# bibtab

bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:2012:MMO
author: Jonathan M. Borwein and Liangjin Yao
title: Maximally monotone operators of negative infimum type are of dense type: the proof revisited
pages: 1--33
month: jun
monthnumber: 6
year: 2012
bibdate: Tue Aug 16 09:56:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:56:38 ???
note: Preprint.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Liangjin Yao
rawnote: Preprint.
rawtitle: Maximally monotone operators of negative infimum type are of dense type: the proof revisited
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Unpublished{Borwein:2012:MMO,
  author =       "Jonathan M. Borwein and Liangjin Yao",
  title =        "Maximally monotone operators of negative infimum type
                 are of dense type: the proof revisited",
  month =        jun,
  year =         "2012",
  bibdate =      "Tue Aug 16 09:56:38 2016",
  bibsource =    "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:2012:MSM
author: J. M. Borwein and L. Yao
title: Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator
journal: ArXiv e-prints
pages: 1--33
month: dec
monthnumber: 12
year: 2012
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/2012arXiv1212.4266B; http://docserver.carma.newcastle.edu.au/1483/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and L. Yao
rawtitle: Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal monotonicity of $ A + B $ provided that $ A, B $ are maximally monotone and $A$ is a linear relation, as soon as Rockafellar's constraint qualification holds: $ dom A cap inte dom B neq varnothing $. Moreover, $ A + B$ is of type (FPV).

keywords:
Mathematics - Functional Analysis, Mathematics - Optimization and Control, Primary 47A06, 47H05, Secondary 47B65, 47N10, 90C25

rawabstract:
The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal monotonicity of $ A + B $ provided that $ A, B $ are maximally monotone and $A$ is a linear relation, as soon as Rockafellar's constraint qualification holds: $ \dom A \cap \inte \dom B \neq \varnothing $. Moreover, $ A + B$ is of type (FPV).

entry:
@Article{Borwein:2012:MSM,
  author =       "J. M. Borwein and L. Yao",
  title =        "Maximality of the sum of a maximally monotone linear
                 relation and a maximally monotone operator",
  journal =      "ArXiv e-prints",
  month =        dec,
  year =         "2012",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2012arXiv1212.4266B;
                 http://docserver.carma.newcastle.edu.au/1483/",
  abstract =     "The most famous open problem in Monotone Operator
                 Theory concerns the maximal monotonicity of the sum of
                 two maximally monotone operators provided that
                 Rockafellar's constraint qualification holds. In this
                 paper, we prove the maximal monotonicity of $ A + B $
                 provided that $ A, B $ are maximally monotone and $A$
                 is a linear relation, as soon as Rockafellar's
                 constraint qualification holds: $ \dom A \cap \inte
                 \dom B \neq \varnothing $. Moreover, $ A + B$ is of
                 type (FPV).",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1212.4266",
  keywords =     "Mathematics - Functional Analysis, Mathematics -
                 Optimization and Control, Primary 47A06, 47H05,
                 Secondary 47B65, 47N10, 90C25",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2012:OMT
author: Jonathan Borwein and Veselin Jungic
title: Organic Mathematics: then and now
journal: j-NAMS
volume: 59
number: 3
pages: 416--419
month: mar
monthnumber: 3
year: 2012
CODEN: AMNOAN
DOI: https://doi.org/10.1090/noti805
ISSN: 0002-9920 (print), 1088-9477 (electronic) OR 00029920 (print), 10889477 (electronic)
ISSNL: 0002-9920 OR 00029920
bibdate: Sat Aug 13 15:39:26 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 15:39:26 ???
URL: http://docserver.carma.newcastle.edu.au/1397/; http://www.ams.org/notices/201203/rtx120300416p.pdf
fjournal: Notices of the American Mathematical Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/notices/
rawauthor: Jonathan Borwein and Veselin Jungi{\'c}
rawtitle: Organic Mathematics: then and now
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2012:OMT,
  author =       "Jonathan Borwein and Veselin Jungi{\'c}",
  title =        "Organic Mathematics: then and now",
  journal =      j-NAMS,
  volume =       "59",
  number =       "3",
  pages =        "416--419",
  month =        mar,
  year =         "2012",
  CODEN =        "AMNOAN",
  DOI =          "https://doi.org/10.1090/noti805",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibdate =      "Sat Aug 13 15:39:26 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1397/;
                 http://www.ams.org/notices/201203/rtx120300416p.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2012:RCS
author: Jonathan Borwein and Peter B. Borwein and Veselin Jungic
title: Remote Collaboration: Six Years of the Coast-To-Coast Seminar Series
journal: Science Communication
volume: 34
number: 3
pages: 419--428
month: jun
monthnumber: 6
year: 2012
DOI: https://doi.org/10.1177/1075547012443020
ISSN: 1075-5470 (print), 1552-8545 (electronic) OR 10755470 (print), 15528545 (electronic)
ISSNL: 1075-5470 OR 10755470
bibdate: Fri Aug 12 08:54:03 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 08:54:03 ???
URL: http://docserver.carma.newcastle.edu.au/1387/; http://scx.sagepub.com/content/34/3/419.abstract
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://scx.sagepub.com/content/by/year
rawauthor: Jonathan Borwein and Peter B. Borwein and Veselin Jungi{\'c}
rawtitle: Remote Collaboration: Six Years of the Coast-To-Coast Seminar Series
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this article, the authors describe the Coast-to-Coast Seminar Series, a pan-Canadian scientific event that has been running since 2005. A short history of the series and a listing of the various stages of its development and related challenges in communicating complex scientific topics to audiences at a number of remote sites is provided. In particular, the authors revisit the original goals of the series and discuss in detail its actual outcomes. They finish by mentioning some present and future applications of their experience as organizers of the series.

rawabstract:
In this article, the authors describe the Coast-to-Coast Seminar Series, a pan-Canadian scientific event that has been running since 2005. A short history of the series and a listing of the various stages of its development and related challenges in communicating complex scientific topics to audiences at a number of remote sites is provided. In particular, the authors revisit the original goals of the series and discuss in detail its actual outcomes. They finish by mentioning some present and future applications of their experience as organizers of the series.

entry:
@Article{Borwein:2012:RCS,
  author =       "Jonathan Borwein and Peter B. Borwein and Veselin
                 Jungi{\'c}",
  title =        "Remote Collaboration: Six Years of the Coast-To-Coast
                 Seminar Series",
  journal =      "Science Communication",
  volume =       "34",
  number =       "3",
  pages =        "419--428",
  month =        jun,
  year =         "2012",
  DOI =          "https://doi.org/10.1177/1075547012443020",
  ISSN =         "1075-5470 (print), 1552-8545 (electronic)",
  ISSN-L =       "1075-5470",
  bibdate =      "Fri Aug 12 08:54:03 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1387/;
                 http://scx.sagepub.com/content/34/3/419.abstract",
  abstract =     "In this article, the authors describe the
                 Coast-to-Coast Seminar Series, a pan-Canadian
                 scientific event that has been running since 2005. A
                 short history of the series and a listing of the
                 various stages of its development and related
                 challenges in communicating complex scientific topics
                 to audiences at a number of remote sites is provided.
                 In particular, the authors revisit the original goals
                 of the series and discuss in detail its actual
                 outcomes. They finish by mentioning some present and
                 future applications of their experience as organizers
                 of the series.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  journal-URL =  "http://scx.sagepub.com/content/by/year",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  unique-id =    "Borwein:2012:RCS",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2012:REA
author: Jonathan M. Borwein and Judy-anne Osborn
title: Response to ``Experimental Approaches to Theoretical Thinking ldots ''
crossref: Hanna:2012:PPM
pages: ??--??
year: 2012
bibdate: Sat Aug 13 15:47:54 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 15:47:54 ???
remark: I cannot find this a the publisher Web site??
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Judy-anne Osborn
rawtitle: Response to {``Experimental Approaches to Theoretical Thinking \ldots{}''}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2012:REA,
  author =       "Jonathan M. Borwein and Judy-anne Osborn",
  title =        "Response to {``Experimental Approaches to Theoretical
                 Thinking \ldots{}''}",
  crossref =     "Hanna:2012:PPM",
  pages =        "??--??",
  year =         "2012",
  bibdate =      "Sat Aug 13 15:47:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "I cannot find this a the publisher Web site??",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2012:RPMa
author: J. M. Borwein and L. Yao
title: Recent progress on Monotone Operator Theory
journal: ArXiv e-prints
pages: ??--??
month: oct
monthnumber: 10
year: 2012
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/2012arXiv1210.3401B; http://docserver.carma.newcastle.edu.au/1457/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and L. Yao
rawtitle: Recent progress on Monotone Operator Theory
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper, we survey recent progress on the theory of maximally monotone operators in general Banach space. We also extend various of the results and leave some open questions.

keywords:
Mathematics - Functional Analysis, Mathematics - Optimization and Control, 47H05 (Primary) 46B10, 47A06, 47B65, 47N10, 90C25 (Secondary)

rawabstract:
In this paper, we survey recent progress on the theory of maximally monotone operators in general Banach space. We also extend various of the results and leave some open questions.

entry:
@Article{Borwein:2012:RPMa,
  author =       "J. M. Borwein and L. Yao",
  title =        "Recent progress on Monotone Operator Theory",
  journal =      "ArXiv e-prints",
  month =        oct,
  year =         "2012",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2012arXiv1210.3401B;
                 http://docserver.carma.newcastle.edu.au/1457/",
  abstract =     "In this paper, we survey recent progress on the theory
                 of maximally monotone operators in general Banach
                 space. We also extend various of the results and leave
                 some open questions.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1210.3401",
  keywords =     "Mathematics - Functional Analysis, Mathematics -
                 Optimization and Control, 47H05 (Primary) 46B10, 47A06,
                 47B65, 47N10, 90C25 (Secondary)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2012:RPS
author: Jonathan M. Borwein
title: Ramanujan and Pi: Srinivasa Ramanujan: Going strong at 125
journal: j-NAMS
volume: 59
number: 11
pages: 1534--1537
month: dec
monthnumber: 12
year: 2012
CODEN: AMNOAN
DOI: https://doi.org/10.1090/noti917
ISSN: 0002-9920 (print), 1088-9477 (electronic) OR 00029920 (print), 10889477 (electronic)
ISSNL: 0002-9920 OR 00029920
bibdate: Fri Aug 12 08:47:51 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 08:47:51 ???
fjournal: Notices of the American Mathematical Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/notices/
rawauthor: Jonathan M. Borwein
rawtitle: {Ramanujan} and {Pi}: {Srinivasa Ramanujan}: Going strong at 125
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1379/; http://www.ams.org/journals/notices/201211/rtx121101522p.pdf

remark:
Section of longer article edited by Krishnaswami Alladi, booktitle Srinivasa Ramanujan: Going strong at 125, Part I, pages 1522--1537.

