greg Martin", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/canjmath.bib", note = "This paper established the result that there are no degree-1 BBP-type formulas for $ \pi $, except when the base is 2 (or an integer power thereof).", URL = "http://docserver.carma.newcastle.edu.au/47/", abstract = "Constants with formulae of the form treated by D. Bailey, P. Borwein, and S. Plouffe (BBP formulae to a given base $b$) have interesting computational properties, such as allowing single digits in their base $b$ expansion to be independently computed, and there are hints that they should be normal numbers, i.e., that their base $b$ digits are randomly distributed. We study a formally limited subset of BBP formulae, which we call Machin-type BBP formulae, for which it is relatively easy to determine whether or not a given constant kappa has a Machin-type BBP formula. In particular, given $b$ is an element of $N$, $ b > 2$, $b$ not a proper power, a $b$-ary Machin-type BBP arctangent formula for $ \kappa $ is a formula of the form $ \kappa = \sum_m a_m \arctan ( - b^{-m})$, $ a_m$ is an element of $Q$, while when $ b = 2$, we also allow terms of the form $ a_m \arctan (1 / (1 - 2^m))$. Of particular interest, we show that $ \pi $ has no Machin-type BBP arctangent formula when $ b \neq 2$. To the best of our knowledge, when there is no Machin-type BBP formula for a constant then no BBP formula of any form is known for that constant.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 2003:195.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2004:FEB", } @Book{Borwein:2004:MEP, author = "Jonathan M. Borwein and David H. Bailey", title = "Mathematics by Experiment: Plausible Reasoning in the {21st Century}", publisher = pub-A-K-PETERS, address = pub-A-K-PETERS:adr, pages = "x + 288", year = "2004", ISBN = "1-56881-211-6", ISBN-13 = "978-1-56881-211-3", LCCN = "QA76.95 .B67 2003", MRclass = "00A35", MRnumber = "2033012", MRreviewer = "John H. Mason", bibdate = "Fri Oct 17 10:38:25 2003", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/master.bib", price = "US\$45.00", URL = "http://docserver.carma.newcastle.edu.au/272/", abstract = "Using examples that truly represent the experimental methodology, this book provides the historical context of, and rationale behind, experimental mathematics. It shows how today, the use of advanced computing technology provides, mathematicians with an amazing, previously unimaginable ``laboratory,'' in which examples can be analyzed, new ideas tested, and patterns discovered. This is a perfect introduction to the history and current state of research and technology in the growing field of experimental mathematics.", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", remark = "Due to an unfortunate error, some of the citations in the book point to the wrong item in the Bibliography. Here is how to find the correct citation number: [1]--[85]: Citation number is correct; [86, page 100]: [86]; [86, page 2]: [87]; [87]--[156]: Add one to citation number; [157]: [159]; [158, page 139]: [158]; [158, page 97]: [160]; [159]--[196]: Add two to citation number", tableofcontents = "What is Experimental Mathematics? \\ Experimental Mathematics in Action \\ Pi and Its Friends \\ Normality of Numbers \\ The Power of Constructive Proofs I \\ Numerical Techniques I \\ Making Sense of Experimental Math", } @Article{Borwein:2004:OPV, author = "Jonathan Borwein and Lixin Cheng and Mari{\'a}n Fabian and Julian P. Revalski", title = "A one perturbation variational principle and applications", journal = j-SET-VALUED-ANAL, volume = "12", number = "1--2", pages = "49--60", year = "2004", CODEN = "SVANEG", DOI = "https://doi.org/10.1023/B:SVAN.0000023400.92518.cb", ISSN = "0927-6947 (print), 1572-932x (electronic)", ISSN-L = "0927-6947", MRclass = "49J53 (46B20 46G05 49J40 49J50)", MRnumber = "2069351", MRreviewer = "John R. Giles", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/14/", abstract = "We study a variational principle in which there is one common perturbation function $ \phi $ for every proper lower semicontinuous extended real-valued function $f$ defined on a metric space $X$. Necessary and sufficient conditions are given in order for the perturbed function $ f + \phi $ to attain its minimum. In the case of a separable Banach space we obtain a specific principle in which the common perturbation function is, in addition, also convex and Hadamard-like differentiable. This allows us to provide applications of the principle to differentiability of convex functions on separable and more general Banach spaces.", acknowledgement = ack-nhfb, fjournal = "Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications", journal-URL = "http://link.springer.com/journal/11228", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 2003:205.", researcherid-numbers = "Fabian, Marian/D-5427-2014 Borwein, Jonathan/A-6082-2009 Cheng, LX/G-3342-2010", unique-id = "Borwein:2004:OPV", } @InProceedings{Borwein:2004:PEN, author = "J. M. Borwein and P. B. Borwein and K. Dilcher", booktitle = "Pi: A Source Book", title = "Pi, {Euler} Numbers, and Asymptotic Expansions", publisher = pub-SV, address = pub-SV:adr, pages = "??--??", year = "2004", DOI = "https://doi.org/10.1007/978-1-4757-4217-6_65", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1583/; http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_65", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2004:RAFa, author = "J. Borwein and R. Crandall and G. Fee", title = "On the {Ramanujan} {AGM} Fraction, {I}: The Real-Parameter Case", journal = j-EXP-MATH, volume = "13", number = "3", pages = "275--285", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1080/10586458.2004.10504540", ISSN = "1058-6458 (print), 1944-950X (electronic)", ISSN-L = "1058-6458", MRclass = "11J70 (11A55 33C05 40A15)", MRnumber = "2103326", MRreviewer = "James G. Mc Laughlin", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://projecteuclid.org/euclid.em; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/expmath.bib", URL = "http://docserver.carma.newcastle.edu.au/27/; http://projecteuclid.org/euclid.em/1103749836", abstract = "The Ramanujan AGM continued fraction is a construct [GRAPHIC] enjoying attractive algebraic properties, such as a striking arithmetic-geometric mean (AGM) relation and elegant connections with elliptic-function theory. But the fraction also presents an intriguing computational challenge. Herein we show how to rapidly evaluate $R$ for any triple of positive reals $a$, $b$, $ \eta $. Even in the problematic scenario when a approximate to $b$ certain transformations allow rapid evaluation. In this process we find, for example, that when $ a_\eta = b_\eta = $ a rational number, $ R_\eta $, is essentially an $L$-series that can be cast as a finite sum of fundamental numbers. We ultimately exhibit an algorithm that yields $D$ good digits of $R$ in $ O(D)$ iterations where the implied big-$O$ constant is independent of the positive-real triple $a$, $b$, $ \eta $. Finally, we address the evidently profound theoretical and computational dilemmas attendant on complex parameters, indicating how one might extend the AGM relation for complex parameter domains.", acknowledgement = ack-nhfb, fjournal = "Experimental Mathematics", journal-URL = "http://www.tandfonline.com/loi/uexm20", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2004:RAFa", } @Article{Borwein:2004:RAFb, author = "J. Borwein and R. Crandall", title = "On the {Ramanujan} {AGM} Fraction, {II}: The Complex-Parameter Case", journal = j-EXP-MATH, volume = "13", number = "3", pages = "287--295", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1080/10586458.2004.10504541", ISSN = "1058-6458 (print), 1944-950X (electronic)", ISSN-L = "1058-6458", MRclass = "11J70 (11A55 33C05)", MRnumber = "2103327", MRreviewer = "James G. Mc Laughlin", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://projecteuclid.org/euclid.em; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/expmath.bib", URL = "http://docserver.carma.newcastle.edu.au/29/; http://projecteuclid.org/euclid.em/1103749837", abstract = "The Ramanujan continued fraction is interesting in many ways; e.g., for certain complex parameters $ (\eta, a, b) $ one has an attractive AGM relation $ R_{\eta }(a.b) + R_\eta (b, a) = 2 R_\eta ((a + b) / 2, \sqrt {a b}) $. Alas, for some parameters the continued fraction $ R_\eta $, does not converge; moreover, there are converging instances where the AGM relation itself does not hold. To unravel these dilemmas we herein establish convergence theorems, the central result being that $ R_1 $ converges whenever $ |a| \neq |b| $. Such analysis leads naturally to the conjecture that divergence occurs whenever $ a = b e^{i \phi } $ with $ c o s^2 \phi \neq 1 $ (which conjecture has been proven in a separate work) [Borwein et al. 04b.] We further conjecture that for $ a / b $ lying in a certain --- and rather picturesque --- complex domain, we have both convergence and the truth of the AGM relation.", acknowledgement = ack-nhfb, fjournal = "Experimental Mathematics", journal-URL = "http://www.tandfonline.com/loi/uexm20", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2004:RAFb", } @InProceedings{Borwein:2004:RME, author = "J. M. Borwein and P. B. Borwein and D. H. Bailey", booktitle = "Pi: A Source Book", title = "{Ramanujan}, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi", publisher = pub-SV, address = pub-SV:adr, pages = "??--??", year = "2004", DOI = "https://doi.org/10.1007/978-1-4757-4217-6_64", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1587/; http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_64", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bailey:2005:EDA, author = "David H. Bailey and Jonathan M. Borwein and David M. Bradley", title = "Experimental determination of {Ap{\'e}ry}-like identities for $ \zeta (2 n + 2) $", journal = "ArXiv Mathematics e-prints", month = may, year = "2005", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2005math......5270B; http://docserver.carma.newcastle.edu.au/295/", abstract = "We document the discovery of two generating functions for the Riemann zeta values $ \zeta (2 n + 2) $, analogous to earlier work for $ \zeta (2 n + 1) $ and $ \zeta (4 n + 3) $. This continues work initiated by Koecher and pursued further by Borwein, Bradley and others.", acknowledgement = ack-nhfb, eprint = "math/0505270", keywords = "Mathematics - Number Theory, Mathematics - Classical Analysis and ODEs, 11M06 (Primary), 33C20 (Secondary)", ORCID-numbers = "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", year = "2005", CODEN = "AMNOAN", ISSN = "0002-9920 (print), 1088-9477 (electronic)", ISSN-L = "0002-9920", MRclass = "00A35", MRnumber = "2140093", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1241/; http://www.ams.org/notices/200505/fea-borwein.pdf", acknowledgement = ack-nhfb, fjournal = "Notices of the American Mathematical Society", journal-URL = "http://www.ams.org/notices/", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", remark = "CoLab Preprint 269.", } @Article{Bailey:2005:FPC, author = "D. H. Bailey and J. M. Borwein", title = "Future Prospects for Computer-assisted Mathematics", journal = j-CMS-NOTES, volume = "37", number = "8", pages = "2--6", month = dec, year = "2005", DOI = "", ISSN = "1193-9273 (print), 1496-4295 (electronic)", ISSN-L = "1193-9273", bibdate = "Sat Aug 13 17:21:21 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/304/; https://cms.math.ca/notes/v37/n8/Notesv37n8.pdf", acknowledgement = ack-nhfb, ajournal = "CMS Notes", fjournal = "Canadian Mathematical Society Notes", journal-URL = "https://cms.math.ca/notes", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:2005:ADC, author = "J. M. Borwein and K. Karamanos", editor = "Andrew Eberhard and Nicolas Hadjisavvas and Dinh The Luc", booktitle = "Generalized Convexity, Generalized Monotonicity and Applications", title = "Algebraic Dynamics of Certain Gamma Function Values", volume = "77", publisher = pub-SV, address = pub-SV:adr, bookpages = "xi + 350", pages = "3--21", year = "2005", DOI = "https://doi.org/10.1007/0-387-23639-2_1", ISBN = "0-387-23638-4", ISBN-13 = "978-0-387-23638-4", MRclass = "11Y60 (33B15 37B99 37N99 94A17)", MRnumber = "2103023", MRreviewer = "Brian L. Burrows", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Nonconvex Optim. Appl.", URL = "http://docserver.carma.newcastle.edu.au/256/; http://link.springer.com/chapter/10.1007/0-387-23639-2_1", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Eberhard, Andrew/0000-0003-2977-3456", } @Article{Borwein:2005:CFT, author = "Jonathan Michael Borwein and Kwok-Kwong Stephen Choi and Wilfried Pigulla", title = "Continued fractions of tails of hypergeometric series", journal = j-AMER-MATH-MONTHLY, volume = "112", number = "6", pages = "493--501", month = jun # "\slash " # jul, year = "2005", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/30037519", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "33C05 (40A15)", MRnumber = "2142600", MRreviewer = "Takao Komatsu", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/39/; http://www.jstor.org/stable/30037519", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 2003:201.", } @Article{Borwein:2005:CMF, author = "Jonathan M. Borwein and Xianfu Wang", title = "Cone-monotone functions: differentiability and continuity", journal = j-CAN-J-MATH, volume = "57", number = "5", pages = "961--982", year = "2005", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2005-037-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "49J50 (26B05 46G05 58C20)", MRnumber = "2164591", MRreviewer = "Lud{\v{e}}k Zaj{\'{\i}}{\v{c}}ek", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "We provide a porosity-based approach to the differentiability and continuity of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone $K$ with non-empty interior. We also show that the set of nowhere $K$-monotone functions has a sigma-porous complement in the space of continuous functions endowed with the uniform metric.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics. Journal Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2005:CMF", } @Article{Borwein:2005:DCF, author = "Jonathan M. Borwein and D. Russell Luke", title = "Dynamics of a continued fraction of {Ramanujan} with random coefficients", journal = j-ABSTR-APPL-ANAL, volume = "2005", number = "5", pages = "449--467", month = "????", year = "2005", DOI = "https://doi.org/10.1155/AAA.2005.449", ISSN = "1085-3375 (print), 1687-0409 (electronic)", ISSN-L = "1085-3375", MRclass = "11J70 (60F15)", MRnumber = "2201037", MRreviewer = "Mary E. Flahive", bibdate = "Fri Aug 12 10:09:56 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2005AbApA2005..449B; http://www.hindawi.com/journals/aaa/2005/162798/abs/", abstract = "We study a generalization of a continued fraction of Ramanujan with random, complex-valued coefficients. A study of the continued fraction is equivalent to an analysis of the convergence of certain stochastic difference equations and the stability of random dynamical systems. We determine the convergence properties of stochastic difference equations and so the divergence of their corresponding continued fractions.", acknowledgement = ack-nhfb, fjournal = "Abstract and Applied Analysis", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", received = "16 November 2004", remark = "CoLab Preprint 275", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2005:DCF", } @Article{Borwein:2005:EBS, author = "Jonathan M. Borwein and Roland Girgensohn", title = "Evaluations of binomial series", journal = j-AEQUATIONES-MATHEMATICAE, volume = "70", number = "1--2", pages = "25--36", year = "2005", CODEN = "AEMABN", DOI = "https://doi.org/10.1007/s00010-005-2774-x", ISSN = "0001-9054 (print), 1420-8903 (electronic)", ISSN-L = "0001-9054", MRclass = "05A10 (11B65 33B30)", MRnumber = "2167981", MRreviewer = "Valery V. Karachik", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/131/", acknowledgement = ack-nhfb, fjournal = "Aequationes Mathematicae", journal-URL = "http://link.springer.com/journal/10", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 02:188.", } @Article{Borwein:2005:EDA, author = "Jonathan M. Borwein and David M. Bradley", title = "Empirically determined {Ap{\'e}ry}-like formulae for $ \zeta (4 n + 3) $", journal = "ArXiv Mathematics e-prints", month = may, year = "2005", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2005math......5124B; http://docserver.carma.newcastle.edu.au/163/", abstract = "Some rapidly convergent formulae for special values of the Riemann zeta function are given. We obtain a generating function formula for $ \zeta (4 n + 3) $ which generalizes Ap{\'e}ry's series for $ \zeta (3) $, and appears to give the best possible series relations of this type, at least for $ n \lt 12 $. The formula reduces to a finite but apparently non-trivial combinatorial identity. The identity is equivalent to an interesting new integral evaluation for the central binomial coefficient. We outline a new technique for transforming and summing certain infinite series. We also derive a beautiful formula which provides strange evaluations of a large new class of non-terminating hypergeometric series. Our main results are shown to be equivalent. At the time this article was submitted for publication back in 1996, these results were only conjectures, but they have subsequently been proved as a result of work due to Gert Almkvist and Andrew Granville.", acknowledgement = ack-nhfb, eprint = "math/0505124", keywords = "Mathematics - Classical Analysis and ODEs, Mathematics - Number Theory, 11M06", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2005:EMPa, author = "J. M. Borwein", title = "The Experimental Mathematician: The Pleasure of Discovery and the Role of Proof", journal = "International Journal of Computers for Mathematical Learning", volume = "10", number = "2", pages = "75--108", month = may, year = "2005", DOI = "https://doi.org/10.1007/s10758-005-5216-x", ISSN = "1382-3892 (print), 1573-1766 (electronic)", ISSN-L = "1382-3892", bibdate = "Fri Aug 12 10:49:11 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Counterpart presentation published in CMESG25 Proceedings, 2002, with lecture slides at \url{http://www.cecm.sfu.ca/personal/jborwein/proof.pdf}.", URL = "http://docserver.carma.newcastle.edu.au/264/; http://link.springer.com/article/10.1007/s10758-005-5216-x; https://web.archive.org/web/20040330173752/http://www.cecm.sfu.ca/personal/jborwein/proof.pdf", acknowledgement = ack-nhfb, journal-URL = "http://link.springer.com/journal/10758", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark-1 = "CECM Preprint 02:178; 264.", remark-2 = "Journal renamed in 2011 to \booktitle{Technology, knowledge and learning}.", } @Article{Borwein:2005:KCM, author = "Jonathan Borwein and Terry Stanway", title = "Knowledge and Community in Mathematics", journal = j-MATH-INTEL, volume = "27", number = "2", pages = "7--16", year = "2005", CODEN = "MAINDC", DOI = "https://doi.org/10.1007/BF02985788", ISSN = "0343-6993 (print), 1866-7414 (electronic)", ISSN-L = "0343-6993", MRclass = "01A80 (00A05)", MRnumber = "2156530", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/274/", acknowledgement = ack-nhfb, fjournal = "The Mathematical Intelligencer", journal-URL = "http://link.springer.com/journal/283", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CoLab Preprint 274.", } @Article{Borwein:2005:LFM, author = "Jonathan M. Borwein and Xianfu Wang", title = "{Lipschitz} functions with maximal {Clarke} subdifferentials are staunch", journal = j-BULL-AUSTRAL-MATH-SOC, volume = "72", number = "3", pages = "491--496", year = "2005", CODEN = "ALNBAB", DOI = "https://doi.org/10.1017/S0004972700035322", ISSN = "0004-9727 (print), 1755-1633 (electronic)", ISSN-L = "0004-9727", MRclass = "49J52 (26B05 26E25 54C30)", MRnumber = "2199651", MRreviewer = "Dariusz Zagrodny", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/302/; http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=4829356", abstract = "In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire's category) have a maximal Clarke sub differential. In the present paper, we show that in a separable Banach space the set of non-expansive Lipschitz functions with a maximal Clarke subdifferential is not only generic, but also staunch in the space of non-expansive functions.", acknowledgement = ack-nhfb, fjournal = "Bulletin of the Australian Mathematical Society", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2005:LFM", } @InProceedings{Borwein:2005:PFW, author = "Jonathan M. Borwein and Mason Macklem and Jaehyun Paek", editor = "????", booktitle = "SIAM Conference on Computational Science and Engineering, Orlando, February 2005", title = "A Prototype for the Federated World Directory of Mathematicians", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "??