# bibtab

bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2001:AWMa
author: Jonathan M. Borwein
title: Aesthetics for the Working Mathematician
type: Report
institution: Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 22
day: 18
month: apr
monthnumber: 4
year: 2001
bibdate: Tue Aug 16 10:19:46 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:19:46 ???
URL: http://docserver.carma.newcastle.edu.au/150/
remark: No abstract available.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawtitle: Aesthetics for the Working Mathematician
ORCID: Borwein, Jonathan/0000-0002-1263-0646
note:
Public Lecture at Queen's University Symposium on Beauty and the Mathematical Beast, April 18--19, Kingston, ON, Canada.

rawnote:
Public Lecture at Queen's University Symposium on Beauty and the Mathematical Beast, April 18--19, Kingston, ON, Canada.

entry:
@TechReport{Borwein:2001:AWMa,
  author =       "Jonathan M. Borwein",
  title =        "Aesthetics for the Working Mathematician",
  type =         "Report",
  institution =  "Simon Fraser University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "22",
  day =          "18",
  month =        apr,
  year =         "2001",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Public Lecture at Queen's University Symposium on
                 Beauty and the Mathematical Beast, April 18--19,
                 Kingston, ON, Canada.",
  URL =          "http://docserver.carma.newcastle.edu.au/150/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "No abstract available.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
DOI: https://doi.org/10.1080/10586458.2001.10504426
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 11G55 (05A10 11M06 33B99)
MRnumber: 1821569
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Experimental Mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.tandfonline.com/loi/uexm20
rawauthor: Jonathan Michael Borwein and David J. Broadhurst and Joel Kamnitzer
rawtitle: Central binomial sums, multiple {Clausen} values, and zeta values
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2001:CBS,
  author =       "Jonathan Michael Borwein and David J. Broadhurst and
                 Joel Kamnitzer",
  title =        "Central binomial sums, multiple {Clausen} values, and
                 zeta values",
  journal =      j-EXP-MATH,
  volume =       "10",
  number =       "1",
  pages =        "25--34",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2001.10504426",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11G55 (05A10 11M06 33B99)",
  MRnumber =     "1821569",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib",
  URL =          "http://arxiv.org/abs/hep-th/0004153;
                 http://docserver.carma.newcastle.edu.au/243/;
                 http://projecteuclid.org/euclid.em/999188418",
  abstract =     "We find and prove relationships between Riemann zeta
                 values and central binomial sums. We also investigate
                 alternating binomial sums (also called Apery sums). The
                 study of nonalternating sums leads to an investigation
                 of different types of sums which we call multiple
                 Clausen values. The study of alternating sums leads to
                 a tower of experimental results involving
                 polylogarithms in the golden ratio.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2001:CBS",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 09446532 (print), 23636394 (electronic)
MRclass: 46G99 (46N10 49J50)
MRnumber: 1915959
MRreviewer: A. B. N{\'e}meth
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Journal of Convex Analysis
remark: CECM Preprint 00:151.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.heldermann.de/JCA/jcacon.htm
rawauthor: Jonathan M. Borwein and Jon D. Vanderwerff
rawtitle: Convex functions of {Legendre} type in general {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/228/; http://www.heldermann.de/JCA/JCA08/JCA082/jca08030.htm

abstract:
Convex functions of Legendre type are constructed on arbitrary open convex sets in Banach spaces that satisfy appropriate rotundity and smoothness conditions. A simple direct proof of the existence of ``universal'' barriers on arbitrary open convex sets in $ mathbb R^n $ is given.

rawabstract:
Convex functions of Legendre type are constructed on arbitrary open convex sets in Banach spaces that satisfy appropriate rotundity and smoothness conditions. A simple direct proof of the existence of ``universal'' barriers on arbitrary open convex sets in $ \mathbb {R}^n $ is given.

entry:
@Article{Borwein:2001:CFL,
  author =       "Jonathan M. Borwein and Jon D. Vanderwerff",
  title =        "Convex functions of {Legendre} type in general
                 {Banach} spaces",
  journal =      j-J-CONVEX-ANAL,
  volume =       "8",
  number =       "2",
  pages =        "569--581",
  year =         "2001",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "46G99 (46N10 49J50)",
  MRnumber =     "1915959",
  MRreviewer =   "A. B. N{\'e}meth",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/228/;
                 http://www.heldermann.de/JCA/JCA08/JCA082/jca08030.htm",
  abstract =     "Convex functions of Legendre type are constructed on
                 arbitrary open convex sets in Banach spaces that
                 satisfy appropriate rotundity and smoothness
                 conditions. A simple direct proof of the existence of
                 ``universal'' barriers on arbitrary open convex sets in
                 $ \mathbb {R}^n $ is given.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Convex Analysis",
  journal-URL =  "http://www.heldermann.de/JCA/jcacon.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 00:151.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2001:CFL",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 5
year: 2001
CODEN: CSENFA
DOI: https://doi.org/10.1109/5992.919266
ISSN: 1521-9615 (print), 1558-366X (electronic) OR 15219615 (print), 1558366X (electronic)
ISSNL: 1521-9615 OR 15219615
bibdate: Wed Aug 10 12:08:56 2016
bibtimestamp: 2016.08.10 12:08:56 ???
fjournal: Computing in Science and Engineering
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992
rawauthor: Jonathan M. Borwein and Peter B. Borwein
rawtitle: Challenges in Mathematical Computing
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/computscieng.bib

URL:
http://dlib.computer.org/cs/books/cs2001/pdf/c3048.pdf; http://docserver.carma.newcastle.edu.au/135/; http://www.computer.org/cse/cs1999c3048abs.htm

abstract:
Almost all interesting mathematical algorithmic questions relate to NP-hard questions. Such computation is prone to explode exponentially. The authors anticipate the greatest benefit will come from mathematical platforms that allow for computer-assisted insight generation, not from solutions of grand-challenge problems.

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

rawabstract:
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.

entry:
@Article{Borwein:2001:CMCa,
  author =       "Jonathan M. Borwein and Peter B. Borwein",
  title =        "Challenges in Mathematical Computing",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "3",
  number =       "3",
  pages =        "48--53",
  month =        may # "\slash " # jun,
  year =         "2001",
  CODEN =        "CSENFA",
  DOI =          "https://doi.org/10.1109/5992.919266",
  ISSN =         "1521-9615 (print), 1558-366X (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Wed Aug 10 12:08:56 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/computscieng.bib",
  URL =          "http://dlib.computer.org/cs/books/cs2001/pdf/c3048.pdf;
                 http://docserver.carma.newcastle.edu.au/135/;
                 http://www.computer.org/cse/cs1999c3048abs.htm",
  abstract =     "Almost all interesting mathematical algorithmic
                 questions relate to NP-hard questions. Such computation
                 is prone to explode exponentially. The authors
                 anticipate the greatest benefit will come from
                 mathematical platforms that allow for computer-assisted
                 insight generation, not from solutions of
                 grand-challenge problems.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
  keywords =     "Algebra; computational complexity; Computer
                 architecture; Computer networks; computer-assisted
                 insight generation; Databases; Encyclopedias;
                 grand-challenge problems; HTML; Java; mathematical
                 algorithmic questions; mathematical computing;
                 mathematical platforms; Mathematics; mathematics
                 computing; NP-hard questions; Packaging; Statistics;
                 symbol manipulation",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2001:CMC",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2001:CMCc
author: Jonathan M. Borwein and Peter B. Borwein
title: Challenges in Mathematical Computing
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 12
day: 19
month: feb
monthnumber: 2
year: 2001
bibdate: Wed Aug 31 12:21:01 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 12:21:01 ???
URL: http://docserver.carma.newcastle.edu.au/135/2/01_160-Borwein-Borwein-ocr.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Peter B. Borwein
rawtitle: Challenges in Mathematical Computing
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Almost all interesting mathematical algorithmic questions relate to NP-hard questions and such computation is prone to explode exponentially. More space, more speed and processors, and even say massive parallelism will have an impact but it will be largely at a ``micro not macro'' level. We anticipate the greatest benefit accruing from mathematical platforms that allow for highly computer assisted insight generation (more ``aha''s per cycle), not from solution of grand challenge problems.

rawabstract:
Almost all interesting mathematical algorithmic questions relate to NP-hard questions and such computation is prone to explode exponentially. More space, more speed and processors, and even say massive parallelism will have an impact but it will be largely at a ``micro not macro'' level. We anticipate the greatest benefit accruing from mathematical platforms that allow for highly computer assisted insight generation (more ``aha''s per cycle), not from solution of grand challenge problems.

entry:
@TechReport{Borwein:2001:CMCc,
  author =       "Jonathan M. Borwein and Peter B. Borwein",
  title =        "Challenges in Mathematical Computing",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "12",
  day =          "19",
  month =        feb,
  year =         "2001",
  bibdate =      "Wed Aug 31 12:21:01 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/135/2/01_160-Borwein-Borwein-ocr.pdf",
  abstract =     "Almost all interesting mathematical algorithmic
                 questions relate to NP-hard questions and such
                 computation is prone to explode exponentially. More
                 space, more speed and processors, and even say massive
                 parallelism will have an impact but it will be largely
                 at a ``micro not macro'' level. We anticipate the
                 greatest benefit accruing from mathematical platforms
                 that allow for highly computer assisted insight
                 generation (more ``aha''s per cycle), not from solution
                 of grand challenge problems.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2001:CSF
author: Jonathan M. Borwein and Adrian S. Lewis and Qiji J. Zhu
booktitle: Optimization and related topics (Ballarat/Melbourne, 1999)
volume: 47
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: 179--196
year: 2001
DOI: https://doi.org/10.1007/978-1-4757-6099-6_12
MRclass: 49N15 (47A10 47B10 90C25)
MRnumber: 1893622
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: Appl. Optim.
URL: http://docserver.carma.newcastle.edu.au/251/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Adrian S. Lewis and Qiji J. Zhu
rawbooktitle: Optimization and related topics ({Ballarat}/{Melbourne}, 1999)
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Convex spectral functions of compact operators. II. Lower semicontinuity and rearrangement invariance

rawtitle:
Convex spectral functions of compact operators. {II}. {Lower} semicontinuity and rearrangement invariance

entry:
@InCollection{Borwein:2001:CSF,
  author =       "Jonathan M. Borwein and Adrian S. Lewis and Qiji J.
                 Zhu",
  booktitle =    "Optimization and related topics
                 ({Ballarat}/{Melbourne}, 1999)",
  title =        "Convex spectral functions of compact operators. {II}.
                 {Lower} semicontinuity and rearrangement invariance",
  volume =       "47",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "179--196",
  year =         "2001",
  DOI =          "https://doi.org/10.1007/978-1-4757-6099-6_12",
  MRclass =      "49N15 (47A10 47B10 90C25)",
  MRnumber =     "1893622",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Appl. Optim.",
  URL =          "http://docserver.carma.newcastle.edu.au/251/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 0362546x (print), 18735215 (electronic)
ISSNL: 0362-546X OR 0362546X
MRclass: 49J53 (49N15 90C46)
MRnumber: 1851858
MRreviewer: Roberto Lucchetti
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
remark: CECM Research Report 98:111.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.sciencedirect.com/journal/nonlinear-analysis
rawauthor: J. M. Borwein and S. P. Fitzpatrick
rawtitle: Duality inequalities and sandwiched functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/204/; http://www.sciencedirect.com/science/article/pii/S0362546X00001292

keywords:
Ekeland variational principle; Fenchel duality; Mean-value inequalities; Nonconvex separation; Sandwich theorem; Schauder fixed-point theorem

entry:
@Article{Borwein:2001:DIS,
  author =       "J. M. Borwein and S. P. Fitzpatrick",
  title =        "Duality inequalities and sandwiched functions",
  journal =      j-NONLINEAR-ANAL,
  volume =       "46",
  number =       "3",
  pages =        "365--380",
  year =         "2001",
  CODEN =        "NOANDD",
  DOI =          "https://doi.org/10.1016/S0362-546X(00)00129-2",
  ISSN =         "0362-546x (print), 1873-5215 (electronic)",
  ISSN-L =       "0362-546X",
  MRclass =      "49J53 (49N15 90C46)",
  MRnumber =     "1851858",
  MRreviewer =   "Roberto Lucchetti",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/204/;
                 http://www.sciencedirect.com/science/article/pii/S0362546X00001292",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Nonlinear Analysis. Theory, Methods \& Applications.
                 An International Multidisciplinary Journal. Series A:
                 Theory and Methods",
  journal-URL =  "https://www.sciencedirect.com/journal/nonlinear-analysis",
  keywords =     "Ekeland variational principle; Fenchel duality;
                 Mean-value inequalities; Nonconvex separation; Sandwich
                 theorem; Schauder fixed-point theorem",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Research Report 98:111.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2001:EM
author: Jonathan M. Borwein
title: Experimental Mathematics
journal: j-AUSTRALIAN-MATH-SOC-GAZ
volume: 28
pages: 77--80
year: 2001
ISSN: 0311-0729 (print), 1326-2297 (electronic) OR 03110729 (print), 13262297 (electronic)
ISSNL: 0311-0729 OR 03110729
bibdate: Fri Aug 12 11:12:55 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 11:12:55 ???
URL: http://docserver.carma.newcastle.edu.au/1527/
fjournal: Australian Mathematical Society Gazette
acknowledgement: ack-nhfb
ajournal: Aust. Math. Soc. Gaz.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.austms.org.au/gazette
rawauthor: Jonathan M. Borwein
rawtitle: Experimental Mathematics
ORCID: Borwein, Jonathan/0000-0002-1263-0646
remark:
The journal has archives only from volume 31 (2004) at url https://austms.org.au/publications/gazette/gazette-past-issues/.

entry:
@Article{Borwein:2001:EM,
  author =       "Jonathan M. Borwein",
  title =        "Experimental Mathematics",
  journal =      j-AUSTRALIAN-MATH-SOC-GAZ,
  volume =       "28",
  number =       "??",
  pages =        "77--80",
  month =        "????",
  year =         "2001",
  DOI =          "",
  ISSN =         "0311-0729 (print), 1326-2297 (electronic)",
  ISSN-L =       "0311-0729",
  bibdate =      "Fri Aug 12 11:12:55 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1527/",
  acknowledgement = ack-nhfb,
  ajournal =     "Aust. Math. Soc. Gaz.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Australian Mathematical Society Gazette",
  journal-URL =  "http://www.austms.org.au/gazette",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "The journal has archives only from volume 31 (2004) at
                 \url{https://austms.org.au/publications/gazette/gazette-past-issues/}.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 00029947 (print), 10886850 (electronic)
ISSNL: 0002-9947 OR 00029947
MRclass: 49J52 (46G05 58C20)
MRnumber: 1837212
MRreviewer: Mari{\'a}n Fabian
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/234/
fjournal: Transactions of the American Mathematical Society
remark: CECM Preprint 99:127.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/journals/tran/
rawauthor: Jonathan M. Borwein and Warren B. Moors and Xianfu Wang
rawtitle: Generalized subdifferentials: a {Baire} categorical approach
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We use Baire categorical arguments to construct pathological locally Lipschitz functions. The origins of this approach can be traced back to Banach and Mazurkiewicz (1931) who independently used similar categorical arguments to show that ``almost every continuous real-valued function defined on [0,1] is nowhere differentiable''. As with the results of Banach and Mazurkiewicz, it appears that it is easier to show that almost every function possesses a certain property than to construct a single concrete example. Among the most striking results contained in this paper are: Almost every 1-Lipschitz function defined on a Banach space has a Clarke subdifferential mapping that is identically equal to the dual ball; if T-1; T-2,ldots ,T-n is a family of maximal cyclically monotone operators defined on a Banach space X then there exists a real-valued locally Lipschitz function g such that partial derivative (0g)(x) =co T-1(x); T-2(x),ldots ,T-n(x) for each x is an element of X; in a separable Banach space each non-empty weak* compact convex subset in the dual space is identically equal to the approximate subdifferential mapping of some Lipschitz function and for locally Lipschitz functions defined on separable spaces the notions of strong and weak integrability coincide.

rawabstract:
We use Baire categorical arguments to construct pathological locally Lipschitz functions. The origins of this approach can be traced back to Banach and Mazurkiewicz (1931) who independently used similar categorical arguments to show that ``almost every continuous real-valued function defined on [0,1] is nowhere differentiable''. As with the results of Banach and Mazurkiewicz, it appears that it is easier to show that almost every function possesses a certain property than to construct a single concrete example. Among the most striking results contained in this paper are: Almost every 1-Lipschitz function defined on a Banach space has a Clarke subdifferential mapping that is identically equal to the dual ball; if \{T-1; T-2,\ldots{},T-n\} is a family of maximal cyclically monotone operators defined on a Banach space X then there exists a real-valued locally Lipschitz function g such that partial derivative (0g)(x) =co \{T-1(x); T-2(x),\ldots{},T-n(x)\} for each x is an element of X; in a separable Banach space each non-empty weak* compact convex subset in the dual space is identically equal to the approximate subdifferential mapping of some Lipschitz function and for locally Lipschitz functions defined on separable spaces the notions of strong and weak integrability coincide.

entry:
@Article{Borwein:2001:GSB,
  author =       "Jonathan M. Borwein and Warren B. Moors and Xianfu
                 Wang",
  title =        "Generalized subdifferentials: a {Baire} categorical
                 approach",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "353",
  number =       "10",
  pages =        "3875--3893",
  year =         "2001",
  CODEN =        "TAMTAM",
  DOI =          "https://doi.org/10.1090/S0002-9947-01-02820-3",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "49J52 (46G05 58C20)",
  MRnumber =     "1837212",
  MRreviewer =   "Mari{\'a}n Fabian",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/234/",
  abstract =     "We use Baire categorical arguments to construct
                 pathological locally Lipschitz functions. The origins
                 of this approach can be traced back to Banach and
                 Mazurkiewicz (1931) who independently used similar
                 categorical arguments to show that ``almost every
                 continuous real-valued function defined on [0,1] is
                 nowhere differentiable''. As with the results of Banach
                 and Mazurkiewicz, it appears that it is easier to show
                 that almost every function possesses a certain property
                 than to construct a single concrete example. Among the
                 most striking results contained in this paper are:
                 Almost every 1-Lipschitz function defined on a Banach
                 space has a Clarke subdifferential mapping that is
                 identically equal to the dual ball; if \{T-1;
                 T-2,\ldots{},T-n\} is a family of maximal cyclically
                 monotone operators defined on a Banach space X then
                 there exists a real-valued locally Lipschitz function g
                 such that partial derivative (0g)(x) =co \{T-1(x);
                 T-2(x),\ldots{},T-n(x)\} for each x is an element of X;
                 in a separable Banach space each non-empty weak*
                 compact convex subset in the dual space is identically
                 equal to the approximate subdifferential mapping of
                 some Lipschitz function and for locally Lipschitz
                 functions defined on separable spaces the notions of
                 strong and weak integrability coincide.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Transactions of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/tran/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 99:127.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2001:GSB",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2001:LLC
author: J. M. Borwein and J. Vanderwerff and Xianfu Wang
title: Local Lipschitz-constant functions and maximal subdifferentials
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 28
year: 2001
MRclass: 49J52 (54E52)
bibdate: Thu Sep 01 10:51:58 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 10:51:58 ???
note: Published in cite Borwein:2003:LLC.
URL: http://docserver.carma.newcastle.edu.au/55/2/01_158-Borwein-Vanderwerff-Wang.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and J. Vanderwerff and Xianfu Wang
rawnote: Published in \cite{Borwein:2003:LLC}.
rawtitle: Local {Lipschitz}-constant functions and maximal subdifferentials
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
It is shown that if k(x) is an upper semicontinuous and quasi lower semicontinuous function on a Banach space X, then k(z)Bx~ is the Clarke subdifferential of some locally Lipschitz function on X. Related results for approximate subdifferentials are also given. Moreover, on smooth Banach spaces, for every locally Lipschitz function with minimal Clarke subdifferential, one can obtain a maximal Clarke subdifferential map via its ``local Lipschitz-constant'' function. Finally, some results concerning the characterization and calculus of local Lipschitz-constant functions are developed.

keywords:
approximate subdifferential; Baire category; Clarke subdifferential; Lipschitz function; local Lipschitz-constant function

rawabstract:
It is shown that if k(x) is an upper semicontinuous and quasi lower semicontinuous function on a Banach space X, then k(z)Bx~ is the Clarke subdifferential of some locally Lipschitz function on X. Related results for approximate subdifferentials are also given. Moreover, on smooth Banach spaces, for every locally Lipschitz function with minimal Clarke subdifferential, one can obtain a maximal Clarke subdifferential map via its ``local Lipschitz-constant'' function. Finally, some results concerning the characterization and calculus of local Lipschitz-constant functions are developed.

entry:
@TechReport{Borwein:2001:LLC,
  author =       "J. M. Borwein and J. Vanderwerff and Xianfu Wang",
  title =        "Local {Lipschitz}-constant functions and maximal
                 subdifferentials",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "28",
  year =         "2001",
  MRclass =      "49J52 (54E52)",
  bibdate =      "Thu Sep 01 10:51:58 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2003:LLC}.",
  URL =          "http://docserver.carma.newcastle.edu.au/55/2/01_158-Borwein-Vanderwerff-Wang.pdf",
  abstract =     "It is shown that if k(x) is an upper semicontinuous
                 and quasi lower semicontinuous function on a Banach
                 space X, then k(z)Bx~ is the Clarke subdifferential of
                 some locally Lipschitz function on X. Related results
                 for approximate subdifferentials are also given.
                 Moreover, on smooth Banach spaces, for every locally
                 Lipschitz function with minimal Clarke subdifferential,
                 one can obtain a maximal Clarke subdifferential map via
                 its ``local Lipschitz-constant'' function. Finally,
                 some results concerning the characterization and
                 calculus of local Lipschitz-constant functions are
                 developed.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "approximate subdifferential; Baire category; Clarke
                 subdifferential; Lipschitz function; local
                 Lipschitz-constant function",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2001:MVS
author: David Borwein and Jonathan M. Borwein and Bernard A. Mares, Jr.
title: Multi-variable sinc integrals and volumes of polyhedra
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 19
day: 9
month: feb
monthnumber: 2
year: 2001
bibdate: Thu Sep 01 10:57:31 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 10:57:31 ???
URL: http://docserver.carma.newcastle.edu.au/56/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David Borwein and Jonathan M. Borwein and Bernard A. {Mares, Jr.}
rawtitle: Multi-variable sinc integrals and volumes of polyhedra
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@TechReport{Borwein:2001:MVS,
  author =       "David Borwein and Jonathan M. Borwein and Bernard A.
                 {Mares, Jr.}",
  title =        "Multi-variable sinc integrals and volumes of
                 polyhedra",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "19",
  day =          "9",
  month =        feb,
  year =         "2001",
  bibdate =      "Thu Sep 01 10:57:31 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/56/",
  abstract =     "We investigate multi-variable integrals of products of
                 sinc functions and show how they may be interpreted as
                 volumes of symmetric convex polyhedra. We then derive
                 an explicit formula for computing such sinc integrals
                 and so equivalently volumes of polyhedra.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2001:NRI
author: J. Borwein and R. Goebel
title: Notions of relative interior in Banach spaces
institution: inst-CECM
address: inst-CECM:adr
pages: 17
day: 10
month: oct
monthnumber: 10
year: 2001
MRclass: 49J53 (46B20 90C48)
MRnumber: 1992991
MRreviewer: Constantin Z{\u{a}}linescu
bibdate: Wed Aug 31 12:30:27 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 12:30:27 ???
note: Published in cite Borwein:2003:NRI.
URL: http://docserver.carma.newcastle.edu.au/138/
fjournal: Journal of Mathematical Sciences (New York)
remark: Special issue on optimization and related topics, 1. CECM Preprint 01:162.
acknowledgement: ack-nhfb
ajournal: J. Math. Sci. (NY)
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. Borwein and R. Goebel
rawnote: Published in \cite{Borwein:2003:NRI}.
rawtitle: Notions of relative interior in {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Extensions to a Banach space of the equivalent notions of relatively absorbing, non-support, and relative interior points of a convex set in $ mathbb R^n $ are presented. The relations between these extensions are studied, and their basic calculus rules are developed. Several explicit examples and counterexamples in general Banach spaces are given; and the tools for development of further examples are explained. Various implications for infinite dimensional optimization are highlighted.

rawabstract:
Extensions to a Banach space of the equivalent notions of relatively absorbing, non-support, and relative interior points of a convex set in $ \mathbb {R}^n $ are presented. The relations between these extensions are studied, and their basic calculus rules are developed. Several explicit examples and counterexamples in general Banach spaces are given; and the tools for development of further examples are explained. Various implications for infinite dimensional optimization are highlighted.