entry:
@Article{Borwein:2012:RPS,
  author =       "Jonathan M. Borwein",
  title =        "{Ramanujan} and {Pi}: {Srinivasa Ramanujan}: Going
                 strong at 125",
  journal =      j-NAMS,
  volume =       "59",
  number =       "11",
  pages =        "1534--1537",
  month =        dec,
  year =         "2012",
  CODEN =        "AMNOAN",
  DOI =          "https://doi.org/10.1090/noti917",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibdate =      "Fri Aug 12 08:47:51 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1379/;
                 http://www.ams.org/journals/notices/201211/rtx121101522p.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Section of longer article edited by Krishnaswami
                 Alladi, \booktitle{Srinivasa Ramanujan: Going strong at
                 125, Part I}, pages 1522--1537.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2012:SRC
author: J. M. Borwein and L. Yao
title: Some results on the convexity of the closure of the domain of a maximally monotone operator
journal: ArXiv e-prints
pages: 1534--1537
month: may
monthnumber: 5
year: 2012
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/2012arXiv1205.4482B; http://docserver.carma.newcastle.edu.au/1373/
keywords: Mathematics - Functional Analysis, 47H05 (Primary) 26B25, 47A05, 47B65 (Secondary)
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and L. Yao
rawtitle: Some results on the convexity of the closure of the domain of a maximally monotone operator
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We provide a concise analysis about what is known regarding when the closure of the domain of a maximally monotone operator on an arbitrary real Banach space is convex. In doing so, we also provide an affirmative answer to a problem posed by Simons.

rawabstract:
We provide a concise analysis about what is known regarding when the closure of the domain of a maximally monotone operator on an arbitrary real Banach space is convex. In doing so, we also provide an affirmative answer to a problem posed by Simons.

entry:
@Article{Borwein:2012:SRC,
  author =       "J. M. Borwein and L. Yao",
  title =        "Some results on the convexity of the closure of the
                 domain of a maximally monotone operator",
  journal =      "ArXiv e-prints",
  month =        may,
  year =         "2012",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2012arXiv1205.4482B;
                 http://docserver.carma.newcastle.edu.au/1373/",
  abstract =     "We provide a concise analysis about what is known
                 regarding when the closure of the domain of a maximally
                 monotone operator on an arbitrary real Banach space is
                 convex. In doing so, we also provide an affirmative
                 answer to a problem posed by Simons.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1205.4482",
  keywords =     "Mathematics - Functional Analysis, 47H05 (Primary)
                 26B25, 47A05, 47B65 (Secondary)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2012:SS
author: David Borwein and Jonathan M. Borwein and Armin Straub
title: A Sinc that Sank
journal: j-AMER-MATH-MONTHLY
volume: 119
number: 7
pages: 535--549
month: aug
monthnumber: 8
year: 2012
CODEN: AMMYAE
DOI: https://doi.org/10.4169/amer.math.monthly.119.07.535
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 33B10 (26A09)
MRnumber: 2956424
MRreviewer: M{\'a}rcia Kashimoto
bibdate: Thu Nov 8 07:34:19 MST 2012
bibtimestamp: 2012.11.08 07:34:19 MST
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: David Borwein and Jonathan M. Borwein and Armin Straub
rawtitle: A Sinc that Sank
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053
bibsource:
https://www.jstor.org/journals/00029890.html; https://www.jstor.org/stable/10.4169/amermathmont.119.issue-7; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib

URL:
http://docserver.carma.newcastle.edu.au/1391/; https://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.119.07.535.pdf

abstract:
We resolve and further study a sinc integral evaluation, first posed in this MONTHLY in [1967, p. 1015], which was solved in [1968, p. 914] and withdrawn in [1970, p. 657]. After a short introduction to the problem and its history, we give a general evaluation which we make entirely explicit in the case of the product of three sinc functions. Finally, we exhibit some more general structure of the integrals in question.

rawabstract:
We resolve and further study a sinc integral evaluation, first posed in this MONTHLY in [1967, p. 1015], which was solved in [1968, p. 914] and withdrawn in [1970, p. 657]. After a short introduction to the problem and its history, we give a general evaluation which we make entirely explicit in the case of the product of three sinc functions. Finally, we exhibit some more general structure of the integrals in question.

entry:
@Article{Borwein:2012:SS,
  author =       "David Borwein and Jonathan M. Borwein and Armin
                 Straub",
  title =        "A Sinc that Sank",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "119",
  number =       "7",
  pages =        "535--549",
  month =        aug,
  year =         "2012",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.119.07.535",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "33B10 (26A09)",
  MRnumber =     "2956424",
  MRreviewer =   "M{\'a}rcia Kashimoto",
  bibdate =      "Thu Nov 8 07:34:19 MST 2012",
  bibsource =    "https://www.jstor.org/journals/00029890.html;
                 https://www.jstor.org/stable/10.4169/amermathmont.119.issue-7;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1391/;
                 https://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.119.07.535.pdf",
  abstract =     "We resolve and further study a sinc integral
                 evaluation, first posed in this MONTHLY in [1967, p.
                 1015], which was solved in [1968, p. 914] and withdrawn
                 in [1970, p. 657]. After a short introduction to the
                 problem and its history, we give a general evaluation
                 which we make entirely explicit in the case of the
                 product of three sinc functions. Finally, we exhibit
                 some more general structure of the integrals in
                 question.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053",
  unique-id =    "Borwein:2012:SS",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2012:STMa
author: J. M. Borwein and L. Yao
title: Structure theory for maximally monotone operators with points of continuity
journal: ArXiv e-prints
pages: 535--549
month: mar
monthnumber: 3
year: 2012
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/2012arXiv1203.1101B; http://docserver.carma.newcastle.edu.au/1375/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and L. Yao
rawtitle: Structure theory for maximally monotone operators with points of continuity
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper, we consider the structure of maximally monotone operators in Banach space whose domains have nonempty interior and we present new and explicit structure formulas for such operators. Along the way, we provide new proofs of the norm-to-weak$^*$ closedness and of property (Q) for these operators (as recently proven by Voisei). Various applications and limiting examples are given.

keywords:
Mathematics - Functional Analysis, Mathematics - Optimization and Control, Primary 47H05, Secondary 47B65, 47N10, 90C25

rawabstract:
In this paper, we consider the structure of maximally monotone operators in Banach space whose domains have nonempty interior and we present new and explicit structure formulas for such operators. Along the way, we provide new proofs of the norm-to-weak$^*$ closedness and of property (Q) for these operators (as recently proven by Voisei). Various applications and limiting examples are given.

entry:
@Article{Borwein:2012:STMa,
  author =       "J. M. Borwein and L. Yao",
  title =        "Structure theory for maximally monotone operators with
                 points of continuity",
  journal =      "ArXiv e-prints",
  month =        mar,
  year =         "2012",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2012arXiv1203.1101B;
                 http://docserver.carma.newcastle.edu.au/1375/",
  abstract =     "In this paper, we consider the structure of maximally
                 monotone operators in Banach space whose domains have
                 nonempty interior and we present new and explicit
                 structure formulas for such operators. Along the way,
                 we provide new proofs of the norm-to-weak$^*$
                 closedness and of property (Q) for these operators (as
                 recently proven by Voisei). Various applications and
                 limiting examples are given.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1203.1101",
  keywords =     "Mathematics - Functional Analysis, Mathematics -
                 Optimization and Control, Primary 47H05, Secondary
                 47B65, 47N10, 90C25",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Piantadosi:2012:CME
author: Julia Piantadosi and Phil Howlett and Jonathan Borwein
title: Copulas with maximum entropy
journal: j-OPTIM-LETT
volume: 6
number: 1
pages: 99--125
year: 2012
DOI: https://doi.org/10.1007/s11590-010-0254-2
ISSN: 1862-4472 (print), 1862-4480 (electronic) OR 18624472 (print), 18624480 (electronic)
ISSNL: 1862-4472 OR 18624472
MRclass: 60E05 (62H05 90C25)
MRnumber: 2886586
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/1394/
fjournal: Optimization Letters
acknowledgement: ack-nhfb
ajournal: Optim. Lett.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11590
rawauthor: Julia Piantadosi and Phil Howlett and Jonathan Borwein
rawtitle: Copulas with maximum entropy
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Howlett, Phil/0000-0003-2382-8137
abstract:
We shall find a multi-dimensional checkerboard copula of maximum entropy that matches an observed set of grade correlation coefficients. This problem is formulated as the maximization of a concave function on a convex polytope. Under mild constraint qualifications we show that a unique solution exists in the core of the feasible region. The theory of Fenchel duality is used to reformulate the problem as an unconstrained minimization which is well solved numerically using a Newton iteration. Finally, we discuss the numerical calculations for some hypothetical examples and describe how this work can be applied to the modelling and simulation of monthly rainfall.

rawabstract:
We shall find a multi-dimensional checkerboard copula of maximum entropy that matches an observed set of grade correlation coefficients. This problem is formulated as the maximization of a concave function on a convex polytope. Under mild constraint qualifications we show that a unique solution exists in the core of the feasible region. The theory of Fenchel duality is used to reformulate the problem as an unconstrained minimization which is well solved numerically using a Newton iteration. Finally, we discuss the numerical calculations for some hypothetical examples and describe how this work can be applied to the modelling and simulation of monthly rainfall.