--??", year = "2005", bibdate = "Sat Aug 13 17:23:15 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2005:SDC, author = "Jonathan M. Borwein", title = "The {SIAM} 100-Digit challenge: a study in high-accuracy numerical computing", journal = j-MATH-INTEL, volume = "27", number = "4", pages = "40--48", year = "2005", CODEN = "MAINDC", DOI = "https://doi.org/10.1007/BF02985860", ISSN = "0343-6993 (print), 1866-7414 (electronic)", ISSN-L = "0343-6993", bibdate = "Fri Aug 12 10:34:00 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "The Mathematical Intelligencer", journal-URL = "http://link.springer.com/journal/283", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "D-drive preprint 285.", } @Article{Borwein:2005:SSA, author = "J. M. Borwein and David M. Bradley", title = "Searching symbolically for {Ap{\'e}ry}-like formulae for values of the {Riemann} zeta function", journal = "ArXiv Mathematics e-prints", month = may, year = "2005", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2005math......5093B; http://docserver.carma.newcastle.edu.au/170/", abstract = "We discuss some aspects of the search for identities using computer algebra and symbolic methods. The focus is on so-called Ap{\'e}ry-like formulae for special values of the Riemann Zeta function. Much work lays ahead in formally proving and properly classifying many of the identities we have uncovered.", acknowledgement = ack-nhfb, eprint = "math/0505093", keywords = "Mathematics - Classical Analysis and ODEs, Mathematics - Number Theory, 11M06", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2005:TFI, author = "Jonathan M. Borwein and David M. Bradley", title = "On Two Fundamental Identities for {Euler} Sums", journal = "arxiv.org", volume = "??", number = "??", pages = "??--??", month = feb, year = "2005", bibdate = "Tue Aug 16 10:16:43 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://arxiv.org/abs/math.NT/0502034/; http://docserver.carma.newcastle.edu.au/279/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "The archive.org URL is wrong: it points to the \title{Thirty-two Goldbach Variations} paper.", } @Article{Borwein:2005:TTG, author = "J. M. Borwein and David M. Bradley", title = "Thirty-two {Goldbach} Variations", journal = "ArXiv Mathematics e-prints", day = "1", month = feb, year = "2005", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2005math......2034B; http://arxiv.org/abs/math/0502034; http://docserver.carma.newcastle.edu.au/301/", abstract = "We give thirty-two diverse proofs of a small mathematical gem --- the fundamental Euler sum identity $$ \zeta (2, 1) = \zeta (3) = 8 \zeta (\bar 2, 1) $$. We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating both the wide variety of techniques fruitfully used to study such sums and the attraction of their study.", acknowledgement = ack-nhfb, eprint = "math/0502034", keywords = "Mathematics - Number Theory, 11M41", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "v1 (1 February 2005): 34 pages AMSLaTeX. v2 (3 November 2005): 41 pages AMSLaTeX. New introductory material added and material on inequalities, Hilbert matrix and Witten zeta functions. Errors in the second section on Complex Line Integrals are corrected. Published in \cite{Borwein:2006:TTG}.", } @Book{Borwein:2005:TVA, author = "Jonathan M. Borwein and Qiji J. Zhu", title = "Techniques of Variational Analysis", publisher = pub-SV, address = pub-SV:adr, pages = "vi + 362", year = "2005", DOI = "https://doi.org/10.1007/0-387-28271-8", ISBN = "0-387-24298-8", ISBN-13 = "978-0-387-24298-9", MRclass = "49-02 (49J52 49J53 90-02)", MRnumber = "2144010", MRreviewer = "Richard B. Vinter", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "CMS Books in Mathematics/Ouvrages de Math{\'e}matiques de la SMC, 20", URL = "http://docserver.carma.newcastle.edu.au/1735/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", tableofcontents = "Front Matter / i--vi \\ Introduction and Notation / 1--4 \\ Variational Principles / 5--36 \\ Variational Techniques in Subdifferential Theory / 37--109 \\ Variational Techniques in Convex Analysis / 111--163 \\ Variational Techniques and Multifunctions / 165--241 \\ Variational Principles in Nonlinear Functional Analysis / 243--289 \\ Variational Techniques In the Presence of Symmetry / 291--338 \\ Back Matter / 339--362", } @InProceedings{Bailey:2006:EBE, author = "D. H. Bailey and J. M. Borwein", booktitle = "20th International Symposium on High-Performance Computing in an Advanced Collaborative Environment (HPCS'06)", title = "Effective Bounds in {Euler--Maclaurin}-Based Quadrature (Summary for {HPCS06})", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "34--34", month = may, year = "2006", DOI = "https://doi.org/10.1109/HPCS.2006.22", ISSN = "1550-5243 (print), 2378-2099 (electronic)", ISSN-L = "1550-5243", bibdate = "Wed Aug 10 12:08:56 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.davidhbailey.com/dhbpapers/hpcs06.pdf", acknowledgement = ack-nhfb, keywords = "Approximation error; Computer errors; Computer science; Concurrent computing; Error analysis; International collaboration; Mathematics; System testing", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bailey:2006:EDA, author = "David H. Bailey and Jonathan M. Borwein and David M. Bradley", title = "Experimental Determination of {Ap{\'e}ry}-like Identities for $ \zeta (2 n + 2) $", journal = j-EXP-MATH, volume = "15", number = "3", pages = "281--289", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1080/10586458.2006.10128968", ISSN = "1058-6458 (print), 1944-950X (electronic)", ISSN-L = "1058-6458", MRclass = "11Y60 (11M06)", MRnumber = "2264467", MRreviewer = "Tanguy Rivoal", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://projecteuclid.org/euclid.em; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/expmath.bib; http://www.tandfonline.com/toc/uexm20/15/3", URL = "http://docserver.carma.newcastle.edu.au/295/; http://projecteuclid.org/euclid.em/1175789759", abstract = "We document the discovery of two generating functions for $ \zeta (2 n + 2) $, analogous to earlier work for $ \zeta (2 n + 1) $ and $ \zeta (4 n + 3) $, initiated by Koecher and pursued further by Borwein, Bradley, and others.", acknowledgement = ack-nhfb, fjournal = "Experimental Mathematics", journal-URL = "http://www.tandfonline.com/loi/uexm20", onlinedate = "30 Jan 2011", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Bailey:2006:EDA", } @TechReport{Bailey:2006:FGE, author = "David H. Bailey and Jonathan M. Borwein", title = "Finding General Explicit Formulas for {Ising} Integral Recursions", type = "Report", institution = "Lawrence Berkeley National Laboratory and Faculty of Computer Science, Dalhousie University", address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5, Canada", day = "2", month = oct, year = "2006", bibdate = "Fri Sep 30 08:18:51 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.davidhbailey.com/dhbpapers/ising-int.pdf", acknowledgement = ack-nhfb, keywords = "$K_0$ modified Bessel function; ARPREC multiprecision software system", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bailey:2006:IIC, author = "D. H. Bailey and J. M. Borwein and R. E. Crandall", title = "Integrals of the {Ising} class", journal = j-J-PHYS-A, volume = "39", number = "40", pages = "12271--12302", month = oct, year = "2006", CODEN = "JPHAC5", DOI = "https://doi.org/10.1088/0305-4470/39/40/001", ISSN = "0305-4470 (print), 1361-6447 (electronic)", ISSN-L = "0305-4470", MRclass = "33F05 (33F10 65D30 82B20 82B80)", MRnumber = "2261886", MRreviewer = "Syamal K. Sen", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib", URL = "http://adsabs.harvard.edu/abs/2006JPhA...39..001B; http://docserver.carma.newcastle.edu.au/324/; http://iopscience.iop.org/article/10.1088/0305-4470/39/40/001; http://stacks.iop.org/0305-4470/39/i=40/a=001", abstract = "From an experimental-mathematical perspective we analyse 'Ising-class' integrals. These are structurally related $n$-dimensional integrals we call $ C_n$, $ D_n$, $ E_n$, where $ D_n$ is a magnetic susceptibility integral central to the Ising theory of solid-state physics. We first analyse $ C_n \coloneq \frac {4}{n!} \int_0^\infty \cdots \int_0^\infty \frac { 1 } { \big (\sum_{ j = 1 }^n (u_j + 1 / u_j) \big)^2 } \frac { d u_1 } { u_1 } \cdots \frac { d u_n } { u_n }$.\par We had conjectured --- on the basis of extreme-precision numerical quadrature --- that $ C_n $ has a finite large-$n$ limit, namely $ C_\infty = 2 e^{-2} $, with $ \gamma $ being the Euler constant. On such a numerological clue we are able to prove the conjecture. We then show that integrals $ D_n $ and $ E_n $ both decay exponentially with $n$, in a certain rigorous sense. While $ C_n $, $ D_n $ remain unresolved for $ n \geq 5 $, we were able to conjecture a closed form for $ E_5 $. Our experimental results involved extreme-precision, multidimensional quadrature on intricate integrands; thus, a highly parallel computation was required.", acknowledgement = ack-nhfb, 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", } @Article{Bailey:2006:TPE, author = "David H. Bailey and Jonathan M. Borwein and Vishaal Kapoor and Eric W. Weisstein", title = "Ten problems in experimental mathematics", journal = j-AMER-MATH-MONTHLY, volume = "113", number = "6", pages = "481--509", month = jun # "\slash " # jul, year = "2006", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/27641975", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "65-02 (11Y60 37E05 37G10 65-05 68-02)", MRnumber = "2231135", MRreviewer = "Vasily A. Chernecky", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1237/; http://www.jstor.org/stable/27641975", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", remark = "CoLab Preprint 270.", } @InCollection{Borwein:2006:AWM, author = "Jonathan M. Borwein", editor = "N. Sinclair and W. Higginson", booktitle = "Mathematics and the aesthetic", title = "Aesthetics for the working mathematician", volume = "25", publisher = pub-SV, address = pub-SV:adr, pages = "21--40", year = "2006", MRclass = "00A05 (00A99 11A99 11Y99)", MRnumber = "2274212", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "CMS Books Math./Ouvrages Math. SMC", URL = "http://docserver.carma.newcastle.edu.au/150/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 01:165.", } @Article{Borwein:2006:BDE, author = "Jonathan Borwein and Vicente Montesinos and Jon Vanderwerff", title = "Boundedness, differentiability and extensions of convex functions", journal = j-J-CONVEX-ANAL, volume = "13", number = "3--4", pages = "587--602", year = "2006", ISSN = "0944-6532 (print), 2363-6394 (electronic)", MRclass = "46G05 (46N10 49J50 52A41)", MRnumber = "2291553", MRreviewer = "Lud{\v{e}}k Zaj{\'{\i}}{\v{c}}ek", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/288/; http://www.heldermann.de/JCA/JCA13/JCA133/jca13046.htm", abstract = "We survey various boundedness, differentiability and extendibility properties of convex functions, and how they are related to sequential convergence with respect to various topologies in the dual space. It is also shown that if $ X / Y $ is separable then every continuous convex function on $Y$ can be extended to a continuous convex function on $X$.", acknowledgement = ack-nhfb, fjournal = "Journal of Convex Analysis", journal-URL = "http://www.heldermann.de/JCA/jcacon.htm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2006:BDE", } @Book{Borwein:2006:CAN, author = "Jonathan M. Borwein and Adrian S. Lewis", title = "Convex analysis and nonlinear optimization", volume = "3", publisher = pub-SV, address = pub-SV:adr, edition = "Second", pages = "xii + 310", year = "2006", DOI = "https://doi.org/10.1007/978-0-387-31256-9", ISBN = "0-387-29570-4", ISBN-13 = "978-0-387-29570-1", MRclass = "49-01 (46N10 47N10 49-02 49J53 90-01)", MRnumber = "2184742", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Theory and examples.", series = "CMS Books in Mathematics\slash Ouvrages de Math{\'e}matiques de la SMC", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", tableofcontents = "Front Matter / i--xii \\ Background / 1--14 \\ Inequality Constraints / 15--32 \\ Fenchel Duality / 33--63 \\ Convex Analysis / 65--96 \\ Special Cases / 97--122 \\ Nonsmooth Optimization / 123--152 \\ Karush--Kuhn--Tucker Theory / 153--177 \\ Fixed Points / 179--211 \\ More Nonsmooth Structure / 213--238 \\ Postscript: Infinite Versus Finite Dimensions / 239--251 \\ List of Results and Notation / 253--273 \\ Back Matter / 275--310", } @Article{Borwein:2006:DLP, author = "Jonathan M. Borwein and Mason S. Macklem", title = "The (digital) life of {Pi}", journal = j-AUSTRALIAN-MATH-SOC-GAZ, volume = "33", number = "4", pages = "243--248", month = sep, year = "2006", ISSN = "0311-0729 (print), 1326-2297 (electronic)", ISSN-L = "0311-0729", MRclass = "11Y60 (65B99)", MRnumber = "2259732", MRreviewer = "Khodabakhsh Hessami Pilehrood", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/267/; http://www.austms.org.au/Publ/Gazette/2006/Sep06/pi.pdf", acknowledgement = ack-nhfb, fjournal = "The Australian Mathematical Society. Gazette", journal-URL = "http://www.austms.org.au/gazette", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Book{Borwein:2006:EM, author = "Jonathan M. Borwein and David H. Bailey and Roland Girgensohn", title = "Experiments in Mathematics", publisher = pub-A-K-PETERS, address = pub-A-K-PETERS:adr, pages = "????", year = "2006", ISBN = "1-56881-283-3, 1-56881-211-6, 1-56881-136-5", ISBN-13 = "978-1-56881-283-0", LCCN = "????", bibdate = "Tue Aug 16 08:45:42 MDT 2016", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Combined interactive CD version.", abstract = "Contains the full text of: Mathematics by experiment: plausible reasoning in the 21st century; and, Experimentation in mathematics: computational paths to discovery, in electronic, searchable form. Includes hyperlinks for all cross references, Internet URLs, and bibliographical references. Enhanced search function helps with particular formulas or expressions.", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2006:FRO, author = "Jonathan M. Borwein", title = "Featured Review: {{\booktitle{Oxford Users' Guide to Mathematics}}. Edited by Eberhard Zeidler. Oxford University Press, Oxford, 2004. \$59.50. xxii + 1285 pp., softcover. ISBN 0-19-850763-1}", journal = j-SIAM-REVIEW, volume = "48", number = "3", pages = "585--594", month = sep, year = "2006", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/SIREAD000048000003000585000001", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Wed Aug 31 09:49:49 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "http://epubs.siam.org/doi/abs/10.1137/SIREAD000048000003000585000001; http://www.jstor.org/stable/20453842", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2006:MMC, author = "Jonathan M. Borwein", title = "Maximal monotonicity via convex analysis", journal = j-J-CONVEX-ANAL, volume = "13", number = "3--4", pages = "561--586", year = "2006", ISSN = "0944-6532 (print), 2363-6394 (electronic)", MRclass = "47H05 (47N10 49J53)", MRnumber = "2291552", MRreviewer = "Andrew C. Eberhard", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1235/; http://www.heldermann.de/JCA/JCA13/JCA133/jca13045.htm", abstract = "In his `23' ``Mathematische Probleme''(1) lecture to the Paris International Congress in 1900, David Hilbert wrote ``Besides it is an error to believe that rigor in the proof is the enemy of simplicity.'' In this spirit, we use simple convex analytic methods, relying on an ingenious function due to Simon Fitzpatrick, to provide a concise proof of the maximality of the sum of two maximal monotone operators on reflexive Banach space under standard transversality conditions. Many other extension, surjectivity, convexity and local boundedness results are likewise established.", acknowledgement = ack-nhfb, fjournal = "Journal of Convex Analysis", journal-URL = "http://www.heldermann.de/JCA/jcacon.htm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2006:MMC", } @Unpublished{Borwein:2006:MS, author = "Jonathan Borwein and Helaman Ferguson", title = "The mathematics of salt", month = dec, year = "2006", bibdate = "Tue Aug 16 10:05:43 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Preprint.