entry:
@TechReport{Borwein:2001:NRI,
  author =       "J. Borwein and R. Goebel",
  title =        "Notions of relative interior in {Banach} spaces",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "17",
  day =          "10",
  month =        oct,
  year =         "2001",
  MRclass =      "49J53 (46B20 90C48)",
  MRnumber =     "1992991",
  MRreviewer =   "Constantin Z{\u{a}}linescu",
  bibdate =      "Wed Aug 31 12:30:27 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2003:NRI}.",
  URL =          "http://docserver.carma.newcastle.edu.au/138/",
  abstract =     "Extensions to a Banach space of the equivalent notions
                 of relatively absorbing, non-support, and relative
                 interior points of a convex set in $ \mathbb {R}^n $
                 are presented. The relations between these extensions
                 are studied, and their basic calculus rules are
                 developed. Several explicit examples and
                 counterexamples in general Banach spaces are given; and
                 the tools for development of further examples are
                 explained. Various implications for infinite
                 dimensional optimization are highlighted.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Math. Sci. (NY)",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Mathematical Sciences (New York)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Special issue on optimization and related topics, 1.
                 CECM Preprint 01:162.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 13314343 (print), 18489966 (electronic)
ISSNL: 1331-4343 OR 13314343
MRclass: 52A38 (26B25 52A40)
MRnumber: 1859668
MRreviewer: Beifang Chen
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/222/
fjournal: Mathematical Inequalities & Applications
remark: CECM Preprint 00:146.
acknowledgement: ack-nhfb
ajournal: Math. Inequal. Appl.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://mia.ele-math.com/
rawauthor: D. Borwein and J. Borwein and G. Fee and R. Girgensohn
rawtitle: Refined convexity and special cases of the {Blaschke--Santalo} inequality
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2001:RCS,
  author =       "D. Borwein and J. Borwein and G. Fee and R.
                 Girgensohn",
  title =        "Refined convexity and special cases of the
                 {Blaschke--Santalo} inequality",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "4",
  number =       "4",
  pages =        "631--638",
  year =         "2001",
  DOI =          "https://doi.org/10.7153/mia-04-56",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  ISSN-L =       "1331-4343",
  MRclass =      "52A38 (26B25 52A40)",
  MRnumber =     "1859668",
  MRreviewer =   "Beifang Chen",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/222/",
  abstract =     "We derive the l(p) version of the classical
                 Blaschke-Santalo inequality for polar volumes as a
                 consequence of more subtle convexity estimates for the
                 volume of the p-ball in Euclidean space. We also give
                 analogs for the (p, q) -substitution norm.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Inequal. Appl.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 00:146.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2001:RCS",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 13454773 (print), 18805221 (electronic)
ISSNL: 1345-4773 OR 13454773
MRclass: 58C20 (46G05 49J53)
MRnumber: 1828155
MRreviewer: Mari{\'a}n Fabian
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
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
fjournal: Journal of Nonlinear and Convex Analysis. An International Journal
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ybook.co.jp/jnca.html
rawauthor: J. M. Borwein and M. Fabian and I. Kortezov and P. D. Loewen
rawnote: Special issue for Professor Ky Fan.
rawtitle: The range of the gradient of a continuously differentiable bump
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2001:RGC,
  author =       "J. M. Borwein and M. Fabian and I. Kortezov and P. D.
                 Loewen",
  title =        "The range of the gradient of a continuously
                 differentiable bump",
  journal =      j-J-NONLINEAR-CONVEX-ANAL,
  volume =       "2",
  number =       "1",
  pages =        "1--19",
  year =         "2001",
  ISSN =         "1345-4773 (print), 1880-5221 (electronic)",
  ISSN-L =       "1345-4773",
  MRclass =      "58C20 (46G05 49J53)",
  MRnumber =     "1828155",
  MRreviewer =   "Mari{\'a}n Fabian",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Special issue for Professor Ky Fan.",
  URL =          "http://docserver.carma.newcastle.edu.au/231/;
                 http://www.ybook.co.jp/online2/opjnca/vol2/p1.html",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Nonlinear and Convex Analysis. An
                 International Journal",
  journal-URL =  "http://www.ybook.co.jp/jnca.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2001:RP
author: Jonathan M. Borwein and Peter B. Borwein
title: Ramanujan and pi
crossref: Berndt:2001:RES
pages: 187--199
year: 2001
MRclass: 11-03 (01A70)
MRnumber: 1862751
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: Reprint of cite Borwein:1988:RP.
series: Hist. Math.
URL: http://docserver.carma.newcastle.edu.au/1379/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Peter B. Borwein
rawnote: Reprint of \cite{Borwein:1988:RP}.
rawtitle: {Ramanujan} and pi
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2001:RP,
  author =       "Jonathan M. Borwein and Peter B. Borwein",
  title =        "{Ramanujan} and pi",
  crossref =     "Berndt:2001:RES",
  pages =        "187--199",
  year =         "2001",
  MRclass =      "11-03 (01A70)",
  MRnumber =     "1862751",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Reprint of \cite{Borwein:1988:RP}.",
  series =       "Hist. Math.",
  URL =          "http://docserver.carma.newcastle.edu.au/1379/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 09276947 (print), 1572932x (electronic)
ISSNL: 0927-6947 OR 09276947
MRclass: 46N10 (49J53 54E52)
MRnumber: 1845933
MRreviewer: Gargi Chakraborty
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: Wellposedness in optimization and related topics (Gargnano, 1999).
URL: http://docserver.carma.newcastle.edu.au/221/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11228
rawauthor: Jonathan M. Borwein and Ivaylo Kortezov
rawnote: Wellposedness in optimization and related topics (Gargnano, 1999).
rawtitle: Some generic results on nonattaining functionals
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2001:SGR,
  author =       "Jonathan M. Borwein and Ivaylo Kortezov",
  title =        "Some generic results on nonattaining functionals",
  journal =      j-SET-VALUED-ANAL,
  volume =       "9",
  number =       "1--2",
  pages =        "35--47",
  year =         "2001",
  CODEN =        "SVANEG",
  DOI =          "https://doi.org/10.1023/A:1011246414064",
  ISSN =         "0927-6947 (print), 1572-932x (electronic)",
  ISSN-L =       "0927-6947",
  MRclass =      "46N10 (49J53 54E52)",
  MRnumber =     "1845933",
  MRreviewer =   "Gargi Chakraborty",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Wellposedness in optimization and related topics
                 (Gargnano, 1999).",
  URL =          "http://docserver.carma.newcastle.edu.au/221/",
  abstract =     "We prove that (a) in a reflexive space, for any
                 linearly bounded but unbounded closed convex subset the
                 nonsupport functionals are a dense G(delta) subset of
                 the polar set, and (b) any non-semicoercive proper
                 convex Isc [weak*-lsc] function in a [dual] Banach
                 space has a generic [dense G(delta)] set of
                 L-infinity-perturbations which do not attain their
                 infimum. We also characterize the proper convex
                 functions that have inf-nonattaining
                 L-infinity-perturbations. This results also in a
                 criterion for reflexivity.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Set-Valued Analysis. An International Journal Devoted
                 to the Theory of Multifunctions and its Applications",
  journal-URL =  "http://link.springer.com/journal/11228",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2001:SGR",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 13824090 (print), 15729303 (electronic)
ISSNL: 1382-4090 OR 13824090
MRclass: 42A38 (26D15 40A05 41A55)
MRnumber: 1829810
MRreviewer: Philip Heywood
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/249/
fjournal: The Ramanujan Journal
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11139
rawauthor: David Borwein and Jonathan M. Borwein
rawtitle: Some remarkable properties of sinc and related integrals
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2001:SRP,
  author =       "David Borwein and Jonathan M. Borwein",
  title =        "Some remarkable properties of sinc and related
                 integrals",
  journal =      j-RAMANUJAN-J,
  volume =       "5",
  number =       "1",
  pages =        "73--89",
  year =         "2001",
  CODEN =        "RAJOF9",
  DOI =          "https://doi.org/10.1023/A:1011497229317",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  MRclass =      "42A38 (26D15 40A05 41A55)",
  MRnumber =     "1829810",
  MRreviewer =   "Philip Heywood",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/249/",
  abstract =     "Using Fourier transform techniques, we establish
                 inequalities for integrals of the form [GRAPHICS] We
                 then give quite striking closed form evaluations of
                 such integrals and finish by discussing various
                 extensions and applications.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The {Ramanujan} Journal",
  journal-URL =  "http://link.springer.com/journal/11139",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2001:SRP",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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 OR 12267228
MRclass: 49J52 (26A24 46G05 46T20)
MRnumber: 1844467
MRreviewer: Yan Gao
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: Nonlinear analysis and its applications (St. John's, NF, 1999).
fjournal: Nonlinear Analysis Forum. An International Journal
acknowledgement: ack-nhfb
ajournal: Nonlinear Anal. Forum
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://prof.ks.ac.kr/bslee/naf/
rawauthor: J. M. Borwein and X. Wang
rawnote: Nonlinear analysis and its applications (St. John's, NF, 1999).
rawtitle: Subdifferentiability of typical continuous functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/241/; http://prof.ks.ac.kr/bslee/naf/table/vol-0601/v0601-05a.PDF

entry:
@Article{Borwein:2001:STC,
  author =       "J. M. Borwein and X. Wang",
  title =        "Subdifferentiability of typical continuous functions",
  journal =      "Nonlinear Analysis Forum",
  volume =       "6",
  number =       "1",
  pages =        "49--58",
  year =         "2001",
  ISSN =         "1226-7228",
  MRclass =      "49J52 (26A24 46G05 46T20)",
  MRnumber =     "1844467",
  MRreviewer =   "Yan Gao",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Nonlinear analysis and its applications (St. John's,
                 NF, 1999).",
  URL =          "http://docserver.carma.newcastle.edu.au/241/;
                 http://prof.ks.ac.kr/bslee/naf/table/vol-0601/v0601-05a.PDF",
  acknowledgement = ack-nhfb,
  ajournal =     "Nonlinear Anal. Forum",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Nonlinear Analysis Forum. An International Journal",
  journal-URL =  "http://prof.ks.ac.kr/bslee/naf/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2001:SVM
author: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lisonek
title: Special values of multiple polylogarithms
journal: j-TRANS-AM-MATH-SOC
volume: 353
number: 3
pages: 907--941
month: mar
monthnumber: 3
year: 2001
CODEN: TAMTAM
DOI: https://doi.org/10.1090/S0002-9947-00-02616-7
ISSN: 0002-9947 (print), 1088-6850 (electronic) OR 00029947 (print), 10886850 (electronic)
ISSNL: 0002-9947 OR 00029947
MRclass: 33B30 (11G55 11Y60 33E20)
MRnumber: 1709772
MRreviewer: P. D. F. Ion
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: https://www.jstor.org/stable/221840
fjournal: Transactions of the American Mathematical Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/journals/tran/
rawauthor: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lison{\v{e}}k
rawtitle: Special values of multiple polylogarithms
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2001:SVM,
  author =       "Jonathan M. Borwein and David M. Bradley and David J.
                 Broadhurst and Petr Lison{\v{e}}k",
  title =        "Special values of multiple polylogarithms",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "353",
  number =       "3",
  pages =        "907--941",
  month =        mar,
  year =         "2001",
  CODEN =        "TAMTAM",
  DOI =          "https://doi.org/10.1090/S0002-9947-00-02616-7",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "33B30 (11G55 11Y60 33E20)",
  MRnumber =     "1709772",
  MRreviewer =   "P. D. F. Ion",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "https://www.jstor.org/stable/221840",
  abstract =     "Historically, the polylogarithm has attracted
                 specialists and nonspecialists alike with its lovely
                 evaluations. Much the same can be said for Euler sums
                 (or multiple harmonic sums), which, within the past
                 decade, have arisen in combinatorics, knot theory and
                 high-energy physics. More recently, we have been forced
                 to consider multidimensional extensions encompassing
                 the classical polylogarithm, Euler sums, and the
                 Riemann zeta function. Here, we provide a general
                 framework within which previously isolated results can
                 now be properly understood. Applying the theory
                 developed herein, we prove several previously
                 conjectured evaluations, including an intriguing
                 conjecture of Don Zagier.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Transactions of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/tran/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2001:SVM",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRnumber: 1544137
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.jstor.org/journals/00029890.html
rawauthor: Peter Lindqvist and Jaak Peetre and Jonathan M. Borwein
rawtitle: Problems and Solutions: Solutions: Generalized Trigonometric Functions: 10744
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Lindqvist:2001:PSS,
  author =       "Peter Lindqvist and Jaak Peetre and Jonathan M.
                 Borwein",
  title =        "Problems and Solutions: Solutions: Generalized
                 Trigonometric Functions: 10744",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "108",
  number =       "5",
  pages =        "473--474",
  year =         "2001",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2695813",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRnumber =     "1544137",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: 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 OR 000710295X
ISBN13: 978-0-00-710295-2 OR 9780007102952
bibdate: Tue Aug 16 09:04:49 MDT 2016
bibtimestamp: 2016.08.16 09:04:49 MDT
subject: Mathematics; Dictionaries; Mathematik; Worterbuch.; Mathematics.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Ephraim J. Borowski and Jonathan M. Borwein
rawtitle: Mathematics: {Collins} dictionary
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Book{Borowski:2002:MCD,
  author =       "Ephraim J. Borowski and Jonathan M. Borwein",
  title =        "Mathematics: {Collins} dictionary",
  publisher =    pub-COLLINS,
  address =      pub-COLLINS:adr,
  edition =      "Second",
  pages =        "633",
  year =         "2002",
  ISBN =         "0-00-710295-X",
  ISBN-13 =      "978-0-00-710295-2",
  LCCN =         "????",
  bibdate =      "Tue Aug 16 09:04:49 MDT 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject =      "Mathematics; Dictionaries; Mathematik;
                 W{\"o}rterbuch.; Mathematics.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2002:ANB
author: J. M. Borwein and M. Jimenez-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) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
MRclass: 46B20 (41A65)
MRnumber: 1880294
MRreviewer: Ioan {\c{S}}erb
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
fjournal: Journal of Approximation Theory
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: J. M. Borwein and M. Jim{\'e}nez-Sevilla and J. P. Moreno
rawtitle: Antiproximinal norms in {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2002:ANB,
  author =       "J. M. Borwein and M. Jim{\'e}nez-Sevilla and J. P.
                 Moreno",
  title =        "Antiproximinal norms in {Banach} spaces",
  journal =      j-J-APPROX-THEORY,
  volume =       "114",
  number =       "1",
  pages =        "57--69",
  year =         "2002",
  CODEN =        "JAXTAZ",
  DOI =          "https://doi.org/10.1006/jath.2001.3636",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  MRclass =      "46B20 (41A65)",
  MRnumber =     "1880294",
  MRreviewer =   "Ioan {\c{S}}erb",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/233/;
                 http://www.sciencedirect.com/science/article/pii/S0021904501936366",
  abstract =     "We prove that every Banach space containing a
                 complemented copy of $ c_0 $ has an antiproximinal body
                 for a suitable norm. If, in addition, the space is
                 separable, there is a pair of antiproximinal norms. In
                 particular, in a separable polyhedral space $X$, the
                 set of all (equivalent) norms on $X$ having an
                 isomorphic antiproximinal norm is dense. In contrast,
                 it is shown that there are no antiproximinal norms in
                 Banach spaces with the convex point of continuity
                 property (CPCP). Other questions related to the
                 existence of antiproximinal bodies are also
                 discussed.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  received =     "CECM Preprint 00:157.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2002:ANB",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2002:ASS
author: Jonathan M. Borwein and Qiji J. Zhu
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) OR 0362546x (print), 18735215 (electronic)
ISSNL: 0362-546X OR 0362546X
MRclass: 49J52 (46G05 46N10 49-02 49J53 58C05)
MRnumber: 1885123
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: See cite Borwein:1999:SSC.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.sciencedirect.com/journal/nonlinear-analysis
rawauthor: Jonathan M. Borwein and Qiji J. Zhu
rawnote: See \cite{Borwein:1999:SSC}.
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Addendum: ``A survey of subdifferential calculus with applications'' [Nonlinear Anal.bf 38 (1999), no.6, Ser.A: Theory Methods, 687--773; (2000j:49024)]

rawtitle:
Addendum: ``{A survey of subdifferential calculus with applications'' [Nonlinear Anal.\ {\bf 38} (1999), no.\ 6, Ser.\ A: Theory Methods, 687--773; (2000j:49024)]}

entry:
@Article{Borwein:2002:ASS,
  author =       "Jonathan M. Borwein and Qiji J. Zhu",
  title =        "Addendum: ``{A survey of subdifferential calculus with
                 applications'' [Nonlinear Anal.\ {\bf 38} (1999), no.\
                 6, Ser.\ A: Theory Methods, 687--773; (2000j:49024)]}",
  journal =      j-NONLINEAR-ANAL,
  volume =       "49",
  number =       "2, Ser. A: Theory Methods",
  pages =        "295--296",
  year =         "2002",
  CODEN =        "NOANDD",
  DOI =          "https://doi.org/10.1016/S0362-546X(01)00099-2",
  ISSN =         "0362-546x (print), 1873-5215 (electronic)",
  ISSN-L =       "0362-546X",
  MRclass =      "49J52 (46G05 46N10 49-02 49J53 58C05)",
  MRnumber =     "1885123",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "See \cite{Borwein:1999:SSC}.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Nonlinear Analysis. Theory, Methods \& Applications.
                 An International Multidisciplinary Journal. Series A:
                 Theory and Methods",
  journal-URL =  "https://www.sciencedirect.com/journal/nonlinear-analysis",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 6
year: 2002
CODEN: PAMYAR
DOI: https://doi.org/10.1090/S0002-9939-01-06249-9
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 46B20 (46N10 52A41)
MRnumber: 1887028
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/230/; https://www.jstor.org/stable/2699775
fjournal: Proceedings of the American Mathematical Society
remark: CECM Preprint 00:154.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/journals/proc
rawauthor: J. M. Borwein and J. D. Vanderwerff
rawtitle: On the continuity of biconjugate convex functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

entry:
@Article{Borwein:2002:CBC,
  author =       "J. M. Borwein and J. D. Vanderwerff",
  title =        "On the continuity of biconjugate convex functions",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "130",
  number =       "6",
  pages =        "1797--1803",
  month =        jun,
  year =         "2002",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/S0002-9939-01-06249-9",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "46B20 (46N10 52A41)",
  MRnumber =     "1887028",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/230/;
                 https://www.jstor.org/stable/2699775",
  abstract =     "We show that a Banach space is a Grothendieck space if
                 and only if every continuous convex function on $X$ has
                 a continuous biconjugate function on $ X**$, thus also
                 answering a question raised by S. Simons. Related
                 characterizations and examples are given.",
  acknowledgement = ack-nhfb,
  article-number = "UNSP S 0002-9939(01)06249-9",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 00:154.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2002:CBC",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2002:DSSc
author: Jonathan Michael Borwein and Kwok-Kwong Stephen Choi
title: On Dirichlet series for sums of squares
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 29
day: 5
month: feb
monthnumber: 2
year: 2002
bibdate: Wed Aug 31 14:12:44 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 14:12:44 ???
note: Published in cite Borwein:2003:DSS.
URL: http://docserver.carma.newcastle.edu.au/142/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Michael Borwein and Kwok-Kwong Stephen Choi
rawnote: Published in \cite{Borwein:2003:DSS}.
rawtitle: On {Dirichlet} series for sums of squares
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In [14], Hardy and Wright recorded elegant closed forms for the generating functions of the divisor functions $ sigma _k(n) $ and $ sigma _k(n)^2 $ in the terms of Riemann Zeta function $ zeta (s) $ only. In this paper, we explore other arithmetical functions enjoying this remarkable property. In Theorem 2.1 below, we are able to generalize the above result and prove that if $ f_i $ and $ g_i $ are completely multiplicative, then we have par $$ sum _n = 1^infty frac (f_1 ast g_1)(n) cdot (f_2 ast g_2)(n)n^s = f r a cL_f_1 f_2(s) L_g_1 g_2(s) L_f_1 g_2(s)L_f_1 f_2 g_1 g_2(2s) $$ par where $ L_f(s) := sum _n = 1^infty f(n) n^-s $ is the Dirichlet series corresponding to $f$. Let $ r_N(n)$ be the number of solutions of $ x_1^2 + cdots + x_N^2 = n$ and $ r_2, P(n)^2$ be the number of solutions of $ x^2 + P y^2 = n$. One of the applications of Theorem 2.1 is to obtain closed forms, in terms of $ zeta (s)$ and Dirichlet $L$-functions, for the generating functions of $ r_N(n)$, $ r_N^2 (n)$, $ r_2, Pp(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.

rawabstract:
In [14], Hardy and Wright recorded elegant closed forms for the generating functions of the divisor functions $ \sigma_k(n) $ and $ \sigma_k(n)^2 $ in the terms of Riemann Zeta function $ \zeta (s) $ only. In this paper, we explore other arithmetical functions enjoying this remarkable property. In Theorem 2.1 below, we are able to generalize the above result and prove that if $ f_i $ and $ g_i $ are completely multiplicative, then we have \par $$ \sum_{n = 1}^\infty \frac {(f_1 \ast g_1)(n) \cdot (f_2 \ast g_2)(n)}{n^s} = f r a c{L_{f_1 f_2}(s) L_{g_1 g_2}(s) L_{f_1 g_2}(s)}{L_{f_1 f_2 g_1 g_2}(2s)} $$ \par where $ L_f(s) := \sum_{n = 1}^\infty f(n) n^{-s} $ is the Dirichlet series corresponding to $f$. Let $ r_N(n)$ be the number of solutions of $ x_1^2 + \cdots + x_N^2 = n$ and $ r_{2, P}(n)^2$ be the number of solutions of $ x^2 + P y^2 = n$. One of the applications of Theorem 2.1 is to obtain closed forms, in terms of $ \zeta (s)$ and Dirichlet $L$-functions, for the generating functions of $ r_N(n)$, $ r_N^2 (n)$, $ r_{2, P}p(n)$ and $ r_{2, p}(n)^2$ for certain $N$ and $P$. We also use these generating functions to obtain asymptotic estimates of the average values for each function for which we obtain a Dirichlet series.

entry:
@TechReport{Borwein:2002:DSSc,
  author =       "Jonathan Michael Borwein and Kwok-Kwong Stephen Choi",
  title =        "On {Dirichlet} series for sums of squares",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "29",
  day =          "5",
  month =        feb,
  year =         "2002",
  bibdate =      "Wed Aug 31 14:12:44 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2003:DSS}.",
  URL =          "http://docserver.carma.newcastle.edu.au/142/",
  abstract =     "In [14], Hardy and Wright recorded elegant closed
                 forms for the generating functions of the divisor
                 functions $ \sigma_k(n) $ and $ \sigma_k(n)^2 $ in the
                 terms of Riemann Zeta function $ \zeta (s) $ only. In
                 this paper, we explore other arithmetical functions
                 enjoying this remarkable property. In Theorem 2.1
                 below, we are able to generalize the above result and
                 prove that if $ f_i $ and $ g_i $ are completely
                 multiplicative, then we have \par

                  $$ \sum_{n = 1}^\infty \frac {(f_1 \ast g_1)(n) \cdot
                 (f_2 \ast g_2)(n)}{n^s} = f r a c{L_{f_1 f_2}(s) L_{g_1
                 g_2}(s) L_{f_1 g_2}(s)}{L_{f_1 f_2 g_1 g_2}(2s)} $$
                 \par

                 where $ L_f(s) := \sum_{n = 1}^\infty f(n) n^{-s} $ is
                 the Dirichlet series corresponding to $f$. Let $
                 r_N(n)$ be the number of solutions of $ x_1^2 + \cdots
                 + x_N^2 = n$ and $ r_{2, P}(n)^2$ be the number of
                 solutions of $ x^2 + P y^2 = n$. One of the
                 applications of Theorem 2.1 is to obtain closed forms,
                 in terms of $ \zeta (s)$ and Dirichlet $L$-functions,
                 for the generating functions of $ r_N(n)$, $ r_N^2
                 (n)$, $ r_{2, P}p(n)$ and $ r_{2, p}(n)^2$ for certain
                 $N$ and $P$. We also use these generating functions to
                 obtain asymptotic estimates of the average values for
                 each function for which we obtain a Dirichlet series.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
pages: 30--31
month: jul
monthnumber: 7
year: 2002
bibdate: Sat Aug 13 17:35:58 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 17:35:58 ???
note: Section Special Theme ERCIMathematics.
URL: https://www.ercim.eu/publication/Ercim_News/enw50/borwein.html
remark: The journal web sites has no online content before volume 86, July 2011.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://ercim-news.ercim.eu/
rawauthor: J. M. Borwein
rawnote: Section Special Theme ERCIMathematics.
rawtitle: Experimental Mathematics and Integer Relations
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2002:EMI,
  author =       "J. M. Borwein",
  title =        "Experimental Mathematics and Integer Relations",
  journal =      "European Research Consortium for Informatics and
                 Mathematics, ERCIM News",
  volume =       "50",
  number =       "??",
  pages =        "30--31",
  month =        jul,
  year =         "2002",
  bibdate =      "Sat Aug 13 17:35:58 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Section Special Theme ERCIMathematics.",
  URL =          "https://www.ercim.eu/publication/Ercim_News/enw50/borwein.html",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  journal-URL =  "http://ercim-news.ercim.eu/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "The journal web sites has no online content before
                 volume 86, July 2011.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2002:FES
author: J. M. Borwein and I. Kortezov and H. Wiersma
title: A $ C^1 $-function that is even on a sphere and has no critical points in the ball
journal: j-J-NONLINEAR-CONVEX-ANAL
volume: 3
number: 1
pages: 1--16
year: 2002
ISSN: 1345-4773 (print), 1880-5221 (electronic) OR 13454773 (print), 18805221 (electronic)
ISSNL: 1345-4773 OR 13454773
MRclass: 49J53 (26B35 47J30)
MRnumber: 1895233
MRreviewer: S. Simons
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/140/; http://www.ybook.co.jp/online2/jncav3.html
fjournal: Journal of Nonlinear and Convex Analysis. An International Journal
remark: CECM Preprint 01:164.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ybook.co.jp/jnca.html
rawauthor: J. M. Borwein and I. Kortezov and H. Wiersma
rawtitle: A {$ C^1 $}-function that is even on a sphere and has no critical points in the ball
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2002:FES,
  author =       "J. M. Borwein and I. Kortezov and H. Wiersma",
  title =        "A {$ C^1 $}-function that is even on a sphere and has
                 no critical points in the ball",
  journal =      j-J-NONLINEAR-CONVEX-ANAL,
  volume =       "3",
  number =       "1",
  pages =        "1--16",
  year =         "2002",
  ISSN =         "1345-4773 (print), 1880-5221 (electronic)",
  ISSN-L =       "1345-4773",
  MRclass =      "49J53 (26B35 47J30)",
  MRnumber =     "1895233",
  MRreviewer =   "S. Simons",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/140/;
                 http://www.ybook.co.jp/online2/jncav3.html",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Nonlinear and Convex Analysis. An
                 International Journal",
  journal-URL =  "http://www.ybook.co.jp/jnca.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 01:164.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 13824090 (print), 15729303 (electronic)
ISSNL: 1382-4090 OR 13824090
MRclass: 52A38 (42B10)
MRnumber: 1908197
MRreviewer: Carla Peri
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/56/
fjournal: The Ramanujan Journal
remark: CECM Preprint 01:159.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11139
rawauthor: David Borwein and Jonathan M. Borwein and Bernard A. {Mares, Jr.}
rawtitle: Multi-variable sinc integrals and volumes of polyhedra
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

entry:
@Article{Borwein:2002:MVS,
  author =       "David Borwein and Jonathan M. Borwein and Bernard A.
                 {Mares, Jr.}",
  title =        "Multi-variable sinc integrals and volumes of
                 polyhedra",
  journal =      j-RAMANUJAN-J,
  volume =       "6",
  number =       "2",
  pages =        "189--208",
  year =         "2002",
  CODEN =        "RAJOF9",
  DOI =          "https://doi.org/10.1023/A:1015727317007",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  MRclass =      "52A38 (42B10)",
  MRnumber =     "1908197",
  MRreviewer =   "Carla Peri",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/56/",
  abstract =     "We investigate multi-variable integrals of products of
                 sinc functions and show how they may be interpreted as
                 volumes of symmetric convex polyhedra. We then derive
                 an explicit formula for computing such sinc integrals
                 and so equivalently volumes of polyhedra.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The {Ramanujan} Journal",
  journal-URL =  "http://link.springer.com/journal/11139",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 01:159.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2002:MVS",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2002:PDA
author: J. Borwein and R. Choksi and P. Marechal
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 19
day: 7
month: jan
monthnumber: 1
year: 2002
bibdate: Wed Aug 31 07:10:33 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 07:10:33 ???
URL: http://docserver.carma.newcastle.edu.au/10/2/02_3A176-Borwein-Choksi-Marechal.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. Borwein and R. Choksi and P. Mar{\'e}chal
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Probability distributions of assets inferred from option prices via the Principle of Maximum Entropy

abstract:
This article revisits the maximum entropy algorithm in the context of recovering the probability distribution of an asset from the prices of finitely many associated European call options, via partially finite convex programming. We are able to provide an effective characterization of the constraint qualification under which the problem reduces to optimizing an explicit function in finitely many variables. We also prove that the value (or objective) function is lower semi-continuous on its domain. Reference is given to a web-site which exploits these ideas for the efficient computation of the maximum entropy solution.