entry:
@Article{Piantadosi:2012:CME,
  author =       "Julia Piantadosi and Phil Howlett and Jonathan
                 Borwein",
  title =        "Copulas with maximum entropy",
  journal =      j-OPTIM-LETT,
  volume =       "6",
  number =       "1",
  pages =        "99--125",
  year =         "2012",
  DOI =          "https://doi.org/10.1007/s11590-010-0254-2",
  ISSN =         "1862-4472 (print), 1862-4480 (electronic)",
  ISSN-L =       "1862-4472",
  MRclass =      "60E05 (62H05 90C25)",
  MRnumber =     "2886586",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1394/",
  abstract =     "We shall find a multi-dimensional checkerboard copula
                 of maximum entropy that matches an observed set of
                 grade correlation coefficients. This problem is
                 formulated as the maximization of a concave function on
                 a convex polytope. Under mild constraint qualifications
                 we show that a unique solution exists in the core of
                 the feasible region. The theory of Fenchel duality is
                 used to reformulate the problem as an unconstrained
                 minimization which is well solved numerically using a
                 Newton iteration. Finally, we discuss the numerical
                 calculations for some hypothetical examples and
                 describe how this work can be applied to the modelling
                 and simulation of monthly rainfall.",
  acknowledgement = ack-nhfb,
  ajournal =     "Optim. Lett.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Optimization Letters",
  journal-URL =  "http://link.springer.com/journal/11590",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Howlett,
                 Phil/0000-0003-2382-8137",
  unique-id =    "Piantadosi:2012:CME",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Piantadosi:2012:MEM
author: Julia Piantadosi and Phil Howlett and Jonathan Borwein and John Henstridge
title: Maximum entropy methods for generating simulated rainfall
journal: j-NUMER-ALGEBRA-CONTROL-OPTIM
volume: 2
number: 2
pages: 233--256
year: 2012
DOI: https://doi.org/10.3934/naco.2012.2.233
ISSN: 2155-3289 (print), 2155-3297 (electronic) OR 21553289 (print), 21553297 (electronic)
ISSNL: 2155-3297 OR 21553297
MRclass: 62H05 (52A41 65C05)
MRnumber: 2929449
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://aimsciences.org/article/doi/10.3934/naco.2012.2.233
fjournal: Numerical Algebra, Control and Optimization
acknowledgement: ack-nhfb
ajournal: Numer. Algebra Control Optim.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://aimsciences.org/journal/2155-3289
rawauthor: Julia Piantadosi and Phil Howlett and Jonathan Borwein and John Henstridge
rawtitle: Maximum entropy methods for generating simulated rainfall
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Howlett, Phil/0000-0003-2382-8137
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/naco.bib

entry:
@Article{Piantadosi:2012:MEM,
  author =       "Julia Piantadosi and Phil Howlett and Jonathan Borwein
                 and John Henstridge",
  title =        "Maximum entropy methods for generating simulated
                 rainfall",
  journal =      j-NUMER-ALGEBRA-CONTROL-OPTIM,
  volume =       "2",
  number =       "2",
  pages =        "233--256",
  month =        "????",
  year =         "2012",
  CODEN =        "????",
  DOI =          "https://doi.org/10.3934/naco.2012.2.233",
  ISSN =         "2155-3289 (print), 2155-3297 (electronic)",
  ISSN-L =       "2155-3297",
  MRclass =      "62H05 (52A41 65C05)",
  MRnumber =     "2929449",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/naco.bib",
  URL =          "http://aimsciences.org/article/doi/10.3934/naco.2012.2.233",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algebra Control Optim.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Numerical Algebra, Control and Optimization",
  journal-URL =  "http://aimsciences.org/journal/2155-3289",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Howlett,
                 Phil/0000-0003-2382-8137",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: AragonArtacho:2013:ACA
author: F. J. Aragon Artacho and J. M. Borwein and V. Martin-Marquez and L. Yao
title: Applications of Convex Analysis within Mathematics
journal: ArXiv e-prints
pages: 233--256
month: feb
monthnumber: 2
year: 2013
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/2013arXiv1302.1978A; http://docserver.carma.newcastle.edu.au/1513/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: F. J. {Arag{\'o}n Artacho} and J. M. Borwein and V. Mart{\'\i}n-M{\'a}rquez and L. Yao
rawtitle: Applications of Convex Analysis within Mathematics
ORCID: Aragon Artacho, Francisco Javier/0000-0002-2445-8011; Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal convolution in Monotone Operator Theory. Among other things, we recapture the Minty surjectivity theorem in Hilbert space, and present a new proof of the sum theorem in reflexive spaces. More technically, we also discuss autoconjugate representers for maximally monotone operators. Finally, we consider various other applications in mathematical analysis.

keywords:
Mathematics - Functional Analysis, Mathematics - Optimization and Control, Primary 47N10, 90C25, Secondary 47H05, 47A06, 47B65

rawabstract:
In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal convolution in Monotone Operator Theory. Among other things, we recapture the Minty surjectivity theorem in Hilbert space, and present a new proof of the sum theorem in reflexive spaces. More technically, we also discuss autoconjugate representers for maximally monotone operators. Finally, we consider various other applications in mathematical analysis.

entry:
@Article{AragonArtacho:2013:ACA,
  author =       "F. J. {Arag{\'o}n Artacho} and J. M. Borwein and V.
                 Mart{\'\i}n-M{\'a}rquez and L. Yao",
  title =        "Applications of Convex Analysis within Mathematics",
  journal =      "ArXiv e-prints",
  month =        feb,
  year =         "2013",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2013arXiv1302.1978A;
                 http://docserver.carma.newcastle.edu.au/1513/",
  abstract =     "In this paper, we study convex analysis and its
                 theoretical applications. We first apply important
                 tools of convex analysis to Optimization and to
                 Analysis. We then show various deep applications of
                 convex analysis and especially infimal convolution in
                 Monotone Operator Theory. Among other things, we
                 recapture the Minty surjectivity theorem in Hilbert
                 space, and present a new proof of the sum theorem in
                 reflexive spaces. More technically, we also discuss
                 autoconjugate representers for maximally monotone
                 operators. Finally, we consider various other
                 applications in mathematical analysis.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1302.1978",
  keywords =     "Mathematics - Functional Analysis, Mathematics -
                 Optimization and Control, Primary 47N10, 90C25,
                 Secondary 47H05, 47A06, 47B65",
  ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
                 Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: AragonArtacho:2013:DRF
author: F. J. Aragon Artacho and J. M. Borwein and M. K. Tam
title: Douglas--Rachford Feasibility Methods for Matrix Completion Problems
journal: ArXiv e-prints
pages: 233--256
month: aug
monthnumber: 8
year: 2013
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/2013arXiv1308.4243A
keywords: Mathematics - Optimization and Control
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: F. J. {Arag{\'o}n Artacho} and J. M. Borwein and M. K. Tam
rawtitle: {Douglas--Rachford} Feasibility Methods for Matrix Completion Problems
ORCID: Aragon Artacho, Francisco Javier/0000-0002-2445-8011; Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper we give general recommendations for successful application of the Douglas--Rachford reflection method to convex and non-convex real matrix-completion problems. These guidelines are demonstrated by various illustrative examples.

rawabstract:
In this paper we give general recommendations for successful application of the Douglas--Rachford reflection method to convex and non-convex real matrix-completion problems. These guidelines are demonstrated by various illustrative examples.

entry:
@Article{AragonArtacho:2013:DRF,
  author =       "F. J. {Arag{\'o}n Artacho} and J. M. Borwein and M. K.
                 Tam",
  title =        "{Douglas--Rachford} Feasibility Methods for Matrix
                 Completion Problems",
  journal =      "ArXiv e-prints",
  month =        aug,
  year =         "2013",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2013arXiv1308.4243A",
  abstract =     "In this paper we give general recommendations for
                 successful application of the Douglas--Rachford
                 reflection method to convex and non-convex real
                 matrix-completion problems. These guidelines are
                 demonstrated by various illustrative examples.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1308.4243",
  keywords =     "Mathematics - Optimization and Control",
  ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
                 Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.OC",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: AragonArtacho:2013:GCN
author: Francisco J. Aragon Artacho and Jonathan M. Borwein
title: Global convergence of a non-convex Douglas--Rachford iteration
journal: j-J-GLOBAL-OPT
volume: 57
number: 3
pages: 753--769
year: 2013
CODEN: JGOPEO
DOI: https://doi.org/10.1007/s10898-012-9958-4
ISSN: 0925-5001 (print), 1573-2916 (electronic) OR 09255001 (print), 15732916 (electronic)
ISSNL: 0925-5001 OR 09255001
MRclass: 47J25 (47H10 90C26)
MRnumber: 3119379
MRreviewer: Patrick L. Combettes
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://arxiv.org/abs/1203.2392; http://docserver.carma.newcastle.edu.au/1061/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/10898
rawauthor: Francisco J. {Arag{\'o}n Artacho} and Jonathan M. Borwein
rawtitle: Global convergence of a non-convex {Douglas--Rachford} iteration
ORCID: Aragon Artacho, Francisco Javier/0000-0002-2445-8011; Borwein, Jonathan/0000-0002-1263-0646
fjournal:
Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering

entry:
@Article{AragonArtacho:2013:GCN,
  author =       "Francisco J. {Arag{\'o}n Artacho} and Jonathan M.
                 Borwein",
  title =        "Global convergence of a non-convex {Douglas--Rachford}
                 iteration",
  journal =      j-J-GLOBAL-OPT,
  volume =       "57",
  number =       "3",
  pages =        "753--769",
  year =         "2013",
  CODEN =        "JGOPEO",
  DOI =          "https://doi.org/10.1007/s10898-012-9958-4",
  ISSN =         "0925-5001 (print), 1573-2916 (electronic)",
  ISSN-L =       "0925-5001",
  MRclass =      "47J25 (47H10 90C26)",
  MRnumber =     "3119379",
  MRreviewer =   "Patrick L. Combettes",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/1203.2392;
                 http://docserver.carma.newcastle.edu.au/1061/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Global Optimization. An International
                 Journal Dealing with Theoretical and Computational
                 Aspects of Seeking Global Optima and Their Applications
                 in Science, Management and Engineering",
  journal-URL =  "http://link.springer.com/journal/10898",
  ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
                 Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: AragonArtacho:2013:RRDa
author: F. J. Aragon Artacho and J. M. Borwein and M. K. Tam
title: Recent Results on Douglas--Rachford Methods for Combinatorial Optimization Problems
journal: ArXiv e-prints
pages: 753--769
month: may
monthnumber: 5
year: 2013
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/2013arXiv1305.2657A; http://docserver.carma.newcastle.edu.au/1510/
keywords: Mathematics - Optimization and Control, Mathematics - Combinatorics, 90C27, 90C59, 47N10
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: F. J. {Arag{\'o}n Artacho} and J. M. Borwein and M. K. Tam
rawtitle: Recent Results on {Douglas--Rachford} Methods for Combinatorial Optimization Problems
ORCID: Aragon Artacho, Francisco Javier/0000-0002-2445-8011; Borwein, Jonathan/0000-0002-1263-0646
abstract:
We discuss recent positive experiences applying convex feasibility algorithms of Douglas--Rachford type to highly combinatorial and far from convex problems.