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2006:MST, author = "Jonathan M. Borwein", title = "Maximality of sums of two maximal monotone operators", journal = j-PROC-AM-MATH-SOC, volume = "134", number = "10", pages = "2951--2955", year = "2006", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/S0002-9939-06-08323-7", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "47H05 (46A22 46N10 47N10 49J53)", MRnumber = "2231619", MRreviewer = "Teemu Pennanen", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1234/; http://www.jstor.org/stable/4098152", abstract = "We use methods from convex analysis, relying on an ingenious function of Simon Fitzpatrick, to prove maximality of the sum of two maximal monotone operators on reflexive Banach space under weak transversality conditions.", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2006:MST", } @Article{Borwein:2006:PES, author = "David Borwein and Jonathan M. Borwein and David M. Bradley", title = "Parametric {Euler} sum identities", journal = j-J-MATH-ANAL-APPL, volume = "316", number = "1", pages = "328--338", month = apr, year = "2006", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/j.jmaa.2005.04.040", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "11M41", MRnumber = "2201764", MRreviewer = "Junesang Choi", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2006JMAA..316..328B; http://docserver.carma.newcastle.edu.au/1236/; http://www.sciencedirect.com/science/article/pii/S0022247X05003811", abstract = "We consider some parametrized classes of multiple sums first studied by Euler. Identities between meromorphic functions of one or more variables in many cases account for reduction formulae for these sums.", acknowledgement = ack-nhfb, eprint = "math/0505058", fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", keywords = "Euler sums; Generating functions; Multiple zeta values; Zeta functions", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Unpublished{Borwein:2006:QCT, author = "Jonathan Borwein and Peter (Liquin) Ye", title = "Quadratic Convergence of the Tanh--Sinh Quadrature Rule", month = feb, year = "2006", bibdate = "Tue Aug 16 10:18:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Preprint.", URL = "http://docserver.carma.newcastle.edu.au/342/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:2006:SCM, author = "Jonathan M. Borwein and Chris H. Hamilton", booktitle = "Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation: {ISSAC 2006}", title = "Symbolic Computation of Multidimensional {Fenchel} Conjugates", publisher = pub-ACM, address = pub-ACM:adr, pages = "23--30", year = "2006", DOI = "https://doi.org/10.1145/1145768.1145780", ISBN = "1-59593-276-3", ISBN-13 = "978-1-59593-276-1", MRclass = "68W30 (65K10)", MRnumber = "2289097", bibdate = "Wed Aug 10 12:08:56 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "ISSAC '06", URL = "http://doi.acm.org/10.1145/1145768.1145780", acknowledgement = ack-nhfb, acmid = "1145780", keywords = "Fenchel conjugate, Legendre--Fenchel transform, computer proofs, inequalities, subdifferential, subgradient", location = "Genoa, Italy", numpages = "8", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2006:SFM, author = "Jonathan Borwein", title = "{Simon Fitzpatrick} memorial volume", journal = j-J-CONVEX-ANAL, volume = "13", number = "3--4", pages = "463--476", year = "2006", ISSN = "0944-6532 (print), 2363-6394 (electronic)", MRclass = "01A70", MRnumber = "2291547", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Introduction to Fitzpatrick memorial volume.", URL = "http://www.heldermann.de/JCA/JCA13/JCA133/jca13040.htm", acknowledgement = ack-nhfb, fjournal = "Journal of Convex Analysis", journal-URL = "http://www.heldermann.de/JCA/jcacon.htm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2006:TTG, author = "Jonathan M. Borwein and David M. Bradley", title = "Thirty-two {Goldbach} variations", journal = j-INT-J-NUMBER-THEORY, volume = "2", number = "1", pages = "65--103", year = "2006", DOI = "https://doi.org/10.1142/S1793042106000383", ISSN = "1793-0421 (print), 1933-8368 (electronic)", MRclass = "11M41 (11M06)", MRnumber = "2217795", MRreviewer = "F. Beukers", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/301/", abstract = "We give thirty-two diverse proofs of a small mathematical gem --- the fundamental Euler sum identity $ \zeta (2, 1) = \zeta (3) = 8 \zeta (\bar {2}, 1) $. We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating both the wide variety of techniques fruitfully used to study such sums and the attraction of their study.", acknowledgement = ack-nhfb, fjournal = "International Journal of Number Theory", journal-URL = "http://www.worldscientific.com/worldscinet/ijnt", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2006:TTG", } @Article{Borwein:2006:VMC, author = "Jonathan M. Borwein and Qiji J. Zhu", title = "Variational methods in convex analysis", journal = j-J-GLOBAL-OPT, volume = "35", number = "2", pages = "197--213", year = "2006", CODEN = "JGOPEO", DOI = "https://doi.org/10.1007/s10898-005-3835-3", ISSN = "0925-5001 (print), 1573-2916 (electronic)", ISSN-L = "0925-5001", MRclass = "49J53 (90C25)", MRnumber = "2242012", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Special issue in honour of Alex Rubinov's 65th birthday.", URL = "http://docserver.carma.newcastle.edu.au/259/", abstract = "We use variational methods to provide a concise development of a number of basic results in convex and functional analysis. This illuminates the parallels between convex analysis and smooth subdifferential theory.", acknowledgement = ack-nhfb, fjournal = "Journal of Global Optimization", journal-URL = "http://link.springer.com/journal/10898", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CoLab Preprint 259.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2006:VMC", } @Article{Bailey:2007:BI, author = "D. H. Bailey and J. M. Borwein and R. E. Crandall", title = "Box integrals", journal = j-J-COMPUT-APPL-MATH, volume = "206", number = "1", pages = "196--208", month = sep, year = "2007", CODEN = "JCAMDI", DOI = "https://doi.org/10.1016/j.cam.2006.06.010", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", MRclass = "65D30 (11Y60 33E20 60E05)", MRnumber = "2337437", MRreviewer = "Michael J. Evans", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2007JCoAM.206..196B; http://docserver.carma.newcastle.edu.au/320/; http://www.sciencedirect.com/science/article/pii/S0377042706004250", abstract = "By a ``box integral'' we mean here an expectation $ \bra | r \to - q \to | s \ket $ where $ r \to $ runs over the unit $n$-cube, with $ q \to $ and $s$ fixed, explicitly: $ \int_0^1 \cdots \int_0^1 ((r 1 - q 1) 2 + \cdots + (r n - q n) 2) s / 2 d r 1 \ldots d r n$. The study of box integrals leads one naturally into several disparate fields of analysis. While previous studies have focused upon symbolic evaluation and asymptotic analysis of special cases (notably $ s = 1$), we work herein more generally --- in interdisciplinary fashion --- developing results such as: (1) analytic continuation (in complex $s$), (2) relevant combinatorial identities, (3) rapidly converging series, (4) statistical inferences, (5) connections to mathematical physics, and (6) extreme-precision quadrature techniques appropriate for these integrals. These intuitions and results open up avenues of experimental mathematics, with a view to new conjectures and theorems on integrals of this type.", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", keywords = "Box integrals; High-precision quadrature; Multi-dimensional integrals", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Book{Bailey:2007:EMA, author = "David H. Bailey and Jonathan M. Borwein and Neil J. Calkin and Roland Girgensohn and D. Russell Luke and Victor Moll", title = "Experimental Mathematics in Action", publisher = pub-A-K-PETERS, address = pub-A-K-PETERS:adr, pages = "xii + 322", year = "2007", ISBN = "1-56881-271-X", ISBN-13 = "978-1-56881-271-7", LCCN = "QA8.7 .E97 2007", bibdate = "Thu Oct 25 18:45:59 MDT 2007", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/master.bib; z3950.loc.gov:7090/Voyager", URL = "http://docserver.carma.newcastle.edu.au/1733/", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", subject = "Experimental mathematics", tableofcontents = "Preface / xi \\ 1 A Philosophical Introduction / 1 \\ 1.1 Introduction / 1 \\ 1.2 Mathematical Knowledge as We View It / 1 \\ 1.3 Mathematical Reasoning / 2 \\ 1.4 Philosophy of Experimental Mathematics / 3 \\ 1.5 Our Experimental Mathodology / 11 \\ 1.6 Finding Things versus Proving Things / 15 \\ 1.7 Conclusions / 24 \\ 2 Algorithms for Experimental Mathematics I / 29 \\ 2.1 The Poetry of Computation / 29 \\ 2.2 High-Precision Arithmetic / 30 \\ 2.3 Integer Relation Detection / 31 \\ 2.4 Illustrations and Examples / 33 \\ 2.5 Definite Integrals and Infinite Series Summations / 43 \\ 2.6 Computation of Multivariate Zeta Values / 44 \\ 2.7 Ramanujan-Type Elliptic Series / 45 \\ 3 Algorithms for Experimental Mathematics II / 53 \\ 3.1 True Scientific Value / 53 \\ 3.2 Prime Number Computations / 55 \\ 3.3 Roots of Polynomials / 58 \\ 3.4 Numerical Quadrature / 61 \\ 3.5 Infinite Series Summation / 67 \\ 3.6 Ap{\'e}ry-Like Summations / 70 \\ 4 Exploration and Discovery in Inverse Scattering / 79 \\ 4.1 Metaphysics and Mechanics / 79 \\ 4.2 The Physical Experiment / 80 \\ 4.3 The Model / 83 \\ 4.4 The Mathematical Experiment: Qualitative Inverse Scattering / 90 \\ 4.5 Current Research / 107 \\ 5 Exploring Strange Functions on the Computer / 113 \\ 5.1 What Is ``Strange''? / 113 \\ 5.2 Nowhere Differentiable Functions / 114 \\ 5.3 Bernoulli Convolutions / 126 \\ 6 Random Vectors and Factoring Integers: A Case Study / 139 \\ 6.1 Learning from Experience / 139 \\ 6.2 Integer Factorization / 140 \\ 6.3 Random Models / 143 \\ 6.4 The Main Questions / 144 \\ 6.5 Bounds / 145 \\ 6.6 Which Model Is Best? / 149 \\ 6.7 Experimental Evidence / 155 \\ 6.8 Conclusions / 158 \\ 7 A Selection of Integrals from a Popular Table / 161 \\ 7.1 The Allure of the Integral / 161 \\ 7.2 The Project and Its Experimental Nature / 163 \\ 7.3 Families and Individuals / 164 \\ 7.4 An Experimental Derivation of Wallis' Formula / 167 \\ 7.5 A Hyperbolic Example / 170 \\ 7.6 A Formula Hidden in the List / 174 \\ 7.7 Some Experiments on Valuations / 177 \\ 7.8 An Error in the Latest Edition / 184 \\ 7.9 Some Examples Involving the Hurwitz Zeta Function / 185 \\ 8 Experimental Mathematics: A Computational Conclusion / 189 \\ 8.1 Mathematicians Are a Kind of Frenchmen / 189 \\ 8.2 Putting Lessons in Action / 190 \\ 8.3 Visual Computing / 191 \\ 8.4 A Preliminary Example: Visualizing DNA Strands / 194 \\ 8.5 What Is a Chaos Game? / 195 \\ 8.6 Hilbert's Inequality and Witten's Zeta Function / 202 \\ 8.7 Computational Challenge Problems / 214 \\ 8.8 Last Words / 222 \\ 9 Exercises / 225 \\ Exercises for Chapter 1 / 225 \\ Exercises for Chapter 2 / 231 \\ Exercises for Chapter 3 / 249 \\ Exercises for Chapter 4 / 256 \\ Exercises for Chapter 5 / 260 \\ Exercises for Chapter 6 / 262 \\ Exercises for Chapter 7 / 265 \\ Exercises for Chapter 8 / 273 \\ Additional Exercises / 280 \\ Bibliography / 301 \\ Index / 317", } @Article{Bailey:2007:HFI, author = "D. H. Bailey and D. Borwein and J. M. Borwein and R. E. Crandall", title = "Hypergeometric Forms for {Ising}-Class Integrals", journal = j-EXP-MATH, volume = "16", number = "3", pages = "257--276", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1080/10586458.2007.10129003", ISSN = "1058-6458 (print), 1944-950X (electronic)", ISSN-L = "1058-6458", MRclass = "33E20 (33C05 33F05 33F10 65D30 82B20)", MRnumber = "2367317", MRreviewer = "Wadim Zudilin", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://projecteuclid.org/euclid.em; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/expmath.bib; http://www.tandfonline.com/toc/uexm20/16/3", URL = "http://docserver.carma.newcastle.edu.au/326/; http://projecteuclid.org/euclid.em/1204928528", abstract = "We apply experimental -mathematical principles to analyze the integrals [complex multiple integral] These are generalizations of a previous integral $ C_n := C_{n, 1} $ relevant to the Ising theory of solid-state physics [Bailey et al. 06]. We find representations of the $ C_{n, k} $ in terms of Meijer $G$-functions and nested Barnes integrals. Our investigations began by computing 500-digit numerical values Of $ C_{n, k}$ for all integers $n$, $k$, where $n$ is an element of $ [2, 12]$ and $k$ is an element of $ [0, 25]$. We found that some $ C_{n, k}$ enjoy exact evaluations involving Dirichlet L-functions or the Riemann zeta function. In the process of analyzing hypergeometric representations, we found-experimentally and strikingly-that the $ C_{n, k}$ almost certainly satisfy certain interindicial relations including discrete k-recurrences. Using generating functions, differential theory, complex analysis, and Wilf--Zeilberger algorithms we are able to prove some central cases of these relations.", acknowledgement = ack-nhfb, fjournal = "Experimental Mathematics", journal-URL = "http://www.tandfonline.com/loi/uexm20", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Bailey:2007:HFI", } @Unpublished{Bailey:2007:HSI, author = "D. Bailey and J. Borwein and R. Crandall and D. Manna", title = "{Heisenberg} spin integrals", month = aug, year = "2007", bibdate = "Tue Aug 16 10:04:46 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib", note = "Preprint.", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Bailey:2007:SPa, author = "David H. Bailey and Jonathan M. Borwein", title = "Solution to Problem 11275", type = "Report", institution = "Lawrence Berkeley National Laboratory and Faculty of Computer Science, Dalhousie University", address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5, Canada", pages = "2", day = "24", month = feb, year = "2007", bibdate = "Fri Sep 30 08:29:49 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.davidhbailey.com/dhbpapers/amm-11275.pdf", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Bailey:2007:SPb, author = "David H. Bailey and Jonathan M. Borwein", title = "Solution to Monthly Problem 11277", type = "Report", institution = "Lawrence Berkeley National Laboratory and Faculty of Computer Science, Dalhousie University", address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5, Canada", pages = "3", day = "23", month = mar, year = "2007", bibdate = "Fri Sep 30 08:30:39 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.davidhbailey.com/dhbpapers/amm-11277.pdf", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bartz:2007:FFC, author = "Sedi Bartz and Heinz H. Bauschke and Jonathan M. Borwein and Simeon Reich and Xianfu Wang", title = "{Fitzpatrick} functions, cyclic monotonicity and {Rockafellar}'s antiderivative", journal = j-NONLINEAR-ANAL, volume = "66", number = "5", pages = "1198--1223", year = "2007", CODEN = "NOANDD", DOI = "https://doi.org/10.1016/j.na.2006.01.013", ISSN = "0362-546x (print), 1873-5215 (electronic)", ISSN-L = "0362-546X", MRclass = "47H05 (47N10 49J53 90C25)", MRnumber = "2286629", MRreviewer = "Patrick L. Combettes", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1232/; http://www.sciencedirect.com/science/article/pii/S0362546X06000435", abstract = "Several deeper results on maximal monotone operators have recently found simpler proofs using Fitzpatrick functions. In this paper, we study a sequence of Fitzpatrick functions associated with a monotone operator. The first term of this sequence coincides with the original Fitzpatrick function, and the other terms turn out to be useful for the identification and characterization of cyclic monotonicity properties. It is shown that for any maximal cyclically monotone operator, the pointwise supremum of the sequence of Fitzpatrick functions is closely related to Rockafellar's antiderivative. Several examples are explicitly computed for the purpose of illustration. In contrast to Rockafellar's result, a maximal 3-cyclically monotone operator need not be maximal monotone. A simplified proof of Asplund's observation that the rotation in the Euclidean plane by $ \pi / n $ is $n$-cyclically monotone but not $ (n + 1)$ -cyclically monotone is provided. The Fitzpatrick family of the subdifferential operator of a sublinear and of an indicator function is studied in detail. We conclude with a new proof of Moreau's result concerning the convexity of the set of proximal mappings.", acknowledgement = ack-nhfb, fjournal = "Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods", journal-URL = "https://www.sciencedirect.com/journal/nonlinear-analysis", keywords = "Convex function; Cyclically monotone operator; Fenchel conjugate; Fitzpatrick function; Maximal monotone operator; Subdifferential operator; Sublinear function", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bauschke:2007:FFC, author = "Heinz H. Bauschke and Jonathan M. Borwein and Xianfu Wang", title = "{Fitzpatrick} functions and continuous linear monotone operators", journal = j-SIAM-J-OPT, volume = "18", number = "3", pages = "789--809", year = "2007", CODEN = "SJOPE8", DOI = "https://doi.org/10.1137/060655468", ISSN = "1052-6234 (print), 1095-7189 (electronic)", ISSN-L = "1052-6234", MRclass = "47H05 (47B65 90C25)", MRnumber = "2345969", MRreviewer = "P. P. Zabre{\u\i}ko", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/319/", abstract = "The notion of a maximal monotone operator is crucial in optimization as it captures both the subdifferential operator of a convex, lower semicontinuous, and proper function and any (not necessarily symmetric) continuous linear positive operator. It was