rawabstract:
This article revisits the maximum entropy algorithm in the context of recovering the probability distribution of an asset from the prices of finitely many associated European call options, via partially finite convex programming. We are able to provide an effective characterization of the constraint qualification under which the problem reduces to optimizing an explicit function in finitely many variables. We also prove that the value (or objective) function is lower semi-continuous on its domain. Reference is given to a web-site which exploits these ideas for the efficient computation of the maximum entropy solution.

rawtitle:
Probability distributions of assets inferred from option prices via the {Principle of Maximum Entropy}

entry:
@TechReport{Borwein:2002:PDA,
  author =       "J. Borwein and R. Choksi and P. Mar{\'e}chal",
  title =        "Probability distributions of assets inferred from
                 option prices via the {Principle of Maximum Entropy}",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "19",
  day =          "7",
  month =        jan,
  year =         "2002",
  bibdate =      "Wed Aug 31 07:10:33 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/10/2/02_3A176-Borwein-Choksi-Marechal.pdf",
  abstract =     "This article revisits the maximum entropy algorithm in
                 the context of recovering the probability distribution
                 of an asset from the prices of finitely many associated
                 European call options, via partially finite convex
                 programming. We are able to provide an effective
                 characterization of the constraint qualification under
                 which the problem reduces to optimizing an explicit
                 function in finitely many variables. We also prove that
                 the value (or objective) function is lower
                 semi-continuous on its domain. Reference is given to a
                 web-site which exploits these ideas for the efficient
                 computation of the maximum entropy solution.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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 $-smooth bump in infinite dimensions
journal: j-ISRAEL-J-MATH
volume: 132
number: 1
pages: 239--251
month: dec
monthnumber: 12
year: 2002
CODEN: ISJMAP
DOI: https://doi.org/10.1007/BF02784514
ISSN: 0021-2172 (print), 1565-8511 (electronic) OR 00212172 (print), 15658511 (electronic)
ISSNL: 0021-2172 OR 00212172
MRclass: 58C05 (46B20 46G05)
MRnumber: 1952623
MRreviewer: Li Xin Cheng
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:36:22 MDT
URL: http://docserver.carma.newcastle.edu.au/144/; http://link.springer.com/article/10.1007/BF02784514
fjournal: Israel Journal of Mathematics
remark: CECM Preprint 01:169.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11856
rawauthor: J. M. Borwein and M. Fabian and P. D. Loewen
rawtitle: The range of the gradient of a {Lipschitz} {$ C^1 $}-smooth bump in infinite dimensions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2002:RGL,
  author =       "J. M. Borwein and M. Fabian and P. D. Loewen",
  title =        "The range of the gradient of a {Lipschitz} {$ C^1
                 $}-smooth bump in infinite dimensions",
  journal =      j-ISRAEL-J-MATH,
  volume =       "132",
  number =       "1",
  pages =        "239--251",
  month =        dec,
  year =         "2002",
  CODEN =        "ISJMAP",
  DOI =          "https://doi.org/10.1007/BF02784514",
  ISSN =         "0021-2172 (print), 1565-8511 (electronic)",
  ISSN-L =       "0021-2172",
  MRclass =      "58C05 (46B20 46G05)",
  MRnumber =     "1952623",
  MRreviewer =   "Li Xin Cheng",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/144/;
                 http://link.springer.com/article/10.1007/BF02784514",
  abstract =     "If a Banach space has a Lipschitz $ C^1$-smooth bump
                 function, then it admits other bumps of the same
                 smoothness whose gradients exactly fill the dual unit
                 ball and other reasonable figures. This strengthens a
                 result of Azagra and Deville who were able to cover the
                 dual unit ball.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Israel Journal of Mathematics",
  journal-URL =  "http://link.springer.com/journal/11856",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 01:169.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Fabian,
                 Marian/D-5427-2014",
  unique-id =    "Borwein:2002:RGL",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 0362546x (print), 18735215 (electronic)
ISSNL: 0362-546X OR 0362546X
MRclass: 49J52 (46B20)
MRnumber: 1870757
MRreviewer: Lionel Thibault
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
keywords: Baire category; Clarke subdifferentials; Extensions; Lipschitz functions; Rotund norms
remark: CECM Preprint 98:126.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.sciencedirect.com/journal/nonlinear-analysis
rawauthor: Jon Borwein and John Giles and Jon Vanderwerff
rawtitle: Rotund norms, {Clarke} subdifferentials and extensions of {Lipschitz} functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/219/; http://www.sciencedirect.com/science/article/pii/S0362546X00001875

entry:
@Article{Borwein:2002:RNC,
  author =       "Jon Borwein and John Giles and Jon Vanderwerff",
  title =        "Rotund norms, {Clarke} subdifferentials and extensions
                 of {Lipschitz} functions",
  journal =      j-NONLINEAR-ANAL,
  volume =       "48",
  number =       "2",
  pages =        "287--301",
  year =         "2002",
  CODEN =        "NOANDD",
  DOI =          "https://doi.org/10.1016/S0362-546X(00)00187-5",
  ISSN =         "0362-546x (print), 1873-5215 (electronic)",
  ISSN-L =       "0362-546X",
  MRclass =      "49J52 (46B20)",
  MRnumber =     "1870757",
  MRreviewer =   "Lionel Thibault",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/219/;
                 http://www.sciencedirect.com/science/article/pii/S0362546X00001875",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Nonlinear Analysis. Theory, Methods \& Applications.
                 An International Multidisciplinary Journal. Series A:
                 Theory and Methods",
  journal-URL =  "https://www.sciencedirect.com/journal/nonlinear-analysis",
  keywords =     "Baire category; Clarke subdifferentials; Extensions;
                 Lipschitz functions; Rotund norms",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 98:126.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 0362546x (print), 18735215 (electronic)
ISSNL: 0362-546X OR 0362546X
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
fjournal: Nonlinear Analysis, Theory, Methods and Applications
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.sciencedirect.com/journal/nonlinear-analysis
rawauthor: Jonathan M. Borwein and Qiji J. Zhu
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/199/; http://www.sciencedirect.com/science/article/pii/S0362546X01000992

rawtitle:
A survey of subdifferential calculus with applications: [Nonlinear Anal. TMA {\bf 38} (1999) 687--773]

entry:
@Article{Borwein:2002:SSC,
  author =       "Jonathan M. Borwein and Qiji J. Zhu",
  title =        "A survey of subdifferential calculus with
                 applications: [Nonlinear Anal. TMA {\bf 38} (1999)
                 687--773]",
  journal =      j-NONLINEAR-ANAL,
  volume =       "49",
  number =       "2",
  pages =        "295--296",
  year =         "2002",
  CODEN =        "NOANDD",
  DOI =          "https://doi.org/10.1016/S0362-546X(01)00099-2",
  ISSN =         "0362-546x (print), 1873-5215 (electronic)",
  ISSN-L =       "0362-546X",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/199/;
                 http://www.sciencedirect.com/science/article/pii/S0362546X01000992",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Nonlinear Analysis, Theory, Methods and Applications",
  journal-URL =  "https://www.sciencedirect.com/journal/nonlinear-analysis",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 03630129 (print), 10957138 (electronic)
ISSNL: 0363-0129 OR 03630129
MRclass: 90C25 (47H05 47N10 90C48)
MRnumber: 1982285
MRreviewer: Simeon Reich
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/127/
fjournal: SIAM Journal on Control and Optimization
remark: CECM Preprint 02:184.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://epubs.siam.org/sicon
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein and Patrick L. Combettes
rawtitle: {Bregman} monotone optimization algorithms
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Bauschke:2003:BMO,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein and Patrick
                 L. Combettes",
  title =        "{Bregman} monotone optimization algorithms",
  journal =      j-SIAM-J-CONTROL-OPTIM,
  volume =       "42",
  number =       "2",
  pages =        "596--636",
  year =         "2003",
  CODEN =        "SJCODC",
  DOI =          "https://doi.org/10.1137/S0363012902407120",
  ISSN =         "0363-0129 (print), 1095-7138 (electronic)",
  ISSN-L =       "0363-0129",
  MRclass =      "90C25 (47H05 47N10 90C48)",
  MRnumber =     "1982285",
  MRreviewer =   "Simeon Reich",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/127/",
  abstract =     "A broad class of optimization algorithms based on
                 Bregman distances in Banach spaces is unified around
                 the notion of Bregman monotonicity. A systematic
                 investigation of this notion leads to a simplified
                 analysis of numerous algorithms and to the development
                 of a new class of parallel block-iterative surrogate
                 Bregman projection schemes. Another key contribution is
                 the introduction of a class of operators that is shown
                 to be intrinsically tied to the notion of Bregman
                 monotonicity and to include the operators commonly
                 found in Bregman optimization methods. Special emphasis
                 is placed on the viability of the algorithms and the
                 importance of Legendre functions in this regard.
                 Various applications are discussed.",
  acknowledgement = ack-nhfb,
  article-number = "PII S0363012902407120",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIAM Journal on Control and Optimization",
  journal-URL =  "http://epubs.siam.org/sicon",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 02:184.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Combettes,
                 Patrick/A-2442-2011 Bauschke, Heinz/D-5582-2009",
  unique-id =    "Bauschke:2003:BMO",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Benoist:2003:CQV
author: Joel 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
monthnumber: 4
year: 2003
CODEN: PAMYAR
DOI: https://doi.org/10.1090/S0002-9939-02-06761-8
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 26B25 (49J53 90C26)
MRnumber: 1948101
MRreviewer: Laura Martein
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/145/; https://www.jstor.org/stable/1194189
fjournal: Proceedings of the American Mathematical Society
remark: CECM Preprint 01:170.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/journals/proc
rawauthor: Jo{\"e}l Benoist and Jonathan M. Borwein and Nicolae Popovici
rawtitle: A characterization of quasiconvex vector-valued functions
abstract:
The aim of this paper is to characterize in terms of scalar quasiconvexity the vector-valued functions which are $K$-quasiconvex with respect to a closed convex cone $K$ in a Banach space. Our main result extends a well-known characterization of $K$-quasiconvexity by means of extreme directions of the polar cone of $K$, obtained by Dinh The Luc in the particular case when $K$ is a polyhedral cone generated by exactly $n$ linearly independent vectors in the Euclidean space $ mathbb R^n$.

rawabstract:
The aim of this paper is to characterize in terms of scalar quasiconvexity the vector-valued functions which are $K$-quasiconvex with respect to a closed convex cone $K$ in a Banach space. Our main result extends a well-known characterization of $K$-quasiconvexity by means of extreme directions of the polar cone of $K$, obtained by Dinh The Luc in the particular case when $K$ is a polyhedral cone generated by exactly $n$ linearly independent vectors in the Euclidean space $ \mathbb {R}^n$.

ORCID:
Popovici, Nicolae/0000-0002-1842-6005; Roohi, Mehdi/0000-0002-8444-042X; Borwein, Jonathan/0000-0002-1263-0646

entry:
@Article{Benoist:2003:CQV,
  author =       "Jo{\"e}l Benoist and Jonathan M. Borwein and Nicolae
                 Popovici",
  title =        "A characterization of quasiconvex vector-valued
                 functions",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "131",
  number =       "4",
  pages =        "1109--1113",
  month =        apr,
  year =         "2003",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/S0002-9939-02-06761-8",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "26B25 (49J53 90C26)",
  MRnumber =     "1948101",
  MRreviewer =   "Laura Martein",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/145/;
                 https://www.jstor.org/stable/1194189",
  abstract =     "The aim of this paper is to characterize in terms of
                 scalar quasiconvexity the vector-valued functions which
                 are $K$-quasiconvex with respect to a closed convex
                 cone $K$ in a Banach space. Our main result extends a
                 well-known characterization of $K$-quasiconvexity by
                 means of extreme directions of the polar cone of $K$,
                 obtained by Dinh The Luc in the particular case when
                 $K$ is a polyhedral cone generated by exactly $n$
                 linearly independent vectors in the Euclidean space $
                 \mathbb {R}^n$.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  ORCID-numbers = "Popovici, Nicolae/0000-0002-1842-6005; Roohi,
                 Mehdi/0000-0002-8444-042X; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 01:170.",
  researcherid-numbers = "Popovici, Nicolae/G-6304-2010 Borwein,
                 Jonathan/A-6082-2009",
  unique-id =    "Benoist:2003:CQV",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Berggren:2003:PP
author: J. Lennart Berggren and Jonathan Borwein and Peter Borwein
title: A Pamphlet on Pi serving as a Supplement for the Third Edition of booktitle Pi: A Source Book
type: CECM Preprint
number: 2003:210
institution: inst-CECM
address: inst-CECM:adr
pages: 65
day: 17
month: jul
monthnumber: 7
year: 2003
bibdate: Tue Aug 16 10:15:54 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:15:54 ???
URL: http://docserver.carma.newcastle.edu.au/33/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. Lennart Berggren and Jonathan Borwein and Peter Borwein
rawtitle: A Pamphlet on Pi serving as a Supplement for the Third Edition of {{\booktitle{Pi: A Source Book}}}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
TOC:
List of Figures / i 1 Pi and Its Friends / 1 1.1 A Recent History of Pi / 1 1.1.1 The ENIAC Integrator and Calculator / 5 1.2 Computing Individual Digits of Pi / 7 1.3 Does Pi Have a Non-Binary BBP Formula? / 13 2 Normality of Numbers / 17 2.1 Normality: A Stubborn Question / 17 2.2 BBP Constants and Normality / 22 2.3 A Class of Provably Normal Constants / 26 3 Historia Cyclometrica / 29 3.1 1 Kings, 2 Chronicles, and Maimonides / 29 3.2 Francois Viete. Book VIII, Chapter XVIII. / 30 3.2.1 Ratio of Regular Polygons, Inscribed in a Circle, to the Circle / 30 3.2.2 Defense Against the New Cyclometry or anti-axe. / 33 3.3 Christian Huygens. Problem IV, Proposition XX. / 43 3.3.1 Determining the Magnitude of the Circle / 43 4 Demotica Cyclometrica / 47 4.1 Irving Kaplansky's ``Song of Pi'' / 47 4.2 Ludolph van Ceulen's Tombstone / 47 Bibliography / 55 Index / 59

rawTOC:
List of Figures / i \\ 1 Pi and Its Friends / 1 \\ 1.1 A Recent History of Pi / 1 \\ 1.1.1 The ENIAC Integrator and Calculator / 5 \\ 1.2 Computing Individual Digits of Pi / 7 \\ 1.3 Does Pi Have a Non-Binary BBP Formula? / 13 \\ \\ 2 Normality of Numbers / 17 \\ 2.1 Normality: A Stubborn Question / 17 \\ 2.2 BBP Constants and Normality / 22 \\ 2.3 A Class of Provably Normal Constants / 26 \\ \\ 3 Historia Cyclometrica / 29 \\ 3.1 1 Kings, 2 Chronicles, and Maimonides / 29 \\ 3.2 Fran{\c{c}}ois Vi{\`e}te. Book VIII, Chapter XVIII. / 30 \\ 3.2.1 Ratio of Regular Polygons, Inscribed in a Circle, to the Circle / 30 \\ 3.2.2 Defense Against the New Cyclometry or anti-axe. / 33 \\ 3.3 Christian Huygens. Problem IV, Proposition XX. / 43 \\ 3.3.1 Determining the Magnitude of the Circle / 43 \\ \\ 4 Demotica Cyclometrica / 47 \\ 4.1 Irving Kaplansky's ``Song of Pi'' / 47 \\ 4.2 Ludolph van Ceulen's Tombstone / 47 \\ \\ Bibliography / 55 \\ Index / 59

entry:
@TechReport{Berggren:2003:PP,
  author =       "J. Lennart Berggren and Jonathan Borwein and Peter
                 Borwein",
  title =        "A Pamphlet on Pi serving as a Supplement for the Third
                 Edition of {{\booktitle{Pi: A Source Book}}}",
  type =         "CECM Preprint",
  number =       "2003:210",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "65",
  day =          "17",
  month =        jul,
  year =         "2003",
  bibdate =      "Tue Aug 16 10:15:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/33/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  tableofcontents = "List of Figures / i \\
                 1 Pi and Its Friends / 1 \\
                 1.1 A Recent History of Pi / 1 \\
                 1.1.1 The ENIAC Integrator and Calculator / 5 \\
                 1.2 Computing Individual Digits of Pi / 7 \\
                 1.3 Does Pi Have a Non-Binary BBP Formula? / 13 \\
                 \\
                 2 Normality of Numbers / 17 \\
                 2.1 Normality: A Stubborn Question / 17 \\
                 2.2 BBP Constants and Normality / 22 \\
                 2.3 A Class of Provably Normal Constants / 26 \\
                 \\
                 3 Historia Cyclometrica / 29 \\
                 3.1 1 Kings, 2 Chronicles, and Maimonides / 29 \\
                 3.2 Fran{\c{c}}ois Vi{\`e}te. Book VIII, Chapter XVIII.
                 / 30 \\
                 3.2.1 Ratio of Regular Polygons, Inscribed in a Circle,
                 to the Circle / 30 \\
                 3.2.2 Defense Against the New Cyclometry or anti-axe. /
                 33 \\
                 3.3 Christian Huygens. Problem IV, Proposition XX. / 43
                 \\
                 3.3.1 Determining the Magnitude of the Circle / 43 \\
                 \\
                 4 Demotica Cyclometrica / 47 \\
                 4.1 Irving Kaplansky's ``Song of Pi'' / 47 \\
                 4.2 Ludolph van Ceulen's Tombstone / 47 \\
                 \\
                 Bibliography / 55 \\
                 Index / 59",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 49J53 (47J20)
MRnumber: 1974655
MRreviewer: Mari{\'a}n Fabian
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/128/
fjournal: Proceedings of the American Mathematical Society
remark: CECM Preprint 02:185.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/journals/proc
rawauthor: J. M. Borwein and A. L. Dontchev
rawtitle: On the {Bartle--Graves} theorem
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2003:BGT,
  author =       "J. M. Borwein and A. L. Dontchev",
  title =        "On the {Bartle--Graves} theorem",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "131",
  number =       "8",
  pages =        "2553--2560",
  year =         "2003",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/S0002-9939-03-07229-0",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "49J53 (47J20)",
  MRnumber =     "1974655",
  MRreviewer =   "Mari{\'a}n Fabian",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/128/",
  abstract =     "The Bartle-Graves theorem extends the Banach open
                 mapping principle to a family of linear and bounded
                 mappings, thus showing that surjectivity of each member
                 of the family is equivalent to the openness of the
                 whole family. In this paper we place this theorem in
                 the perspective of recent concepts and results, and
                 present a general Bartle-Graves theorem for set-valued
                 mappings. As applications, we obtain versions of this
                 theorem for mappings defined by systems of
                 inequalities, and for monotone variational
                 inequalities.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 02:185.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Dontchev,
                 Assen/J-6833-2017",
  unique-id =    "Borwein:2003:BGT",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 13314343 (print), 18489966 (electronic)
ISSNL: 1331-4343 OR 13314343
MRclass: 26D15
MRnumber: 1992480
MRreviewer: Feng Qi
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/148/
fjournal: Mathematical Inequalities & Applications
remark: CECM Preprint 01:174.
acknowledgement: ack-nhfb
ajournal: Math. Inequal. Appl.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://mia.ele-math.com/
rawauthor: Jonathan Borwein and Roland Girgensohn
rawtitle: A class of exponential inequalities
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2003:CEI,
  author =       "Jonathan Borwein and Roland Girgensohn",
  title =        "A class of exponential inequalities",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "6",
  number =       "3",
  pages =        "397--411",
  year =         "2003",
  DOI =          "https://doi.org/10.7153/mia-06-37",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  ISSN-L =       "1331-4343",
  MRclass =      "26D15",
  MRnumber =     "1992480",
  MRreviewer =   "Feng Qi",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/148/",
  abstract =     "We prove that for reals $ x_i $ with $ \sum x_i \geq 0
                 $, the estimate $ \sum x_i e^{x_i} \geq (C_N / N) \sum
                 x_i^2 $ holds, where $ C_N = \max \{ 2, e (1 - 1 / N)
                 \} $. We also prove analogues for the $I$-norm and for
                 Lebesgue-integrable functions.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Inequal. Appl.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 01:174.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2003:CEI",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2003:DB
author: Jonathan M. Borwein
editor: Alex C. Michalos
booktitle: The best teacher I ever had: personal reports from highly productive scholars
title: On David Borwein
crossref: Michalos:2003:BTE
chapter: 14
pages: ??--??
year: 2003
bibdate: Sat Aug 13 17:29:16 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 17:29:16 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawbooktitle: The best teacher {I} ever had: personal reports from highly productive scholars
raweditor: Alex C. Michalos
rawtitle: On {David Borwein}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2003:DB,
  author =       "Jonathan M. Borwein",
  editor =       "Alex C. Michalos",
  booktitle =    "The best teacher {I} ever had: personal reports from
                 highly productive scholars",
  title =        "On {David Borwein}",
  crossref =     "Michalos:2003:BTE",
  chapter =      "14",
  pages =        "??--??",
  year =         "2003",
  bibdate =      "Sat Aug 13 17:29:16 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 13824090 (print), 15729303 (electronic)
ISSNL: 1382-4090 OR 13824090
MRclass: 11M41 (11E25)
MRnumber: 2035795
MRreviewer: Don Redmond
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: Rankin memorial issues.
URL: http://docserver.carma.newcastle.edu.au/142/
fjournal: The Ramanujan Journal
remark: CECM Preprint 01:167.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11139
rawauthor: Jonathan Michael Borwein and Kwok-Kwong Stephen Choi
rawnote: Rankin memorial issues.
rawtitle: On {Dirichlet} series for sums of squares
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2003:DSS,
  author =       "Jonathan Michael Borwein and Kwok-Kwong Stephen Choi",
  title =        "On {Dirichlet} series for sums of squares",
  journal =      j-RAMANUJAN-J,
  volume =       "7",
  number =       "1--3",
  pages =        "95--127",
  year =         "2003",
  CODEN =        "RAJOF9",
  DOI =          "https://doi.org/10.1023/A:1026230709945",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  MRclass =      "11M41 (11E25)",
  MRnumber =     "2035795",
  MRreviewer =   "Don Redmond",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Rankin memorial issues.",
  URL =          "http://docserver.carma.newcastle.edu.au/142/",
  abstract =     "Hardy and Wright (\booktitle{An Introduction to the
                 Theory of Numbers}, 5th edn., Oxford, 1979) recorded
                 elegant closed forms for the generating functions of
                 the divisor functions $ \sigma_k(n) $ and $
                 \sigma^2_k(n) $ in the terms of Riemann Zeta function $
                 \zeta (s) $ only. In this paper, we explore other
                 arithmetical functions enjoying this remarkable
                 property. In Theorem 2.1 below, we are able to
                 generalize the above result and prove that if $ f_i $
                 and $ g_i $ are completely multiplicative, then we have
                 [large equation] where $ L_f(s) := \sum_{n = 1}^\infty
                 f(n) n^{-s} $ is the Dirichlet series corresponding to
                 $f$. Let $ r_N(n)$ be the number of solutions of $
                 x_1^2 + \ldots {} + x_N^2 = n$ and $ r_{2, P}(n)$ be
                 the number of solutions of $ x^2 + P y^2 = n$. One of
                 the applications of Theorem 2.1 is to obtain closed
                 forms, in terms of $ \zeta (s)$ and Dirichlet
                 $L$-functions, for the generating functions of $
                 r_N(n)$, $ r_N^2 (n)$, $ r_{2, P}(n)$ and $ r_{2,
                 P}(n)^2$ for certain $N$ and $P$. We also use these
                 generating functions to obtain asymptotic estimates of
                 the average values for each function for which we
                 obtain a Dirichlet series.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The {Ramanujan} Journal",
  journal-URL =  "http://link.springer.com/journal/11139",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 01:167.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2003:DSS",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2003:LFL
author: J. M. Borwein and Xianfu Wang
title: Lipschitz functions on the line with prescribed Holder subdifferentials
journal: Advanced Studies in Contemporary Mathematics (Kyungshang).
volume: 7
number: 2
pages: 93--117
year: 2003
ISSN: 1229-3067 OR 12293067
ISSNL: 1229-3067 OR 12293067
MRclass: 49J52 (26A16 26A24 26A27)
MRnumber: 2005859
MRreviewer: Mari{\'a}n Fabian
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1526/
remark: Article archive requires login access.
acknowledgement: ack-nhfb
ajournal: Adv. Stud. Contemp. Math. (Kyungshang)
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.jangjeon.or.kr/etc/Search.html?division=ASCM
rawauthor: J. M. Borwein and Xianfu Wang
rawtitle: {Lipschitz} functions on the line with prescribed {H{\"o}lder} subdifferentials
ORCID: Borwein, Jonathan/0000-0002-1263-0646
fjournal:
Advanced Studies in Contemporary Mathematics (Kyungshang). Memoirs of the Jangjeon Mathematical Society