rawabstract:
We discuss recent positive experiences applying convex feasibility algorithms of Douglas--Rachford type to highly combinatorial and far from convex problems.

entry:
@Article{AragonArtacho:2013:RRDa,
  author =       "F. J. {Arag{\'o}n Artacho} and J. M. Borwein and M. K.
                 Tam",
  title =        "Recent Results on {Douglas--Rachford} Methods for
                 Combinatorial Optimization Problems",
  journal =      "ArXiv e-prints",
  month =        may,
  year =         "2013",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2013arXiv1305.2657A;
                 http://docserver.carma.newcastle.edu.au/1510/",
  abstract =     "We discuss recent positive experiences applying convex
                 feasibility algorithms of Douglas--Rachford type to
                 highly combinatorial and far from convex problems.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1305.2657",
  keywords =     "Mathematics - Optimization and Control, Mathematics -
                 Combinatorics, 90C27, 90C59, 47N10",
  ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
                 Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.OC",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: AragonArtacho:2013:RRDb
author: Francisco J. Aragon Artacho and Jonathan M. Borwein and Matthew K. Tam
title: Recent results on Douglas--Rachford methods
journal: j-SERDICA-MATH-J
volume: 39
number: 3--4
pages: 313--330
year: 2013
ISSN: 1310-6600 OR 13106600
MRclass: 90C27 (90C59)
MRnumber: 3203190
MRreviewer: Patrick L. Combettes
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: Serdica. Mathematical Journal. Serdika. Matematichesko Spisanie
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.math.bas.bg/serdica/
rawauthor: Francisco J. {Arag{\'o}n Artacho} and Jonathan M. Borwein and Matthew K. Tam
rawtitle: Recent results on {Douglas--Rachford} methods
ORCID: Aragon Artacho, Francisco Javier/0000-0002-2445-8011; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{AragonArtacho:2013:RRDb,
  author =       "Francisco J. {Arag{\'o}n Artacho} and Jonathan M.
                 Borwein and Matthew K. Tam",
  title =        "Recent results on {Douglas--Rachford} methods",
  journal =      j-SERDICA-MATH-J,
  volume =       "39",
  number =       "3--4",
  pages =        "313--330",
  year =         "2013",
  ISSN =         "1310-6600",
  MRclass =      "90C27 (90C59)",
  MRnumber =     "3203190",
  MRreviewer =   "Patrick L. Combettes",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "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 =     "Serdica. Mathematical Journal. Serdika. Matematichesko
                 Spisanie",
  journal-URL =  "http://www.math.bas.bg/serdica/",
  ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
                 Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: AragonArtacho:2013:WRN
author: Francisco J. Aragon Artacho and David H. Bailey and Jonathan M. Borwein and Peter B. Borwein
title: Walking on Real Numbers
journal: j-MATH-INTEL
volume: 35
number: 1
pages: 42--60
month: mar
monthnumber: 3
year: 2013
CODEN: MAINDC
DOI: https://doi.org/10.1007/s00283-012-9340-x
ISSN: 0343-6993 (print), 1866-7414 (electronic) OR 03436993 (print), 18667414 (electronic)
ISSNL: 0343-6993 OR 03436993
MRclass: 11Y60 (60A99 60F05)
MRnumber: 3041991
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: The Mathematical Intelligencer
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/283
rawauthor: Francisco J. {Arag{\'o}n Artacho} and David H. Bailey and Jonathan M. Borwein and Peter B. Borwein
rawtitle: Walking on Real Numbers
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib

URL:
http://docserver.carma.newcastle.edu.au/1475/; http://gigapan.com/gigapans/106803; http://link.springer.com/article/10.1007/s00283-012-9340-x; http://www.davidhbailey.com/dhbpapers/tools-walk.pdf

keywords:
Catalan's constant; Champernowne numbers; continued fractions; Copeland--Erdos numbers; DNA genome numbers; dragon curves; Erdos--Borwein numbers; Euler--Mascherino constant ($gamma $); expected random-walk distance; exponential constant ($e$); Fibonacci constant ($F$); Gauss--Kuzmin distribution; irrational numbers; Koch snowflakes; Liouville number ($lambda _2$); logarithmic constant ($log 2$); Minkowski--Bouligand dimension; normal numbers; normalized random-walk distance; paper-folding constant; paper-folding numbers; pi (number); random walks; Riemann zeta numbers ($zeta (n)$); self-similarity; Stoneham numbers; strong normality; Thue--Morse numbers; transcendental numbers; turtle plots

ORCID:
Aragon Artacho, Francisco Javier/0000-0002-2445-8011; Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646

entry:
@Article{AragonArtacho:2013:WRN,
  author =       "Francisco J. {Arag{\'o}n Artacho} and David H. Bailey
                 and Jonathan M. Borwein and Peter B. Borwein",
  title =        "Walking on Real Numbers",
  journal =      j-MATH-INTEL,
  volume =       "35",
  number =       "1",
  pages =        "42--60",
  month =        mar,
  year =         "2013",
  CODEN =        "MAINDC",
  DOI =          "https://doi.org/10.1007/s00283-012-9340-x",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  MRclass =      "11Y60 (60A99 60F05)",
  MRnumber =     "3041991",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1475/;
                 http://gigapan.com/gigapans/106803;
                 http://link.springer.com/article/10.1007/s00283-012-9340-x;
                 http://www.davidhbailey.com/dhbpapers/tools-walk.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The Mathematical Intelligencer",
  journal-URL =  "http://link.springer.com/journal/283",
  keywords =     "Catalan's constant; Champernowne numbers; continued
                 fractions; Copeland--Erd{\H{o}}s numbers; DNA genome
                 numbers; dragon curves; Erd{\H{o}}s--Borwein numbers;
                 Euler--Mascherino constant ($\gamma$); expected
                 random-walk distance; exponential constant ($e$);
                 Fibonacci constant ($F$); Gauss--Kuzmin distribution;
                 irrational numbers; Koch snowflakes; Liouville number
                 ($\lambda_2$); logarithmic constant ($\log 2$);
                 Minkowski--Bouligand dimension; normal numbers;
                 normalized random-walk distance; paper-folding
                 constant; paper-folding numbers; pi (number); random
                 walks; Riemann zeta numbers ($\zeta(n)$);
                 self-similarity; Stoneham numbers; strong normality;
                 Thue--Morse numbers; transcendental numbers; turtle
                 plots",
  ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
                 Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2013:CLS
author: David H. Bailey and Jonathan M. Borwein
title: Compressed lattice sums arising from the Poisson equation
journal: j-BOUND-VALUE-PROBL
volume: 75
number: 1
pages: 1--18
year: 2013
DOI: https://doi.org/10.1186/1687-2770-2013-75
ISSN: 1687-2770 OR 16872770
MRclass: 35J15 (35C10)
MRnumber: 3055839
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 volume in honour of Hari Srivastava.
fjournal: Boundary Value Problems
acknowledgement: ack-nhfb
ajournal: Bound. Value Probl.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://boundaryvalueproblems.springeropen.com/
onlinedate: 13 May 2013
rawauthor: David H. Bailey and Jonathan M. Borwein
rawnote: Special volume in honour of Hari Srivastava.
rawtitle: Compressed lattice sums arising from the {Poisson} equation
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://boundaryvalueproblems.springeropen.com/articles/10.1186/1687-2770-2013-75; http://docserver.carma.newcastle.edu.au/1476/; http://www.boundaryvalueproblems.com/content/2013/1/75

abstract:
In recent years attention has been directed to the problem of solving the Poisson equation, either in engineering scenarios (computational) or in regard to crystal structure (theoretical). Methods: In (Bailey et al. in J. Phys. A, Math. Theor. 46:115201, 2013, doi:10.1088/1751-8113/46/11/115201) we studied a class of lattice sums that amount to solutions of Poisson's equation, utilizing some striking connections between these sums and Jacobi I-function values, together with high-precision numerical computations and the PSLQ algorithm to find certain polynomials associated with these sums. We take a similar approach in this study. Results: We were able to develop new closed forms for certain solutions and to extend such analysis to related lattice sums. We also alluded to results for the compressed sum phi(2)(x,y,d):=1/pi(2) Sigma(m,n is an element of O) cos(pi mx)cos(pi n root dy)/m(2) + dn(2) , (1) where , x, y are real numbers and denotes the odd integers. In this paper we first survey the earlier work and then discuss the sum (1) more completely. Conclusions: As in the previous study, we find some surprisingly simple closed-form evaluations of these sums. In particular, we find that in some cases these sums are given by , where A is an algebraic number. These evaluations suggest that a deep theory interconnects all such summations.

rawabstract:
In recent years attention has been directed to the problem of solving the Poisson equation, either in engineering scenarios (computational) or in regard to crystal structure (theoretical). Methods: In (Bailey et al. in J. Phys. A, Math. Theor. 46:115201, 2013, doi:10.1088/1751-8113/46/11/115201) we studied a class of lattice sums that amount to solutions of Poisson's equation, utilizing some striking connections between these sums and Jacobi I-function values, together with high-precision numerical computations and the PSLQ algorithm to find certain polynomials associated with these sums. We take a similar approach in this study. Results: We were able to develop new closed forms for certain solutions and to extend such analysis to related lattice sums. We also alluded to results for the compressed sum phi(2)(x,y,d):=1/pi(2) Sigma(m,n is an element of O) cos(pi mx)cos(pi n root dy)/m(2) + dn(2) , (1) where , x, y are real numbers and denotes the odd integers. In this paper we first survey the earlier work and then discuss the sum (1) more completely. Conclusions: As in the previous study, we find some surprisingly simple closed-form evaluations of these sums. In particular, we find that in some cases these sums are given by , where A is an algebraic number. These evaluations suggest that a deep theory interconnects all such summations.