recently discovered that most fundamental results on maximal monotone operators allow simpler proofs utilizing Fitzpatrick functions. In this paper, we study Fitzpatrick functions of continuous linear monotone operators defined on a Hilbert space. A novel characterization of skew operators is presented. A result by Brezis and Haraux is reproved using the Fitzpatrick function. We investigate the Fitzpatrick function of the sum of two operators, and we show that a known upper bound is actually exact in finite-dimensional and more general settings. Cyclic monotonicity properties are also analyzed, and closed forms of the Fitzpatrick functions of all orders are provided for all rotators in the Euclidean plane.", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Optimization", journal-URL = "http://epubs.siam.org/siopt", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Bauschke, Heinz/D-5582-2009", unique-id = "Bauschke:2007:FFC", } @Article{Borwein:2007:ADMa, author = "Jonathan Borwein and Herre Wiersma", title = "{Asplund} decomposition of monotone operators", journal = j-SIAM-J-OPT, volume = "18", number = "3", pages = "946--960", year = "2007", CODEN = "SJOPE8", DOI = "https://doi.org/10.1137/060658357", ISSN = "1052-6234 (print), 1095-7189 (electronic)", ISSN-L = "1052-6234", MRclass = "47H05 (47N10 49J53 52A41)", MRnumber = "2345978", MRreviewer = "Hong Kun Xu", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/321/", abstract = "We establish representations of a monotone mapping as the sum of a maximal subdifferential mapping and a ``remainder'' monotone mapping, where the remainder is ``acyclic'' in the sense that it contains no nontrivial subdifferential component. This is the nonlinear analogue of a skew linear operator. Examples of indecomposable and acyclic operators are given. In particular, we present an explicit nonlinear acyclic operator.", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Optimization", journal-URL = "http://epubs.siam.org/siopt", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2007:ADM", } @InCollection{Borwein:2007:ADMb, author = "Jonathan M. Borwein", editor = "Alain Pietrus and Michel H. Geoffroy", booktitle = "{CSVAA} 2004---control set-valued analysis and applications, ESAIM: Proceedings", title = "{Asplund} decompositions of monotone operators", volume = "17", publisher = "EDP Sci.", address = "Les Ulis, France", pages = "19--25", year = "2007", DOI = "https://doi.org/10.1051/proc:071703", MRclass = "47H05 (41A50 46B03 46B20 46G05 47N10 49J53)", MRnumber = "2362689", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "ESAIM Proc.", URL = "http://docserver.carma.newcastle.edu.au/299/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Borwein:2007:CCS, author = "Jonathan M. Borwein and David Langstroth and Mason Macklem and Scott Wilson and V. Jungi{\'c}", booktitle = "{21st International Symposium on High Performance Computing Systems and Applications. HPCS 2007, Saskatoon, SK, Canada, 13--16 May 2007}", title = "The Coast-to-Coast Seminar and Remote Mathematical Collaboration", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "23--29", month = may, year = "2007", DOI = "https://doi.org/10.1109/HPCS.2007.30", bibdate = "Wed Aug 10 12:08:56 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, book-isbn = "0-7695-2813-9", keywords = "AccessGrid; Australia; Canadian universities; coast-to-coast seminar; Collaboration; Collaborative work; computer aided instruction; Computer displays; Computer networks; Dalhousie University; Distributed computing; grid computing; groupware; Mathematics; mathematics computing; Production; remote mathematical collaboration; seminar series; Seminars; Simon Fraser University; Virtual environment", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2007:CDS, author = "Jonathan M. Borwein", title = "A class of {Dirichlet} series integrals", journal = j-AMER-MATH-MONTHLY, volume = "114", number = "1", pages = "70--76", month = jan, year = "2007", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "40A10 (26A42)", MRnumber = "2283644", MRreviewer = "Ilaria Mantellini", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/262/; http://www.jstor.org/stable/27642121", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CoLab Preprint 262.", } @InCollection{Borwein:2007:CNS, author = "Jonathan M. Borwein and Warren B. Moors", editor = "Elliott Pearl", booktitle = "Open Problems in Topology {II}", title = "Chapter 50: {Non-smooth} analysis, optimisation theory and {Banach} space theory", publisher = pub-ELSEVIER, address = pub-ELSEVIER:adr, pages = "549--559", year = "2007", DOI = "https://doi.org/10.1016/B978-044452208-5/50050-8", ISBN = "0-444-52208-5", ISBN-13 = "978-0-444-52208-5", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.sciencedirect.com/science/article/pii/B9780444522085500508", abstract = "This chapter discusses about nonsmooth analysis, optimization theory, and Banach space theory. A Banach space X is called a weak Asplund space [G{\^a}teaux differentiability space] if each continuous convex function defined on it is G{\^a}teaux differentiable at the points of a residual subset (that is, a subset that contains the intersection of countably many dense open subsets of X) [dense subset] of its domain. For a Banach space (X, || \cdot || ), with closed unit ball BX, the Bishop--Phelps set is the set of all linear functionals in the dual X* that attain their maximum value over BX; that is, the set {x* \subset X*: x*(x) = || x*|| for some x \subset BX}. The Bishop--Phelps Theorem says that the Bishop--Phelps set is always dense in X*. A Banach space X has the attainable approximation property (AAP) if the set of support functionals for any closed bounded convex subset W \subseteq X is norm dense in X*. The concepts related to the Bishop--Phelps problem and the complex Bishop--Phelps property are also discussed. Concepts of biorthogonal sequences and support points are also elaborated.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2007:DCR, author = "D. Borwein and J. Borwein and R. Crandall and R. Mayer", title = "On the dynamics of certain recurrence relations", journal = j-RAMANUJAN-J, volume = "13", number = "1--3", pages = "63--101", year = "2007", CODEN = "RAJOF9", DOI = "https://doi.org/10.1007/s11139-006-0243-3", ISSN = "1382-4090 (print), 1572-9303 (electronic)", ISSN-L = "1382-4090", MRclass = "11B37 (11A55 11Y16 37C99 37E99 39A10 65Q05)", MRnumber = "2281157", MRreviewer = "James G. Mc Laughlin", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/253/; http://link.springer.com/article/10.1007/s11139-006-0243-3", abstract = "In recent analyses [ 3, 4] the remarkable AGM continued fraction of Ramanujan - denoted R-1(a, b) - was proven to converge for almost all complex parameter pairs (a, b). It was conjectured that R-1 diverges if and only if (0 not equal a = be(i phi) with cos(2) phi not equal 1) or (a(2) = b(2) is an element of (-infinity, 0)). In the present treatment we resolve this conjecture to the positive, thus establishing the precise convergence domain for R-1. This is accomplished by analyzing, using various special functions, the dynamics of sequences such as (t(n)) satisfying a recurrence t(n) = (t(n-1)(n-1) \kappa(n-1)t(n-2))/n. where \kappa(n):= a(2), b(2) as n be even, odd respectively. As a byproduct, we are able to give, in some cases, exact expressions for the n-th convergent to the fraction R-1, thus establishing some precise convergence rates. It is of interest that this final resolution of convergence depends on rather intricate theorems for complex-matrix products, which theorems evidently being extensible to more general continued fractions.", acknowledgement = ack-nhfb, fjournal = "The {Ramanujan} Journal", journal-URL = "http://link.springer.com/journal/11139", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CoLab Preprint 253.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2007:DCR", } @TechReport{Borwein:2007:ELAa, author = "David Borwein and Jonathan Borwein and Richard Crandall", title = "Effective {Laguerre} asymptotics", type = "Report", institution = "Department of Computer Science, Dalhousie University", address = "Halifax, NS, Canada B3H 4R2", year = "2007", bibdate = "Thu Aug 11 08:24:07 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib", URL = "http://docserver.carma.newcastle.edu.au/334/; http://locutus.cs.dal.ca:8088/archive/00000334/; http://web.archive.org/web/20070208032521/http://locutus.cs.dal.ca:8088/archive/00000334/", abstract = "It is known that the generalized Laguerre polynomials can enjoy sub-exponential growth for large primary index. Specifically, for certain fixed parameter pairs $ (a, z) $ one has the large-$n$ asymptotic $$ L_n^{( - a)}( - z) \sim C(a, z) n^{-a / 2 - 1 / 4} e^{2 \sqrt {nz}}. $$ We introduce a computationally motivated contour integral that allows highly efficient numerical evaluation of $ L_n$, yet also leads to general asymptotic series over the full domain for sub-exponential behavior. We eventually lay out a fast algorithm for generation of the rather formidable expansion coefficients. Along the way we address the difficult problem of establishing effective (i.e., rigorous and explicit) error bounds on the general expansion. To this end, we avoid classical stationary-phase and steepest-descent techniques in favor of an ``exp-arc'' method that amounts to a natural bridge between converging series and effective asymptotics. Finally, we exhibit an absolutely convergent exp-arc series for Bessel-function evaluation as an alternative to conventional ascending-asymptotic switching.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2007:IPA, author = "Jonathan M. Borwein and Marc Chamberland", title = "Integer powers of arcsin", journal = j-INT-J-MATH-MATH-SCI, pages = "Art. ID 19381, 10", month = jun, year = "2007", DOI = "https://doi.org/10.1155/2007/19381", ISSN = "0161-1712 (print), 1687-0425 (electronic)", ISSN-L = "0161-1712", MRclass = "33B10 (11B65 33B30)", MRnumber = "2320777", MRreviewer = "Stefan Gerhold", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/287/", acknowledgement = ack-nhfb, fjournal = "International Journal of Mathematics and Mathematical Sciences", journal-URL = "https://www.hindawi.com/journals/ijmms/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2007:MST, author = "Jonathan M. Borwein", title = "Maximality of sums of two maximal monotone operators in general {Banach} space", journal = j-PROC-AM-MATH-SOC, volume = "135", number = "12", pages = "3917--3924", month = dec, year = "2007", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/S0002-9939-07-08960-5", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "47H05 (46N10 52A41)", MRnumber = "2341941", MRreviewer = "S{\'a}ndor Z. N{\'e}meth", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/322/; http://www.jstor.org/stable/20535029", abstract = "We combine methods from convex analysis, based on a function of Simon Fitzpatrick, with a fine recent idea due to Voisei, to prove maximality of the sum of two maximal monotone operators in Banach space under various natural domain and transversality conditions.", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2007:MST", } @InCollection{Borwein:2007:NAA, author = "Jonathan M. Borwein and Warren B. Moors", title = "Nonsmooth Analysis, Approximation Theory and {Banach} Space Theory", crossref = "Pearl:2007:OPT", pages = "557--566", year = "2007", bibdate = "Sat Aug 13 17:04:44 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2007:PCS, author = "Jonathan M. Borwein", title = "Proximality and {Chebyshev} sets", journal = j-OPTIM-LETT, volume = "1", number = "1", pages = "21--32", year = "2007", DOI = "https://doi.org/10.1007/s11590-006-0014-5", ISSN = "1862-4472 (print), 1862-4480 (electronic)", ISSN-L = "1862-4472", MRclass = "41A50 (46A55 46N10 47J20 49J53)", MRnumber = "2357605", MRreviewer = "John R. Giles", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/323/", abstract = "This paper is a companion to a lecture given at the Prague Spring School in Analysis in April 2006. It highlights four distinct variational methods of proving that a finite dimensional Chebyshev set is convex and hopes to inspire renewed work on the open question of whether every Chebyshev set in Hilbert space is convex.", acknowledgement = ack-nhfb, ajournal = "Optim. Lett.", fjournal = "Optimization Letters", journal-URL = "http://link.springer.com/journal/11590", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2007:PCS", } @Article{Borwein:2007:PRB, author = "J. M. Borwein and B. Salvy", title = "A Proof of a Recursion for {Bessel} Moments", journal = "ArXiv e-prints", month = jun, year = "2007", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2007arXiv0706.1409B; http://docserver.carma.newcastle.edu.au/346/", abstract = "We provide a proof of a conjecture in (Bailey, Borwein, Borwein, Crandall 2007) on the existence and form of linear recursions for moments of powers of the Bessel function $ K_0 $.", acknowledgement = ack-nhfb, eprint = "0706.1409", keywords = "Computer Science - Symbolic Computation, Mathematics - Classical Analysis and ODEs", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Salvy, Bruno/0000-0002-4313-0679", primaryclass = "cs.SC", } @Unpublished{Borwein:2007:REM, author = "J. M. Borwein and Mason Macklem", title = "Retro-enhancement of Mathematical Literature", month = mar, year = "2007", bibdate = "Tue Aug 16 10:05:13 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Preprint.", URL = "http://docserver.carma.newcastle.edu.au/339/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2007:VPE, author = "David Borwein and Jonathan Borwein", title = "{van der Pol} Expansions of {$L$}-Series", journal = j-CAN-MATH-BULL, volume = "50", number = "1", pages = "11--23", month = mar, year = "2007", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-2007-002-0", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", MRclass = "11M35 (11M41)", MRnumber = "2296621", MRreviewer = "Saulius Zamarys", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://cms.math.ca/cmb/v50/; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/canmathbull.bib", URL = "http://docserver.carma.newcastle.edu.au/283/", abstract = "We provide concise series representations for various L-series integrals. Different techniques are needed below and above the abscissa of absolute convergence of the underlying L-series.", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2007:VPE", } @InCollection{Bailey:2008:CAD, author = "David H. Bailey and Jonathan M. Borwein", booktitle = "Tapas in experimental mathematics", title = "Computer-assisted discovery and proof", volume = "457", publisher = pub-AMS, address = pub-AMS:adr, pages = "21--52", year = "2008", DOI = "https://doi.org/10.1090/conm/457/08901", MRclass = "11Y99 (68T15 68U35 68W30)", MRnumber = "2427663", MRreviewer = "Jeffrey O. Shallit", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Contemp. Math.", URL = "http://docserver.carma.newcastle.edu.au/338/", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @InProceedings{Bailey:2008:EEB, author = "David H. Bailey and Jonathan M. Borwein", title = "Effective Error Bounds for {Euler--Maclaurin}-Based Quadrature Schemes", crossref = "IEEE:2008:HIS", pages = "??--??", year = "2008", bibdate = "Sat Aug 13 17:20:17 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", pagecount = "7", } @Article{Bailey:2008:EIE, author = "David H. Bailey and Jonathan M. Borwein and David Broadhurst and M. L. Glasser", title = "Elliptic integral evaluations of {Bessel} moments and applications", journal = j-J-PHYS-A-MATH-THEOR, volume = "41", number = "20", pages = "205203", month = may, year = "2008", CODEN = "JPAMB5", DOI = "https://doi.org/10.1088/1751-8113/41/20/205203", ISSN = "1751-8113 (print), 1751-8121 (electronic)", ISSN-L = "1751-8113", MRclass = "33C10 (33E05 33F05)", MRnumber = "2450513", MRreviewer = "Subuhi Khan", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2008JPhA...41t5203B; http://arxiv.org/abs/0801.0891; http://iopscience.iop.org/article/10.1088/1751-8113/41/20/205203; http://stacks.iop.org/1751-8121/41/i=20/a=205203", abstract = "We record and substantially extend what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical physics. In particular, we develop formulae for integrals of products of six or fewer Bessel functions. In consequence, we are able to discover and prove closed forms for $ c_{n, k} \coloneq {\int }^\infty_0 t^k K^n_0 (t) d t $ with integers $ n = 1, 2, 3, 4 $ and $ k \geq 0 $, obtaining new results for the even moments $ c_{3, 2k} $ and $ c_{4, 2k} $. We also derive new closed forms for the odd moments $ s_{n, 2k + 1} \coloneq \int^\infty_0 t^{2k + 1} I_0 (t) K^{n - 1}_0 (t) \, d t $ with $ n = 3, 4 $ and for $ t_{n, 2k + 1} \coloneq \int^\infty_0 t^{2k + 1} I^2_0 (t) K^{n - 2}_0 (t) \, d t $ with $ n = 5 $, relating the latter to Green functions on hexagonal, diamond and cubic lattices. We conjecture the values of $ s_{5, 2k + 1} $, make substantial progress on the evaluation of $ c_{5, 2k + 1} $, $ s_{6, 2k + 1} $ and $ t_{6, 2k + 1} $ and report more limited progress regarding $ c_{5, 2k} $, $ c_{6, 2k + 1} $ and $ c_{6, 2k} $. In the process, we obtain eight conjectural evaluations, each of which has been checked to 1200 decimal places. One of these lies deep in four-dimensional quantum field theory and two are probably provable by delicate combinatorics. There remains a hard core of five conjectures whose proofs would be most instructive, to mathematicians and physicists alike.", acknowledgement = ack-nhfb, eid = "205203", eprint = "0801.0891", fjournal = "Journal of Physics. A. Mathematical and Theoretical", journal-URL = "http://iopscience.iop.org/1751-8121", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", pagecount = "46", primaryclass = "hep-th", } @InProceedings{Bailey:2008:HPC, author = "D. H. Bailey and J. M. Borwein", booktitle = "Proceedings of {XII} Advanced Computing and Analysis Techniques in Physics Research", title = "High-Precision Computation and Mathematical Physics", publisher = "????", address = "????", pages = "14", year = "2008", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2008acat.confE..14B; http://docserver.carma.newcastle.edu.au/386/", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Bailey:2008:HPH, author = "David H. Bailey and Jonathan M. Borwein", title = "Highly Parallel, High-Precision Numerical Integration", type = "Report", institution = "Lawrence Berkeley National Laboratory and Faculty of Computer Science, Dalhousie University", address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5, Canada", pages = "18", day = "1", month = apr, year = "2008", bibdate = "Fri Sep 30 08:30:39 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.davidhbailey.com/dhbpapers/quadparallel.pdf", abstract = "This paper describes schemes for rapidly computing numerical values of definite integrals to very high accuracy (hundreds to thousands of digits) on highly parallel computer systems. Such schemes are of interest not only in computational physics and computational chemistry, but also in experimental mathematics, where high-precision numerical values of definite integrals can be used to numerically discover new identities. This paper presents performance results for 1-D and 2-D integral test suites on highly parallel computer systems. Results are also given for certain problems that derive from mathematical physics. One of these results confirms a conjecture to 20,000 digit accuracy. The performance rate for this calculation is 690 Gflop/s on 1024 CPUs of a state-of-the-art parallel system. Other results, which range in precision from 120 to 500 digits, and for 1-D, 2-D, 3-D and 4-D integrals, derive from Ising theory. The largest of these calculations required 28 hours on 256 CPUs. We believe that these are the first instances of evaluations of nontrivial 3-D and 4-D integrals to multi-hundred-digit accuracy.", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Bailey:2008:HPN, author = "D. H. Bailey and J. M. Borwein", booktitle = "MICA conference May 2008", title = "High-Precision Numerical Integration: Progress and Challenges", publisher = "????", address = "????", pages = "??