entry:
@Article{Borwein:2003:LFL,
  author =       "J. M. Borwein and Xianfu Wang",
  title =        "{Lipschitz} functions on the line with prescribed
                 {H{\"o}lder} subdifferentials",
  journal =      "Advanced Studies in Contemporary Mathematics
                 (Kyungshang).",
  volume =       "7",
  number =       "2",
  pages =        "93--117",
  year =         "2003",
  ISSN =         "1229-3067",
  ISSN-L =       "1229-3067",
  MRclass =      "49J52 (26A16 26A24 26A27)",
  MRnumber =     "2005859",
  MRreviewer =   "Mari{\'a}n Fabian",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1526/",
  acknowledgement = ack-nhfb,
  ajournal =     "Adv. Stud. Contemp. Math. (Kyungshang)",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Advanced Studies in Contemporary Mathematics
                 (Kyungshang). Memoirs of the Jangjeon Mathematical
                 Society",
  journal-URL =  "http://www.jangjeon.or.kr/etc/Search.html?division=ASCM",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Article archive requires login access.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 09276947 (print), 1572932X (electronic)
ISSNL: 0927-6947 OR 09276947
MRclass: 49J52 (54E40 54E52)
MRnumber: 1954034
MRreviewer: John R. Giles
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:36:22 MDT
URL: http://link.springer.com/article/10.1023/A%3A1021975622768
remark: CECM Preprint 01:158.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11228
rawauthor: J. M. Borwein and J. Vanderwerff and Xianfu Wang
rawtitle: Local {Lipschitz}-constant functions and maximal subdifferentials
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2003:LLC,
  author =       "J. M. Borwein and J. Vanderwerff and Xianfu Wang",
  title =        "Local {Lipschitz}-constant functions and maximal
                 subdifferentials",
  journal =      j-SET-VALUED-ANAL,
  volume =       "11",
  number =       "1",
  pages =        "37--67",
  year =         "2003",
  CODEN =        "SVANEG",
  DOI =          "https://doi.org/10.1023/A:1021975622768",
  ISSN =         "0927-6947 (print), 1572-932X (electronic)",
  ISSN-L =       "0927-6947",
  MRclass =      "49J52 (54E40 54E52)",
  MRnumber =     "1954034",
  MRreviewer =   "John R. Giles",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://link.springer.com/article/10.1023/A%3A1021975622768",
  abstract =     "It is shown that if $ k(x) $ is an upper
                 semicontinuous and quasi lower semicontinuous function
                 on a Banach space $X$, then $ k(x) B - X*$ is the
                 Clarke subdifferential of some locally Lipschitz
                 function on $X$. Related results for approximate
                 subdifferentials are also given. Moreover, on smooth
                 Banach spaces, for every locally Lipschitz function
                 with minimal Clarke subdifferential, one can obtain a
                 maximal Clarke subdifferential map via its `local
                 Lipschitz-constant' function. Finally, some results
                 concerning the characterization and calculus of local
                 Lipschitz-constant functions are developed.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Set-Valued Analysis. An International Journal Devoted
                 to the Theory of Multifunctions and its Applications",
  journal-URL =  "http://link.springer.com/journal/11228",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 01:158.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2003:LLC",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2003:MDM
author: J. M. Borwein and T. Stanway
title: Managing Digital Mathematical Discourse
crossref: Asperti:2003:MKM
pages: 45--55
year: 2003
bibdate: Sat Aug 13 17:26:56 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 17:26:56 ???
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and T. Stanway
rawtitle: Managing Digital Mathematical Discourse
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@InProceedings{Borwein:2003:MDM,
  author =       "J. M. Borwein and T. Stanway",
  title =        "Managing Digital Mathematical Discourse",
  crossref =     "Asperti:2003:MKM",
  pages =        "45--55",
  year =         "2003",
  bibdate =      "Sat Aug 13 17:26:56 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  abstract =     "In this paper, we propose that the present state of
                 Mathematical Knowledge Management (MKM) derives from
                 two main imperatives: the desire to organize and
                 encapsulate mathematical knowledge after it is produced
                 and the desire to encapsulate the act of production.
                 While progress in digital network technology has
                 facilitated a confluence of these efforts, their
                 original separation imposes an approximate rubric on
                 MKM which may be used to help define the challenges
                 facing the field. We propose that one of the main
                 challenges lies in the question of fixed versus
                 flexible ontologies and the related question of
                 ontology resolution between applications. Finally, we
                 describe Emkara, an application which adopts a flexible
                 metadata definition in the archiving and retrieval of
                 digital mathematical exchanges, queries, and grey
                 literature.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2003:MDM",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2003:MEP
author: Jonathan M. Borwein and David H. Bailey and Roland Girgensohn
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: iv + 67
day: 28
month: aug
monthnumber: 8
year: 2003
bibdate: Mon Sep 05 06:29:13 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.05 06:29:13 ???
URL: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.187.5170&rep=rep1&type=pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David H. Bailey and Roland Girgensohn
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
title:
Mathematics by Experiment: Plausible Reasoning in the 21st Century and Experiments in Mathematics: Computational Paths to Discovery

rawtitle:
Mathematics by Experiment: Plausible Reasoning in the 21st Century and Experiments in Mathematics: Computational Paths to Discovery

entry:
@TechReport{Borwein:2003:MEP,
  author =       "Jonathan M. Borwein and David H. Bailey and Roland
                 Girgensohn",
  title =        "Mathematics by Experiment: Plausible Reasoning in the
                 21st Century and Experiments in Mathematics:
                 Computational Paths to Discovery",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "iv + 67",
  day =          "28",
  month =        aug,
  year =         "2003",
  bibdate =      "Mon Sep 05 06:29:13 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.187.5170&rep=rep1&type=pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2003:NRI
author: J. Borwein and R. Goebel
title: Notions of relative interior in Banach spaces
journal: Journal of Mathematical Sciences (New York)
volume: 115
number: 4
pages: 2542--2553
year: 2003
CODEN: JMTSEW
DOI: https://doi.org/10.1023/A:1022988116044
ISSN: 1072-3374 (print), 1573-8795 (electronic) OR 10723374 (print), 15738795 (electronic)
MRclass: 49J53 (46B20 90C48)
MRnumber: 1992991
MRreviewer: Constantin Z{\u{a}}linescu
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: Special issue on optimization and related topics, 1.
fjournal: Journal of Mathematical Sciences (New York)
remark: CECM Preprint 01:162.
acknowledgement: ack-nhfb
ajournal: J. Math. Sci. (NY)
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. Borwein and R. Goebel
rawnote: Special issue on optimization and related topics, 1.
rawtitle: Notions of relative interior in {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/138/; http://link.springer.com/article/10.1023/A%3A1022988116044

entry:
@Article{Borwein:2003:NRI,
  author =       "J. Borwein and R. Goebel",
  title =        "Notions of relative interior in {Banach} spaces",
  journal =      "Journal of Mathematical Sciences (New York)",
  volume =       "115",
  number =       "4",
  pages =        "2542--2553",
  year =         "2003",
  CODEN =        "JMTSEW",
  DOI =          "https://doi.org/10.1023/A:1022988116044",
  ISSN =         "1072-3374 (print), 1573-8795 (electronic)",
  MRclass =      "49J53 (46B20 90C48)",
  MRnumber =     "1992991",
  MRreviewer =   "Constantin Z{\u{a}}linescu",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Special issue on optimization and related topics, 1.",
  URL =          "http://docserver.carma.newcastle.edu.au/138/;
                 http://link.springer.com/article/10.1023/A%3A1022988116044",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Math. Sci. (NY)",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Mathematical Sciences (New York)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 01:162.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2003:PDA
author: J. Borwein and R. Choksi and P. Marechal
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) OR 10526234 (print), 10957189 (electronic)
ISSNL: 1052-6234 OR 10526234
MRclass: 90C25 (91B28)
MRnumber: 2048161
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/10/
fjournal: SIAM Journal on Optimization
remark: CECM Preprint 02:176.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://epubs.siam.org/siopt
rawauthor: J. Borwein and R. Choksi and P. Mar{\'e}chal
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Probability distributions of assets inferred from option prices via the principle of maximum entropy

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).

rawabstract:
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).

rawtitle:
Probability distributions of assets inferred from option prices via the principle of maximum entropy

entry:
@Article{Borwein:2003:PDA,
  author =       "J. Borwein and R. Choksi and P. Mar{\'e}chal",
  title =        "Probability distributions of assets inferred from
                 option prices via the principle of maximum entropy",
  journal =      j-SIAM-J-OPT,
  volume =       "14",
  number =       "2",
  pages =        "464--478",
  year =         "2003",
  CODEN =        "SJOPE8",
  DOI =          "https://doi.org/10.1137/S1052623401400324",
  ISSN =         "1052-6234 (print), 1095-7189 (electronic)",
  ISSN-L =       "1052-6234",
  MRclass =      "90C25 (91B28)",
  MRnumber =     "2048161",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/10/",
  abstract =     "This article revisits the maximum entropy algorithm in
                 the context of recovering the probability distribution
                 of an asset from the prices of finitely many associated
                 European call options via partially finite
                 convex-programming. We are able to provide an effective
                 characterization of the constraint qualification under
                 which the problem reduces to optimizing an explicit
                 function in finitely many variables. We also prove that
                 the value (or objective) function is lower
                 semicontinuous on its domain. Reference is given to a
                 website which exploits these ideas for the efficient
                 computation of the maximum entropy solution (MES).",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIAM Journal on Optimization",
  journal-URL =  "http://epubs.siam.org/siopt",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 02:176.",
  researcherid-numbers = "Choksi, Rustum/A-9985-2009 Borwein,
                 Jonathan/A-6082-2009",
  unique-id =    "Borwein:2003:PDA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 12
year: 2003
CODEN: CMBUA3
DOI: https://doi.org/10.4153/CMB-2003-051-5
ISSN: 0008-4395 (print), 1496-4287 (electronic) OR 00084395 (print), 14964287 (electronic)
ISSNL: 0008-4395 OR 00084395
MRclass: 49J52 (46N10 47H05 90C48)
MRnumber: 2011392
MRreviewer: John R. Giles
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://cms.math.ca/10.4153/CMB-2003-051-5; http://docserver.carma.newcastle.edu.au/149/
fjournal: Canadian Mathematical Bulletin. Bulletin Canadien de Mathematiques
remark: CECM Preprint 01:175.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://cms.math.ca/cmb/
rawauthor: Jonathan Borwein and Simon Fitzpatrick and Roland Girgensohn
rawtitle: Subdifferentials whose graphs are not norm $ \times $ weak$^*$ closed
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
http://cms.math.ca/cmb/v46/; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib

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.

rawabstract:
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.

entry:
@Article{Borwein:2003:SWG,
  author =       "Jonathan Borwein and Simon Fitzpatrick and Roland
                 Girgensohn",
  title =        "Subdifferentials whose graphs are not norm $ \times $
                 weak$^*$ closed",
  journal =      j-CAN-MATH-BULL,
  volume =       "46",
  number =       "4",
  pages =        "538--545",
  month =        dec,
  year =         "2003",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-2003-051-5",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  MRclass =      "49J52 (46N10 47H05 90C48)",
  MRnumber =     "2011392",
  MRreviewer =   "John R. Giles",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://cms.math.ca/cmb/v46/;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/canmathbull.bib",
  URL =          "http://cms.math.ca/10.4153/CMB-2003-051-5;
                 http://docserver.carma.newcastle.edu.au/149/",
  abstract =     "In this note we give examples of convex functions
                 whose subdifferentials have unpleasant properties.
                 Particularly, we exhibit a proper lower semicontinuous
                 convex function on a separable Hilbert space such that
                 the graph of its subdifferential is not dosed in the
                 product of the norm and bounded weak topologies. We
                 also exhibit a set whose sequential normal cone is not
                 norm dosed.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Canadian Mathematical Bulletin. Bulletin Canadien de
                 Math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cmb/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 01:175.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2003:SWG",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Kellar:2003:DCM
title: Dynamic Composition of Math Lessons
journal: Journal of Educational Technology & Society
volume: 6
number: 4
pages: 100--111
year: 2003
ISSN: 1176-3647 (print), 1436-4522 (electronic) OR 11763647 (print), 14364522 (electronic)
ISSNL: 1176-3647 OR 11763647
bibdate: Tue Feb 06 09:20:39 2018
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2018.02.06 09:20:39 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.jstor.org/journal/jeductechsoci
rawtitle: Dynamic Composition of Math Lessons
ORCID: Borwein, Jonathan/0000-0002-1263-0646
author:
Melanie Kellar and Bonnie MacKay and Rui Zhang and Carolyn Watters and David Kaufman and Jonathan Borwein

URL:
http://docserver.carma.newcastle.edu.au/1525/; http://ifets.ieee.org/periodical/6_4/10.pdf; https://www.jstor.org/stable/jeductechsoci.6.4.100

rawauthor:
Melanie Kellar and Bonnie MacKay and Rui Zhang and Carolyn Watters and David Kaufman and Jonathan Borwein

entry:
@Article{Kellar:2003:DCM,
  author =       "Melanie Kellar and Bonnie MacKay and Rui Zhang and
                 Carolyn Watters and David Kaufman and Jonathan
                 Borwein",
  title =        "Dynamic Composition of Math Lessons",
  journal =      "Journal of Educational Technology \& Society",
  volume =       "6",
  number =       "4",
  pages =        "100--111",
  month =        "????",
  year =         "2003",
  ISSN =         "1176-3647 (print), 1436-4522 (electronic)",
  ISSN-L =       "1176-3647",
  bibdate =      "Tue Feb 06 09:20:39 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1525/;
                 http://ifets.ieee.org/periodical/6_4/10.pdf;
                 https://www.jstor.org/stable/jeductechsoci.6.4.100",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  journal-URL =  "https://www.jstor.org/journal/jeductechsoci",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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 Theorie des Nombres de Bordeaux
volume: 16
number: 3
pages: 487--518
year: 2004
ISSN: 1246-7405 (print), 2118-8572 (electronic) OR 12467405 (print), 21188572 (electronic)
ISSNL: 1246-7405 OR 12467405
MRclass: 11K16 (11J25 11J91)
MRnumber: 2144954
MRreviewer: John H. Loxton
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/36/; http://jtnb.cedram.org/item?id=JTNB_2004__16_3_487_0
fjournal: Journal de Theorie des Nombres de Bordeaux
remark: CECM Preprint 2003:204.
acknowledgement: ack-nhfb
ajournal: J. Theor. Nombres Bordeaux
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein and Richard E. Crandall and Carl Pomerance
rawtitle: On the binary expansions of algebraic numbers
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bailey:2004:BEA,
  author =       "David H. Bailey and Jonathan M. Borwein and Richard E.
                 Crandall and Carl Pomerance",
  title =        "On the binary expansions of algebraic numbers",
  journal =      "Journal de Th{\'e}orie des Nombres de {Bordeaux}",
  volume =       "16",
  number =       "3",
  pages =        "487--518",
  year =         "2004",
  ISSN =         "1246-7405 (print), 2118-8572 (electronic)",
  ISSN-L =       "1246-7405",
  MRclass =      "11K16 (11J25 11J91)",
  MRnumber =     "2144954",
  MRreviewer =   "John H. Loxton",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/36/;
                 http://jtnb.cedram.org/item?id=JTNB_2004__16_3_487_0",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Th{\'e}or. Nombres Bordeaux",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal de Th{\'e}orie des Nombres de Bordeaux",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 2003:204.",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2004:AGMa
author: J. M. Borwein and P. B. Borwein
title: The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions
crossref: Berggren:2004:PSB
pages: 537--552
year: 2004
DOI: https://doi.org/10.1007/978-1-4757-4217-6_56
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibtimestamp: 2016.08.11 09:36:22 MDT
note: Reprint of cite Borwein:1984:AGM.
URL: http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_56
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein
rawnote: Reprint of \cite{Borwein:1984:AGM}.
rawtitle: The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InCollection{Borwein:2004:AGMa,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:2004:PSB",
  pages =        "537--552",
  year =         "2004",
  DOI =          "https://doi.org/10.1007/978-1-4757-4217-6_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Borwein:1984:AGM}.",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_56",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 3
year: 2004
CODEN: SVANEG
DOI: https://doi.org/10.1023/B:SVAN.0000023393.75251.05
ISSN: 0927-6947 (print), 1572-932x (electronic) OR 09276947 (print), 1572932x (electronic)
ISSNL: 0927-6947 OR 09276947
MRclass: 49J53 (46B20 46N10 90C25 90C48)
MRnumber: 2069352
MRreviewer: Diethard Pallaschke
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/38/
remark: CECM Preprint 2003:202.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11228
rawauthor: Jonathan M. Borwein and Jon D. Vanderwerff
rawtitle: Constructible convex sets
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2004:CCS,
  author =       "Jonathan M. Borwein and Jon D. Vanderwerff",
  title =        "Constructible convex sets",
  journal =      j-SET-VALUED-ANAL,
  volume =       "12",
  number =       "1--2",
  pages =        "61--77",
  month =        mar # "\slash " # jun,
  year =         "2004",
  CODEN =        "SVANEG",
  DOI =          "https://doi.org/10.1023/B:SVAN.0000023393.75251.05",
  ISSN =         "0927-6947 (print), 1572-932x (electronic)",
  ISSN-L =       "0927-6947",
  MRclass =      "49J53 (46B20 46N10 90C25 90C48)",
  MRnumber =     "2069352",
  MRreviewer =   "Diethard Pallaschke",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/38/",
  abstract =     "We investigate when closed convex sets can be written
                 as countable intersections of closed half-spaces in
                 Banach spaces. It is reasonable to consider this class
                 to comprise the constructible convex sets since such
                 sets are precisely those that can be defined by a
                 countable number of linear inequalities, hence are
                 accessible to techniques of semi-infinite convex
                 programming. We also explore some model theoretic
                 implications. Applications to set convergence are given
                 as limiting examples.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Set-Valued Analysis. An International Journal Devoted
                 to the Theory of Multifunctions and its Applications",
  journal-URL =  "http://link.springer.com/journal/11228",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 2003:202.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2004:CCS",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 13101331 (print), 23675535 (electronic)
ISSNL: 1310-1331 OR 13101331
MRclass: 49J53 (54C60)
MRnumber: 2117234
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/273/
remark: CoLab Preprint 273. The journal web site only has an abstract for this paper.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.proceedings.bas.bg/
rawauthor: J. Borwein and I. Kortezov
rawtitle: Constructive minimal uscos
ORCID: Borwein, Jonathan/0000-0002-1263-0646
fjournal:
Dokladi na Bcdprime lgarskata Akademiya na Naukite. Comptes Rendus de l'Academie Bulgare des Sciences

entry:
@Article{Borwein:2004:CMU,
  author =       "J. Borwein and I. Kortezov",
  title =        "Constructive minimal uscos",
  journal =      j-C-R-ACAD-BULGARE-SCI,
  volume =       "57",
  number =       "12",
  pages =        "9--12",
  year =         "2004",
  CODEN =        "DBANAD",
  ISSN =         "1310-1331 (print), 2367-5535 (electronic)",
  ISSN-L =       "1310-1331",
  MRclass =      "49J53 (54C60)",
  MRnumber =     "2117234",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/273/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Dokladi na B\cdprime lgarskata Akademiya na Naukite.
                 Comptes Rendus de l'Acad{\'e}mie Bulgare des Sciences",
  journal-URL =  "http://www.proceedings.bas.bg/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CoLab Preprint 273. The journal web site only has an
                 abstract for this paper.",
  xxtitle =      "Constructive minimal cuscos",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 4
year: 2004
CODEN: PAMYAR
DOI: https://doi.org/10.1090/S0002-9939-03-07149-1
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 49J50 (46G05 46N10)
MRnumber: 2045422
MRreviewer: Jes{\'u}s A. Jaramillo
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Proceedings of the American Mathematical Society
remark: CECM Preprint 02:183.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/journals/proc
rawauthor: Jonathan M. Borwein and James V. Burke and Adrian S. Lewis
rawtitle: Differentiability of cone-monotone functions on separable {Banach} space
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/123/1/; http://docserver.carma.newcastle.edu.au/1242/; https://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.

rawabstract:
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.

entry:
@Article{Borwein:2004:DCM,
  author =       "Jonathan M. Borwein and James V. Burke and Adrian S.
                 Lewis",
  title =        "Differentiability of cone-monotone functions on
                 separable {Banach} space",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "132",
  number =       "4",
  pages =        "1067--1076",
  month =        apr,
  year =         "2004",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/S0002-9939-03-07149-1",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "49J50 (46G05 46N10)",
  MRnumber =     "2045422",
  MRreviewer =   "Jes{\'u}s A. Jaramillo",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/123/1/;
                 http://docserver.carma.newcastle.edu.au/1242/;
                 https://www.jstor.org/stable/4097135",
  abstract =     "Motivated by applications to (directionally) Lipschitz
                 functions, we provide a general result on the almost
                 everywhere Gateaux differentiability of real-valued
                 functions on separable Banach spaces, when the function
                 is monotone with respect to an ordering induced by a
                 convex cone with nonempty interior. This seemingly
                 arduous restriction is useful, since it covers the case
                 of directionally Lipschitz functions, and necessary. We
                 show by way of example that most results fail more
                 generally.",
  acknowledgement = ack-nhfb,
  article-number = "PII S0002-9939(03)07149-1",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 02:183.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2004:DCM",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2004:DSS
author: Jonathan Michael Borwein and Kwok-Kwong Stephen Choi
title: Dirichlet series for squares of sums of squares: a summary
crossref: Kisilevsky:2004:NTP
volume: 36
pages: 27--34
year: 2004
MRclass: 11M41 (11E25)
MRnumber: 2076564
MRreviewer: Don Redmond
bibdate: Sat Aug 13 17:30:35 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 17:30:35 ???
series: CRM Proc. Lecture Notes
ZMnumber: 1078.11055
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Michael Borwein and Kwok-Kwong Stephen Choi
rawtitle: {Dirichlet} series for squares of sums of squares: a summary
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InProceedings{Borwein:2004:DSS,
  author =       "Jonathan Michael Borwein and Kwok-Kwong Stephen Choi",
  title =        "{Dirichlet} series for squares of sums of squares: a
                 summary",
  crossref =     "Kisilevsky:2004:NTP",
  volume =       "36",
  pages =        "27--34",
  year =         "2004",
  MRclass =      "11M41 (11E25)",
  MRnumber =     "2076564",
  MRreviewer =   "Don Redmond",
  bibdate =      "Sat Aug 13 17:30:35 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "CRM Proc. Lecture Notes",
  ZMnumber =     "1078.11055",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: 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 OR 1568811365
ISBN13: 978-1-56881-136-9 OR 9781568811369
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
bibtimestamp: 2016.08.10 11:09:47 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David H. Bailey and Roland Girgensohn
rawtitle: Experimentation in mathematics: computational paths to discovery
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

shortTOC:
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

rawshortTOC:
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

entry:
@Book{Borwein:2004:EMCa,
  author =       "Jonathan M. Borwein and David H. Bailey and Roland
                 Girgensohn",
  title =        "Experimentation in mathematics: computational paths to
                 discovery",
  publisher =    pub-A-K-PETERS,
  address =      pub-A-K-PETERS:adr,
  pages =        "x + 357",
  year =         "2004",
  ISBN =         "1-56881-136-5",
  ISBN-13 =      "978-1-56881-136-9",
  LCCN =         "QA12 .B67 2004",
  MRclass =      "11-01 (11Yxx 40-01 42A16 42A38 68W30)",
  MRnumber =     "2051473",
  MRreviewer =   "F. Beukers",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  shorttableofcontents = "Sequences, series, products and integrals / 1
                 \\
                 Fourier series and integrals / 69 \\
                 Zeta functions and multizeta functions / 131 \\
                 Partitions and powers / 183 \\
                 Primes and polynomials / 225 \\
                 The power of constructive proofs II / 263 \\
                 Numerical techniques II / 299",
  tableofcontents = "",
  xxyear =       "2003",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
year: 2004
CODEN: CJMAAB
DOI: https://doi.org/10.4153/CJM-2004-041-2
ISSN: 0008-414X (print), 1496-4279 (electronic) OR 0008414X (print), 14964279 (electronic)
ISSNL: 0008-414X OR 0008414X
MRclass: 11Y60 (11A67 11G55 33B30)
MRnumber: 2085627
MRreviewer: Greg Martin
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/47/
fjournal: Canadian Journal of Mathematics = Journal canadien de mathematiques
remark: CECM Preprint 2003:195.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://cms.math.ca/cjm/
rawauthor: Jonathan M. Borwein and David Borwein and William F. Galway
rawtitle: Finding and excluding $b$-ary {Machin}-type individual digit formulae
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/canjmath.bib

note:
This paper established the result that there are no degree-1 BBP-type formulas for $ pi $, except when the base is 2 (or an integer power thereof).