entry:
@Article{Bailey:2013:CLS,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Compressed lattice sums arising from the {Poisson}
                 equation",
  journal =      j-BOUND-VALUE-PROBL,
  volume =       "75",
  number =       "1",
  pages =        "1--18",
  year =         "2013",
  DOI =          "https://doi.org/10.1186/1687-2770-2013-75",
  ISSN =         "1687-2770",
  MRclass =      "35J15 (35C10)",
  MRnumber =     "3055839",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Special volume in honour of Hari Srivastava.",
  URL =          "http://boundaryvalueproblems.springeropen.com/articles/10.1186/1687-2770-2013-75;
                 http://docserver.carma.newcastle.edu.au/1476/;
                 http://www.boundaryvalueproblems.com/content/2013/1/75",
  abstract =     "In recent years attention has been directed to the
                 problem of solving the Poisson equation, either in
                 engineering scenarios (computational) or in regard to
                 crystal structure (theoretical). Methods: In (Bailey et
                 al. in J. Phys. A, Math. Theor. 46:115201, 2013,
                 doi:10.1088/1751-8113/46/11/115201) we studied a class
                 of lattice sums that amount to solutions of Poisson's
                 equation, utilizing some striking connections between
                 these sums and Jacobi I-function values, together with
                 high-precision numerical computations and the PSLQ
                 algorithm to find certain polynomials associated with
                 these sums. We take a similar approach in this study.
                 Results: We were able to develop new closed forms for
                 certain solutions and to extend such analysis to
                 related lattice sums. We also alluded to results for
                 the compressed sum phi(2)(x,y,d):=1/pi(2) Sigma(m,n is
                 an element of O) cos(pi mx)cos(pi n root dy)/m(2) +
                 dn(2) , (1) where , x, y are real numbers and denotes
                 the odd integers. In this paper we first survey the
                 earlier work and then discuss the sum (1) more
                 completely. Conclusions: As in the previous study, we
                 find some surprisingly simple closed-form evaluations
                 of these sums. In particular, we find that in some
                 cases these sums are given by , where A is an algebraic
                 number. These evaluations suggest that a deep theory
                 interconnects all such summations.",
  acknowledgement = ack-nhfb,
  ajournal =     "Bound. Value Probl.",
  article-number = "75",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Boundary Value Problems",
  journal-URL =  "http://boundaryvalueproblems.springeropen.com/",
  onlinedate =   "13 May 2013",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  unique-id =    "Bailey:2013:CLS",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Bailey:2013:CPF
author: D. H. Bailey and J. M. Borwein and M. Lopez de Prado and Qiji Zhu
pages: 1--18
month: sep
monthnumber: 9
year: 2013
bibdate: Tue Aug 16 09:54:19 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:54:19 ???
note: Preprint.
URL: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2308659
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. H. Bailey and J. M. Borwein and M. {L{\'o}pez de Prado} and Qiji Zhu
rawnote: Preprint.
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
title:
Computing the Probability of Over-Fitting in the Back-Testing and Optimization of Investment Strategies

rawtitle:
Computing the Probability of Over-Fitting in the Back-Testing and Optimization of Investment Strategies

entry:
@Unpublished{Bailey:2013:CPF,
  author =       "D. H. Bailey and J. M. Borwein and M. {L{\'o}pez de
                 Prado} and Qiji Zhu",
  title =        "Computing the Probability of Over-Fitting in the
                 Back-Testing and Optimization of Investment
                 Strategies",
  month =        sep,
  year =         "2013",
  bibdate =      "Tue Aug 16 09:54:19 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Preprint.",
  URL =          "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2308659",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2013:CPI
author: David H. Bailey and Jonathan M. Borwein and Andrew Mattingly and Glenn Wightwick
title: The computation of previously inaccessible digits of $ pi ^2 $ and Catalan's constant
journal: j-NAMS
volume: 60
number: 7
pages: 844--854
month: aug
monthnumber: 8
year: 2013
CODEN: AMNOAN
DOI: https://doi.org/10.1090/noti1015
ISSN: 0002-9920 (print), 1088-9477 (electronic) OR 00029920 (print), 10889477 (electronic)
ISSNL: 0002-9920 OR 00029920
MRclass: 11Y60 (65-04)
MRnumber: 3086394
MRreviewer: Michael M. Dediu
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1436/; http://www.ams.org/notices/201307/rnoti-p844.pdf
fjournal: Notices of the American Mathematical Society
acknowledgement: ack-nhfb
ajournal: Notices Amer. Math. Soc.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/notices/
rawauthor: David H. Bailey and Jonathan M. Borwein and Andrew Mattingly and Glenn Wightwick
rawtitle: The computation of previously inaccessible digits of $ \pi^2 $ and {Catalan}'s constant
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bailey:2013:CPI,
  author =       "David H. Bailey and Jonathan M. Borwein and Andrew
                 Mattingly and Glenn Wightwick",
  title =        "The computation of previously inaccessible digits of
                 $ \pi^2 $ and {Catalan}'s constant",
  journal =      j-NAMS,
  volume =       "60",
  number =       "7",
  pages =        "844--854",
  month =        aug,
  year =         "2013",
  CODEN =        "AMNOAN",
  DOI =          "https://doi.org/10.1090/noti1015",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  MRclass =      "11Y60 (65-04)",
  MRnumber =     "3086394",
  MRreviewer =   "Michael M. Dediu",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1436/;
                 http://www.ams.org/notices/201307/rnoti-p844.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ajournal =     "Notices Amer. Math. Soc.",
  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",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2013:EFS
author: David H. Bailey and Jonathan M. Borwein and Richard E. Crandall and Michael G. Rose
title: Expectations on fractal sets
journal: j-APPL-MATH-COMP
volume: 220
pages: 695--721
day: 1
month: sep
monthnumber: 9
year: 2013
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/j.amc.2013.06.078
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
MRclass: 28A80 (60G18 60G50)
MRnumber: 3091892
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: Applied Mathematics and Computation
keywords: Expectations; Fractals; Monte Carlo methods; Numerical quadrature; Self-similarity
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: David H. Bailey and Jonathan M. Borwein and Richard E. Crandall and Michael G. Rose
rawtitle: Expectations on fractal sets
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1454/; http://www.sciencedirect.com/science/article/pii/S0096300313007273

abstract:
Using fractal self-similarity and functional-expectation relations, the classical theory of box integrals -- being expectations on unit hypercubes -- is extended to a class of fractal ``string-generated Cantor sets'' (SCSs) embedded in unit hypercubes of arbitrary dimension. Motivated by laboratory studies on the distribution of brain synapses, these SCSs were designed for dimensional freedom -- a suitable choice of generating string allows for fine-tuning the fractal dimension of the corresponding set. We also establish closed forms for certain statistical moments on SCSs, develop a precision algorithm for high embedding dimensions, and report various numerical results. The underlying numerical quadrature issues are in themselves quite challenging.

rawabstract:
Using fractal self-similarity and functional-expectation relations, the classical theory of box integrals -- being expectations on unit hypercubes -- is extended to a class of fractal ``string-generated Cantor sets'' (SCSs) embedded in unit hypercubes of arbitrary dimension. Motivated by laboratory studies on the distribution of brain synapses, these SCSs were designed for dimensional freedom -- a suitable choice of generating string allows for fine-tuning the fractal dimension of the corresponding set. We also establish closed forms for certain statistical moments on SCSs, develop a precision algorithm for high embedding dimensions, and report various numerical results. The underlying numerical quadrature issues are in themselves quite challenging.

entry:
@Article{Bailey:2013:EFS,
  author =       "David H. Bailey and Jonathan M. Borwein and Richard E.
                 Crandall and Michael G. Rose",
  title =        "Expectations on fractal sets",
  journal =      j-APPL-MATH-COMP,
  volume =       "220",
  number =       "??",
  pages =        "695--721",
  day =          "1",
  month =        sep,
  year =         "2013",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2013.06.078",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "28A80 (60G18 60G50)",
  MRnumber =     "3091892",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1454/;
                 http://www.sciencedirect.com/science/article/pii/S0096300313007273",
  abstract =     "Using fractal self-similarity and
                 functional-expectation relations, the classical theory
                 of box integrals -- being expectations on unit
                 hypercubes -- is extended to a class of fractal
                 ``string-generated Cantor sets'' (SCSs) embedded in
                 unit hypercubes of arbitrary dimension. Motivated by
                 laboratory studies on the distribution of brain
                 synapses, these SCSs were designed for dimensional
                 freedom -- a suitable choice of generating string
                 allows for fine-tuning the fractal dimension of the
                 corresponding set. We also establish closed forms for
                 certain statistical moments on SCSs, develop a
                 precision algorithm for high embedding dimensions, and
                 report various numerical results. The underlying
                 numerical quadrature issues are in themselves quite
                 challenging.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "Expectations; Fractals; Monte Carlo methods; Numerical
                 quadrature; Self-similarity",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Bailey:2013:HPA
author: David H. Bailey and Jonathan M. Borwein
title: High-Precision Arithmetic: Opportunities and Challenges
pages: 695--721
month: aug
monthnumber: 8
year: 2013
bibdate: Tue Aug 16 09:53:03 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:53:03 ???
note: Preprint.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawnote: Preprint.
rawtitle: High-Precision Arithmetic: Opportunities and Challenges
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Unpublished{Bailey:2013:HPA,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "High-Precision Arithmetic: Opportunities and
                 Challenges",
  month =        aug,
  year =         "2013",
  bibdate =      "Tue Aug 16 09:53:03 2016",
  bibsource =    "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 = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2013:LSA
author: David H. Bailey and Jonathan M. Borwein and Richard E. Crandall and I. John Zucker
title: Lattice sums arising from the Poisson equation
journal: j-J-PHYS-A-MATH-THEOR
volume: 46
number: 11
pages: 115201
month: mar
monthnumber: 3
year: 2013
CODEN: JPAMB5
DOI: https://doi.org/10.1088/1751-8113/46/11/115201
ISSN: 1751-8113 (print), 1751-8121 (electronic) OR 17518113 (print), 17518121 (electronic)
ISSNL: 1751-8113 OR 17518113
MRclass: 35J05 (11Y40 35C05)
MRnumber: 3030150
bibdate: Fri Sep 30 09:24:58 2016
bibtimestamp: 2016.09.30 09:24:58 ???
fjournal: Journal of Physics A: Mathematical and Theoretical
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://iopscience.iop.org/1751-8121
onlinedate: 25 February 2013
rawauthor: David H. Bailey and Jonathan M. Borwein and Richard E. Crandall and I. John Zucker
rawtitle: Lattice sums arising from the {Poisson} equation
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://adsabs.harvard.edu/abs/2013JPhA...46k5201B; http://docserver.carma.newcastle.edu.au/1458/; http://iopscience.iop.org/article/10.1088/1751-8113/46/11/115201; http://stacks.iop.org/1751-8121/46/i=11/a=115201; http://www.davidhbailey.com/dhbpapers/PoissonLattice.pdf

abstract:
In recent times, attention has been directed to the problem of solving the Poisson equation, either in engineering scenarios (computational) or in regard to crystal structure (theoretical). Herein we study a class of lattice sums that amount to Poisson solutions, namely the $n$-dimensional forms $ phi _n(r_1, dots , r_n) = frac 1pi ^2 sum _ m_1, dots , m_n rm odd frac e^ i pi (m_1 r_1 + cdots + m_n r_n)m_1^2 + cdots + m_n^2 $. par By virtue of striking connections with Jacobi $ thetav $-function values, we are able to develop new closed forms for certain values of the coordinates r$_k$, and extend such analysis to similar lattice sums. A primary result is that for rational $x$, $y$, the natural potential $ phiv _2 (x, y)$ is $ frac 1pi log A$ where $A$ is an algebraic number. Various extensions and explicit evaluations are given. Such work is made possible by number-theoretical analysis, symbolic computation and experimental mathematics, including extensive numerical computations using up to 20,000-digit arithmetic.