--??", year = "2008", bibdate = "Sat Aug 13 16:39:19 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1444/", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Bailey:2008:PSP, author = "David H. Bailey and Jonathan M. Borwein", title = "Proposed {SIAM} Problem", type = "Report", institution = "Lawrence Berkeley National Laboratory and Faculty of Computer Science, Dalhousie University", address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5, Canada", pages = "2", day = "12", month = aug, year = "2008", bibdate = "Fri Sep 30 08:36:07 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.davidhbailey.com/dhbpapers/siam-bessel.pdf", abstract = "[From the introduction:] A recent paper by the present authors, together with mathematical physicists David Broadhurst and M. Larry Glasser, explored Bessel moment integrals, namely definite integrals of the general form $ \int_0^\infty t^m f^n(t) \, d t $, where the function $ f(t) $ is one of the classical Bessel functions [2]. In that paper, numerous previously unknown analytic evaluations were obtained, using a combination of analytic methods together with some fairly high-powered numerical computations, often performed on highly parallel computers.", acknowledgement = ack-nhfb, keywords = "Bessel moment integrals", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Baillie:2008:SSS, author = "Robert Baillie and David Borwein and Jonathan M. Borwein", title = "Surprising sinc sums and integrals", journal = j-AMER-MATH-MONTHLY, volume = "115", number = "10", pages = "888--901", month = dec, year = "2008", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "33B10 (26D05 40A25 42A05)", MRnumber = "2468551", MRreviewer = "Valery V. Karachik", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/332/; http://www.jstor.org/stable/27642636", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Unpublished{Borwein:2008:BST, author = "J. M. Borwein and A. C. Eberhard", title = "{Banach} spaces of type ({NI}) and monotone operators on non-reflexive spaces", month = jun, year = "2008", bibdate = "Tue Aug 16 10:02:34 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Preprint.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Eberhard, Andrew/0000-0003-2977-3456", } @InCollection{Borwein:2008:CCC, author = "J. Borwein and V. Jungi{\'c} and D. Langstroth and M. Macklem and S. Wilson", title = "Coast-to-Coast (C2C) Seminar: Background, History, and Practice", crossref = "Borwein:2008:CMD", chapter = "9", pages = "127--140", year = "2008", DOI = "https://doi.org/10.1201/b10587-12", bibdate = "Sat Aug 13 16:51:32 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.crcnetbase.com/doi/pdfplus/10.1201/b10587-12", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2008:DRT, author = "Jonathan M. Borwein and D. Russell Luke", title = "Dynamics of a {Ramanujan}-type continued fraction with cyclic coefficients", journal = j-RAMANUJAN-J, volume = "16", number = "3", pages = "285--304", year = "2008", CODEN = "RAJOF9", DOI = "https://doi.org/10.1007/s11139-007-9096-7", ISSN = "1382-4090 (print), 1572-9303 (electronic)", ISSN-L = "1382-4090", MRclass = "40A15 (11J70)", MRnumber = "2429902", MRreviewer = "Haakon S. Waadeland", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1480/", abstract = "We study several generalizations of the AGM continued fraction of Ramanujan inspired by a series of recent articles in which the validity of the AGM relation and the domain of convergence of the continued fraction were determined for certain complex parameters (Borwein et al., Exp. Math. 13, 275-286, 2004, Ramanujan J., in press, 2004; Borwein and Crandall, Exp. Math. 12, 287-296, 2004). A study of the AGM continued fraction is equivalent to an analysis of the convergence of certain difference equations and the stability of dynamical systems. Using the matrix analytical tools developed in 2004, we determine the convergence properties of deterministic difference equations and so divergence of their corresponding continued fractions.", acknowledgement = ack-nhfb, fjournal = "The {Ramanujan} Journal", journal-URL = "http://link.springer.com/journal/11139", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CoLab Preprint 261.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2008:DRT", } @Article{Borwein:2008:EBF, author = "David Borwein and Jonathan M. Borwein and O-Yeat Chan", title = "The evaluation of {Bessel} functions via exp--arc integrals", journal = j-J-MATH-ANAL-APPL, volume = "341", number = "1", pages = "478--500", month = may, year = "2008", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/j.jmaa.2007.10.003", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "33C10 (33F05 65D20)", MRnumber = "2394100", MRreviewer = "Richard B. Paris", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/elefunt.bib", URL = "http://adsabs.harvard.edu/abs/2008JMAA..341..478B; http://docserver.carma.newcastle.edu.au/1231/; http://www.sciencedirect.com/science/article/pii/S0022247X07012346", abstract = "A standard method for computing values of Bessel functions has been to use the well-known ascending series for small argument, and to use an asymptotic series for large argument; with the choice of the series changing at some appropriate argument magnitude, depending on the number of digits required. In a recent paper, D. Borwein, J. Borwein, and R. Crandall [D. Borwein, J. M. Borwein, R. Crandall, Effective Laguerre asymptotics, preprint at http://locutus.cs.dal.ca:8088/archive/00000334/] derived a series for an ``exp-arc'' integral which gave rise to an absolutely convergent series for the J and I Bessel functions with integral order. Such series can be rapidly evaluated via recursion and elementary operations, and provide a viable alternative to the conventional ascending-asymptotic switching. In the present work, we extend the method to deal with Bessel functions of general (non-integral) order, as well as to deal with the Y and K Bessel functions.", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", keywords = "Bessel function; Exponential-hyperbolic expansions; Uniform series expansion", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2008:ECE, author = "J. M. Borwein and I. J. Zucker and J. Boersma", title = "The evaluation of character {Euler} double sums", journal = j-RAMANUJAN-J, volume = "15", number = "3", pages = "377--405", year = "2008", CODEN = "RAJOF9", DOI = "https://doi.org/10.1007/s11139-007-9083-z", ISSN = "1382-4090 (print), 1572-9303 (electronic)", ISSN-L = "1382-4090", MRclass = "11M41 (11M06)", MRnumber = "2390277", MRreviewer = "Stamatis Koumandos", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/255/; http://link.springer.com/article/10.1007/s11139-007-9083-z", abstract = "Euler considered sums of the form [GRAPHICS] Here natural generalizations of these sums namely [complex equation] are investigated, where chi(p) and chi(q) are characters, and s and t are positive integers. The cases when p and q are either 1, 2a, 2b or -4 are examined in detail, and closed-form expressions are found for t = 1 and general s in terms of the Riemann zeta function and the Catalan zeta function-the Dirichlet series L(-4)(s) = 1(-s) - 3(-s) + 5(-s) - 7(-s) + center dot center dot center dot. Some results for arbitrary p and q are obtained as well.", acknowledgement = ack-nhfb, fjournal = "The {Ramanujan} Journal", journal-URL = "http://link.springer.com/journal/11139", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CoLab Preprint 260.", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2008:ECE", } @Article{Borwein:2008:ELA, author = "David Borwein and Jonathan M. Borwein and Richard E. Crandall", title = "Effective {Laguerre} asymptotics", journal = j-SIAM-J-NUMER-ANAL, volume = "46", number = "6", pages = "3285--3312", year = "2008", CODEN = "SJNAAM", DOI = "https://doi.org/10.1137/07068031X", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "33C65 (30E20 34E05)", MRnumber = "2448665", MRreviewer = "Yu-Qiu Zhao", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/elefunt.bib", URL = "http://docserver.carma.newcastle.edu.au/334/", abstract = "It is known that the generalized Laguerre polynomials can enjoy subexponential growth for large primary index. In particular, for certain fixed parameter pairs (a, z) one has the large-n asymptotic behavior L-n((-a)) (-z) similar to C(a, z)(n)(-a)/2-1/ (4)e(2) root nz. We introduce a computationally motivated contour integral that allows efficient numerical Laguerre evaluations yet also leads to the complete asymptotic series over the full parameter domain of subexponential behavior. We present a fast algorithm for symbolic generation of the rather formidable expansion coefficients. Along the way we address the difficult problem of establishing effective (i. e., rigorous and explicit) error bounds on the general expansion. A primary tool for these developments is an ``exp-arc'' method giving a natural bridge between converging series and effective asymptotics.", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2008:ELA", } @Article{Borwein:2008:HIW, author = "Jonathan M. Borwein", title = "{Hilbert}'s Inequality and {Witten}'s Zeta-Function", journal = j-AMER-MATH-MONTHLY, volume = "115", number = "2", pages = "125--137", month = feb, year = "2008", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jan 30 12:00:30 MST 2012", bibsource = "http://www.jstor.org/journals/00029890.html; http://www.jstor.org/stable/i27642413; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib", URL = "http://www.jstor.org/stable/27642418", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:2008:IEM, author = "Jonathan Borwein", title = "Implications of experimental mathematics for the philosophy of mathematics", crossref = "Gold:2008:POD", chapter = "2", publisher = pub-LONGMAN, address = pub-LONGMAN:adr, pages = "33--61", year = "2008", MRclass = "00A30 (03A05)", MRnumber = "2452073", bibdate = "Sat Aug 13 16:37:59 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "MAA Spectrum", URL = "http://docserver.carma.newcastle.edu.au/280/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", xxpages = "33--59", } @Book{Borwein:2008:ME, author = "Jonathan Borwein and David Bailey", title = "Mathematics by Experiment", publisher = pub-A-K-PETERS, address = pub-A-K-PETERS:adr, edition = "Second", pages = "xii + 377", year = "2008", DOI = "https://doi.org/10.1201/b10704", ISBN = "1-56881-442-9, 1-4398-6536-1 (PDF e-book)", ISBN-13 = "978-1-56881-442-1, 978-1-4398-6536-1 (PDF e-book)", LCCN = "QA76.95 .B67 2008", MRclass = "00A35 (37-04)", MRnumber = "2473161", MRreviewer = "Michael Otte", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Plausible reasoning in the 21st Century.", URL = "http://docserver.carma.newcastle.edu.au/272/", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", tableofcontents = "Front matter / i \\ 1. What is experimental mathematics? / 1 \\ 2. Experimental mathematics in action / 47 \\ 3. Pi and its friends / 103 \\ 4. Normality of numbers / 143 \\ 5. The power of constructive proofs / 175 \\ 6. Numerical techniques / 215 \\ 7. Recent experiences / 243 \\ Bibliography / 349", } @Article{Borwein:2008:PRB, author = "Jonathan M. Borwein and Bruno Salvy", title = "A Proof of a Recurrence for {Bessel} Moments", journal = j-EXP-MATH, volume = "17", number = "2", pages = "223--230", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1080/10586458.2008.10129032", ISSN = "1058-6458 (print), 1944-950X (electronic)", ISSN-L = "1058-6458", MRclass = "68W30 (33C10 33E30 33F10)", MRnumber = "2433887", MRreviewer = "Carsten Schneider", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://projecteuclid.org/euclid.em; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/expmath.bib; http://www.tandfonline.com/toc/uexm20/17/2", URL = "http://docserver.carma.newcastle.edu.au/346/; http://projecteuclid.org/euclid.em/1227118973", abstract = "We provide a proof of a conjecture in [Bailey et al. 07a] on the existence and form of linear recurrences for moments of powers of the Bessel function K-0.", acknowledgement = ack-nhfb, fjournal = "Experimental Mathematics", journal-URL = "http://www.tandfonline.com/loi/uexm20", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Salvy, Bruno/0000-0002-4313-0679", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2008:PRB", } @InProceedings{Borwein:2008:VPG, author = "J. M. Borwein", editor = "????", booktitle = "Mathematics and Culture, La matematica: Problemi e teoremi", title = "La vita di pi greco. ({Italian}) [{The} life of {Greek} pi]", publisher = "Guilio Einaudi Editori", address = "Turino, Italy", pages = "??--??", year = "2008", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/pi.bib", URL = "http://www.carma.newcastle.edu.au/~jb616/pi-2010.pdf", acknowledgement = ack-nhfb, language = "Italian", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CoLab Preprint 265", } @InCollection{Borwein:2008:WEM, author = "J. M. Borwein and D. H. Bailey", editor = "Giovanni Treccani", booktitle = "Enciclopedia della Scienza e della Tecnica", title = "What is Experimental Mathematics", publisher = "????", address = "Roma, Italia", pages = "??--??", year = "2008", bibdate = "Sat Aug 13 16:32:55 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Reprint of \cite[Chapter 1]{Borwein:2004:MEP}.", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", xxnote = "Check: is Treccani the editor or publisher?? I cannot find this book in library catalogs or large booksellers.", } @Article{Eberhard:2008:SOC, author = "A. C. Eberhard and J. M. Borwein", title = "Second Order Cones for Maximal Monotone Operators via Representative Functions", journal = j-SET-VALUED-ANAL, volume = "16", number = "2--3", pages = "157--184", year = "2008", CODEN = "SVANEG", DOI = "https://doi.org/10.1007/s11228-008-0075-y", ISSN = "0927-6947 (print), 1572-932X (electronic)", ISSN-L = "0927-6947", MRclass = "49J53 (46N10 47H04 47H05 47N10)", MRnumber = "2399200", MRreviewer = "Nicolas Hadjisavvas", bibdate = "Thu Aug 11 09:36:22 MDT 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/348/; http://link.springer.com/article/10.1007/s11228-008-0075-y", abstract = "It is shown that various first and second order derivatives of the Fitzpatrick and Penot representative functions for a maximal monotone operator T, in a reflexive Banach space, can be used to represent differential information associated with the tangent and normal cones to the Graph T. In particular we obtain formula for the proto-derivative, as well as its polar, the normal cone to the graph of T. First order derivatives are shown to be useful in recognising points of single-valuedness of T. We show that a strong form of proto-differentiability to the graph of T, is often associated with single-valuedness of T.", acknowledgement = ack-nhfb, fjournal = "Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications", journal-URL = "http://link.springer.com/journal/11228", ORCID-numbers = "Eberhard, Andrew/0000-0003-2977-3456; Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009; Eberhard, Andrew/B-5576-2013", unique-id = "Eberhard:2008:SOC", } @Article{Bailey:2009:EMCa, author = "David H. Bailey and Jonathan M. Borwein", title = "Experimental mathematics and computational statistics", journal = "Wiley Interdisciplinary Reviews: Computational Statistics", volume = "1", number = "1", pages = "12--24", year = "2009", DOI = "https://doi.org/10.1002/wics.1", ISSN = "1939-0068 (print), 1939-5108 (electronic)", ISSN-L = "1939-0068", bibdate = "Thu Aug 11 11:01:49 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1227/", abstract = "The field of statistics has long been noted for techniques to detect patterns and regularities in numerical data. In this article, we explore connections between statistics and the emerging field of experimental mathematics. These include both applications of experimental mathematics in statistics as well as statistical methods applied to computational mathematics.", acknowledgement = ack-nhfb, keywords = "experimental mathematics, numerical integration, numerical analysis, computational statistics", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Bailey:2009:EMCb, author = "D. H. Bailey and J. M. Borwein", booktitle = "Online Encyclopedia of Computational Statistics. {A} {Wiley} Interdisciplinary Review", title = "Experimental Mathematics and Computational Statistics", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "??--??", month = jul, year = "2009", DOI = "", LCCN = "", bibdate = "Fri Aug 12 09:29:41 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://ca.wiley.com/WileyCDA/Section/id-390445.html; http://docserver.carma.newcastle.edu.au/1227/; http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470973889.html", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", remark = "Probably identical to \cite{Bailey:2009:EMCa}. Appears to be first edition, but not available at publisher site.", xxISBN = "0-470-97388-9 (second edition)", xxisbn-13 = "978-0-470-97388-2 (second edition)", } @Article{Bailey:2009:HPH, author = "David Bailey and Jonathan Borwein", title = "Highly parallel, high precision integration", journal = "International Journal of Computational Science and Engineering", volume = "4", number = "??", pages = "??--??", month = "????", year = "2009", ISSN = "1742-7185 (print), 1742-7193 (electronic)", ISSN-L = "1742-7185", bibdate = "Fri Aug 12 09:16:29 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/294/", acknowledgement = ack-nhfb, journal-URL = "http://www.inderscience.com/jhome.php?jcode=ijcse", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", remark = "I cannot find this article at the publisher site, which lacks metadata by volume, and fails to find author or title values.", } @Article{Bailey:2009:PAD, author = "David H. Bailey and Jonathan M. Borwein", title = "{PSLQ}: an Algorithm to Discover to Integer Relations", journal = "Computeralgebra Rundbrief", volume = "45", number = "??", pages = "8--11", month = oct, year = "2009", ISSN = "0933-5994", ISSN-L = "0933-5994", bibdate = "Sat Aug 13 16:11:51 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.fachgruppe-computeralgebra.de/cms/tiki-index.php?page=Rundbrief", acknowledgement = ack-nhfb, journal-URL = "http://www.fachgruppe-computeralgebra.de/rundbrief/", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bailey:2009:RQR, author = "D. H. Bailey and J. M. Borwein and R. E. Crandall", title = "Resolution of the {Quinn--Rand--Strogatz} Constant of Nonlinear Physics", journal = j-EXP-MATH, volume = "18", number = "1", pages = "107--116", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1080/10586458.2009.10128885", ISSN = "1058-6458 (print), 1944-950X (electronic)", ISSN-L = "1058-6458", MRclass = "11Y60 (11M35 11Z05)", MRnumber = "2548991", MRreviewer = "Herman J. J. te Riele", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://projecteuclid.org/euclid.em; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/expmath.bib; http://www.tandfonline.com/toc/uexm20/18/1", URL = "http://docserver.carma.newcastle.edu.au/345/; http://projecteuclid.org/euclid.em/1243430534", abstract = "Herein we develop connections between zeta functions and some recent ``mysterious'' constants of nonlinear physics. In an important analysis of coupled Winfree oscillators, Quinn, Rand, and Strogatz [Quinn et al. 07] developed a certain N-oscillator scenario whose bifurcation phase offset small phi is implicitly defined, with a conjectured asymptotic behavior sin phi similar to 1 - c(1)/N, with experimental estimate c(1) = 0.605443657.... We are able to derive the exact theoretical value of this ``QRS constant'' c(1) as a real zero of a particular Hurwitz zeta function. This discovery enables, for example, the rapid resolution of cl to extreme precision. Results and conjectures are provided in regard to higher-order terms of the sin phi asymptotic, and to yet more physics constants emerging from the original QRS work.", acknowledgement = ack-nhfb, fjournal = "Experimental Mathematics", journal-URL = "http://www.tandfonline.com/loi/uexm20", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Bailey:2009:RQR", } @TechReport{Bailey:2009:SMPa, author = "David H. Bailey and Jonathan M. Borwein", title = "Solution to {{\booktitle{Monthly}}} Problem \#11418", type = "Report", institution = "Lawrence Berkeley National Laboratory and Faculty of Computer Science, Dalhousie University and School of Mathematical and Physical Sciences, University of Newcastle", address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5, Canada and Callaghan, NSW 2308, Australia", day = "6", month = jul, year = "2009", bibdate = "Fri Sep 30 08:40:15 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.davidhbailey.com/dhbpapers/amm-11418.pdf", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", remark = "The report evaluates the integral $ J = \int_\infty^\infty \frac {t^2 \sech^2(t)}{a - \tanh (t)} \, d t $ for complex $ |a| > 1 $.", } @TechReport{Bailey:2009:SMPb, author = "David H. Bailey and Jonathan M. Borwein", title = "Solutions to {{\booktitle{Monthly}}} Problems 11456 and 11457", type = "Report", institution = "Lawrence Berkeley National Laboratory and Faculty of Computer Science, Dalhousie University", address = "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5, Canada", pages = "2", day = "10", month = oct, year = "2009", bibdate = "Fri Sep 30 08:34:31 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.davidhbailey.com/dhbpapers/amm-11456.pdf", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Book{Borwein:2009:CCI, author = "Jonathan M. Borwein and Keith J. Devlin", title = "The computer as crucible: an introduction to experimental mathematics", publisher = pub-A-K-PETERS, address = pub-A-K-PETERS:adr, pages = "xi + 158", year = "2009", ISBN = "1-56881-343-0", ISBN-13 = "978-1-56881-343-1", LCCN = "QA8.7 .B67 2009", MRclass = "00A35 (11-04 11Y16 11Y60)", MRnumber = "2464847", MRreviewer = "Samuel S. Wagstaff, Jr.", bibdate = "Tue Nov 10 17:48:24 MST 2009", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/master.bib; z3950.loc.gov:7090/Voyager", URL = "http://docserver.carma.newcastle.edu.au/1730/; http://www.loc.gov/catdir/toc/fy0904/2008022180.html", acknowledgement = ack-nhfb, libnote = "Not in my library.", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", subject = "Experimental mathematics", tableofcontents = "What is experimental mathematics? \\ What is the quadrillionth decimal place of $pi$? \\ What is that number? \\ The most important function in mathematics \\ Evaluate the following integral \\ Serendipity \\ Calculating [pi] \\ The computer knows more math than you do \\ Take it to the limit \\ Danger! Always exercise caution when using the computer \\ Stuff we left out (until now)", } @InProceedings{Borwein:2009:DAD, author = "J. M. Borwein", title = "Digitally-assisted discovery and proof", crossref = "Lin:2009:PPM", pages = "I.3--I.11", year = "2009", bibdate = "Sat Aug 13 16:21:36 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Plenary address.", URL = "http://docserver.carma.newcastle.edu.au/390/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2009:DCF, author = "Jonathan Borwein and Jon Vanderwerff", title = "Differentiability of conjugate functions and perturbed minimization principles", journal = j-J-CONVEX-ANAL, volume = "16", number = "3--4", pages = "707--711", year = "2009", ISSN = "0944-6532 (print), 2363-6394 (electronic)", MRclass = "49K40 (46G05 46N10 49J50 52A41 58E30 90C46)", MRnumber = "2583890", MRreviewer = "Philip D. Loewen", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/383/; http://www.heldermann.de/JCA/JCA16/JCA163/jca16042.htm", abstract = "We survey the tight connection between differentiability of conjugate functions and perturbed optimization principles", acknowledgement = ack-nhfb, fjournal = "Journal of Convex Analysis", journal-URL = "http://www.heldermann.de/JCA/jcacon.htm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2009:DCF", xxpages = "699--706", } @Article{Borwein:2009:EBS, author = "Jonathan M. Borwein and Neil J. Calkin and Dante Manna", title = "{Euler--Boole} summation revisited", journal = j-AMER-MATH-MONTHLY, volume = "116", number = "5", pages = "387--412", year = "2009", CODEN = "AMMYAE", DOI = "https://doi.org/10.4169/193009709X470290", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "11B68 (11B73 26A06)", MRnumber = "2510837", MRreviewer = "Samuel S. Wagstaff, Jr.", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2009:MME, author = "Jonathan M. Borwein", title = "Maths Matters: Exploratory experimentation: digitally-assisted discovery and proof", journal = j-AUSTRALIAN-MATH-SOC-GAZ, volume = "36", number = "3", pages = "166--175", month = jul, year = "2009", ISSN = "0311-0729 (print), 1326-2297 (electronic)", ISSN-L = "0311-0729", MRclass = "00A35 68W30 97U50 00A30", MRnumber = "2543725", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", ZMnumber = "1175.00028", acknowledgement = ack-nhfb, fjournal = "The Australian Mathematical Society. Gazette", journal-URL = "http://www.austms.org.au/gazette", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark-1 = "This material is largely excerpted from a longer paper written for ICMI Study 19 `On Proof and Proving in Mathematics Education', and a plenary talk given in May 2009 at the corresponding Workshop at National Taiwan Normal University. [NHFB remarks: It appears that the longer paper did not appear in ICMI [International Commission on Mathematical Instruction] Study 19, which is published in \booktitle{ZDM Mathematics Education} {\bf 40}(2) May 2008, \url{http://link.springer.com/journal/11858/40/2/page/1}, and in the Chinese\slash English proceedings with ISBN 986-01-8210-8.]", remark-2 = "From page 166: ``The computer offers to provide scaffolding both to enhance mathematical reasoning and to restrain mathematical error.''", remark-3 = "From page 174: ``We live in an information-rich, judgement-poor world and the explosion of information and tools is not going to diminish.''", } @InCollection{Borwein:2009:NCM, author = "Jonathan Borwein and Rafal Goebel", booktitle = "Optimization", title = "On the nondifferentiability of cone-monotone functions in {Banach} spaces", volume = "32", publisher = pub-SV, address = pub-SV:adr, pages = "3--14", year = "2009", DOI = "https://doi.org/10.1007/978-0-387-98096-6_1", MRclass = "49J50 (47G10 47N10)", MRnumber = "2599222", MRreviewer = "John R. Giles", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Springer Optim. Appl.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CECM Preprint 02:179.", } @Article{Borwein:2009:PCM, author = "Jonathan M. Borwein", title = "{{\booktitle{The Princeton companion to mathematics}}. Timothy Gowers, with June Barrow Green and Imre Leader. Princeton University Press, Princeton, NJ, 2008. \$99.00. xxii + 1034 pp., hardcover. ISBN 978-0-691-1 1880-2. [book review of \refcno 2467561]}", journal = j-SIAM-REVIEW, volume = "51", number = "4", pages = "790--794", month = dec, year = "2009", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/SIREAD000051000004000785000001", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "00A17", MRnumber = "2573944", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "http://docserver.carma.newcastle.edu.au/1228/; http://www.jstor.org/stable/25662346", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2009:SCC, author = "Jonathan M. Borwein and Warren B. Moors", title = "Stability of closedness of convex cones under linear mappings", journal = j-J-CONVEX-ANAL, volume = "16", number = "3--4", pages = "699--705", year = "2009", ISSN = "0944-6532 (print), 2363-6394 (electronic)", MRclass = "47N10 (90C25 90C31)", MRnumber = "2583889", MRreviewer = "John R. Giles", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1229/; http://www.heldermann.de/JCA/JCA16/JCA163/jca16041.htm", abstract = "In this paper we reconsider the question of when the continuous linear image of a closed convex cone is closed in Euclidean space. In particular, we show that although it is not true that the closedness of the image is preserved under small perturbations of the linear mappings it is ``almost'' true that the closedness of the image is preserved under small perturbations, in the sense that, for ``almost all'' linear mappings from R(n) into R(m) if the image of the cone is closed then there is a small neighbourhood around it whose members also preserve the closedness of the cone.", acknowledgement = ack-nhfb, fjournal = "Journal of Convex Analysis", journal-URL = "http://www.heldermann.de/JCA/jcacon.htm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2009:SCC", xxpages = "707--713", } @Article{Borwein:2009:SFC, author = "Jonathan M. Borwein and Chris H. Hamilton", title = "Symbolic {Fenchel} conjugation", journal = j-MATH-PROG, volume = "116", number = "1--2", pages = "17--35", year = "2009", CODEN = "MHPGA4", DOI = "https://doi.org/10.1007/s10107-007-0134-4", ISSN = "0025-5610 (print), 1436-4646 (electronic)", ISSN-L = "0025-5610", MRclass = "90-04 (44A15 49J52 65K10 90C25 90C46)", MRnumber = "2421271", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Special issue in honor of Alfred Auslender.", URL = "http://docserver.carma.newcastle.edu.au/1479/", abstract = "Of key importance in convex analysis and optimization is the notion of duality, and in particular that of Fenchel duality. This work explores improvements to existing algorithms for the symbolic calculation of subdifferentials and Fenchel conjugates of convex functions defined on the real line. More importantly, these algorithms are extended to enable the symbolic calculation of Fenchel conjugates on a class of real-valued functions defined on the real line. More importantly, these algorithms are extended to enable the symbolic calculation of Fenchel conjugates on a class of real-valued functions defined on R(n). These algorithms are realized in the form of the Maple package SCAT.", acknowledgement = ack-nhfb, fjournal = "Mathematical Programming", journal-URL = "http://link.springer.com/journal/10107", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2009:SFC", } @Article{Borwein:2009:UBC, author = "Jonathan M. Borwein and O-Yeat Chan", title = "Uniform bounds for the complementary incomplete gamma function", journal = j-MATH-INEQUAL-APPL, volume = "12", number = "1", pages = "115--121", year = "2009", DOI = "https://doi.org/10.7153/mia-12-10", ISSN = "1331-4343 (print), 1848-9966 (electronic)", ISSN-L = "1331-4343", MRclass = "33B20", MRnumber = "2489355", MRreviewer = "Necdet Batir", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/335/", abstract = "We prove upper and lower bounds for the complementary incomplete gamma function Gamma(a, z) with complex parameters a and z. Our bounds are refined within the circular hyperboloid of one sheet \{(a, z) : vertical bar z vertical bar > c vertical bar a - 1 vertical bar\} with a real and z complex. Our results show that within the hyperboloid, vertical bar Gamma(a, z)vertical bar is of order vertical bar Z vertical bar(a-1)e(-Re(z)), and extends an upper estimate of Natalini and Palumbo to complex values of z.", acknowledgement = ack-nhfb, ajournal = "Math. Inequal. Appl.", fjournal = "Mathematical Inequalities \& Applications", journal-URL = "http://mia.ele-math.com/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2009:UBC", } @Article{Borwein:2009:UCF, author = "J. Borwein and A. J. Guirao and P. H{\'a}jek and J. Vanderwerff", title = "Uniformly convex functions on {Banach} spaces", journal = j-PROC-AM-MATH-SOC, volume = "137", number = "3", pages = "1081--1091", year = "2009", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/S0002-9939-08-09630-5", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "46B20 (46G05 46N10 49J50 52A41 90C48)", MRnumber = "2457450", MRreviewer = "Doug Ward", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/340/", abstract = "Given a Banach space $ (X, || \cdot ||) $, we study the connection between uniformly convex functions $ f \colon X \to R $ bounded above by $ || \cdot ||^p $ and the existence of norms on $X$ with moduli of convexity of power type. In particular, we show that there exists a uniformly convex function $ f \colon X \to R$ bounded above $ || \cdot ||^2$ if and only if $X$ admits an equivalent norm with modulus of convexity of power type 2", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Hajek, Petr/D-5429-2014", unique-id = "Borwein:2009:UCF", } @Article{Jackson:2009:JER, author = "Allyn Jackson", title = "{John Ewing} retires from the {AMS}", journal = j-NAMS, volume = "56", number = "1", pages = "48--51", month = jan, year = "2009", CODEN = "AMNOAN", ISSN = "0002-9920 (print), 1088-9477 (electronic)", ISSN-L = "0002-9920", bibdate = "Tue Aug 16 09:18:13 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "With contributions by Jonathan Borwein and Jane Kister.", URL = "", acknowledgement = ack-nhfb, fjournal = "Notices of the American Mathematical Society", journal-URL = "http://www.ams.org/notices/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Unpublished{Bacak:2010:DCF, author = "M. Bac{\'a}k and J. Borwein and B. Sims", title = "Differentiability of convex functions in {CAT(0)} spaces.", month = aug, year = "2010", bibdate = "Tue Aug 16 10:01:41 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Preprint.