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.

rawabstract:
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.

rawnote:
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).

entry:
@Article{Borwein:2004:FEA,
  author =       "Jonathan M. Borwein and David Borwein and William F.
                 Galway",
  title =        "Finding and excluding $b$-ary {Machin}-type individual
                 digit formulae",
  journal =      j-CAN-J-MATH,
  volume =       "56",
  number =       "5",
  pages =        "897--925",
  month =        "????",
  year =         "2004",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-2004-041-2",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  MRclass =      "11Y60 (11A67 11G55 33B30)",
  MRnumber =     "2085627",
  MRreviewer =   "Greg Martin",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/canjmath.bib",
  note =         "This paper established the result that there are no
                 degree-1 BBP-type formulas for $ \pi $, except when the
                 base is 2 (or an integer power thereof).",
  URL =          "http://docserver.carma.newcastle.edu.au/47/",
  abstract =     "Constants with formulae of the form treated by D.
                 Bailey, P. Borwein, and S. Plouffe (BBP formulae to a
                 given base $b$) have interesting computational
                 properties, such as allowing single digits in their
                 base $b$ expansion to be independently computed, and
                 there are hints that they should be normal numbers,
                 i.e., that their base $b$ digits are randomly
                 distributed. We study a formally limited subset of BBP
                 formulae, which we call Machin-type BBP formulae, for
                 which it is relatively easy to determine whether or not
                 a given constant kappa has a Machin-type BBP formula.
                 In particular, given $b$ is an element of $N$, $ b >
                 2$, $b$ not a proper power, a $b$-ary Machin-type BBP
                 arctangent formula for $ \kappa $ is a formula of the
                 form $ \kappa = \sum_m a_m \arctan ( - b^{-m})$, $ a_m$
                 is an element of $Q$, while when $ b = 2$, we also
                 allow terms of the form $ a_m \arctan (1 / (1 - 2^m))$.
                 Of particular interest, we show that $ \pi $ has no
                 Machin-type BBP arctangent formula when $ b \neq 2$. To
                 the best of our knowledge, when there is no Machin-type
                 BBP formula for a constant then no BBP formula of any
                 form is known for that constant.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Canadian Journal of Mathematics = Journal canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 2003:195.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2004:FEB",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: 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 OR 1568812116
ISBN13: 978-1-56881-211-3 OR 9781568812113
LCCN: QA76.95 .B67 2003
MRclass: 00A35
MRnumber: 2033012
MRreviewer: John H. Mason
bibdate: Fri Oct 17 10:38:25 2003
bibtimestamp: 2003.10.17 10:38:25 ???
URL: http://docserver.carma.newcastle.edu.au/272/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David H. Bailey
rawtitle: Mathematics by Experiment: Plausible Reasoning in the {21st Century}
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

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.

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

TOC:
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

rawabstract:
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.

rawTOC:
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

entry:
@Book{Borwein:2004:MEP,
  author =       "Jonathan M. Borwein and David H. Bailey",
  title =        "Mathematics by Experiment: Plausible Reasoning in the
                 {21st Century}",
  publisher =    pub-A-K-PETERS,
  address =      pub-A-K-PETERS:adr,
  pages =        "x + 288",
  year =         "2004",
  ISBN =         "1-56881-211-6",
  ISBN-13 =      "978-1-56881-211-3",
  LCCN =         "QA76.95 .B67 2003",
  MRclass =      "00A35",
  MRnumber =     "2033012",
  MRreviewer =   "John H. Mason",
  bibdate =      "Fri Oct 17 10:38:25 2003",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$45.00",
  URL =          "http://docserver.carma.newcastle.edu.au/272/",
  abstract =     "Using examples that truly represent the experimental
                 methodology, this book provides the historical context
                 of, and rationale behind, experimental mathematics. It
                 shows how today, the use of advanced computing
                 technology provides, mathematicians with an amazing,
                 previously unimaginable ``laboratory,'' in which
                 examples can be analyzed, new ideas tested, and
                 patterns discovered. This is a perfect introduction to
                 the history and current state of research and
                 technology in the growing field of experimental
                 mathematics.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "Due to an unfortunate error, some of the citations in
                 the book point to the wrong item in the Bibliography.
                 Here is how to find the correct citation number:
                 [1]--[85]: Citation number is correct; [86, page 100]:
                 [86]; [86, page 2]: [87]; [87]--[156]: Add one to
                 citation number; [157]: [159]; [158, page 139]: [158];
                 [158, page 97]: [160]; [159]--[196]: Add two to
                 citation number",
  tableofcontents = "What is Experimental Mathematics? \\
                 Experimental Mathematics in Action \\
                 Pi and Its Friends \\
                 Normality of Numbers \\
                 The Power of Constructive Proofs I \\
                 Numerical Techniques I \\
                 Making Sense of Experimental Math",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2004:OPV
author: Jonathan Borwein and Lixin Cheng and Marian 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) OR 09276947 (print), 1572932x (electronic)
ISSNL: 0927-6947 OR 09276947
MRclass: 49J53 (46B20 46G05 49J40 49J50)
MRnumber: 2069351
MRreviewer: John R. Giles
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/14/
remark: CECM Preprint 2003:205.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11228
rawauthor: Jonathan Borwein and Lixin Cheng and Mari{\'a}n Fabian and Julian P. Revalski
rawtitle: A one perturbation variational principle and applications
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2004:OPV,
  author =       "Jonathan Borwein and Lixin Cheng and Mari{\'a}n Fabian
                 and Julian P. Revalski",
  title =        "A one perturbation variational principle and
                 applications",
  journal =      j-SET-VALUED-ANAL,
  volume =       "12",
  number =       "1--2",
  pages =        "49--60",
  year =         "2004",
  CODEN =        "SVANEG",
  DOI =          "https://doi.org/10.1023/B:SVAN.0000023400.92518.cb",
  ISSN =         "0927-6947 (print), 1572-932x (electronic)",
  ISSN-L =       "0927-6947",
  MRclass =      "49J53 (46B20 46G05 49J40 49J50)",
  MRnumber =     "2069351",
  MRreviewer =   "John R. Giles",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/14/",
  abstract =     "We study a variational principle in which there is one
                 common perturbation function $ \phi $ for every proper
                 lower semicontinuous extended real-valued function $f$
                 defined on a metric space $X$. Necessary and sufficient
                 conditions are given in order for the perturbed
                 function $ f + \phi $ to attain its minimum. In the
                 case of a separable Banach space we obtain a specific
                 principle in which the common perturbation function is,
                 in addition, also convex and Hadamard-like
                 differentiable. This allows us to provide applications
                 of the principle to differentiability of convex
                 functions on separable and more general Banach
                 spaces.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Set-Valued Analysis. An International Journal Devoted
                 to the Theory of Multifunctions and its Applications",
  journal-URL =  "http://link.springer.com/journal/11228",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 2003:205.",
  researcherid-numbers = "Fabian, Marian/D-5427-2014 Borwein,
                 Jonathan/A-6082-2009 Cheng, LX/G-3342-2010",
  unique-id =    "Borwein:2004:OPV",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2004:PEN
author: J. M. Borwein and P. B. Borwein and K. Dilcher
title: Pi, Euler Numbers, and Asymptotic Expansions
crossref: Berggren:2004:PSB
pages: 642--648
year: 2004
DOI: https://doi.org/10.1007/978-1-4757-4217-6_65
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:36:22 MDT
note: Reprint of cite Borwein:1989:PEN.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein and K. Dilcher
rawnote: Reprint of \cite{Borwein:1989:PEN}.
rawtitle: Pi, {Euler} Numbers, and Asymptotic Expansions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1583/; http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_65

entry:
@InCollection{Borwein:2004:PEN,
  author =       "J. M. Borwein and P. B. Borwein and K. Dilcher",
  title =        "Pi, {Euler} Numbers, and Asymptotic Expansions",
  crossref =     "Berggren:2004:PSB",
  pages =        "642--648",
  year =         "2004",
  DOI =          "https://doi.org/10.1007/978-1-4757-4217-6_65",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Reprint of \cite{Borwein:1989:PEN}.",
  URL =          "http://docserver.carma.newcastle.edu.au/1583/;
                 http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_65",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
DOI: https://doi.org/10.1080/10586458.2004.10504540
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 11J70 (11A55 33C05 40A15)
MRnumber: 2103326
MRreviewer: James G. Mc Laughlin
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/27/; http://projecteuclid.org/euclid.em/1103749836
fjournal: Experimental Mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.tandfonline.com/loi/uexm20
rawauthor: J. Borwein and R. Crandall and G. Fee
rawtitle: On the {Ramanujan} {AGM} Fraction, {I}: The Real-Parameter Case
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2004:RAFa,
  author =       "J. Borwein and R. Crandall and G. Fee",
  title =        "On the {Ramanujan} {AGM} Fraction, {I}: The
                 Real-Parameter Case",
  journal =      j-EXP-MATH,
  volume =       "13",
  number =       "3",
  pages =        "275--285",
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2004.10504540",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11J70 (11A55 33C05 40A15)",
  MRnumber =     "2103326",
  MRreviewer =   "James G. Mc Laughlin",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/27/;
                 http://projecteuclid.org/euclid.em/1103749836",
  abstract =     "The Ramanujan AGM continued fraction is a construct
                 [GRAPHIC] enjoying attractive algebraic properties,
                 such as a striking arithmetic-geometric mean (AGM)
                 relation and elegant connections with elliptic-function
                 theory. But the fraction also presents an intriguing
                 computational challenge. Herein we show how to rapidly
                 evaluate $R$ for any triple of positive reals $a$, $b$,
                 $ \eta $. Even in the problematic scenario when a
                 approximate to $b$ certain transformations allow rapid
                 evaluation. In this process we find, for example, that
                 when $ a_\eta = b_\eta = $ a rational number, $ R_\eta
                 $, is essentially an $L$-series that can be cast as a
                 finite sum of fundamental numbers. We ultimately
                 exhibit an algorithm that yields $D$ good digits of $R$
                 in $ O(D)$ iterations where the implied big-$O$
                 constant is independent of the positive-real triple
                 $a$, $b$, $ \eta $. Finally, we address the evidently
                 profound theoretical and computational dilemmas
                 attendant on complex parameters, indicating how one
                 might extend the AGM relation for complex parameter
                 domains.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2004:RAFa",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
DOI: https://doi.org/10.1080/10586458.2004.10504541
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 11J70 (11A55 33C05)
MRnumber: 2103327
MRreviewer: James G. Mc Laughlin
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/29/; http://projecteuclid.org/euclid.em/1103749837
fjournal: Experimental Mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.tandfonline.com/loi/uexm20
rawauthor: J. Borwein and R. Crandall
rawtitle: On the {Ramanujan} {AGM} Fraction, {II}: The Complex-Parameter Case
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2004:RAFb,
  author =       "J. Borwein and R. Crandall",
  title =        "On the {Ramanujan} {AGM} Fraction, {II}: The
                 Complex-Parameter Case",
  journal =      j-EXP-MATH,
  volume =       "13",
  number =       "3",
  pages =        "287--295",
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2004.10504541",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11J70 (11A55 33C05)",
  MRnumber =     "2103327",
  MRreviewer =   "James G. Mc Laughlin",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/29/;
                 http://projecteuclid.org/euclid.em/1103749837",
  abstract =     "The Ramanujan continued fraction is interesting in
                 many ways; e.g., for certain complex parameters $
                 (\eta, a, b) $ one has an attractive AGM relation $
                 R_{\eta }(a.b) + R_\eta (b, a) = 2 R_\eta ((a + b) / 2,
                 \sqrt {a b}) $. Alas, for some parameters the continued
                 fraction $ R_\eta $, does not converge; moreover, there
                 are converging instances where the AGM relation itself
                 does not hold. To unravel these dilemmas we herein
                 establish convergence theorems, the central result
                 being that $ R_1 $ converges whenever $ |a| \neq |b| $.
                 Such analysis leads naturally to the conjecture that
                 divergence occurs whenever $ a = b e^{i \phi } $ with $
                 c o s^2 \phi \neq 1 $ (which conjecture has been proven
                 in a separate work) [Borwein et al. 04b.] We further
                 conjecture that for $ a / b $ lying in a certain ---
                 and rather picturesque --- complex domain, we have both
                 convergence and the truth of the AGM relation.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2004:RAFb",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2004:RME
author: J. M. Borwein and P. B. Borwein and D. H. Bailey
title: Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
crossref: Berggren:2004:PSB
pages: 623--641
year: 2004
DOI: https://doi.org/10.1007/978-1-4757-4217-6_64
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:36:22 MDT
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein and D. H. Bailey
rawtitle: {Ramanujan}, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1587/; http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_64

entry:
@InCollection{Borwein:2004:RME,
  author =       "J. M. Borwein and P. B. Borwein and D. H. Bailey",
  title =        "{Ramanujan}, Modular Equations, and Approximations to
                 Pi or How to Compute One Billion Digits of Pi",
  crossref =     "Berggren:2004:PSB",
  pages =        "623--641",
  year =         "2004",
  DOI =          "https://doi.org/10.1007/978-1-4757-4217-6_64",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1587/;
                 http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_64",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2005:EDA
author: David H. Bailey and Jonathan M. Borwein and David M. Bradley
title: Experimental determination of Apery-like identities for $ zeta (2 n + 2) $
journal: ArXiv Mathematics e-prints
pages: 623--641
month: may
monthnumber: 5
year: 2005
bibdate: Thu Aug 11 07:19:54 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 07:19:54 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein and David M. Bradley
rawtitle: Experimental determination of {Ap{\'e}ry}-like identities for $ \zeta (2 n + 2) $
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://adsabs.harvard.edu/abs/2005math......5270B; http://docserver.carma.newcastle.edu.au/163/; http://docserver.carma.newcastle.edu.au/295/

abstract:
We document the discovery of two generating functions for the Riemann zeta values $ zeta (2 n + 2) $, analogous to earlier work for $ zeta (2 n + 1) $ and $ zeta (4 n + 3) $. This continues work initiated by Koecher and pursued further by Borwein, Bradley and others.

keywords:
Mathematics - Number Theory, Mathematics - Classical Analysis and ODEs, 11M06 (Primary), 33C20 (Secondary)

rawabstract:
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.

entry:
@Article{Bailey:2005:EDA,
  author =       "David H. Bailey and Jonathan M. Borwein and David M.
                 Bradley",
  title =        "Experimental determination of {Ap{\'e}ry}-like
                 identities for $ \zeta (2 n + 2) $",
  journal =      "ArXiv Mathematics e-prints",
  month =        may,
  year =         "2005",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2005math......5270B;
                 http://docserver.carma.newcastle.edu.au/163/;
                 http://docserver.carma.newcastle.edu.au/295/",
  abstract =     "We document the discovery of two generating functions
                 for the Riemann zeta values $ \zeta (2 n + 2) $,
                 analogous to earlier work for $ \zeta (2 n + 1) $ and $
                 \zeta (4 n + 3) $. This continues work initiated by
                 Koecher and pursued further by Borwein, Bradley and
                 others.",
  abstract-2 =   "Some rapidly convergent formulae for special values of
                 the Riemann Zeta function are given. We obtain a
                 generating function formula for $ \zeta (4 n + 3) $
                 which generalizes Ap{\'e}ry's series for $ \zeta (3) $,
                 and appears to give the best possible series relations
                 of this type, at least for $ n < 12 $. The formula
                 reduces to a finite but apparently non-trivial
                 combinatorial identity. The identity is equivalent to
                 an interesting new integral evaluation for the central
                 binomial coefficient. We outline a new technique for
                 transforming and summing certain infinite series. We
                 also derive a beautiful formula which provides strange
                 evaluations of a large new class of non-terminating
                 hypergeometric series. It should be emphasized that our
                 main results are shown equivalent but are still only
                 conjectures.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "math/0505270",
  keywords =     "Mathematics - Number Theory, Mathematics - Classical
                 Analysis and ODEs, 11M06 (Primary), 33C20 (Secondary)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2005:EME
author: David H. Bailey and Jonathan M. Borwein
title: Experimental mathematics: examples, methods and implications
journal: j-NAMS
volume: 52
number: 5
pages: 502--514
month: may
monthnumber: 5
year: 2005
CODEN: AMNOAN
ISSN: 0002-9920 (print), 1088-9477 (electronic) OR 00029920 (print), 10889477 (electronic)
ISSNL: 0002-9920 OR 00029920
MRclass: 00A35
MRnumber: 2140093
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1241/; http://www.ams.org/notices/200505/fea-borwein.pdf
fjournal: Notices of the American Mathematical Society
remark: CoLab Preprint 269.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/notices/
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Experimental mathematics: examples, methods and implications
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bailey:2005:EME,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Experimental mathematics: examples, methods and
                 implications",
  journal =      j-NAMS,
  volume =       "52",
  number =       "5",
  pages =        "502--514",
  month =        may,
  year =         "2005",
  CODEN =        "AMNOAN",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  MRclass =      "00A35",
  MRnumber =     "2140093",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1241/;
                 http://www.ams.org/notices/200505/fea-borwein.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "CoLab Preprint 269.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 12
year: 2005
ISSN: 1193-9273 (print), 1496-4295 (electronic) OR 11939273 (print), 14964295 (electronic)
ISSNL: 1193-9273 OR 11939273
bibdate: Sat Aug 13 17:21:21 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 17:21:21 ???
URL: http://docserver.carma.newcastle.edu.au/304/; https://cms.math.ca/notes/v37/n8/Notesv37n8.pdf
fjournal: Canadian Mathematical Society Notes
acknowledgement: ack-nhfb
ajournal: CMS Notes
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://cms.math.ca/notes
rawauthor: D. H. Bailey and J. M. Borwein
rawtitle: Future Prospects for Computer-assisted Mathematics
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bailey:2005:FPC,
  author =       "D. H. Bailey and J. M. Borwein",
  title =        "Future Prospects for Computer-assisted Mathematics",
  journal =      j-CMS-NOTES,
  volume =       "37",
  number =       "8",
  pages =        "2--6",
  month =        dec,
  year =         "2005",
  DOI =          "",
  ISSN =         "1193-9273 (print), 1496-4295 (electronic)",
  ISSN-L =       "1193-9273",
  bibdate =      "Sat Aug 13 17:21:21 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/304/;
                 https://cms.math.ca/notes/v37/n8/Notesv37n8.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "CMS Notes",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Canadian Mathematical Society Notes",
  journal-URL =  "https://cms.math.ca/notes",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: 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
pages: 3--21
year: 2005
DOI: https://doi.org/10.1007/0-387-23639-2_1
ISBN: 0-387-23638-4 OR 0387236384
ISBN13: 978-0-387-23638-4 OR 9780387236384
MRclass: 11Y60 (33B15 37B99 37N99 94A17)
MRnumber: 2103023
MRreviewer: Brian L. Burrows
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:36:22 MDT
series: Nonconvex Optim. Appl.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
bookpages: xi + 350
rawauthor: J. M. Borwein and K. Karamanos
rawbooktitle: Generalized Convexity, Generalized Monotonicity and Applications
raweditor: Andrew Eberhard and Nicolas Hadjisavvas and Dinh The Luc
rawtitle: Algebraic Dynamics of Certain Gamma Function Values
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Eberhard, Andrew/0000-0003-2977-3456
URL:
http://docserver.carma.newcastle.edu.au/256/; http://link.springer.com/chapter/10.1007/0-387-23639-2_1

entry:
@InCollection{Borwein:2005:ADC,
  author =       "J. M. Borwein and K. Karamanos",
  editor =       "Andrew Eberhard and Nicolas Hadjisavvas and Dinh The
                 Luc",
  booktitle =    "Generalized Convexity, Generalized Monotonicity and
                 Applications",
  title =        "Algebraic Dynamics of Certain Gamma Function Values",
  volume =       "77",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "xi + 350",
  pages =        "3--21",
  year =         "2005",
  DOI =          "https://doi.org/10.1007/0-387-23639-2_1",
  ISBN =         "0-387-23638-4",
  ISBN-13 =      "978-0-387-23638-4",
  MRclass =      "11Y60 (33B15 37B99 37N99 94A17)",
  MRnumber =     "2103023",
  MRreviewer =   "Brian L. Burrows",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Nonconvex Optim. Appl.",
  URL =          "http://docserver.carma.newcastle.edu.au/256/;
                 http://link.springer.com/chapter/10.1007/0-387-23639-2_1",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Eberhard,
                 Andrew/0000-0003-2977-3456",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2005:BRS
author: Jonathan M. Borwein
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) OR 03436993 (print), 18667414 (electronic)
ISSNL: 0343-6993 OR 03436993
bibdate: Fri Aug 12 10:34:00 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 10:34:00 ???
fjournal: The Mathematical Intelligencer
remark: D-drive preprint 285.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/283
rawauthor: Jonathan M. Borwein
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Book Review: booktitle The SIAM 100-Digit challenge: a study in high-accuracy numerical computing, Folkmar Bornemann, Dirk Laurie, Stan Wagon, and JSrg Waldvogel, SIAM, Philadelphia, PA, USA 2004, xil + 306 pp. softcover, ISBN 0-89871 561-X, US$57.00

rawtitle:
Book Review: {{\booktitle{The SIAM 100-Digit challenge: a study in high-accuracy numerical computing}}, Folkmar Bornemann, Dirk Laurie, Stan Wagon, and JSrg Waldvogel, SIAM, Philadelphia, PA, USA 2004, xil + 306 pp. softcover, ISBN 0-89871 561-X, US\$57.00}