rawabstract:
In recent times, attention has been directed to the problem of solving the Poisson equation, either in engineering scenarios (computational) or in regard to crystal structure (theoretical). Herein we study a class of lattice sums that amount to Poisson solutions, namely the $n$-dimensional forms $ \phi_n(r_1, \dots, r_n) = \frac {1}{\pi^2} \sum_{ m_1, \dots, m_n {\rm odd}} \frac { e^{ i \pi (m_1 r_1 + \cdots + m_n r_n)}}{m_1^2 + \cdots + m_n^2} $. \par By virtue of striking connections with Jacobi $ \thetav $-function values, we are able to develop new closed forms for certain values of the coordinates r$_k$, and extend such analysis to similar lattice sums. A primary result is that for rational $x$, $y$, the natural potential $ \phiv_2 (x, y)$ is $ \frac {1}{\pi } \log A$ where $A$ is an algebraic number. Various extensions and explicit evaluations are given. Such work is made possible by number-theoretical analysis, symbolic computation and experimental mathematics, including extensive numerical computations using up to 20,000-digit arithmetic.

entry:
@Article{Bailey:2013:LSA,
  author =       "David H. Bailey and Jonathan M. Borwein and Richard E.
                 Crandall and I. John Zucker",
  title =        "Lattice sums arising from the {Poisson} equation",
  journal =      j-J-PHYS-A-MATH-THEOR,
  volume =       "46",
  number =       "11",
  pages =        "115201",
  month =        mar,
  year =         "2013",
  CODEN =        "JPAMB5",
  DOI =          "https://doi.org/10.1088/1751-8113/46/11/115201",
  ISSN =         "1751-8113 (print), 1751-8121 (electronic)",
  ISSN-L =       "1751-8113",
  MRclass =      "35J05 (11Y40 35C05)",
  MRnumber =     "3030150",
  bibdate =      "Fri Sep 30 09:24:58 2016",
  bibsource =    "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/2013JPhA...46k5201B;
                 http://docserver.carma.newcastle.edu.au/1458/;
                 http://iopscience.iop.org/article/10.1088/1751-8113/46/11/115201;
                 http://stacks.iop.org/1751-8121/46/i=11/a=115201;
                 http://www.davidhbailey.com/dhbpapers/PoissonLattice.pdf",
  abstract =     "In recent times, attention has been directed to the
                 problem of solving the Poisson equation, either in
                 engineering scenarios (computational) or in regard to
                 crystal structure (theoretical). Herein we study a
                 class of lattice sums that amount to Poisson solutions,
                 namely the $n$-dimensional forms $ \phi_n(r_1, \dots,
                 r_n) = \frac {1}{\pi^2} \sum_{ m_1, \dots, m_n {\rm
                 odd}} \frac { e^{ i \pi (m_1 r_1 + \cdots + m_n
                 r_n)}}{m_1^2 + \cdots + m_n^2} $. \par

                 By virtue of striking connections with Jacobi $ \thetav
                 $-function values, we are able to develop new closed
                 forms for certain values of the coordinates r$_k$, and
                 extend such analysis to similar lattice sums. A primary
                 result is that for rational $x$, $y$, the natural
                 potential $ \phiv_2 (x, y)$ is $ \frac {1}{\pi } \log
                 A$ where $A$ is an algebraic number. Various extensions
                 and explicit evaluations are given. Such work is made
                 possible by number-theoretical analysis, symbolic
                 computation and experimental mathematics, including
                 extensive numerical computations using up to
                 20,000-digit arithmetic.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eid =          "115201",
  fjournal =     "Journal of Physics A: Mathematical and Theoretical",
  journal-URL =  "http://iopscience.iop.org/1751-8121",
  onlinedate =   "25 February 2013",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  pagecount =    "31",
  unique-id =    "Bailey:2013:LSA",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Bailey:2013:NNP
author: David H. Bailey and Jonathan M. Borwein
title: Normal numbers and pseudorandom generators
crossref: Bailey:2013:CAM
volume: 50
pages: 1--18
year: 2013
DOI: https://doi.org/10.1007/978-1-4614-7621-4_1
MRclass: 11K16 (11A63 11K45)
MRnumber: 3108419
MRreviewer: John H. Loxton
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
series: Springer Proc. Math. Stat.
URL: http://docserver.carma.newcastle.edu.au/1448/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Normal numbers and pseudorandom generators
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/prng.bib

entry:
@InCollection{Bailey:2013:NNP,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Normal numbers and pseudorandom generators",
  crossref =     "Bailey:2013:CAM",
  volume =       "50",
  pages =        "1--18",
  year =         "2013",
  DOI =          "https://doi.org/10.1007/978-1-4614-7621-4_1",
  MRclass =      "11K16 (11A63 11K45)",
  MRnumber =     "3108419",
  MRreviewer =   "John H. Loxton",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  series =       "Springer Proc. Math. Stat.",
  URL =          "http://docserver.carma.newcastle.edu.au/1448/",
  acknowledgement = ack-nhfb,
  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:2013:OSD
author: D. H. Bailey and J. M. Borwein and Victoria Stodden
title: Opinion: Set the default to ``open''
journal: j-NAMS
volume: 60
number: 6
pages: 679--680
month: jun
monthnumber: 6
year: 2013
CODEN: AMNOAN
DOI: https://doi.org/10.1090/noti1014
ISSN: 0002-9920 (print), 1088-9477 (electronic) OR 00029920 (print), 10889477 (electronic)
ISSNL: 0002-9920 OR 00029920
bibdate: Sat Aug 13 15:29:13 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 15:29:13 ???
URL: http://www.ams.org/notices/201306/rnoti-p679.pdf
fjournal: Notices of the American Mathematical Society
remark: Commentary on reproducibility in Computational and Experimental Mathematics.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/notices/
rawauthor: D. H. Bailey and J. M. Borwein and Victoria Stodden
rawtitle: Opinion: Set the default to ``open''
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bailey:2013:OSD,
  author =       "D. H. Bailey and J. M. Borwein and Victoria Stodden",
  title =        "Opinion: Set the default to ``open''",
  journal =      j-NAMS,
  volume =       "60",
  number =       "6",
  pages =        "679--680",
  month =        jun # "\slash " # jul,
  year =         "2013",
  CODEN =        "AMNOAN",
  DOI =          "https://doi.org/10.1090/noti1014",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibdate =      "Sat Aug 13 15:29:13 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.ams.org/notices/201306/rnoti-p679.pdf",
  acknowledgement = ack-nhfb,
  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 =       "Commentary on reproducibility in Computational and
                 Experimental Mathematics.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:2013:PDU
author: David H. Bailey and Jonathan M. Borwein
title: Pi Day is upon us again and we still do not know if Pi is normal
type: Report
address: Berkeley, CA 94720, USA and Callaghan, NSW 2308, Australia
pages: 20
day: 29
month: may
monthnumber: 5
year: 2013
bibdate: Fri Aug 12 18:29:28 2016
bibtimestamp: 2016.08.12 18:29:28 ???
URL: http://www.carma.newcastle.edu.au/jon/pi-monthly.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Pi Day is upon us again and we still do not know if Pi is normal
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
institution:
Lawrence Berkeley National Laboratory and Centre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle

entry:
@TechReport{Bailey:2013:PDU,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Pi Day is upon us again and we still do not know if Pi
                 is normal",
  type =         "Report",
  institution =  "Lawrence Berkeley National Laboratory and Centre for
                 Computer Assisted Research Mathematics and its
                 Applications (CARMA), University of Newcastle",
  address =      "Berkeley, CA 94720, USA and Callaghan, NSW 2308,
                 Australia",
  pages =        "20",
  day =          "29",
  month =        may,
  year =         "2013",
  bibdate =      "Fri Aug 12 18:29:28 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  URL =          "http://www.carma.newcastle.edu.au/jon/pi-monthly.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: unpublished
filename: borwein-jonathan-m.bib
label: Bailey:2013:SDRa
author: D. H. Bailey and J. Borwein and R. J. LeVeque and W. Rider and W. Stein and V. Stodden
pages: 20
month: jan
monthnumber: 1
year: 2013
bibdate: Tue Aug 16 09:54:58 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:54:58 ???
note: Preprint in collaboration with the workshop participants.
URL: http://www.carma.newcastle.edu.au/jon/icerm12.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. H. Bailey and J. Borwein and R. J. LeVeque and W. Rider and W. Stein and V. Stodden
rawnote: Preprint in collaboration with the workshop participants.
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
title:
Setting the Default to Reproducible. Report on the ICERM Workshop: Reproducibility in Computational and Experimental Mathematics, December 10--14, 2012

rawtitle:
Setting the Default to Reproducible. {Report} on the {ICERM} Workshop: Reproducibility in Computational and Experimental Mathematics, {December 10--14, 2012}