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bacak:2010:ICL, author = "Miroslav Ba{\v{c}}{\'a}k and Jonathan M. Borwein and Andrew Eberhard and Boris S. Mordukhovich", title = "Infimal convolutions and {Lipschitzian} properties of subdifferentials for prox-regular functions in {Hilbert} spaces", journal = j-J-CONVEX-ANAL, volume = "17", number = "3--4", pages = "737--763", year = "2010", ISSN = "0944-6532 (print), 2363-6394 (electronic)", MRclass = "49J52 (46G05)", MRnumber = "2731276", MRreviewer = "Shawn Xianfu Wang", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Special volume in honour of Hedi Attouch.", URL = "http://docserver.carma.newcastle.edu.au/1224/; http://www.heldermann.de/JCA/JCA17/JCA173/jca17049.htm", abstract = "In this paper we study infimal convolutions of extended-real-valued functions in Hilbert spaces paying a special attention to the rather broad and remarkable class of prox-regular functions. Such functions have been well recognized as highly important in many aspects of variational analysis and its applications in both finite-dimensional and infinite-dimensional settings. Based on advanced variational techniques, we discover some new subdifferential properties of infimal convolutions and apply them to the study of Lipschitzian behavior of subdifferentials for prox-regular functions in Hilbert spaces. It is shown, in particular, that the fulfillment of a natural Lipschitz-like property for (set-valued) subdifferentials of prox-regular functions forces such functions, under weak assumptions, actually to be locally smooth with single-valued subdifferentials reduced to Lipschitz continuous gradient mappings.", acknowledgement = ack-nhfb, fjournal = "Journal of Convex Analysis", journal-URL = "http://www.heldermann.de/JCA/jcacon.htm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Eberhard, Andrew/0000-0003-2977-3456", researcherid-numbers = "Eberhard, Andrew/B-5576-2013", unique-id = "Bacak:2010:ICL", } @Article{Bailey:2010:ATB, author = "D. H. Bailey and J. M. Borwein and R. E. Crandall", title = "Advances in the theory of box integrals", journal = j-MATH-COMPUT, volume = "79", number = "271", pages = "1839--1866", month = jul, year = "2010", CODEN = "MCMPAF", DOI = "https://doi.org/10.1090/S0025-5718-10-02338-0", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "11Y60 (65D30)", MRnumber = "2630017", MRreviewer = "Michael J. Evans", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/389/; http://www.jstor.org/stable/20779125", abstract = "Box integrals--expectations $ \langle \vert \vec r \vert^s \rangle $ or $ \langle \vert \vec r - \vec q \vert^s \rangle $ over the unit $ n$-cube--have over three decades been occasionally given closed forms for isolated $ n, s$. By employing experimental mathematics together with a new, global analytic strategy, we prove that for each of $ n = 1, 2, 3, 4$ dimensions the box integrals are for any integer $ s$ hypergeometrically closed (hyperclosed'') in an explicit sense we clarify herein. For $ n = 5$ dimensions, such a complete hyperclosure proof is blocked by a single, unresolved integral we call $ {\mathcal K}_5$; although we do prove that all but a finite set of ($ n = 5$) cases enjoy hyperclosure. We supply a compendium of exemplary closed forms that arise naturally from the theory.", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", remark = "D-drive preprint 389 (March 2009).", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Bailey:2010:ATB", } @InCollection{Bailey:2010:ECO, author = "David H. Bailey and Jonathan M. Borwein", booktitle = "Gems in experimental mathematics", title = "Experimental computation with oscillatory integrals", volume = "517", publisher = pub-AMS, address = pub-AMS:adr, pages = "25--40", year = "2010", DOI = "https://doi.org/10.1090/conm/517/10131", MRclass = "11Y35 (42B20)", MRnumber = "2731059", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Contemp. Math.", URL = "http://docserver.carma.newcastle.edu.au/391/", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bailey:2010:EMMa, author = "David H. Bailey and Jonathan M. Borwein and David J. Broadhurst and Wadim Zudilin", title = "Experimental Mathematics and Mathematical Physics", journal = "ArXiv e-prints", month = may, year = "2010", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2010arXiv1005.0414B; http://docserver.carma.newcastle.edu.au/1215/", abstract = "One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.", acknowledgement = ack-nhfb, eprint = "1005.0414", keywords = "Mathematical Physics, High Energy Physics - Phenomenology, Mathematics - Classical Analysis and ODEs, Mathematics - Number Theory", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646; Zudilin, Wadim/0000-0001-9551-2903", primaryclass = "math-ph", } @InCollection{Bailey:2010:EMMb, author = "David H. Bailey and Jonathan M. Borwein and David Broadhurst and Wadim Zudilin", booktitle = "Gems in experimental mathematics", title = "Experimental mathematics and mathematical physics", volume = "517", publisher = pub-AMS, address = pub-AMS:adr, pages = "41--58", year = "2010", DOI = "https://doi.org/10.1090/conm/517/10132", MRclass = "33F05 (11Y60 33F10 65D30)", MRnumber = "2731060", MRreviewer = "Zhonghua Li", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Contemp. Math.", URL = "http://docserver.carma.newcastle.edu.au/1215/", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646; Zudilin, Wadim/0000-0001-9551-2903", } @TechReport{Bailey:2010:SMP, author = "David H. Bailey and Jonathan M. Borwein", title = "Solution to {{\booktitle{Monthly}}} Problem 11515", type = "Report", institution = "Lawrence Berkeley National Laboratory and School of Mathematical and Physical Sciences, University of Newcastle", address = "Berkeley, CA 94720, USA and Callaghan, NSW 2308, Australia", pages = "2", day = "15", month = jun, year = "2010", bibdate = "Fri Sep 30 08:23:00 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.davidhbailey.com/dhbpapers/amm-11515.pdf", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", remark = "The problem of evaluating $ S(t) = \sum_{n = 1}^\infty 4^n \sin^4 (t / 2^n) $ is shown to be equal to the simple closed form $ T(t) = t^2 - \sin^2 (t) $.", } @Book{Borwein:2010:CFC, author = "Jonathan M. Borwein and Jon D. Vanderwerff", title = "Convex functions: constructions, characterizations and counterexamples", volume = "109", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "x + 521", year = "2010", DOI = "https://doi.org/10.1017/CBO9781139087322", ISBN = "0-521-85005-3", ISBN-13 = "978-0-521-85005-6", MRclass = "49-02 (46B20 46N10 49J53 52A41 90C25)", MRnumber = "2596822", MRreviewer = "Heinz H. Bauschke", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Encyclopedia of Mathematics and its Applications", URL = "http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139087322", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", tableofcontents = "Frontmatter / i--vi \\ Contents / vii--viii \\ Preface / ix--x \\ 1: Why convex? / 1--17 \\ 2: Convex functions on Euclidean spaces / 18--93 \\ 3: Finer structure of Euclidean spaces / 94--125 \\ 4: Convex functions on Banach spaces / 126--208 \\ 5: Duality between smoothness and strict convexity / 209--275 \\ 6: Further analytic topics / 276--337 \\ 7: Barriers and Legendre functions / 338--376 \\ 8: Convex functions and classifications of Banach spaces / 377--402 \\ 9: Monotone operators and the Fitzpatrick function / 403--459 \\ 10: Further remarks and notes / 460--482 \\ List of symbols / 483--484 \\ References / 485--507", } @Article{Borwein:2010:DTM, author = "Jonathan M. Borwein and O-Yeat Chan", title = "Duality in tails of multiple-zeta values", journal = j-INT-J-NUMBER-THEORY, volume = "6", number = "3", pages = "501--514", year = "2010", DOI = "https://doi.org/10.1142/S1793042110003058", ISSN = "1793-0421 (print), 1933-8368 (electronic)", MRclass = "11M32 (33C20 33F05)", MRnumber = "2652893", MRreviewer = "Zhonghua Li", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1218/", abstract = "Duality relations are deduced for tails of multiple-zeta values using elementary methods. These formulas extend the classical duality formulas for multiple-zeta values.", acknowledgement = ack-nhfb, fjournal = "International Journal of Number Theory", journal-URL = "http://www.worldscientific.com/worldscinet/ijnt", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", researcherid-numbers = "Borwein, Jonathan/A-6082-2009", unique-id = "Borwein:2010:DTM", } @Book{Borwein:2010:ECM, author = "Jonathan Borwein and Peter B. Borwein", title = "Experimental and computational mathematics: selected writings", publisher = "Perfectly Scientific Press", address = "Portland, OR, USA", pages = "viii + 297", year = "2010", ISBN = "1-935638-05-X", ISBN-13 = "978-1-935638-05-6", MRclass = "11-06 (11-04 33-06)", MRnumber = "2841256", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:2010:ENE, author = "Jonathan M. Borwein and Scott Sciffer", booktitle = "Nonlinear analysis and optimization {II}. {Optimization}", title = "An explicit non-expansive function whose subdifferential is the entire dual ball", volume = "514", publisher = pub-AMS, address = pub-AMS:adr, pages = "99--103", year = "2010", DOI = "https://doi.org/10.1090/conm/514/10101", MRclass = "49J52", MRnumber = "2668255", MRreviewer = "Shawn Xianfu Wang", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Contemp. Math.", URL = "http://docserver.carma.newcastle.edu.au/385/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @InCollection{Borwein:2010:FCV, author = "Jonathan M. Borwein", booktitle = "Variational analysis and generalized differentiation in optimization and control", title = "Future challenges for variational analysis", volume = "47", publisher = pub-SV, address = pub-SV:adr, pages = "95--107", year = "2010", DOI = "https://doi.org/10.1007/978-1-4419-0437-9_4", MRclass = "49J53", MRnumber = "2766756", MRreviewer = "B. Mordukhovich", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Springer Optim. Appl.", URL = "http://docserver.carma.newcastle.edu.au/396/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2010:FLF, author = "Jonathan M. Borwein and Jon Vanderwerff", title = "{Fr{\'e}chet--Legendre} functions and reflexive {Banach} spaces", journal = j-J-CONVEX-ANAL, volume = "17", number = "3--4", pages = "915--924", year = "2010", ISSN = "0944-6532 (print), 2363-6394 (electronic)", MRclass = "52A41 (46G05 46N10 49J53 90C25)", MRnumber = "2731284", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Special volume in honour of Hedi Attouch.", URL = "http://www.heldermann.de/JCA/JCA17/JCA173/jca17057.htm", abstract = "A 2001 article by Bauschke, Borwein and Combettes [2] showed how to extend naturally the classical definitions of essential smoothness and essential strict convexity from functions on R(n) in a compatible fashion to any Banach space. They were able, among other things, to show that substantial duality results hold for Legendre functions in reflexive spaces. That article focused on essential smoothness in the Gateaux sense. Our goal herein is to show that similar results hold for Frechet smoothness and to study related properties of such functions on reflexive Banach spaces.", acknowledgement = ack-nhfb, fjournal = "Journal of Convex Analysis", journal-URL = "http://www.heldermann.de/JCA/jcacon.htm", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", unique-id = "Borwein:2010:FLF", } @Article{Borwein:2010:FYM, author = "Jonathan M. Borwein", title = "Fifty years of maximal monotonicity", journal = j-OPTIM-LETT, volume = "4", number = "4", pages = "473--490", year = "2010", DOI = "https://doi.org/10.1007/s11590-010-0178-x", ISSN = "1862-4472 (print), 1862-4480 (electronic)", ISSN-L = "1862-4472", MRclass = "47H05 (47H09 49-02 49J53 90C25 90C33)", MRnumber = "2719898", MRreviewer = "Simeon Reich", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1221/", abstract = "Maximal monotone operator theory is about to turn (or just has turned) 50. I intend to briefly survey the history of the subject. I shall try to explain why maximal monotone operators are both interesting and important-culminating with a description of the remarkable progress made during the past decade.", acknowledgement = ack-nhfb, ajournal = "Optim. Lett.", fjournal = "Optimization Letters", journal-URL = "http://link.springer.com/journal/11590", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", unique-id = "Borwein:2010:FYM", } @Article{Borwein:2010:HDB, author = "Jonathan M. Borwein and O-Yeat Chan and R. E. Crandall", title = "Higher-Dimensional Box Integrals", journal = j-EXP-MATH, volume = "19", number = "4", pages = "431--446", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1080/10586458.2010.10390634", ISSN = "1058-6458 (print), 1944-950X (electronic)", ISSN-L = "1058-6458", MRclass = "33B30", MRnumber = "2778656", MRreviewer = "Cristinel Mortici", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://projecteuclid.org/euclid.em; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/expmath.bib; http://www.tandfonline.com/toc/uexm20/19/4", URL = "http://docserver.carma.newcastle.edu.au/1223/; http://projecteuclid.org/euclid.em/1317758103", abstract = "Herein, with the aid of substantial symbolic computation, we solve previously open problems in the theory of n-dimensional box integrals B(n)(s) := <vertical bar(r) over bar vertical bar(s)>, (r) over bar is an element of [0, 1](n). In particular, we resolve an elusive integral called kappa(5) that previously acted as a ``blockade'' against closed-form evaluation in n = 5 dimensions. In consequence, we now know that B(n) (integer) can be given a closed form for n = 1, 2, 3, 4, 5. We also find the general residue at the pole at s = n, this leading to new relations and definite integrals; for example, we are able to give the first nontrivial closed forms for six-dimensional box integrals and to show hyperclosure of B(6)(even). The Clausen function and its generalizations play a central role in these higher-dimensional evaluations. Our results provide stringent test scenarios for symbolic-algebra simplification methods.", acknowledgement = ack-nhfb, fjournal = "Experimental Mathematics", journal-URL = "http://www.tandfonline.com/loi/uexm20", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", unique-id = "Borwein:2010:HDB", } @InProceedings{Borwein:2010:MEPa, author = "J. M. Borwein", booktitle = "ICME10 Proceedings, July 2010", title = "Mathematics by Experiment: Plausible Reasoning in the 21st Century", publisher = "????", address = "????", pages = "??--??", year = "2010", bibdate = "Sat Aug 13 16:42:06 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/272/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "CoLab Preprint 272.", } @Article{Borwein:2010:NSF, author = "David Borwein and Jonathan M. Borwein and Isaac E. Leonard", title = "{$ L_p $} norms and the sinc function", journal = j-AMER-MATH-MONTHLY, volume = "117", number = "6", pages = "528--539", year = "2010", CODEN = "AMMYAE", DOI = "https://doi.org/10.4169/000298910X492817", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "26A09", MRnumber = "2662705", MRreviewer = "Timo A. J. Tossavainen", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", abstract = "It's everywhere! It's everywhere! .... In this note we give elementary proofs of some of the striking asymptotic properties of the p-norm of the ubiquitous sinc function. Based on experimental evidence we conjecture some enticing further properties of the p-norm as a function of p. See, for example, http://www.carma.newcastle.edu.au/(similar to)jb616/oscillatory.pdf.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", unique-id = "Borwein:2010:PNS", } @InCollection{Borwein:2010:RWP, author = "Jonathan M. Borwein and Dirk Nuyens and Armin Straub and James Wan", booktitle = "{22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)}", title = "Random walks in the plane", publisher = "Assoc. Discrete Math. Theor. Comput. Sci.", address = "Nancy, France", pages = "191--202", year = "2010", MRclass = "05C81 (05A15)", MRnumber = "2673835", MRreviewer = "Manuel Batista Branco", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Discrete Math. Theor. Comput. Sci. Proc., AN", acknowledgement = ack-nhfb, book-URL = "http://math.sfsu.edu/fpsac/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Nuyens, Dirk/0000-0002-4555-2314; Straub, Armin/0000-0001-6802-6053", } @Article{Borwein:2010:SCC, author = "Jonathan M. Borwein and Warren B. Moors", title = "Stability of closedness of convex cones under linear mappings {II}", journal = "Journal of Nonlinear Analysis and Optimization: Theory \& Applications", volume = "1", number = "1", pages = "1--7", year = "2010", ISSN = "1906-9685", ISSN-L = "1906-9685", MRclass = "49J53 (47N10 90C05 90C31)", MRnumber = "2911681", MRreviewer = "John R. Giles", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1226/; http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/5", acknowledgement = ack-nhfb, ajournal = "J. Nonlinear Anal. Optim.", fjournal = "Journal of Nonlinear Analysis and Optimization. Theory and Applications", journal-URL = "http://www.sci.nu.ac.th/jnao", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Unpublished{Borwein:2010:TTT, author = "Jonathan M. Borwein", title = "Talking to {Telstra}: Two weeks spent with {Australia}'s largest {Telco}", day = "27", month = sep, year = "2010", bibdate = "Tue Aug 16 10:00:52 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Response to Australian Communications and Media Authority (ACMA) enquiry, Reconnecting the Customer, Sept 27, 2010.", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "The background for this document is provided by Jon's daughter, Naomi, in a talk at his funeral, and recorded at \url{http://jonborwein.org/2016/08/my-father-by-naomi-borwein/}: ``In 2010 Jon changed his Internet and telephone provider to Telstra, the leading national telecommunications provider in Australia. Telstra started by providing service to J Brow-ein, and things went down hill from there. So Jon chronicled his month-long quest to fix his Internet and telephone connection in a highly amusing, but frustratingly bureaucratic, sixty page document. It ended up being obligatory reading for all the vice presidents at Telstra, and was sent as part of a package to the Australian Government's royal commission on the dysfunction of Big Telcos in the country. This was under the umbrella of the Australian Communications and Media Authority, which is an Australian Government statutory authority. Jon was personally thanked in the final report that was lodged in parliament.''", } @Article{Bacak:2011:DCL, author = "Miroslav Ba{\v{c}}{\'a}k and Jonathan M. Borwein", title = "On difference convexity of locally {Lipschitz} functions", journal = j-OPTIMIZATION, volume = "60", number = "8--9", pages = "961--978", year = "2011", CODEN = "OPTZDQ", DOI = "https://doi.org/10.1080/02331931003770411", ISSN = "0233-1934, 0323-3898", ISSN-L = "0233-1934", MRclass = "49J53 (49-02)", MRnumber = "2860286", MRreviewer = "Shawn Xianfu Wang", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1446/", abstract = "We survey and enhance salient parts of the literature about difference convex (DC) functions with specific regard to current knowledge and applications of DC functions.", acknowledgement = ack-nhfb, fjournal = "Optimization", journal-URL = "http://www.tandfonline.com/loi/gopt20", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", unique-id = "Bacak:2011:DCL", } @TechReport{Bailey:2011:CPI, author = "David H. Bailey and Jonathan M. Borwein and Andrew Mattingly and Glenn Wightwick", title = "The Computation of Previously Inaccessible Digits of $ \pi^2 $ and {Catalan}'s Constant", type = "Report", institution = "Lawrence Berkeley National Laboratory; Centre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle; IBM Australia", address = "Berkeley, CA, USA; Callaghan, NSW 2308, Australia; St. Leonards, NSW 2065, Australia; Pyrmont, NSW 2009, Australia", pages = "18", day = "11", month = apr, year = "2011", bibdate = "Sat Apr 23 08:58:45 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/pi.bib", URL = "http://crd.lbl.gov/~dhbailey/dhbpapers/bbp-bluegene.pdf", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", remark = "Submitted to Notices of the AMS.", } @TechReport{Bailey:2011:EAN, author = "David H. Bailey and Jonathan M. Borwein and Cristian S. Calude and Michael J. Dinneen and Monica Dumitrescu and Alex Yee", title = "An Empirical Approach to the Normality of $ \pi $", type = "Report", number = "CDMTCS-413", institution = "Centre for Discrete Mathematics and Theoretical Computer Science, University of Auckland", address = "Auckland, New Zealand", pages = "i + 31", month = nov, year = "2011", bibdate = "Tue Aug 23 06:50:08 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1382/; http://www.cs.auckland.ac.nz/research/groups/CDMTCS/researchreports/?download&paper_file=413", acknowledgement = ack-nhfb, ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646; Calude, Cristian Sorin/0000-0002-8711-6799", } @Article{Bailey:2011:EEC, author = "David H. Bailey and Jonathan M. Borwein", title = "Exploratory experimentation and computation", journal = j-NAMS, volume = "58", number = "10", pages = "1410--1419", month = oct, year = "2011", CODEN = "AMNOAN", ISSN = "0002-9920 (print), 1088-9477 (electronic)", ISSN-L = "0002-9920", MRclass = "00A35", MRnumber = "2884022", MRreviewer = "Eduard Glas", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "Chinese translation in Mathematical Advances in Translation (Chinese Academy of Science), June 2012.", URL = "http://docserver.carma.newcastle.edu.au/1396/", acknowledgement = ack-nhfb, fjournal = "Notices of the American Mathematical Society", journal-URL = "http://www.ams.org/notices/", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @TechReport{Bailey:2011:GMDa, author = "David H. Bailey and Jonathan M. Borwein", title = "The Greatest Mathematical Discovery?", type = "Report", institution = "Lawrence Berkeley National Laboratory and Centre for Computer Assisted RMA, University of Newcastle", address = "Berkeley, CA 94720, USA and Callaghan, NSW 2308, Australia", pages = "10", day = "8", month = may, year = "2011", bibdate = "Fri Aug 12 18:29:28 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.davidhbailey.com/dhbpapers/decimal.pdf", acknowledgement = ack-nhfb, keywords = "decimal arithmetic history", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bailey:2011:HPN, author = "D. H. Bailey and J. M. Borwein", title = "High-precision numerical integration: Progress and challenges", journal = j-J-SYMBOLIC-COMP, volume = "46", number = "7", pages = "741--754", month = jul, year = "2011", CODEN = "JSYCEH", DOI = "https://doi.org/10.1016/j.jsc.2010.08.010", ISSN = "0747-7171 (print), 1095-855x (electronic)", ISSN-L = "0747-7171", MRclass = "65D30 (65Y05 68W30)", MRnumber = "2795208", MRreviewer = "G. A. Evans", bibdate = "Thu Aug 11 10:27:38 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib", note = "Special Issue in Honour of Keith Geddes on his 60th Birthday.", URL = "http://docserver.carma.newcastle.edu.au/1444/; http://www.sciencedirect.com/science/article/pii/S0747717110001409", abstract = "One of the most fruitful advances in the field of experimental mathematics has been the development of practical methods for very high-precision numerical integration, a quest initiated by Keith Geddes and other researchers in the 1980s and 1990s. These techniques, when coupled with equally powerful integer relation detection methods, have resulted in the analytic evaluation of many integrals that previously were beyond the realm of symbolic techniques. This paper presents a survey of the current state-of-the-art in this area (including results by the present authors and others), mentions some new results, and then sketches what challenges lie ahead.", acknowledgement = ack-nhfb, fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", keywords = "High-precision arithmetic; Ising theory; Numerical integration; Quadrature; Quantum field theory", ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646", } @Article{Bauschke:2011:BBT, author = "H. H. Bauschke and J. M. Borwein and X. Wang and L. Yao", title = "The {Br{\'e}zis--Browder} Theorem in a general {Banach} space", journal = "ArXiv e-prints", month = oct, year = "2011", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2011arXiv1110.5706B", abstract = "During the 1970s Br{\'e}zis and Browder presented a now classical characterization of maximal monotonicity of monotone linear relations in reflexive spaces. In this paper, we extend and refine their result to a general Banach space.", acknowledgement = ack-nhfb, eprint = "1110.5706", keywords = "Mathematics - Functional Analysis, 47A06 (Primary), 47H05, 47B65 (Secondary), 47N10, 90C25", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", primaryclass = "math.FA", } @Article{Bauschke:2011:CPM, author = "H. H. Bauschke and J. M. Borwein and X. Wang and L. Yao", title = "Construction of pathological maximally monotone operators on non-reflexive {Banach} spaces", journal = "ArXiv e-prints", month = aug, year = "2011", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2011arXiv1108.1463B; http://docserver.carma.newcastle.edu.au/1090/", abstract = "In this paper, we construct maximally monotone operators that are not of Gossez's dense-type (D) in many nonreflexive spaces. Many of these operators also fail to possess the Br{\o}nsted--Rockafellar (BR) property. Using these operators, we show that the partial inf-convolution of two BC--functions will not always be a BC--function. This provides a negative answer to a challenging question posed by Stephen Simons. Among other consequences, we deduce that every Banach space which contains an isomorphic copy of the James space $ \mathbf {J} $ or its dual $ \mathbf {J}^* $, or $ c_0 $ or its dual $ \ell^1 $, admits a non type (D) operator.", acknowledgement = ack-nhfb, eprint = "1108.1463", keywords = "Mathematics - Functional Analysis, Primary 47A06, 47H05, Secondary 47B65, 47N1, 90C25", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", primaryclass = "math.FA", } @Article{Bauschke:2011:EMM, author = "H. H. Bauschke and J. M. Borwein and X. Wang and L. Yao", title = "Every maximally monotone operator of {Fitzpatrick--Phelps} type is actually of dense type", journal = "ArXiv e-prints", month = apr, year = "2011", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2011arXiv1104.0750B; http://docserver.carma.newcastle.edu.au/1442/", abstract = "We show that every maximally monotone operator of Fitzpatrick--Phelps type defined on a real Banach space must be of dense type. This provides an affirmative answer to a question posed by Stephen Simons in 2001 and implies that various important notions of monotonicity coincide.", acknowledgement = ack-nhfb, eprint = "1104.0750", keywords = "Mathematics - Functional Analysis, Primary 47H05, Secondary 46B10, 47N10, 90C25", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", primaryclass = "math.FA", } @Article{Bauschke:2011:MML, author = "Heinz H. Bauschke and Jonathan M. Borwein and Xianfu Wang and Liangjin Yao", title = "For maximally monotone linear relations, dense type, negative-infimum type, and {Fitzpatrick--Phelps} type all coincide with monotonicity of the adjoint", journal = "ArXiv e-prints", pages = "15", day = "21", month = mar, year = "2011", bibdate = "Tue Aug 16 09:57:56 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2011arXiv1103.6239B; http://arxiv.org/abs/1103.6239", abstract = "It is shown that, for maximally monotone linear relations defined on a general Banach space, the monotonicities of dense type, of negative-infimum type, and of Fitzpatrick--Phelps type are the same and equivalent to monotonicity of the adjoint. This result also provides affirmative answers to two problems: one posed by Phelps and Simons, and the other by Simons.", acknowledgement = ack-nhfb, eprint = "1103.6239", keywords = "Mathematics - Functional Analysis, Primary 47A06, 47H05, Secondary 47B65, 47N10, 90C25", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", primaryclass = "math.FA", } @Article{Bauschke:2011:MOB, author = "H. H. Bauschke and J. M. Borwein and X. Wang and L. Yao", title = "Monotone operators and ``bigger conjugate'' functions", journal = "ArXiv e-prints", month = aug, year = "2011", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2011arXiv1108.2578B; http://docserver.carma.newcastle.edu.au/1477/", abstract = "We study a question posed by Stephen Simons in his 2008 monograph involving ``bigger conjugate'' (BC) functions and the partial infimal convolution. As Simons demonstrated in his monograph, these function have been crucial to the understanding and advancement of the state-of-the-art of harder problems in monotone operator theory, especially the sum problem. In this paper, we provide some tools for further analysis of BC--functions which allow us to answer Simons' problem in the negative. We are also able to refute a similar but much harder conjecture which would have generalized a classical result of Br{\'e}zis, Crandall and Pazy. Our work also reinforces the importance of understanding unbounded skew linear relations to construct monotone operators with unexpected properties.", acknowledgement = ack-nhfb, eprint = "1108.2578", keywords = "Mathematics - Functional Analysis, Primary 47A06, 47H05, Secondary 47B65, 47N10, 90C25", ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646", primaryclass = "math.FA", } @Article{Borwein:2011:CBF, author = "Jonathan M. Borwein and Simeon Reich and Shoham Sabach", title = "A characterization of {Bregman} firmly nonexpansive operators using a new monotonicity concept", journal = j-J-NONLINEAR-CONVEX-ANAL, volume = "12", number = "1", pages = "161--184", year = "2011", ISSN = "1345-4773 (print), 1880-5221 (electronic)", ISSN-L = "1345-4773", MRclass = "47H05 (26B25 47H09 94A17)", MRnumber = "2816416", MRreviewer = "Patrick L. Combettes", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://docserver.carma.newcastle.edu.au/1445/", abstract = "The property of nonexpansivity (1-Lipschitz) is very important in the analysis of many optimization problems. In this paper we study a more general notion of nonexpansivity - Bregman nonexpansivity. We present a characterization of Bregman firmly nonexpansive operators in general reflexive Banach spaces. This characterization allows us to construct Bregman firmly nonexpansive operators explicitly. We provide several examples of such operators with respect to the Boltzmann-Shannon entropy and the Fermi-Dirac entropy in Euclidean spaces. We also compute resolvents with respect to these functions.", acknowledgement = ack-nhfb, fjournal = "Journal of Nonlinear and Convex Analysis", journal-URL = "http://www.ybook.co.jp/jnca.html", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", unique-id = "Borwein:2011:CBF", } @InCollection{Borwein:2011:DRA, author = "Jonathan M. Borwein and Brailey Sims", title = "The {Douglas--Rachford} Algorithm in the Absence of Convexity", crossref = "Bauschke:2011:FPA", pages = "93--109", year = "2011", DOI = "https://doi.org/10.1007/978-1-4419-9569-8_6", MRclass = "47N10 (47H10 47J25 65J15 90C26)", MRnumber = "2858834", MRreviewer = "A. G. Kartsatos", bibdate = "Sat Aug 13 16:00:55 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Springer Optim. Appl.", URL = "http://link.springer.com/chapter/10.1007/978-1-4419-9569-8_6", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2011:DSU, author = "Jonathan M. Borwein and A. Straub and J. Wan and Wadim Zudilin", title = "Densities of short uniform random walks", journal = "ArXiv e-prints", month = mar, year = "2011", bibdate = "Thu Aug 11 07:19:54 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://adsabs.harvard.edu/abs/2011arXiv1103.2995B; http://docserver.carma.newcastle.edu.au/1388/", abstract = "We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and less completely those with five steps. As one of the main results, we obtain a hypergeometric representation of the density for four steps, which complements the classical elliptic representation in the case of three steps. It appears unrealistic to expect similar results for more than five steps. New results are also presented concerning the moments of uniform random walks and, in particular, their derivatives. Relations with Mahler measures are discussed.", acknowledgement = ack-nhfb, eprint = "1103.2995", keywords = "Mathematics - Classical Analysis and ODEs, Mathematics - Number Theory, 60G50 (Primary) 33C20, 34M25, 44A10 (Secondary)", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053; Zudilin, Wadim/0000-0001-9551-2903", primaryclass = "math.CA", } @Book{Borwein:2011:EMB, author = "Jonathan Borwein and Keith Devlin", title = "{Experimentelle Mathematik: Eine beispielorientierte Einf{\"u}hrung}. ({German}) [{Experimental} mathematics: an example-oriented introduction]", publisher = "Spektrum Akademischer Verlag", address = "Heidelberg, Germany", pages = "xii + 158", year = "2011", DOI = "https://doi.org/10.1007/978-3-8274-2662-8", ISBN = "3-8274-2661-8, 3-8274-2662-6 (e-book)", ISBN-13 = "978-3-8274-2661-1, 978-3-8274-2662-8 (e-book)", LCCN = "QA8.7 .B67 2011", MRclass = "00A35 (01A75 11-04 11Y16 11Y60)", MRnumber = "3052999", bibdate = "Thu Aug 11 17:05:04 MDT 2016", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", note = "German translation by Roland Girgensohn of \cite{Borwein:2009:CCI}, with updates.", URL = "http://link.springer.com/book/10.1007/978-3-8274-2662-8", acknowledgement = ack-nhfb, language = "German", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", remark = "Life Science and Basic Disciplines (German Language) (Springer-11777).", subject = "Mathematics, general; Computermathematik", tableofcontents = "Front Matter / i--xii \\ Was ist Experimentelle Mathematik? / 1-16 \\ Was ist die billiardste Dezimalstelle von $\pi$? / 17---28 \\ Was ist diese Zahl? / 29--38 \\ Die wichtigste Funktion in der Mathematik / 39--48 \\ Werten Sie das folgende Integral aus! / 49--60 \\ Gl{\"u}ckstreffer / 61--69 \\ Berechnungen von $\pi$ / 71--79 \\ Der Computer kennt mehr Mathematik als Sie / 81--91 \\ Treib es bis zum Limit! / 93--104 \\ Vorsicht! Gefahr beim Gebrauch des Computers! / 105--113 \\ Was wir Ihnen bisher nicht verraten haben / 115--130 \\ Back Matter / 131--158", } @InCollection{Borwein:2011:ERF, author = "Jonathan M. Borwein and D. Russell Luke", title = "Entropic Regularization of the $ \ell_0 $ Function", crossref = "Bauschke:2011:FPA", pages = "65--92", year = "2011", DOI = "https://doi.org/10.1007/978-1-4419-9569-8_5", MRclass = "49M20 (49N15 65K10 90C30)", MRnumber = "2858833", MRreviewer = "Aris Daniilidis", bibdate = "Sat Aug 13 16:00:55 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", series = "Springer Optim. Appl.", URL = "http://docserver.carma.newcastle.edu.au/1451/; http://link.springer.com/chapter/10.1007/978-1-4419-9569-8_5", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2011:IFS, author = "Jonathan Michael Borwein", title = "{{\it Implicit functions and solution mappings}} [book review of \refcno 2515104]", journal = j-IEEE-CONTROL-SYST-MAG, volume = "31", number = "1", pages = "74--77", year = "2011", CODEN = "ISMAD7", DOI = "https://doi.org/10.1109/MCS.2010.939261", ISSN = "1066-033X (print), 1941-000X (electronic)", ISSN-L = "1066-033X", MRclass = "00A17", MRnumber = "2789813", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", acknowledgement = ack-nhfb, fjournal = "IEEE Control Systems Magazine", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Book{Borwein:2011:IMM, author = "Jonathan M. Borwein and Matthew P. Skerritt", title = "An introduction to modern mathematical computing: with {Maple}", publisher = pub-SV, address = pub-SV:adr, pages = "xvi + 216", year = "2011", DOI = "https://doi.org/10.1007/978-1-4614-0122-3", ISBN = "1-4614-0121-6", ISBN-13 = "978-1-4614-0121-6", LCCN = "QA76.6 .B665 2011", MRclass = "65-01 (15-01 26-01 68-01)", MRnumber = "2808248", bibdate = "Wed Aug 10 11:09:47 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/tex/bib/maple-extract.bib", series = "Springer Undergraduate Texts in Mathematics and Technology", URL = "http://docserver.carma.newcastle.edu.au/1727/", acknowledgement = ack-nhfb, ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", tableofcontents = "Front Matter / i--xvi \\ Number Theory / 1--65 \\ Calculus / 67--128 \\ Linear Algebra / 129--185 \\ Visualization and Geometry: A Postscript / 187--201 \\ Back Matter / 211--216", } @Article{Borwein:2011:LEW, author = "J. M. Borwein", title = "Letter to the {Editor}: Why are mathematics papers so dull?", journal = j-SIAM-NEWS, volume = "44", number = "6", pages = "7--7", month = jul # "\slash " # aug, year = "2011", ISSN = "0036-1437", ISSN-L = "0036-1437", bibdate = "Sat Aug 13 15:55:33 2016", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib", URL = "http://www.siam.org/news/news.php?id=1903", acknowledgement = ack-nhfb, fjournal = "SIAM News", journal-URL = "http://www.siam.org/news/", ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646", } @Article{Borwein:2011:LHM, author = "Jonathan M. Borwein and Judy-Anne Osborn", title = "{{\booktitle{Loving and hating mathematics}}, by Reuben Hersh and Vera John-Steiner. Princeton and Oxford: Princeton University Press, 2010, 428 pp., US\$29.95. ISBN-10: 0-691-14247-5, ISBN-13: 978-0-691-14247-0 [book review of \refcno 2731560]}", journal = j-MATH-INTEL, volume = "33", number = "4", pages = "63--69", month = dec, year = "2011", CODEN = "MAINDC", DOI = "https://doi.org/10.1007/s00283-011-9260-1", ISSN = "0343-6993 (print), 1866-7414 (electronic)", ISSN-L = "0343-6993", MRclass = "00A17", MRnumber = "2906477", bibdate = "