entry:
@Article{Borwein:2005:BRS,
  author =       "Jonathan M. Borwein",
  title =        "Book Review: {{\booktitle{The SIAM 100-Digit
                 challenge: a study in high-accuracy numerical
                 computing}}, Folkmar Bornemann, Dirk Laurie, Stan
                 Wagon, and JSrg Waldvogel, SIAM, Philadelphia, PA, USA
                 2004, xil + 306 pp. softcover, ISBN 0-89871 561-X,
                 US\$57.00}",
  journal =      j-MATH-INTEL,
  volume =       "27",
  number =       "4",
  pages =        "40--48",
  year =         "2005",
  CODEN =        "MAINDC",
  DOI =          "https://doi.org/10.1007/BF02985860",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  bibdate =      "Fri Aug 12 10:34:00 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The Mathematical Intelligencer",
  journal-URL =  "http://link.springer.com/journal/283",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "D-drive preprint 285.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 6
year: 2005
CODEN: AMMYAE
DOI: https://doi.org/10.2307/30037519
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 33C05 (40A15)
MRnumber: 2142600
MRreviewer: Takao Komatsu
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/39/; https://www.jstor.org/stable/30037519
fjournal: American Mathematical Monthly
remark: CECM Preprint 2003:201.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.jstor.org/journals/00029890.html
rawauthor: Jonathan Michael Borwein and Kwok-Kwong Stephen Choi and Wilfried Pigulla
rawtitle: Continued fractions of tails of hypergeometric series
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2005:CFT,
  author =       "Jonathan Michael Borwein and Kwok-Kwong Stephen Choi
                 and Wilfried Pigulla",
  title =        "Continued fractions of tails of hypergeometric
                 series",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "112",
  number =       "6",
  pages =        "493--501",
  month =        jun # "\slash " # jul,
  year =         "2005",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/30037519",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "33C05 (40A15)",
  MRnumber =     "2142600",
  MRreviewer =   "Takao Komatsu",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/39/;
                 https://www.jstor.org/stable/30037519",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 2003:201.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 0008414X (print), 14964279 (electronic)
ISSNL: 0008-414X OR 0008414X
MRclass: 49J50 (26B05 46G05 58C20)
MRnumber: 2164591
MRreviewer: Lud{\v{e}}k Zaj{\'{\i}}{\v{c}}ek
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Canadian Journal of Mathematics. Journal Canadien de Mathematiques
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://cms.math.ca/cjm/
rawauthor: Jonathan M. Borwein and Xianfu Wang
rawtitle: Cone-monotone functions: differentiability and continuity
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2005:CMF,
  author =       "Jonathan M. Borwein and Xianfu Wang",
  title =        "Cone-monotone functions: differentiability and
                 continuity",
  journal =      j-CAN-J-MATH,
  volume =       "57",
  number =       "5",
  pages =        "961--982",
  year =         "2005",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-2005-037-5",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  MRclass =      "49J50 (26B05 46G05 58C20)",
  MRnumber =     "2164591",
  MRreviewer =   "Lud{\v{e}}k Zaj{\'{\i}}{\v{c}}ek",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  abstract =     "We provide a porosity-based approach to the
                 differentiability and continuity of real-valued
                 functions on separable Banach spaces, when the function
                 is monotone with respect to an ordering induced by a
                 convex cone $K$ with non-empty interior. We also show
                 that the set of nowhere $K$-monotone functions has a
                 sigma-porous complement in the space of continuous
                 functions endowed with the uniform metric.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Canadian Journal of Mathematics. Journal Canadien de
                 Math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2005:CMF",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
year: 2005
DOI: https://doi.org/10.1155/AAA.2005.449
ISSN: 1085-3375 (print), 1687-0409 (electronic) OR 10853375 (print), 16870409 (electronic)
ISSNL: 1085-3375 OR 10853375
MRclass: 11J70 (60F15)
MRnumber: 2201037
MRreviewer: Mary E. Flahive
bibdate: Fri Aug 12 10:09:56 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 10:09:56 ???
fjournal: Abstract and Applied Analysis
remark: CoLab Preprint 275
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and D. Russell Luke
rawtitle: Dynamics of a continued fraction of {Ramanujan} with random coefficients
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2005:DCF,
  author =       "Jonathan M. Borwein and D. Russell Luke",
  title =        "Dynamics of a continued fraction of {Ramanujan} with
                 random coefficients",
  journal =      j-ABSTR-APPL-ANAL,
  volume =       "2005",
  number =       "5",
  pages =        "449--467",
  month =        "????",
  year =         "2005",
  DOI =          "https://doi.org/10.1155/AAA.2005.449",
  ISSN =         "1085-3375 (print), 1687-0409 (electronic)",
  ISSN-L =       "1085-3375",
  MRclass =      "11J70 (60F15)",
  MRnumber =     "2201037",
  MRreviewer =   "Mary E. Flahive",
  bibdate =      "Fri Aug 12 10:09:56 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2005AbApA2005..449B;
                 http://www.hindawi.com/journals/aaa/2005/162798/abs/",
  abstract =     "We study a generalization of a continued fraction of
                 Ramanujan with random, complex-valued coefficients. A
                 study of the continued fraction is equivalent to an
                 analysis of the convergence of certain stochastic
                 difference equations and the stability of random
                 dynamical systems. We determine the convergence
                 properties of stochastic difference equations and so
                 the divergence of their corresponding continued
                 fractions.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Abstract and Applied Analysis",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  received =     "16 November 2004",
  remark =       "CoLab Preprint 275",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2005:DCF",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 00019054 (print), 14208903 (electronic)
ISSNL: 0001-9054 OR 00019054
MRclass: 05A10 (11B65 33B30)
MRnumber: 2167981
MRreviewer: Valery V. Karachik
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/131/
fjournal: Aequationes Mathematicae
remark: CECM Preprint 02:188.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/10
rawauthor: Jonathan M. Borwein and Roland Girgensohn
rawtitle: Evaluations of binomial series
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We give closed forms, recursion formulas and experimental results for the series $ sum n^k / binom 2nn $ and $ sum 2^-n n^k / binom 3nn $ with $ k in mathbb Z $.

rawabstract:
We give closed forms, recursion formulas and experimental results for the series $ \sum n^k / \binom {2n}{n} $ and $ \sum 2^{-n} n^k / \binom {3n}{n} $ with $ k \in \mathbb {Z} $.

entry:
@Article{Borwein:2005:EBS,
  author =       "Jonathan M. Borwein and Roland Girgensohn",
  title =        "Evaluations of binomial series",
  journal =      j-AEQUATIONES-MATHEMATICAE,
  volume =       "70",
  number =       "1--2",
  pages =        "25--36",
  year =         "2005",
  CODEN =        "AEMABN",
  DOI =          "https://doi.org/10.1007/s00010-005-2774-x",
  ISSN =         "0001-9054 (print), 1420-8903 (electronic)",
  ISSN-L =       "0001-9054",
  MRclass =      "05A10 (11B65 33B30)",
  MRnumber =     "2167981",
  MRreviewer =   "Valery V. Karachik",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/131/",
  abstract =     "We give closed forms, recursion formulas and
                 experimental results for the series $ \sum n^k / \binom
                 {2n}{n} $ and $ \sum 2^{-n} n^k / \binom {3n}{n} $ with
                 $ k \in \mathbb {Z} $.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Aequationes Mathematicae",
  journal-URL =  "http://link.springer.com/journal/10",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 02:188.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2005:EDA
author: Jonathan M. Borwein and David M. Bradley
title: Empirically determined Apery-like formulae for $ zeta (4 n + 3) $
journal: ArXiv Mathematics e-prints
pages: 25--36
month: may
monthnumber: 5
year: 2005
bibdate: Thu Aug 11 07:19:54 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 07:19:54 ???
URL: http://adsabs.harvard.edu/abs/2005math......5124B; http://docserver.carma.newcastle.edu.au/163/
keywords: Mathematics - Classical Analysis and ODEs, Mathematics - Number Theory, 11M06
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David M. Bradley
rawtitle: Empirically determined {Ap{\'e}ry}-like formulae for $ \zeta (4 n + 3) $
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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 Apery'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.

rawabstract:
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.

entry:
@Article{Borwein:2005:EDA,
  author =       "Jonathan M. Borwein and David M. Bradley",
  title =        "Empirically determined {Ap{\'e}ry}-like formulae for $
                 \zeta (4 n + 3) $",
  journal =      "ArXiv Mathematics e-prints",
  month =        may,
  year =         "2005",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2005math......5124B;
                 http://docserver.carma.newcastle.edu.au/163/",
  abstract =     "Some rapidly convergent formulae for special values of
                 the Riemann zeta function are given. We obtain a
                 generating function formula for $ \zeta (4 n + 3) $
                 which generalizes Ap{\'e}ry's series for $ \zeta (3) $,
                 and appears to give the best possible series relations
                 of this type, at least for $ n \lt 12 $. The formula
                 reduces to a finite but apparently non-trivial
                 combinatorial identity. The identity is equivalent to
                 an interesting new integral evaluation for the central
                 binomial coefficient. We outline a new technique for
                 transforming and summing certain infinite series. We
                 also derive a beautiful formula which provides strange
                 evaluations of a large new class of non-terminating
                 hypergeometric series. Our main results are shown to be
                 equivalent. At the time this article was submitted for
                 publication back in 1996, these results were only
                 conjectures, but they have subsequently been proved as
                 a result of work due to Gert Almkvist and Andrew
                 Granville.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "math/0505124",
  keywords =     "Mathematics - Classical Analysis and ODEs, Mathematics
                 - Number Theory, 11M06",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 5
year: 2005
DOI: https://doi.org/10.1007/s10758-005-5216-x
ISSN: 1382-3892 (print), 1573-1766 (electronic) OR 13823892 (print), 15731766 (electronic)
ISSNL: 1382-3892 OR 13823892
bibdate: Fri Aug 12 10:49:11 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 10:49:11 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/10758
rawauthor: J. M. Borwein
rawtitle: The Experimental Mathematician: The Pleasure of Discovery and the Role of Proof
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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/

rawnote:
Counterpart presentation published in CMESG25 Proceedings, 2002, with lecture slides at \url{http://www.cecm.sfu.ca/personal/jborwein/proof.pdf}.

entry:
@Article{Borwein:2005:EMPa,
  author =       "J. M. Borwein",
  title =        "The Experimental Mathematician: The Pleasure of
                 Discovery and the Role of Proof",
  journal =      "International Journal of Computers for Mathematical
                 Learning",
  volume =       "10",
  number =       "2",
  pages =        "75--108",
  month =        may,
  year =         "2005",
  DOI =          "https://doi.org/10.1007/s10758-005-5216-x",
  ISSN =         "1382-3892 (print), 1573-1766 (electronic)",
  ISSN-L =       "1382-3892",
  bibdate =      "Fri Aug 12 10:49:11 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Counterpart presentation published in CMESG25
                 Proceedings, 2002, with lecture slides at
                 \url{http://www.cecm.sfu.ca/personal/jborwein/proof.pdf}.",
  URL =          "http://docserver.carma.newcastle.edu.au/264/;
                 http://link.springer.com/article/10.1007/s10758-005-5216-x;
                 https://web.archive.org/web/20040330173752/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  journal-URL =  "http://link.springer.com/journal/10758",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark-1 =     "CECM Preprint 02:178; 264.",
  remark-2 =     "Journal renamed in 2011 to \booktitle{Technology,
                 knowledge and learning}.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 03436993 (print), 18667414 (electronic)
ISSNL: 0343-6993 OR 03436993
MRclass: 01A80 (00A05)
MRnumber: 2156530
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/274/
fjournal: The Mathematical Intelligencer
remark: CoLab Preprint 274.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/283
rawauthor: Jonathan Borwein and Terry Stanway
rawtitle: Knowledge and Community in Mathematics
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2005:KCM,
  author =       "Jonathan Borwein and Terry Stanway",
  title =        "Knowledge and Community in Mathematics",
  journal =      j-MATH-INTEL,
  volume =       "27",
  number =       "2",
  pages =        "7--16",
  year =         "2005",
  CODEN =        "MAINDC",
  DOI =          "https://doi.org/10.1007/BF02985788",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  MRclass =      "01A80 (00A05)",
  MRnumber =     "2156530",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/274/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The Mathematical Intelligencer",
  journal-URL =  "http://link.springer.com/journal/283",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CoLab Preprint 274.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 00049727 (print), 17551633 (electronic)
ISSNL: 0004-9727 OR 00049727
MRclass: 49J52 (26B05 26E25 54C30)
MRnumber: 2199651
MRreviewer: Dariusz Zagrodny
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Bulletin of the Australian Mathematical Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://journals.cambridge.org/action/displayJournal?jid=BAZ
rawauthor: Jonathan M. Borwein and Xianfu Wang
rawtitle: {Lipschitz} functions with maximal {Clarke} subdifferentials are staunch
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2005:LFM,
  author =       "Jonathan M. Borwein and Xianfu Wang",
  title =        "{Lipschitz} functions with maximal {Clarke}
                 subdifferentials are staunch",
  journal =      j-BULL-AUSTRAL-MATH-SOC,
  volume =       "72",
  number =       "3",
  pages =        "491--496",
  year =         "2005",
  CODEN =        "ALNBAB",
  DOI =          "https://doi.org/10.1017/S0004972700035322",
  ISSN =         "0004-9727 (print), 1755-1633 (electronic)",
  ISSN-L =       "0004-9727",
  MRclass =      "49J52 (26B05 26E25 54C30)",
  MRnumber =     "2199651",
  MRreviewer =   "Dariusz Zagrodny",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/302/;
                 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=4829356",
  abstract =     "In a recent paper we have shown that most
                 non-expansive Lipschitz functions (in the sense of
                 Baire's category) have a maximal Clarke sub
                 differential. In the present paper, we show that in a
                 separable Banach space the set of non-expansive
                 Lipschitz functions with a maximal Clarke
                 subdifferential is not only generic, but also staunch
                 in the space of non-expansive functions.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Bulletin of the Australian Mathematical Society",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=BAZ",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2005:LFM",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2005:PFW
author: Jonathan M. Borwein and Mason Macklem and Jaehyun Paek
booktitle: SIAM Conference on Computational Science and Engineering, Orlando, February 2005
title: A Prototype for the Federated World Directory of Mathematicians
publisher: pub-SIAM
address: pub-SIAM:adr
pages: ??--??
year: 2005
bibdate: Sat Aug 13 17:23:15 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 17:23:15 ???
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Mason Macklem and Jaehyun Paek
rawbooktitle: SIAM Conference on Computational Science and Engineering, Orlando, February 2005
rawtitle: A Prototype for the Federated World Directory of Mathematicians
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InProceedings{Borwein:2005:PFW,
  author =       "Jonathan M. Borwein and Mason Macklem and Jaehyun
                 Paek",
  editor =       "????",
  booktitle =    "SIAM Conference on Computational Science and
                 Engineering, Orlando, February 2005",
  title =        "A Prototype for the Federated World Directory of
                 Mathematicians",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Sat Aug 13 17:23:15 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2005:SSA
author: J. M. Borwein and David M. Bradley
title: Searching symbolically for Apery-like formulae for values of the Riemann zeta function
journal: ArXiv Mathematics e-prints
pages: ??--??
month: may
monthnumber: 5
year: 2005
bibdate: Thu Aug 11 07:19:54 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 07:19:54 ???
URL: http://adsabs.harvard.edu/abs/2005math......5093B; http://docserver.carma.newcastle.edu.au/170/
keywords: Mathematics - Classical Analysis and ODEs, Mathematics - Number Theory, 11M06
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and David M. Bradley
rawtitle: Searching symbolically for {Ap{\'e}ry}-like formulae for values of the {Riemann} zeta function
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We discuss some aspects of the search for identities using computer algebra and symbolic methods. The focus is on so-called Apery-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.

rawabstract:
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.

entry:
@Article{Borwein:2005:SSA,
  author =       "J. M. Borwein and David M. Bradley",
  title =        "Searching symbolically for {Ap{\'e}ry}-like formulae
                 for values of the {Riemann} zeta function",
  journal =      "ArXiv Mathematics e-prints",
  month =        may,
  year =         "2005",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2005math......5093B;
                 http://docserver.carma.newcastle.edu.au/170/",
  abstract =     "We discuss some aspects of the search for identities
                 using computer algebra and symbolic methods. The focus
                 is on so-called Ap{\'e}ry-like formulae for special
                 values of the Riemann Zeta function. Much work lays
                 ahead in formally proving and properly classifying many
                 of the identities we have uncovered.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "math/0505093",
  keywords =     "Mathematics - Classical Analysis and ODEs, Mathematics
                 - Number Theory, 11M06",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2005:TFI
author: Jonathan M. Borwein and David M. Bradley
title: On Two Fundamental Identities for Euler Sums
journal: arxiv.org
pages: ??--??
month: feb
monthnumber: 2
year: 2005
bibdate: Tue Aug 16 10:16:43 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:16:43 ???
URL: http://arxiv.org/abs/math.NT/0502034/; http://docserver.carma.newcastle.edu.au/279/
remark: The archive.org URL is wrong: it points to the title Thirty-two Goldbach Variations paper.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David M. Bradley
rawtitle: On Two Fundamental Identities for {Euler} Sums
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2005:TFI,
  author =       "Jonathan M. Borwein and David M. Bradley",
  title =        "On Two Fundamental Identities for {Euler} Sums",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        feb,
  year =         "2005",
  bibdate =      "Tue Aug 16 10:16:43 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/math.NT/0502034/;
                 http://docserver.carma.newcastle.edu.au/279/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "The archive.org URL is wrong: it points to the
                 \title{Thirty-two Goldbach Variations} paper.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2005:TTG
author: J. M. Borwein and David M. Bradley
title: Thirty-two Goldbach Variations
journal: ArXiv Mathematics e-prints
pages: ??--??
day: 1
month: feb
monthnumber: 2
year: 2005
bibdate: Thu Aug 11 07:19:54 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 07:19:54 ???
keywords: Mathematics - Number Theory, 11M41
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and David M. Bradley
rawtitle: Thirty-two {Goldbach} Variations
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

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.

rawabstract:
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.

entry:
@Article{Borwein:2005:TTG,
  author =       "J. M. Borwein and David M. Bradley",
  title =        "Thirty-two {Goldbach} Variations",
  journal =      "ArXiv Mathematics e-prints",
  day =          "1",
  month =        feb,
  year =         "2005",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2005math......2034B;
                 http://arxiv.org/abs/math/0502034;
                 http://docserver.carma.newcastle.edu.au/301/",
  abstract =     "We give thirty-two diverse proofs of a small
                 mathematical gem --- the fundamental Euler sum identity
                 $$ \zeta (2, 1) = \zeta (3) = 8 \zeta (\bar 2, 1) $$.
                 We also discuss various generalizations for multiple
                 harmonic (Euler) sums and some of their many
                 connections, thereby illustrating both the wide variety
                 of techniques fruitfully used to study such sums and
                 the attraction of their study.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "math/0502034",
  keywords =     "Mathematics - Number Theory, 11M41",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "v1 (1 February 2005): 34 pages AMSLaTeX. v2 (3
                 November 2005): 41 pages AMSLaTeX. New introductory
                 material added and material on inequalities, Hilbert
                 matrix and Witten zeta functions. Errors in the second
                 section on Complex Line Integrals are corrected.
                 Published in \cite{Borwein:2006:TTG}.",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: 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 OR 0387242988
ISBN13: 978-0-387-24298-9 OR 9780387242989
MRclass: 49-02 (49J52 49J53 90-02)
MRnumber: 2144010
MRreviewer: Richard B. Vinter
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: CMS Books in Mathematics/Ouvrages de Mathematiques de la SMC, 20
URL: http://docserver.carma.newcastle.edu.au/1735/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Qiji J. Zhu
rawtitle: Techniques of Variational Analysis
ORCID: Borwein, Jonathan/0000-0002-1263-0646
TOC:
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

rawTOC:
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

entry:
@Book{Borwein:2005:TVA,
  author =       "Jonathan M. Borwein and Qiji J. Zhu",
  title =        "Techniques of Variational Analysis",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "vi + 362",
  year =         "2005",
  DOI =          "https://doi.org/10.1007/0-387-28271-8",
  ISBN =         "0-387-24298-8",
  ISBN-13 =      "978-0-387-24298-9",
  MRclass =      "49-02 (49J52 49J53 90-02)",
  MRnumber =     "2144010",
  MRreviewer =   "Richard B. Vinter",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "CMS Books in Mathematics/Ouvrages de Math{\'e}matiques
                 de la SMC, 20",
  URL =          "http://docserver.carma.newcastle.edu.au/1735/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  tableofcontents = "Front Matter / i--vi \\
                 Introduction and Notation / 1--4 \\
                 Variational Principles / 5--36 \\
                 Variational Techniques in Subdifferential Theory /
                 37--109 \\
                 Variational Techniques in Convex Analysis / 111--163
                 \\
                 Variational Techniques and Multifunctions / 165--241
                 \\
                 Variational Principles in Nonlinear Functional Analysis
                 / 243--289 \\
                 Variational Techniques In the Presence of Symmetry /
                 291--338 \\
                 Back Matter / 339--362",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Bailey:2006:EBE
author: D. H. Bailey and J. M. Borwein
title: Effective Bounds in Euler--Maclaurin-Based Quadrature (Summary for HPCS06)
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 34--34
month: may
monthnumber: 5
year: 2006
DOI: https://doi.org/10.1109/HPCS.2006.22
ISSN: 1550-5243 (print), 2378-2099 (electronic) OR 15505243 (print), 23782099 (electronic)
ISSNL: 1550-5243 OR 15505243
bibdate: Wed Aug 10 12:08:56 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 12:08:56 ???
URL: http://www.davidhbailey.com/dhbpapers/hpcs06.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. H. Bailey and J. M. Borwein
rawtitle: Effective Bounds in {Euler--Maclaurin}-Based Quadrature (Summary for {HPCS06})
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
booktitle:
20th International Symposium on High-Performance Computing in an Advanced Collaborative Environment (HPCS'06)

keywords:
Approximation error; Computer errors; Computer science; Concurrent computing; Error analysis; International collaboration; Mathematics; System testing

rawbooktitle:
20th International Symposium on High-Performance Computing in an Advanced Collaborative Environment (HPCS'06)

entry:
@InProceedings{Bailey:2006:EBE,
  author =       "D. H. Bailey and J. M. Borwein",
  booktitle =    "20th International Symposium on High-Performance
                 Computing in an Advanced Collaborative Environment
                 (HPCS'06)",
  title =        "Effective Bounds in {Euler--Maclaurin}-Based
                 Quadrature (Summary for {HPCS06})",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "34--34",
  month =        may,
  year =         "2006",
  DOI =          "https://doi.org/10.1109/HPCS.2006.22",
  ISSN =         "1550-5243 (print), 2378-2099 (electronic)",
  ISSN-L =       "1550-5243",
  bibdate =      "Wed Aug 10 12:08:56 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/hpcs06.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Approximation error; Computer errors; Computer
                 science; Concurrent computing; Error analysis;
                 International collaboration; Mathematics; System
                 testing",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2006:EDA
author: David H. Bailey and Jonathan M. Borwein and David M. Bradley
title: Experimental Determination of Apery-like Identities for $ zeta (2 n + 2) $
journal: j-EXP-MATH
volume: 15
number: 3
pages: 281--289
year: 2006
DOI: https://doi.org/10.1080/10586458.2006.10128968
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 11Y60 (11M06)
MRnumber: 2264467
MRreviewer: Tanguy Rivoal
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/295/; http://projecteuclid.org/euclid.em/1175789759
fjournal: Experimental Mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.tandfonline.com/loi/uexm20
onlinedate: 30 Jan 2011
rawauthor: David H. Bailey and Jonathan M. Borwein and David M. Bradley
rawtitle: Experimental Determination of {Ap{\'e}ry}-like Identities for $ \zeta (2 n + 2) $
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
http://projecteuclid.org/euclid.em; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/expmath.bib; http://www.tandfonline.com/toc/uexm20/15/3

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.

rawabstract:
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.

entry:
@Article{Bailey:2006:EDA,
  author =       "David H. Bailey and Jonathan M. Borwein and David M.
                 Bradley",
  title =        "Experimental Determination of {Ap{\'e}ry}-like
                 Identities for $ \zeta (2 n + 2) $",
  journal =      j-EXP-MATH,
  volume =       "15",
  number =       "3",
  pages =        "281--289",
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2006.10128968",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11Y60 (11M06)",
  MRnumber =     "2264467",
  MRreviewer =   "Tanguy Rivoal",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib;
                 http://www.tandfonline.com/toc/uexm20/15/3",
  URL =          "http://docserver.carma.newcastle.edu.au/295/;
                 http://projecteuclid.org/euclid.em/1175789759",
  abstract =     "We document the discovery of two generating functions
                 for $ \zeta (2 n + 2) $, analogous to earlier work for
                 $ \zeta (2 n + 1) $ and $ \zeta (4 n + 3) $, initiated
                 by Koecher and pursued further by Borwein, Bradley, and
                 others.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  onlinedate =   "30 Jan 2011",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Bailey:2006:EDA",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: 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
pages: 281--289
day: 2
month: oct
monthnumber: 10
year: 2006
bibdate: Fri Sep 30 08:18:51 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 08:18:51 ???
URL: http://www.davidhbailey.com/dhbpapers/ising-int.pdf
keywords: $K_0$ modified Bessel function; ARPREC multiprecision software system
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Finding General Explicit Formulas for {Ising} Integral Recursions
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@TechReport{Bailey:2006:FGE,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Finding General Explicit Formulas for {Ising} Integral
                 Recursions",
  type =         "Report",
  institution =  "Lawrence Berkeley National Laboratory and Faculty of
                 Computer Science, Dalhousie University",
  address =      "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5,
                 Canada",
  day =          "2",
  month =        oct,
  year =         "2006",
  bibdate =      "Fri Sep 30 08:18:51 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/ising-int.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "$K_0$ modified Bessel function; ARPREC multiprecision
                 software system",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 10
year: 2006
CODEN: JPHAC5
DOI: https://doi.org/10.1088/0305-4470/39/40/001
ISSN: 0305-4470 (print), 1361-6447 (electronic) OR 03054470 (print), 13616447 (electronic)
ISSNL: 0305-4470 OR 03054470
MRclass: 33F05 (33F10 65D30 82B20 82B80)
MRnumber: 2261886
MRreviewer: Syamal K. Sen
bibdate: Thu Aug 11 07:19:54 2016
bibtimestamp: 2016.08.11 07:19:54 ???
fjournal: Journal of Physics A (Mathematical and General)
remark: See improvements in cite Dolgov:2020:PCI.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://iopscience.iop.org/1751-8121
onlinedate: 19 September 2006
rawauthor: D. H. Bailey and J. M. Borwein and R. E. Crandall
rawtitle: Integrals of the {Ising} class
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib

URL:
http://adsabs.harvard.edu/abs/2006JPhA...39..001B; http://docserver.carma.newcastle.edu.au/324/; http://iopscience.iop.org/article/10.1088/0305-4470/39/40/001; http://stacks.iop.org/0305-4470/39/i=40/a=001

abstract:
From an experimental-mathematical perspective we analyse 'Ising-class' integrals. These are structurally related $n$-dimensional integrals we call $ C_n$, $ D_n$, $ E_n$, where $ D_n$ is a magnetic susceptibility integral central to the Ising theory of solid-state physics. We first analyse $ C_n coloneq frac 4n! 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.

rawabstract:
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.

entry:
@Article{Bailey:2006:IIC,
  author =       "D. H. Bailey and J. M. Borwein and R. E. Crandall",
  title =        "Integrals of the {Ising} class",
  journal =      j-J-PHYS-A,
  volume =       "39",
  number =       "40",
  pages =        "12271--12302",
  month =        oct,
  year =         "2006",
  CODEN =        "JPHAC5",
  DOI =          "https://doi.org/10.1088/0305-4470/39/40/001",
  ISSN =         "0305-4470 (print), 1361-6447 (electronic)",
  ISSN-L =       "0305-4470",
  MRclass =      "33F05 (33F10 65D30 82B20 82B80)",
  MRnumber =     "2261886",
  MRreviewer =   "Syamal K. Sen",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
  URL =          "http://adsabs.harvard.edu/abs/2006JPhA...39..001B;
                 http://docserver.carma.newcastle.edu.au/324/;
                 http://iopscience.iop.org/article/10.1088/0305-4470/39/40/001;
                 http://stacks.iop.org/0305-4470/39/i=40/a=001",
  abstract =     "From an experimental-mathematical perspective we
                 analyse 'Ising-class' integrals. These are structurally
                 related $n$-dimensional integrals we call $ C_n$, $
                 D_n$, $ E_n$, where $ D_n$ is a magnetic susceptibility
                 integral central to the Ising theory of solid-state
                 physics. We first analyse $ C_n \coloneq \frac {4}{n!}
                 \int_0^\infty \cdots \int_0^\infty \frac { 1 } { \big
                 (\sum_{ j = 1 }^n (u_j + 1 / u_j) \big)^2 } \frac { d
                 u_1 } { u_1 } \cdots \frac { d u_n } { u_n }$.\par

                 We had conjectured --- on the basis of
                 extreme-precision numerical quadrature --- that $ C_n $
                 has a finite large-$n$ limit, namely $ C_\infty = 2
                 e^{-2} $, with $ \gamma $ being the Euler constant. On
                 such a numerological clue we are able to prove the
                 conjecture. We then show that integrals $ D_n $ and $
                 E_n $ both decay exponentially with $n$, in a certain
                 rigorous sense. While $ C_n $, $ D_n $ remain
                 unresolved for $ n \geq 5 $, we were able to conjecture
                 a closed form for $ E_5 $. Our experimental results
                 involved extreme-precision, multidimensional quadrature
                 on intricate integrands; thus, a highly parallel
                 computation was required.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Physics A (Mathematical and General)",
  journal-URL =  "http://iopscience.iop.org/1751-8121",
  onlinedate =   "19 September 2006",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "See improvements in \cite{Dolgov:2020:PCI}.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 6
year: 2006
CODEN: AMMYAE
DOI: https://doi.org/10.2307/27641975
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 65-02 (11Y60 37E05 37G10 65-05 68-02)
MRnumber: 2231135
MRreviewer: Vasily A. Chernecky
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1237/; https://www.jstor.org/stable/27641975
fjournal: American Mathematical Monthly
remark: CoLab Preprint 270.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.jstor.org/journals/00029890.html
rawauthor: David H. Bailey and Jonathan M. Borwein and Vishaal Kapoor and Eric W. Weisstein
rawtitle: Ten problems in experimental mathematics
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bailey:2006:TPE,
  author =       "David H. Bailey and Jonathan M. Borwein and Vishaal
                 Kapoor and Eric W. Weisstein",
  title =        "Ten problems in experimental mathematics",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "113",
  number =       "6",
  pages =        "481--509",
  month =        jun # "\slash " # jul,
  year =         "2006",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/27641975",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "65-02 (11Y60 37E05 37G10 65-05 68-02)",
  MRnumber =     "2231135",
  MRreviewer =   "Vasily A. Chernecky",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1237/;
                 https://www.jstor.org/stable/27641975",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://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.",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2006:AWM
author: Jonathan M. Borwein
editor: N. Sinclair and W. Higginson
booktitle: Mathematics and the aesthetic
title: Aesthetics for the working mathematician
volume: 25
publisher: pub-SV
address: pub-SV:adr
pages: 21--40
year: 2006
MRclass: 00A05 (00A99 11A99 11Y99)
MRnumber: 2274212
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: CMS Books Math./Ouvrages Math. SMC
URL: http://docserver.carma.newcastle.edu.au/150/
remark: CECM Preprint 01:165.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawbooktitle: Mathematics and the aesthetic
raweditor: N. Sinclair and W. Higginson
rawtitle: Aesthetics for the working mathematician
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2006:AWM,
  author =       "Jonathan M. Borwein",
  editor =       "N. Sinclair and W. Higginson",
  booktitle =    "Mathematics and the aesthetic",
  title =        "Aesthetics for the working mathematician",
  volume =       "25",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "21--40",
  year =         "2006",
  MRclass =      "00A05 (00A99 11A99 11Y99)",
  MRnumber =     "2274212",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "CMS Books Math./Ouvrages Math. SMC",
  URL =          "http://docserver.carma.newcastle.edu.au/150/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 01:165.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 09446532 (print), 23636394 (electronic)
MRclass: 46G05 (46N10 49J50 52A41)
MRnumber: 2291553
MRreviewer: Lud{\v{e}}k Zaj{\'{\i}}{\v{c}}ek
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Journal of Convex Analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.heldermann.de/JCA/jcacon.htm
rawauthor: Jonathan Borwein and Vicente Montesinos and Jon Vanderwerff
rawtitle: Boundedness, differentiability and extensions of convex functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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 $X$.

rawabstract:
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 $X$.

entry:
@Article{Borwein:2006:BDE,
  author =       "Jonathan Borwein and Vicente Montesinos and Jon
                 Vanderwerff",
  title =        "Boundedness, differentiability and extensions of
                 convex functions",
  journal =      j-J-CONVEX-ANAL,
  volume =       "13",
  number =       "3--4",
  pages =        "587--602",
  year =         "2006",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "46G05 (46N10 49J50 52A41)",
  MRnumber =     "2291553",
  MRreviewer =   "Lud{\v{e}}k Zaj{\'{\i}}{\v{c}}ek",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/288/;
                 http://www.heldermann.de/JCA/JCA13/JCA133/jca13046.htm",
  abstract =     "We survey various boundedness, differentiability and
                 extendibility properties of convex functions, and how
                 they are related to sequential convergence with respect
                 to various topologies in the dual space. It is also
                 shown that if $ X / Y $ is separable then every
                 continuous convex function on $Y$ can be extended to a
                 continuous convex function on $X$.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Convex Analysis",
  journal-URL =  "http://www.heldermann.de/JCA/jcacon.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2006:BDE",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: 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 OR 0387295704
ISBN13: 978-0-387-29570-1 OR 9780387295701
MRclass: 49-01 (46N10 47N10 49-02 49J53 90-01)
MRnumber: 2184742
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: Theory and examples.
series: CMS Books in Mathematics / Ouvrages de Mathematiques de la SMC
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Adrian S. Lewis
rawnote: Theory and examples.
rawtitle: Convex analysis and nonlinear optimization
ORCID: Borwein, Jonathan/0000-0002-1263-0646
TOC:
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

rawTOC:
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

entry:
@Book{Borwein:2006:CAN,
  author =       "Jonathan M. Borwein and Adrian S. Lewis",
  title =        "Convex analysis and nonlinear optimization",
  volume =       "3",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xii + 310",
  year =         "2006",
  DOI =          "https://doi.org/10.1007/978-0-387-31256-9",
  ISBN =         "0-387-29570-4",
  ISBN-13 =      "978-0-387-29570-1",
  MRclass =      "49-01 (46N10 47N10 49-02 49J53 90-01)",
  MRnumber =     "2184742",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Theory and examples.",
  series =       "CMS Books in Mathematics\slash Ouvrages de
                 Math{\'e}matiques de la SMC",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  tableofcontents = "Front Matter / i--xii \\
                 Background / 1--14 \\
                 Inequality Constraints / 15--32 \\
                 Fenchel Duality / 33--63 \\
                 Convex Analysis / 65--96 \\
                 Special Cases / 97--122 \\
                 Nonsmooth Optimization / 123--152 \\
                 Karush--Kuhn--Tucker Theory / 153--177 \\
                 Fixed Points / 179--211 \\
                 More Nonsmooth Structure / 213--238 \\
                 Postscript: Infinite Versus Finite Dimensions /
                 239--251 \\
                 List of Results and Notation / 253--273 \\
                 Back Matter / 275--310",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 9
year: 2006
ISSN: 0311-0729 (print), 1326-2297 (electronic) OR 03110729 (print), 13262297 (electronic)
ISSNL: 0311-0729 OR 03110729
MRclass: 11Y60 (65B99)
MRnumber: 2259732
MRreviewer: Khodabakhsh Hessami Pilehrood
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: The Australian Mathematical Society. Gazette
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.austms.org.au/gazette
rawauthor: Jonathan M. Borwein and Mason S. Macklem
rawtitle: The (digital) life of {Pi}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/267/; http://www.austms.org.au/Publ/Gazette/2006/Sep06/pi.pdf

entry:
@Article{Borwein:2006:DLP,
  author =       "Jonathan M. Borwein and Mason S. Macklem",
  title =        "The (digital) life of {Pi}",
  journal =      j-AUSTRALIAN-MATH-SOC-GAZ,
  volume =       "33",
  number =       "4",
  pages =        "243--248",
  month =        sep,
  year =         "2006",
  ISSN =         "0311-0729 (print), 1326-2297 (electronic)",
  ISSN-L =       "0311-0729",
  MRclass =      "11Y60 (65B99)",
  MRnumber =     "2259732",
  MRreviewer =   "Khodabakhsh Hessami Pilehrood",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/267/;
                 http://www.austms.org.au/Publ/Gazette/2006/Sep06/pi.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The Australian Mathematical Society. Gazette",
  journal-URL =  "http://www.austms.org.au/gazette",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borwein:2006:EM
author: Jonathan M. Borwein and David H. Bailey and Roland Girgensohn
title: Experiments in Mathematics
publisher: pub-A-K-PETERS
address: pub-A-K-PETERS:adr
pages: 14 + vi + 294 + viii + 363
year: 2006
ISBN: 1-56881-283-3, 1-56881-211-6, 1-56881-136-5 OR 1568812833, 1568812116, 1568811365
LCCN: QA76.95 .E9 2006
bibdate: Tue Aug 16 08:45:42 MDT 2016
bibtimestamp: 2016.08.16 08:45:42 MDT
note: Combined interactive CD version.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David H. Bailey and Roland Girgensohn
rawnote: Combined interactive CD version.
rawtitle: Experiments in Mathematics
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
ISBN13:
978-1-56881-283-0, 978-1-56881-211-3, 978-1-56881-136-9 OR 9781568812830, 9781568812113, 9781568811369

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.

TOC:
Preface to the CD-ROM edition Mathematics by experiment: plausible reasoning in the 21st century / Jonathan Borwein and David Bailey Experimentation in mathematics: computational paths to discovery / Jonathan Borwein, David Bailey, and Roland Girgensohn

rawabstract:
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.

rawTOC:
Preface to the CD-ROM edition \\ Mathematics by experiment: plausible reasoning in the 21st century / Jonathan Borwein and David Bailey \\ Experimentation in mathematics: computational paths to discovery / Jonathan Borwein, David Bailey, and Roland Girgensohn

entry:
@Book{Borwein:2006:EM,
  author =       "Jonathan M. Borwein and David H. Bailey and Roland
                 Girgensohn",
  title =        "Experiments in Mathematics",
  publisher =    pub-A-K-PETERS,
  address =      pub-A-K-PETERS:adr,
  pages =        "14 + vi + 294 + viii + 363",
  year =         "2006",
  ISBN =         "1-56881-283-3, 1-56881-211-6, 1-56881-136-5",
  ISBN-13 =      "978-1-56881-283-0, 978-1-56881-211-3,
                 978-1-56881-136-9",
  LCCN =         "QA76.95 .E9 2006",
  bibdate =      "Tue Aug 16 08:45:42 MDT 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Combined interactive CD version.",
  abstract =     "Contains the full text of: Mathematics by experiment:
                 plausible reasoning in the 21st century; and,
                 Experimentation in mathematics: computational paths to
                 discovery, in electronic, searchable form. Includes
                 hyperlinks for all cross references, Internet URLs, and
                 bibliographical references. Enhanced search function
                 helps with particular formulas or expressions.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  tableofcontents = "Preface to the CD-ROM edition \\
                 Mathematics by experiment: plausible reasoning in the
                 21st century / Jonathan Borwein and David Bailey \\
                 Experimentation in mathematics: computational paths to
                 discovery / Jonathan Borwein, David Bailey, and Roland
                 Girgensohn",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2006:FRO
author: Jonathan M. Borwein
journal: j-SIAM-REVIEW
volume: 48
number: 3
pages: 585--594
month: sep
monthnumber: 9
year: 2006
CODEN: SIREAD
DOI: https://doi.org/10.1137/SIREAD000048000003000585000001
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Wed Aug 31 09:49:49 2016
bibtimestamp: 2016.08.31 09:49:49 ???
fjournal: SIAM Review
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://epubs.siam.org/sirev
rawauthor: Jonathan M. Borwein
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

URL:
http://epubs.siam.org/doi/abs/10.1137/SIREAD000048000003000585000001; https://www.jstor.org/stable/20453842

rawtitle:
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}

entry:
@Article{Borwein:2006:FRO,
  author =       "Jonathan M. Borwein",
  title =        "Featured Review: {{\booktitle{Oxford Users' Guide to
                 Mathematics}}. Edited by Eberhard Zeidler. Oxford
                 University Press, Oxford, 2004. \$59.50. xxii + 1285
                 pp., softcover. ISBN 0-19-850763-1}",
  journal =      j-SIAM-REVIEW,
  volume =       "48",
  number =       "3",
  pages =        "585--594",
  month =        sep,
  year =         "2006",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/SIREAD000048000003000585000001",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Wed Aug 31 09:49:49 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/doi/abs/10.1137/SIREAD000048000003000585000001;
                 https://www.jstor.org/stable/20453842",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 09446532 (print), 23636394 (electronic)
MRclass: 47H05 (47N10 49J53)
MRnumber: 2291552
MRreviewer: Andrew C. Eberhard
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Journal of Convex Analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.heldermann.de/JCA/jcacon.htm
rawauthor: Jonathan M. Borwein
rawtitle: Maximal monotonicity via convex analysis
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2006:MMC,
  author =       "Jonathan M. Borwein",
  title =        "Maximal monotonicity via convex analysis",
  journal =      j-J-CONVEX-ANAL,
  volume =       "13",
  number =       "3--4",
  pages =        "561--586",
  year =         "2006",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "47H05 (47N10 49J53)",
  MRnumber =     "2291552",
  MRreviewer =   "Andrew C. Eberhard",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1235/;
                 http://www.heldermann.de/JCA/JCA13/JCA133/jca13045.htm",
  abstract =     "In his `23' ``Mathematische Probleme''(1) lecture to
                 the Paris International Congress in 1900, David Hilbert
                 wrote ``Besides it is an error to believe that rigor in
                 the proof is the enemy of simplicity.'' In this spirit,
                 we use simple convex analytic methods, relying on an
                 ingenious function due to Simon Fitzpatrick, to provide
                 a concise proof of the maximality of the sum of two
                 maximal monotone operators on reflexive Banach space
                 under standard transversality conditions. Many other
                 extension, surjectivity, convexity and local
                 boundedness results are likewise established.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Convex Analysis",
  journal-URL =  "http://www.heldermann.de/JCA/jcacon.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2006:MMC",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:2006:MS
author: Jonathan Borwein and Helaman Ferguson
title: The mathematics of salt
pages: 561--586
month: dec
monthnumber: 12
year: 2006
bibdate: Tue Aug 16 10:05:43 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:05:43 ???
note: Preprint.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein and Helaman Ferguson
rawnote: Preprint.
rawtitle: The mathematics of salt
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Unpublished{Borwein:2006:MS,
  author =       "Jonathan Borwein and Helaman Ferguson",
  title =        "The mathematics of salt",
  month =        dec,
  year =         "2006",
  bibdate =      "Tue Aug 16 10:05:43 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Preprint.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 47H05 (46A22 46N10 47N10 49J53)
MRnumber: 2231619
MRreviewer: Teemu Pennanen
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1234/; https://www.jstor.org/stable/4098152
fjournal: Proceedings of the American Mathematical Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/journals/proc
rawauthor: Jonathan M. Borwein
rawtitle: Maximality of sums of two maximal monotone operators
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2006:MST,
  author =       "Jonathan M. Borwein",
  title =        "Maximality of sums of two maximal monotone operators",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "134",
  number =       "10",
  pages =        "2951--2955",
  year =         "2006",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/S0002-9939-06-08323-7",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "47H05 (46A22 46N10 47N10 49J53)",
  MRnumber =     "2231619",
  MRreviewer =   "Teemu Pennanen",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1234/;
                 https://www.jstor.org/stable/4098152",
  abstract =     "We use methods from convex analysis, relying on an
                 ingenious function of Simon Fitzpatrick, to prove
                 maximality of the sum of two maximal monotone operators
                 on reflexive Banach space under weak transversality
                 conditions.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2006:MST",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 4
year: 2006
CODEN: JMANAK
DOI: https://doi.org/10.1016/j.jmaa.2005.04.040
ISSN: 0022-247X (print), 1096-0813 (electronic) OR 0022247X (print), 10960813 (electronic)
ISSNL: 0022-247X OR 0022247X
MRclass: 11M41
MRnumber: 2201764
MRreviewer: Junesang Choi
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
fjournal: Journal of Mathematical Analysis and Applications
keywords: Euler sums; Generating functions; Multiple zeta values; Zeta functions
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/0022247X
rawauthor: David Borwein and Jonathan M. Borwein and David M. Bradley
rawtitle: Parametric {Euler} sum identities
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@Article{Borwein:2006:PES,
  author =       "David Borwein and Jonathan M. Borwein and David M.
                 Bradley",
  title =        "Parametric {Euler} sum identities",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "316",
  number =       "1",
  pages =        "328--338",
  month =        apr,
  year =         "2006",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/j.jmaa.2005.04.040",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "11M41",
  MRnumber =     "2201764",
  MRreviewer =   "Junesang Choi",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2006JMAA..316..328B;
                 http://docserver.carma.newcastle.edu.au/1236/;
                 http://www.sciencedirect.com/science/article/pii/S0022247X05003811",
  abstract =     "We consider some parametrized classes of multiple sums
                 first studied by Euler. Identities between meromorphic
                 functions of one or more variables in many cases
                 account for reduction formulae for these sums.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "math/0505058",
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "Euler sums; Generating functions; Multiple zeta
                 values; Zeta functions",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:2006:QCT
author: Jonathan Borwein and Peter (Liquin) Ye
title: Quadratic Convergence of the Tanh--Sinh Quadrature Rule
pages: 328--338
month: feb
monthnumber: 2
year: 2006
bibdate: Tue Aug 16 10:18:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:18:38 ???
note: Preprint.
URL: http://docserver.carma.newcastle.edu.au/342/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein and Peter (Liquin) Ye
rawnote: Preprint.
rawtitle: Quadratic Convergence of the Tanh--Sinh Quadrature Rule
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Unpublished{Borwein:2006:QCT,
  author =       "Jonathan Borwein and Peter (Liquin) Ye",
  title =        "Quadratic Convergence of the Tanh--Sinh Quadrature
                 Rule",
  month =        feb,
  year =         "2006",
  bibdate =      "Tue Aug 16 10:18:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Preprint.",
  URL =          "http://docserver.carma.newcastle.edu.au/342/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: 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 OR 1595932763
ISBN13: 978-1-59593-276-1 OR 9781595932761
MRclass: 68W30 (65K10)
MRnumber: 2289097
bibdate: Wed Aug 10 12:08:56 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 12:08:56 ???
series: ISSAC '06
URL: http://doi.acm.org/10.1145/1145768.1145780
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Chris H. Hamilton
rawbooktitle: Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation: {ISSAC 2006}
rawtitle: Symbolic Computation of Multidimensional {Fenchel} Conjugates
ORCID: Borwein, Jonathan/0000-0002-1263-0646
keywords:
Fenchel conjugate, Legendre--Fenchel transform, computer proofs, inequalities, subdifferential, subgradient

entry:
@InProceedings{Borwein:2006:SCM,
  author =       "Jonathan M. Borwein and Chris H. Hamilton",
  booktitle =    "Proceedings of the 2006 International Symposium on
                 Symbolic and Algebraic Computation: {ISSAC 2006}",
  title =        "Symbolic Computation of Multidimensional {Fenchel}
                 Conjugates",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "23--30",
  year =         "2006",
  DOI =          "https://doi.org/10.1145/1145768.1145780",
  ISBN =         "1-59593-276-3",
  ISBN-13 =      "978-1-59593-276-1",
  MRclass =      "68W30 (65K10)",
  MRnumber =     "2289097",
  bibdate =      "Wed Aug 10 12:08:56 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "ISSAC '06",
  URL =          "http://doi.acm.org/10.1145/1145768.1145780",
  acknowledgement = ack-nhfb,
  acmid =        "1145780",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Fenchel conjugate, Legendre--Fenchel transform,
                 computer proofs, inequalities, subdifferential,
                 subgradient",
  location =     "Genoa, Italy",
  numpages =     "8",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 09446532 (print), 23636394 (electronic)
MRclass: 01A70
MRnumber: 2291547
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: Introduction to Fitzpatrick memorial volume.
URL: http://www.heldermann.de/JCA/JCA13/JCA133/jca13040.htm
fjournal: Journal of Convex Analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.heldermann.de/JCA/jcacon.htm
rawauthor: Jonathan Borwein
rawnote: Introduction to Fitzpatrick memorial volume.
rawtitle: {Simon Fitzpatrick} memorial volume
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2006:SFM,
  author =       "Jonathan Borwein",
  title =        "{Simon Fitzpatrick} memorial volume",
  journal =      j-J-CONVEX-ANAL,
  volume =       "13",
  number =       "3--4",
  pages =        "463--476",
  year =         "2006",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "01A70",
  MRnumber =     "2291547",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Introduction to Fitzpatrick memorial volume.",
  URL =          "http://www.heldermann.de/JCA/JCA13/JCA133/jca13040.htm",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Convex Analysis",
  journal-URL =  "http://www.heldermann.de/JCA/jcacon.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2006:TTG
author: Jonathan M. Borwein and David M. Bradley
title: Thirty-two Goldbach variations
journal: j-INT-J-NUMBER-THEORY
volume: 2
number: 1
pages: 65--103
month: mar
monthnumber: 3
year: 2006
DOI: https://doi.org/10.1142/S1793042106000383
ISSN: 1793-0421 (print), 1793-7310 (electronic) OR 17930421 (print), 17937310 (electronic)
ISSNL: 1793-0421 OR 17930421
MRclass: 11M41 (11M06)
MRnumber: 2217795
MRreviewer: F. Beukers
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: International Journal of Number Theory (IJNT)
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.worldscientific.com/worldscinet/ijnt
rawauthor: Jonathan M. Borwein and David M. Bradley
rawtitle: Thirty-two {Goldbach} variations
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/ijnt.bib

URL:
http://docserver.carma.newcastle.edu.au/301/; https://www.worldscientific.com/doi/10.1142/S1793042106000383

abstract:
We give thirty-two diverse proofs of a small mathematical gem --- the fundamental Euler sum identity $ zeta (2, 1) = zeta (3) = 8 zeta (bar 2, 1) $. We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating both the wide variety of techniques fruitfully used to study such sums and the attraction of their study.

rawabstract:
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.