entry:
@Unpublished{Bailey:2013:SDRa,
  author =       "D. H. Bailey and J. Borwein and R. J. LeVeque and W.
                 Rider and W. Stein and V. Stodden",
  title =        "Setting the Default to Reproducible. {Report} on the
                 {ICERM} Workshop: Reproducibility in Computational and
                 Experimental Mathematics, {December 10--14, 2012}",
  month =        jan,
  year =         "2013",
  bibdate =      "Tue Aug 16 09:54:58 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Preprint in collaboration with the workshop
                 participants.",
  URL =          "http://www.carma.newcastle.edu.au/jon/icerm12.pdf",
  acknowledgement = ack-nhfb,
  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: Bauschke:2013:MOB
author: Heinz H. Bauschke and Jonathan M. Borwein and Xianfu Wang and Liangjin Yao
title: Monotone operators and ``bigger conjugate'' functions
journal: j-J-CONVEX-ANAL
volume: 20
number: 1
pages: 143--155
year: 2013
ISSN: 0944-6532 (print), 2363-6394 (electronic) OR 09446532 (print), 23636394 (electronic)
MRclass: 47H05 (47N10 49J53)
MRnumber: 3086445
MRreviewer: Aris Daniilidis
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: Heinz H. Bauschke and Jonathan M. Borwein and Xianfu Wang and Liangjin Yao
rawtitle: Monotone operators and ``bigger conjugate'' functions
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1477/; http://www.heldermann.de/JCA/JCA20/JCA201/jca20009.htm

abstract:
We study a question posed by Stephen Simons in his 2008 monograph involving ``bigger conjugate'' (BC) functions and the partial infimal convolution. As Simons demonstrated in his monograph, these function have been crucial to the understanding and advancement of the state-of-the-art of harder problems in monotone operator theory, especially the sum problem. In this paper, we provide some tools for further analysis of BC-functions which allow us to answer Simons' problem in the negative. We are also able to refute a similar but much harder conjecture which would have generalized a classical result of Brezis, Crandall and Pazy. Our work also reinforces the importance of understanding unbounded skew linear relations to construct monotone operators with unexpected properties.

rawabstract:
We study a question posed by Stephen Simons in his 2008 monograph involving ``bigger conjugate'' (BC) functions and the partial infimal convolution. As Simons demonstrated in his monograph, these function have been crucial to the understanding and advancement of the state-of-the-art of harder problems in monotone operator theory, especially the sum problem. In this paper, we provide some tools for further analysis of BC-functions which allow us to answer Simons' problem in the negative. We are also able to refute a similar but much harder conjecture which would have generalized a classical result of Brezis, Crandall and Pazy. Our work also reinforces the importance of understanding unbounded skew linear relations to construct monotone operators with unexpected properties.

entry:
@Article{Bauschke:2013:MOB,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein and Xianfu
                 Wang and Liangjin Yao",
  title =        "Monotone operators and ``bigger conjugate''
                 functions",
  journal =      j-J-CONVEX-ANAL,
  volume =       "20",
  number =       "1",
  pages =        "143--155",
  year =         "2013",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "47H05 (47N10 49J53)",
  MRnumber =     "3086445",
  MRreviewer =   "Aris Daniilidis",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1477/;
                 http://www.heldermann.de/JCA/JCA20/JCA201/jca20009.htm",
  abstract =     "We study a question posed by Stephen Simons in his
                 2008 monograph involving ``bigger conjugate'' (BC)
                 functions and the partial infimal convolution. As
                 Simons demonstrated in his monograph, these function
                 have been crucial to the understanding and advancement
                 of the state-of-the-art of harder problems in monotone
                 operator theory, especially the sum problem. In this
                 paper, we provide some tools for further analysis of
                 BC-functions which allow us to answer Simons' problem
                 in the negative. We are also able to refute a similar
                 but much harder conjecture which would have generalized
                 a classical result of Brezis, Crandall and Pazy. Our
                 work also reinforces the importance of understanding
                 unbounded skew linear relations to construct monotone
                 operators with unexpected properties.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Convex Analysis",
  journal-URL =  "http://www.heldermann.de/JCA/jcacon.htm",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
  unique-id =    "Bauschke:2013:MOB",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2013:ACR
author: J. M. Borwein and G. Li and L. Yao
journal: ArXiv e-prints
pages: 143--155
month: apr
monthnumber: 4
year: 2013
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/2013arXiv1304.7965B; http://docserver.carma.newcastle.edu.au/1508/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and G. Li and L. Yao
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Analysis of the convergence rate for the cyclic projection algorithm applied to basic semi-algebraic convex sets

abstract:
In this paper, we study the rate of convergence of the cyclic projection algorithm applied to finitely many basic semi-algebraic convex sets. We establish an explicit convergence rate estimate which relies on the maximum degree of the polynomials that generate the basic semi-algebraic convex sets and the dimension of the underlying space. We achieve our results by exploiting the algebraic structure of the basic semi-algebraic convex sets.

keywords:
Mathematics - Functional Analysis, Mathematics - Optimization and Control, Primary 41A25, 90C25, Secondary 41A50, 90C31

rawabstract:
In this paper, we study the rate of convergence of the cyclic projection algorithm applied to finitely many basic semi-algebraic convex sets. We establish an explicit convergence rate estimate which relies on the maximum degree of the polynomials that generate the basic semi-algebraic convex sets and the dimension of the underlying space. We achieve our results by exploiting the algebraic structure of the basic semi-algebraic convex sets.

rawtitle:
Analysis of the convergence rate for the cyclic projection algorithm applied to basic semi-algebraic convex sets

entry:
@Article{Borwein:2013:ACR,
  author =       "J. M. Borwein and G. Li and L. Yao",
  title =        "Analysis of the convergence rate for the cyclic
                 projection algorithm applied to basic semi-algebraic
                 convex sets",
  journal =      "ArXiv e-prints",
  month =        apr,
  year =         "2013",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2013arXiv1304.7965B;
                 http://docserver.carma.newcastle.edu.au/1508/",
  abstract =     "In this paper, we study the rate of convergence of the
                 cyclic projection algorithm applied to finitely many
                 basic semi-algebraic convex sets. We establish an
                 explicit convergence rate estimate which relies on the
                 maximum degree of the polynomials that generate the
                 basic semi-algebraic convex sets and the dimension of
                 the underlying space. We achieve our results by
                 exploiting the algebraic structure of the basic
                 semi-algebraic convex sets.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1304.7965",
  keywords =     "Mathematics - Functional Analysis, Mathematics -
                 Optimization and Control, Primary 41A25, 90C25,
                 Secondary 41A50, 90C31",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:2013:C
author: J. M. Borwein
title: CARMA
pages: 70--72
month: jul
monthnumber: 7
year: 2013
bibdate: Sat Aug 13 15:27:06 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 15:27:06 ???
URL: http://www.international-innovation-northamerica.com
remark: The URL domain no longer exists, and the reference from CV.pdf is uncertain.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein
rawtitle: CARMA
ORCID: Borwein, Jonathan/0000-0002-1263-0646
note:
One of a small selected number of researchers featured in an issue with a focus on ``Mathematics, Statistics, Numerical and Computational Mathematics,'' International Innovation.

rawnote:
One of a small selected number of researchers featured in an issue with a focus on ``Mathematics, Statistics, Numerical and Computational Mathematics,'' International Innovation.

entry:
@Unpublished{Borwein:2013:C,
  author =       "J. M. Borwein",
  title =        "CARMA",
  pages =        "70--72",
  month =        jul,
  year =         "2013",
  bibdate =      "Sat Aug 13 15:27:06 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "One of a small selected number of researchers featured
                 in an issue with a focus on ``Mathematics, Statistics,
                 Numerical and Computational Mathematics,''
                 International Innovation.",
  URL =          "http://www.international-innovation-northamerica.com",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "The URL domain no longer exists, and the reference
                 from CV.pdf is uncertain.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2013:CDRa
author: J. M. Borwein and M. K. Tam
title: A Cyclic Douglas--Rachford Iteration Scheme
journal: ArXiv e-prints
pages: 70--72
month: mar
monthnumber: 3
year: 2013
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/2013arXiv1303.1859B; http://docserver.carma.newcastle.edu.au/1469/
keywords: Mathematics - Optimization and Control, Mathematics - Functional Analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and M. K. Tam
rawtitle: A Cyclic {Douglas--Rachford} Iteration Scheme
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper we present two Douglas--Rachford inspired iteration schemes which can be applied directly to $N$-set convex feasibility problems in Hilbert space. Our main results are weak convergence of the methods to a point whose nearest point projections onto each of the $N$ sets coincide. For affine subspaces, convergence is in norm. Initial results from numerical experiments, comparing our methods to the classical (product-space) Douglas--Rachford scheme, are promising.

rawabstract:
In this paper we present two Douglas--Rachford inspired iteration schemes which can be applied directly to $N$-set convex feasibility problems in Hilbert space. Our main results are weak convergence of the methods to a point whose nearest point projections onto each of the $N$ sets coincide. For affine subspaces, convergence is in norm. Initial results from numerical experiments, comparing our methods to the classical (product-space) Douglas--Rachford scheme, are promising.

entry:
@Article{Borwein:2013:CDRa,
  author =       "J. M. Borwein and M. K. Tam",
  title =        "A Cyclic {Douglas--Rachford} Iteration Scheme",
  journal =      "ArXiv e-prints",
  month =        mar,
  year =         "2013",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2013arXiv1303.1859B;
                 http://docserver.carma.newcastle.edu.au/1469/",
  abstract =     "In this paper we present two Douglas--Rachford
                 inspired iteration schemes which can be applied
                 directly to $N$-set convex feasibility problems in
                 Hilbert space. Our main results are weak convergence of
                 the methods to a point whose nearest point projections
                 onto each of the $N$ sets coincide. For affine
                 subspaces, convergence is in norm. Initial results from
                 numerical experiments, comparing our methods to the
                 classical (product-space) Douglas--Rachford scheme, are
                 promising.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1303.1859",
  keywords =     "Mathematics - Optimization and Control, Mathematics -
                 Functional Analysis",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.OC",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2013:CDRb
author: J. M. Borwein and M. K. Tam
title: The Cyclic Douglas--Rachford Method for Inconsistent Feasibility Problems
journal: ArXiv e-prints
pages: 70--72
month: oct
monthnumber: 10
year: 2013
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/2013arXiv1310.2195B
keywords: Mathematics - Optimization and Control
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and M. K. Tam
rawtitle: The Cyclic {Douglas--Rachford} Method for Inconsistent Feasibility Problems
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We analyse the behaviour of the newly introduced cyclic Douglas--Rachford algorithm for finding a point in the intersection of a finite number of closed convex sets. This work considers the case in which the target intersection set is possibly empty.