entry:
@Article{Borwein:2006:TTG,
  author =       "Jonathan M. Borwein and David M. Bradley",
  title =        "Thirty-two {Goldbach} variations",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "2",
  number =       "1",
  pages =        "65--103",
  month =        mar,
  year =         "2006",
  DOI =          "https://doi.org/10.1142/S1793042106000383",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  MRclass =      "11M41 (11M06)",
  MRnumber =     "2217795",
  MRreviewer =   "F. Beukers",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/301/;
                 https://www.worldscientific.com/doi/10.1142/S1793042106000383",
  abstract =     "We give thirty-two diverse proofs of a small
                 mathematical gem --- the fundamental Euler sum identity
                 $ \zeta (2, 1) = \zeta (3) = 8 \zeta (\bar {2}, 1) $.
                 We also discuss various generalizations for multiple
                 harmonic (Euler) sums and some of their many
                 connections, thereby illustrating both the wide variety
                 of techniques fruitfully used to study such sums and
                 the attraction of their study.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2006:TTG",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 09255001 (print), 15732916 (electronic)
ISSNL: 0925-5001 OR 09255001
MRclass: 49J53 (90C25)
MRnumber: 2242012
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: Special issue in honour of Alex Rubinov's 65th birthday.
URL: http://docserver.carma.newcastle.edu.au/259/
fjournal: Journal of Global Optimization
remark: CoLab Preprint 259.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/10898
rawauthor: Jonathan M. Borwein and Qiji J. Zhu
rawnote: Special issue in honour of Alex Rubinov's 65th birthday.
rawtitle: Variational methods in convex analysis
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Special issue in honour of Alex Rubinov's 65th
                 birthday.",
  URL =          "http://docserver.carma.newcastle.edu.au/259/",
  abstract =     "We use variational methods to provide a concise
                 development of a number of basic results in convex and
                 functional analysis. This illuminates the parallels
                 between convex analysis and smooth subdifferential
                 theory.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Global Optimization",
  journal-URL =  "http://link.springer.com/journal/10898",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CoLab Preprint 259.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2006:VMC",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 9
year: 2007
CODEN: JCAMDI
DOI: https://doi.org/10.1016/j.cam.2006.06.010
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 65D30 (11Y60 33E20 60E05)
MRnumber: 2337437
MRreviewer: Michael J. Evans
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
fjournal: Journal of Computational and Applied Mathematics
keywords: Box integrals; High-precision quadrature; Multi-dimensional integrals
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: D. H. Bailey and J. M. Borwein and R. E. Crandall
rawtitle: Box integrals
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2007JCoAM.206..196B;
                 http://docserver.carma.newcastle.edu.au/320/;
                 http://www.sciencedirect.com/science/article/pii/S0377042706004250",
  abstract =     "By a ``box integral'' we mean here an expectation $
                 \bra | r \to - q \to | s \ket $ where $ r \to $ runs
                 over the unit $n$-cube, with $ q \to $ and $s$ fixed,
                 explicitly: $ \int_0^1 \cdots \int_0^1 ((r 1 - q 1) 2 +
                 \cdots + (r n - q n) 2) s / 2 d r 1 \ldots d r n$. The
                 study of box integrals leads one naturally into several
                 disparate fields of analysis. While previous studies
                 have focused upon symbolic evaluation and asymptotic
                 analysis of special cases (notably $ s = 1$), we work
                 herein more generally --- in interdisciplinary fashion
                 --- developing results such as: (1) analytic
                 continuation (in complex $s$), (2) relevant
                 combinatorial identities, (3) rapidly converging
                 series, (4) statistical inferences, (5) connections to
                 mathematical physics, and (6) extreme-precision
                 quadrature techniques appropriate for these integrals.
                 These intuitions and results open up avenues of
                 experimental mathematics, with a view to new
                 conjectures and theorems on integrals of this type.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "Box integrals; High-precision quadrature;
                 Multi-dimensional integrals",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Bailey:2007:EMA
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 OR 156881271X
ISBN13: 978-1-56881-271-7 OR 9781568812717
LCCN: QA8.7 .E97 2007
MRnumber: 2320374
bibdate: Thu Oct 25 18:45:59 MDT 2007
bibtimestamp: 2007.10.25 18:45:59 MDT
URL: http://docserver.carma.newcastle.edu.au/1733/
subject: Experimental mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawtitle: Experimental Mathematics in Action
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
author:
David H. Bailey and Jonathan M. Borwein and Neil J. Calkin and Roland Girgensohn and D. Russell Luke and Victor Moll

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; z3950.loc.gov:7090/Voyager

TOC:
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 Apery-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

rawauthor:
David H. Bailey and Jonathan M. Borwein and Neil J. Calkin and Roland Girgensohn and D. Russell Luke and Victor Moll

rawTOC:
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

entry:
@Book{Bailey:2007:EMA,
  author =       "David H. Bailey and Jonathan M. Borwein and Neil J.
                 Calkin and Roland Girgensohn and D. Russell Luke and
                 Victor Moll",
  title =        "Experimental Mathematics in Action",
  publisher =    pub-A-K-PETERS,
  address =      pub-A-K-PETERS:adr,
  pages =        "xii + 322",
  year =         "2007",
  ISBN =         "1-56881-271-X",
  ISBN-13 =      "978-1-56881-271-7",
  LCCN =         "QA8.7 .E97 2007",
  MRnumber =     "2320374",
  bibdate =      "Thu Oct 25 18:45:59 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://docserver.carma.newcastle.edu.au/1733/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  subject =      "Experimental mathematics",
  tableofcontents = "Preface / xi \\
                 1 A Philosophical Introduction / 1 \\
                 1.1 Introduction / 1 \\
                 1.2 Mathematical Knowledge as We View It / 1 \\
                 1.3 Mathematical Reasoning / 2 \\
                 1.4 Philosophy of Experimental Mathematics / 3 \\
                 1.5 Our Experimental Mathodology / 11 \\
                 1.6 Finding Things versus Proving Things / 15 \\
                 1.7 Conclusions / 24 \\
                 2 Algorithms for Experimental Mathematics I / 29 \\
                 2.1 The Poetry of Computation / 29 \\
                 2.2 High-Precision Arithmetic / 30 \\
                 2.3 Integer Relation Detection / 31 \\
                 2.4 Illustrations and Examples / 33 \\
                 2.5 Definite Integrals and Infinite Series Summations /
                 43 \\
                 2.6 Computation of Multivariate Zeta Values / 44 \\
                 2.7 Ramanujan-Type Elliptic Series / 45 \\
                 3 Algorithms for Experimental Mathematics II / 53 \\
                 3.1 True Scientific Value / 53 \\
                 3.2 Prime Number Computations / 55 \\
                 3.3 Roots of Polynomials / 58 \\
                 3.4 Numerical Quadrature / 61 \\
                 3.5 Infinite Series Summation / 67 \\
                 3.6 Ap{\'e}ry-Like Summations / 70 \\
                 4 Exploration and Discovery in Inverse Scattering / 79
                 \\
                 4.1 Metaphysics and Mechanics / 79 \\
                 4.2 The Physical Experiment / 80 \\
                 4.3 The Model / 83 \\
                 4.4 The Mathematical Experiment: Qualitative Inverse
                 Scattering / 90 \\
                 4.5 Current Research / 107 \\
                 5 Exploring Strange Functions on the Computer / 113 \\
                 5.1 What Is ``Strange''? / 113 \\
                 5.2 Nowhere Differentiable Functions / 114 \\
                 5.3 Bernoulli Convolutions / 126 \\
                 6 Random Vectors and Factoring Integers: A Case Study /
                 139 \\
                 6.1 Learning from Experience / 139 \\
                 6.2 Integer Factorization / 140 \\
                 6.3 Random Models / 143 \\
                 6.4 The Main Questions / 144 \\
                 6.5 Bounds / 145 \\
                 6.6 Which Model Is Best? / 149 \\
                 6.7 Experimental Evidence / 155 \\
                 6.8 Conclusions / 158 \\
                 7 A Selection of Integrals from a Popular Table / 161
                 \\
                 7.1 The Allure of the Integral / 161 \\
                 7.2 The Project and Its Experimental Nature / 163 \\
                 7.3 Families and Individuals / 164 \\
                 7.4 An Experimental Derivation of Wallis' Formula / 167
                 \\
                 7.5 A Hyperbolic Example / 170 \\
                 7.6 A Formula Hidden in the List / 174 \\
                 7.7 Some Experiments on Valuations / 177 \\
                 7.8 An Error in the Latest Edition / 184 \\
                 7.9 Some Examples Involving the Hurwitz Zeta Function /
                 185 \\
                 8 Experimental Mathematics: A Computational Conclusion
                 / 189 \\
                 8.1 Mathematicians Are a Kind of Frenchmen / 189 \\
                 8.2 Putting Lessons in Action / 190 \\
                 8.3 Visual Computing / 191 \\
                 8.4 A Preliminary Example: Visualizing DNA Strands /
                 194 \\
                 8.5 What Is a Chaos Game? / 195 \\
                 8.6 Hilbert's Inequality and Witten's Zeta Function /
                 202 \\
                 8.7 Computational Challenge Problems / 214 \\
                 8.8 Last Words / 222 \\
                 9 Exercises / 225 \\
                 Exercises for Chapter 1 / 225 \\
                 Exercises for Chapter 2 / 231 \\
                 Exercises for Chapter 3 / 249 \\
                 Exercises for Chapter 4 / 256 \\
                 Exercises for Chapter 5 / 260 \\
                 Exercises for Chapter 6 / 262 \\
                 Exercises for Chapter 7 / 265 \\
                 Exercises for Chapter 8 / 273 \\
                 Additional Exercises / 280 \\
                 Bibliography / 301 \\
                 Index / 317",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
DOI: https://doi.org/10.1080/10586458.2007.10129003
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 33E20 (33C05 33F05 33F10 65D30 82B20)
MRnumber: 2367317
MRreviewer: Wadim Zudilin
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/326/; http://projecteuclid.org/euclid.em/1204928528
fjournal: Experimental Mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.tandfonline.com/loi/uexm20
rawauthor: D. H. Bailey and D. Borwein and J. M. Borwein and R. E. Crandall
rawtitle: Hypergeometric Forms for {Ising}-Class Integrals
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
http://projecteuclid.org/euclid.em; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/expmath.bib; http://www.tandfonline.com/toc/uexm20/16/3

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.

rawabstract:
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.

entry:
@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;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib;
                 http://www.tandfonline.com/toc/uexm20/16/3",
  URL =          "http://docserver.carma.newcastle.edu.au/326/;
                 http://projecteuclid.org/euclid.em/1204928528",
  abstract =     "We apply experimental -mathematical principles to
                 analyze the integrals [complex multiple integral] These
                 are generalizations of a previous integral $ C_n :=
                 C_{n, 1} $ relevant to the Ising theory of solid-state
                 physics [Bailey et al. 06]. We find representations of
                 the $ C_{n, k} $ in terms of Meijer $G$-functions and
                 nested Barnes integrals. Our investigations began by
                 computing 500-digit numerical values Of $ C_{n, k}$ for
                 all integers $n$, $k$, where $n$ is an element of $ [2,
                 12]$ and $k$ is an element of $ [0, 25]$. We found that
                 some $ C_{n, k}$ enjoy exact evaluations involving
                 Dirichlet L-functions or the Riemann zeta function. In
                 the process of analyzing hypergeometric
                 representations, we found-experimentally and
                 strikingly-that the $ C_{n, k}$ almost certainly
                 satisfy certain interindicial relations including
                 discrete k-recurrences. Using generating functions,
                 differential theory, complex analysis, and
                 Wilf--Zeilberger algorithms we are able to prove some
                 central cases of these relations.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Bailey:2007:HFI",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Bailey:2007:HSI
author: D. Bailey and J. Borwein and R. Crandall and D. Manna
title: Heisenberg spin integrals
pages: 257--276
month: aug
monthnumber: 8
year: 2007
bibdate: Tue Aug 16 10:04:46 2016
bibtimestamp: 2016.08.16 10:04:46 ???
note: Preprint.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. Bailey and J. Borwein and R. Crandall and D. Manna
rawnote: Preprint.
rawtitle: {Heisenberg} spin integrals
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib

entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
  note =         "Preprint.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 2
year: 2007
bibdate: Fri Sep 30 08:29:49 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 08:29:49 ???
URL: http://www.davidhbailey.com/dhbpapers/amm-11275.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Solution to Problem 11275
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/amm-11275.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 3
year: 2007
bibdate: Fri Sep 30 08:30:39 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 08:30:39 ???
URL: http://www.davidhbailey.com/dhbpapers/amm-11277.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Solution to Monthly Problem 11277
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/amm-11277.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 0362546x (print), 18735215 (electronic)
ISSNL: 0362-546X OR 0362546X
MRclass: 47H05 (47N10 49J53 90C25)
MRnumber: 2286629
MRreviewer: Patrick L. Combettes
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.sciencedirect.com/journal/nonlinear-analysis
rawauthor: Sedi Bartz and Heinz H. Bauschke and Jonathan M. Borwein and Simeon Reich and Xianfu Wang
rawtitle: {Fitzpatrick} functions, cyclic monotonicity and {Rockafellar}'s antiderivative
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
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.

keywords:
Convex function; Cyclically monotone operator; Fenchel conjugate; Fitzpatrick function; Maximal monotone operator; Subdifferential operator; Sublinear function

rawabstract:
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.

entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1232/;
                 http://www.sciencedirect.com/science/article/pii/S0362546X06000435",
  abstract =     "Several deeper results on maximal monotone operators
                 have recently found simpler proofs using Fitzpatrick
                 functions. In this paper, we study a sequence of
                 Fitzpatrick functions associated with a monotone
                 operator. The first term of this sequence coincides
                 with the original Fitzpatrick function, and the other
                 terms turn out to be useful for the identification and
                 characterization of cyclic monotonicity properties. It
                 is shown that for any maximal cyclically monotone
                 operator, the pointwise supremum of the sequence of
                 Fitzpatrick functions is closely related to
                 Rockafellar's antiderivative. Several examples are
                 explicitly computed for the purpose of illustration. In
                 contrast to Rockafellar's result, a maximal
                 3-cyclically monotone operator need not be maximal
                 monotone. A simplified proof of Asplund's observation
                 that the rotation in the Euclidean plane by $ \pi / n $
                 is $n$-cyclically monotone but not $ (n + 1)$
                 -cyclically monotone is provided. The Fitzpatrick
                 family of the subdifferential operator of a sublinear
                 and of an indicator function is studied in detail. We
                 conclude with a new proof of Moreau's result concerning
                 the convexity of the set of proximal mappings.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Nonlinear Analysis. Theory, Methods \& Applications.
                 An International Multidisciplinary Journal. Series A:
                 Theory and Methods",
  journal-URL =  "https://www.sciencedirect.com/journal/nonlinear-analysis",
  keywords =     "Convex function; Cyclically monotone operator; Fenchel
                 conjugate; Fitzpatrick function; Maximal monotone
                 operator; Subdifferential operator; Sublinear
                 function",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 10526234 (print), 10957189 (electronic)
ISSNL: 1052-6234 OR 10526234
MRclass: 47H05 (47B65 90C25)
MRnumber: 2345969
MRreviewer: P. P. Zabre{\u\i}ko
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/319/
fjournal: SIAM Journal on Optimization
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://epubs.siam.org/siopt
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein and Xianfu Wang
rawtitle: {Fitzpatrick} functions and continuous linear monotone operators
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/319/",
  abstract =     "The notion of a maximal monotone operator is crucial
                 in optimization as it captures both the subdifferential
                 operator of a convex, lower semicontinuous, and proper
                 function and any (not necessarily symmetric) continuous
                 linear positive operator. It was recently discovered
                 that most fundamental results on maximal monotone
                 operators allow simpler proofs utilizing Fitzpatrick
                 functions. In this paper, we study Fitzpatrick
                 functions of continuous linear monotone operators
                 defined on a Hilbert space. A novel characterization of
                 skew operators is presented. A result by Brezis and
                 Haraux is reproved using the Fitzpatrick function. We
                 investigate the Fitzpatrick function of the sum of two
                 operators, and we show that a known upper bound is
                 actually exact in finite-dimensional and more general
                 settings. Cyclic monotonicity properties are also
                 analyzed, and closed forms of the Fitzpatrick functions
                 of all orders are provided for all rotators in the
                 Euclidean plane.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIAM Journal on Optimization",
  journal-URL =  "http://epubs.siam.org/siopt",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Bauschke,
                 Heinz/D-5582-2009",
  unique-id =    "Bauschke:2007:FFC",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 10526234 (print), 10957189 (electronic)
ISSNL: 1052-6234 OR 10526234
MRclass: 47H05 (47N10 49J53 52A41)
MRnumber: 2345978
MRreviewer: Hong Kun Xu
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/321/
fjournal: SIAM Journal on Optimization
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://epubs.siam.org/siopt
rawauthor: Jonathan Borwein and Herre Wiersma
rawtitle: {Asplund} decomposition of monotone operators
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/321/",
  abstract =     "We establish representations of a monotone mapping as
                 the sum of a maximal subdifferential mapping and a
                 ``remainder'' monotone mapping, where the remainder is
                 ``acyclic'' in the sense that it contains no nontrivial
                 subdifferential component. This is the nonlinear
                 analogue of a skew linear operator. Examples of
                 indecomposable and acyclic operators are given. In
                 particular, we present an explicit nonlinear acyclic
                 operator.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIAM Journal on Optimization",
  journal-URL =  "http://epubs.siam.org/siopt",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2007:ADM",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: 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: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: ESAIM Proc.
URL: http://docserver.carma.newcastle.edu.au/299/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawbooktitle: {CSVAA} 2004---control set-valued analysis and applications, ESAIM: Proceedings
raweditor: Alain Pietrus and Michel H. Geoffroy
rawtitle: {Asplund} decompositions of monotone operators
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "ESAIM Proc.",
  URL =          "http://docserver.carma.newcastle.edu.au/299/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2007:CCS
author: Jonathan M. Borwein and David Langstroth and Mason Macklem and Scott Wilson and V. Jungic
title: The Coast-to-Coast Seminar and Remote Mathematical Collaboration
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 23--29
month: may
monthnumber: 5
year: 2007
DOI: https://doi.org/10.1109/HPCS.2007.30
bibdate: Wed Aug 10 12:08:56 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 12:08:56 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David Langstroth and Mason Macklem and Scott Wilson and V. Jungi{\'c}
rawtitle: The Coast-to-Coast Seminar and Remote Mathematical Collaboration
ORCID: Borwein, Jonathan/0000-0002-1263-0646
booktitle:
21st International Symposium on High Performance Computing Systems and Applications. HPCS 2007, Saskatoon, SK, Canada, 13--16 May 2007

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

rawbooktitle:
{21st International Symposium on High Performance Computing Systems and Applications. HPCS 2007, Saskatoon, SK, Canada, 13--16 May 2007}

entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  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",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 1
year: 2007
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 40A10 (26A42)
MRnumber: 2283644
MRreviewer: Ilaria Mantellini
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/262/; https://www.jstor.org/stable/27642121
fjournal: American Mathematical Monthly
remark: CoLab Preprint 262.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.jstor.org/journals/00029890.html
rawauthor: Jonathan M. Borwein
rawtitle: A class of {Dirichlet} series integrals
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/262/;
                 https://www.jstor.org/stable/27642121",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CoLab Preprint 262.",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: 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 OR 0444522085
ISBN13: 978-0-444-52208-5 OR 9780444522085
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
URL: http://www.sciencedirect.com/science/article/pii/B9780444522085500508
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Warren B. Moors
rawbooktitle: Open Problems in Topology {II}
raweditor: Elliott Pearl
rawtitle: Chapter 50: {Non-smooth} analysis, optimisation theory and {Banach} space theory
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
This chapter discusses about nonsmooth analysis, optimization theory, and Banach space theory. A Banach space X is called a weak Asplund space [Gateaux differentiability space] if each continuous convex function defined on it is Gateaux 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.

rawabstract:
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.

entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/B9780444522085500508",
  abstract =     "This chapter discusses about nonsmooth analysis,
                 optimization theory, and Banach space theory. A Banach
                 space X is called a weak Asplund space [G{\^a}teaux
                 differentiability space] if each continuous convex
                 function defined on it is G{\^a}teaux differentiable at
                 the points of a residual subset (that is, a subset that
                 contains the intersection of countably many dense open
                 subsets of X) [dense subset] of its domain. For a
                 Banach space (X, || \cdot || ), with closed unit ball
                 BX, the Bishop--Phelps set is the set of all linear
                 functionals in the dual X* that attain their maximum
                 value over BX; that is, the set {x* \subset X*: x*(x) =
                 || x*|| for some x \subset BX}. The Bishop--Phelps
                 Theorem says that the Bishop--Phelps set is always
                 dense in X*. A Banach space X has the attainable
                 approximation property (AAP) if the set of support
                 functionals for any closed bounded convex subset W
                 \subseteq X is norm dense in X*. The concepts related
                 to the Bishop--Phelps problem and the complex
                 Bishop--Phelps property are also discussed. Concepts of
                 biorthogonal sequences and support points are also
                 elaborated.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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) OR 13824090 (print), 15729303 (electronic)
ISSNL: 1382-4090 OR 13824090
MRclass: 11B37 (11A55 11Y16 37C99 37E99 39A10 65Q05)
MRnumber: 2281157
MRreviewer: James G. Mc Laughlin
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: The Ramanujan Journal
remark: CoLab Preprint 253.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11139
rawauthor: D. Borwein and J. Borwein and R. Crandall and R. Mayer
rawtitle: On the dynamics of certain recurrence relations
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/253/;
                 http://link.springer.com/article/10.1007/s11139-006-0243-3",
  abstract =     "In recent analyses [ 3, 4] the remarkable AGM
                 continued fraction of Ramanujan - denoted R-1(a, b) -
                 was proven to converge for almost all complex parameter
                 pairs (a, b). It was conjectured that R-1 diverges if
                 and only if (0 not equal a = be(i phi) with cos(2) phi
                 not equal 1) or (a(2) = b(2) is an element of
                 (-infinity, 0)). In the present treatment we resolve
                 this conjecture to the positive, thus establishing the
                 precise convergence domain for R-1. This is
                 accomplished by analyzing, using various special
                 functions, the dynamics of sequences such as (t(n))
                 satisfying a recurrence t(n) = (t(n-1)(n-1)
                 \kappa(n-1)t(n-2))/n. where \kappa(n):= a(2), b(2) as n
                 be even, odd respectively. As a byproduct, we are able
                 to give, in some cases, exact expressions for the n-th
                 convergent to the fraction R-1, thus establishing some
                 precise convergence rates. It is of interest that this
                 final resolution of convergence depends on rather
                 intricate theorems for complex-matrix products, which
                 theorems evidently being extensible to more general
                 continued fractions.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The {Ramanujan} Journal",
  journal-URL =  "http://link.springer.com/journal/11139",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CoLab Preprint 253.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2007:DCR",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: 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
pages: 63--101
year: 2007
bibdate: Thu Aug 11 08:24:07 2016
bibtimestamp: 2016.08.11 08:24:07 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David Borwein and Jonathan Borwein and Richard Crandall
rawtitle: Effective {Laguerre} asymptotics
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/334/; http://locutus.cs.dal.ca:8088/archive/00000334/; http://web.archive.org/web/20070208032521/h

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.

rawabstract:
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.

entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/334/;
                 http://locutus.cs.dal.ca:8088/archive/00000334/;
                 http://web.archive.org/web/20070208032521/h",
  abstract =     "It is known that the generalized Laguerre polynomials
                 can enjoy sub-exponential growth for large primary
                 index. Specifically, for certain fixed parameter pairs
                 $ (a, z) $ one has the large-$n$ asymptotic $$ L_n^{( -
                 a)}( - z) \sim C(a, z) n^{-a / 2 - 1 / 4} e^{2 \sqrt
                 {nz}}. $$ We introduce a computationally motivated
                 contour integral that allows highly efficient numerical
                 evaluation of $ L_n$, yet also leads to general
                 asymptotic series over the full domain for
                 sub-exponential behavior. We eventually lay out a fast
                 algorithm for generation of the rather formidable
                 expansion coefficients. Along the way we address the
                 difficult problem of establishing effective (i.e.,
                 rigorous and explicit) error bounds on the general
                 expansion. To this end, we avoid classical
                 stationary-phase and steepest-descent techniques in
                 favor of an ``exp-arc'' method that amounts to a
                 natural bridge between converging series and effective
                 asymptotics. Finally, we exhibit an absolutely
                 convergent exp-arc series for Bessel-function
                 evaluation as an alternative to conventional
                 ascending-asymptotic switching.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 6
year: 2007
DOI: https://doi.org/10.1155/2007/19381
ISSN: 0161-1712 (print), 1687-0425 (electronic) OR 01611712 (print), 16870425 (electronic)
ISSNL: 0161-1712 OR 01611712
MRclass: 33B10 (11B65 33B30)
MRnumber: 2320777
MRreviewer: Stefan Gerhold
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/287/
fjournal: International Journal of Mathematics and Mathematical Sciences
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.hindawi.com/journals/ijmms/
rawauthor: Jonathan M. Borwein and Marc Chamberland
rawtitle: Integer powers of arcsin
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/287/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "International Journal of Mathematics and Mathematical
                 Sciences",
  journal-URL =  "https://www.hindawi.com/journals/ijmms/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: 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
monthnumber: 12
year: 2007
CODEN: PAMYAR
DOI: https://doi.org/10.1090/S0002-9939-07-08960-5
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 47H05 (46N10 52A41)
MRnumber: 2341941
MRreviewer: S{\'a}ndor Z. N{\'e}meth
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/322/; https://www.jstor.org/stable/20535029
fjournal: Proceedings of the American Mathematical Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/journals/proc
rawauthor: Jonathan M. Borwein
rawtitle: Maximality of sums of two maximal monotone operators in general {Banach} space
ORCID: Borwein, Jonathan/0000-0002-1263-0646
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.

rawabstract:
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.

entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/322/;
                 https://www.jstor.org/stable/20535029",
  abstract =     "We combine methods from convex analysis, based on a
                 function of Simon Fitzpatrick, with a fine recent idea
                 due to Voisei, to prove maximality of the sum of two
                 maximal monotone operators in Banach space under
                 various natural domain and transversality conditions.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2007:MST",
}