rawabstract:
We analyse the behaviour of the newly introduced cyclic Douglas--Rachford algorithm for finding a point in the intersection of a finite number of closed convex sets. This work considers the case in which the target intersection set is possibly empty.

entry:
@Article{Borwein:2013:CDRb,
  author =       "J. M. Borwein and M. K. Tam",
  title =        "The Cyclic {Douglas--Rachford} Method for Inconsistent
                 Feasibility Problems",
  journal =      "ArXiv e-prints",
  month =        oct,
  year =         "2013",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2013arXiv1310.2195B",
  abstract =     "We analyse the behaviour of the newly introduced
                 cyclic Douglas--Rachford algorithm for finding a point
                 in the intersection of a finite number of closed convex
                 sets. This work considers the case in which the target
                 intersection set is possibly empty.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1310.2195",
  keywords =     "Mathematics - Optimization and Control",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.OC",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2013:CFW
author: Jonathan M. Borwein and Richard E. Crandall
title: Closed forms: what they are and why we care
journal: j-NAMS
volume: 60
number: 1
pages: 50--65
month: jan
monthnumber: 1
year: 2013
CODEN: AMNOAN
DOI: https://doi.org/10.1090/noti936
ISSN: 0002-9920 (print), 1088-9477 (electronic) OR 00029920 (print), 10889477 (electronic)
ISSNL: 0002-9920 OR 00029920
MRclass: 33F05
MRnumber: 3052463
MRreviewer: Allan J. Mac Leod
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/767/; http://www.ams.org/notices/201301/rnoti-p50.pdf
fjournal: Notices of the American Mathematical Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/notices/
rawauthor: Jonathan M. Borwein and Richard E. Crandall
rawtitle: Closed forms: what they are and why we care
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2013:CFW,
  author =       "Jonathan M. Borwein and Richard E. Crandall",
  title =        "Closed forms: what they are and why we care",
  journal =      j-NAMS,
  volume =       "60",
  number =       "1",
  pages =        "50--65",
  month =        jan,
  year =         "2013",
  CODEN =        "AMNOAN",
  DOI =          "https://doi.org/10.1090/noti936",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  MRclass =      "33F05",
  MRnumber =     "3052463",
  MRreviewer =   "Allan J. Mac Leod",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/767/;
                 http://www.ams.org/notices/201301/rnoti-p50.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2013:CIL
author: Jonathan Borwein and Christopher Maitland and Matthew Skerritt
title: Computation of an improved lower bound to Giuga's primality conjecture
journal: j-INTEGERS
volume: 13
pages: Paper No. A67, 14
year: 2013
CODEN: INTEHN
ISSN: 1553-1732 OR 15531732
MRclass: 11A25
MRnumber: 3118385
MRreviewer: Samuel S. Wagstaff, Jr.
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/1511/
fjournal: Integers. Electronic Journal of Combinatorial Number Theory
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.degruyter.com/view/j/integ
rawauthor: Jonathan Borwein and Christopher Maitland and Matthew Skerritt
rawtitle: Computation of an improved lower bound to {Giuga}'s primality conjecture
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2013:CIL,
  author =       "Jonathan Borwein and Christopher Maitland and Matthew
                 Skerritt",
  title =        "Computation of an improved lower bound to {Giuga}'s
                 primality conjecture",
  journal =      j-INTEGERS,
  volume =       "13",
  pages =        "Paper No. A67, 14",
  year =         "2013",
  CODEN =        "INTEHN",
  ISSN =         "1553-1732",
  MRclass =      "11A25",
  MRnumber =     "3118385",
  MRreviewer =   "Samuel S. Wagstaff, Jr.",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1511/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Integers. Electronic Journal of Combinatorial Number
                 Theory",
  journal-URL =  "http://www.degruyter.com/view/j/integ",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2013:CLB
author: Jonathan M. Borwein and Matthew Skerritt and Christopher Maitland
title: Computation of a lower bound to Giuga's primality conjecture
journal: j-INTEGERS
volume: 13
pages: ??--??
year: 2013
CODEN: INTEHN
ISSN: 1867-0652 (print), 1867-0660 (electronic) OR 18670652 (print), 18670660 (electronic)
bibdate: Fri Aug 12 08:29:15 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 08:29:15 ???
URL: http://docserver.carma.newcastle.edu.au/1511/
fjournal: Integers
remark: I cannot find this online; it seems that no volumes after v12n6 has been published.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.degruyter.com/view/j/integ
rawauthor: Jonathan M. Borwein and Matthew Skerritt and Christopher Maitland
rawtitle: Computation of a lower bound to {Giuga}'s primality conjecture
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2013:CLB,
  author =       "Jonathan M. Borwein and Matthew Skerritt and
                 Christopher Maitland",
  title =        "Computation of a lower bound to {Giuga}'s primality
                 conjecture",
  journal =      j-INTEGERS,
  volume =       "13",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2013",
  CODEN =        "INTEHN",
  DOI =          "",
  ISSN =         "1867-0652 (print), 1867-0660 (electronic)",
  bibdate =      "Fri Aug 12 08:29:15 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1511/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Integers",
  journal-URL =  "http://www.degruyter.com/view/j/integ",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "I cannot find this online; it seems that no volumes
                 after v12n6 has been published.",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2013:EWC
author: Jonathan Borwein and Michael Rose
title: Explainer: what is Chaos Theory
crossref: Tressider:2013:EDV
pages: ??--??
year: 2013
bibdate: Sat Aug 13 15:19:55 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 15:19:55 ???
URL: https://theconversation.com/explainer-what-is-chaos-theory-10620
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein and Michael Rose
rawtitle: Explainer: what is Chaos Theory
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2013:EWC,
  author =       "Jonathan Borwein and Michael Rose",
  title =        "Explainer: what is Chaos Theory",
  crossref =     "Tressider:2013:EDV",
  pages =        "??--??",
  year =         "2013",
  bibdate =      "Sat Aug 13 15:19:55 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "https://theconversation.com/explainer-what-is-chaos-theory-10620",
  acknowledgement = ack-nhfb,
  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:2013:LST
author: J. M. Borwein and M. L. Glasser and R. C. McPhedran and J. G. Wan and I. J. Zucker
title: Lattice Sums: Then and Now
volume: 150
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: xx + 368
year: 2013
DOI: https://doi.org/10.1017/CBO9781139626804
ISBN: 1-107-03990-8 OR 1107039908
ISBN13: 978-1-107-03990-2 OR 9781107039902
MRclass: 11Mxx (11H06 11K99 11Lxx 11P21 82D25)
MRnumber: 3135109
MRreviewer: S. L. Kalla
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: With a foreword by Helaman Ferguson and Claire Ferguson.
series: Encyclopedia of Mathematics and its Applications
URL: http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139626804
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and M. L. Glasser and R. C. McPhedran and J. G. Wan and I. J. Zucker
rawnote: With a foreword by Helaman Ferguson and Claire Ferguson.
rawtitle: Lattice Sums: Then and Now
ORCID: Borwein, Jonathan/0000-0002-1263-0646
TOC:
Frontmatter / i--iv Dedication / v--vi Contents / vii--x Foreword by Helaman and Claire Ferguson / xi--xvi Preface / xvii--xx 1: Lattice sums / 1--86 2: Convergence of lattice sums and Madelung's constant / 87--124 3: Angular lattice sums / 125--156 4: Use of Dirichlet series with complex characters / 157--185 5: Lattice sums and Ramanujan's modular equations / 186--201 6: Closed-form evaluations of three- and four-dimensional sums / 202--225 7: Electron sums / 226--246 8: Madelung sums in higher dimensions / 247--293 9: Seventy years of the Watson integrals / 294--323 Appendix / 324--349 References / 350--363 Index / 364--368

rawTOC:
Frontmatter / i--iv \\ Dedication / v--vi \\ Contents / vii--x \\ Foreword by Helaman and Claire Ferguson / xi--xvi \\ Preface / xvii--xx \\ 1: Lattice sums / 1--86 \\ 2: Convergence of lattice sums and Madelung's constant / 87--124 \\ 3: Angular lattice sums / 125--156 \\ 4: Use of Dirichlet series with complex characters / 157--185 \\ 5: Lattice sums and Ramanujan's modular equations / 186--201 \\ 6: Closed-form evaluations of three- and four-dimensional sums / 202--225 \\ 7: Electron sums / 226--246 \\ 8: Madelung sums in higher dimensions / 247--293 \\ 9: Seventy years of the Watson integrals / 294--323 \\ Appendix / 324--349 \\ References / 350--363 \\ Index / 364--368

entry:
@Book{Borwein:2013:LST,
  author =       "J. M. Borwein and M. L. Glasser and R. C. McPhedran
                 and J. G. Wan and I. J. Zucker",
  title =        "Lattice Sums: Then and Now",
  volume =       "150",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xx + 368",
  year =         "2013",
  DOI =          "https://doi.org/10.1017/CBO9781139626804",
  ISBN =         "1-107-03990-8",
  ISBN-13 =      "978-1-107-03990-2",
  MRclass =      "11Mxx (11H06 11K99 11Lxx 11P21 82D25)",
  MRnumber =     "3135109",
  MRreviewer =   "S. L. Kalla",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "With a foreword by Helaman Ferguson and Claire
                 Ferguson.",
  series =       "Encyclopedia of Mathematics and its Applications",
  URL =          "http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139626804",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  tableofcontents = "Frontmatter / i--iv \\
                 Dedication / v--vi \\
                 Contents / vii--x \\
                 Foreword by Helaman and Claire Ferguson / xi--xvi \\
                 Preface / xvii--xx \\
                 1: Lattice sums / 1--86 \\
                 2: Convergence of lattice sums and Madelung's constant
                 / 87--124 \\
                 3: Angular lattice sums / 125--156 \\
                 4: Use of Dirichlet series with complex characters /
                 157--185 \\
                 5: Lattice sums and Ramanujan's modular equations /
                 186--201 \\
                 6: Closed-form evaluations of three- and
                 four-dimensional sums / 202--225 \\
                 7: Electron sums / 226--246 \\
                 8: Madelung sums in higher dimensions / 247--293 \\
                 9: Seventy years of the Watson integrals / 294--323 \\
                 Appendix / 324--349 \\
                 References / 350--363 \\
                 Index / 364--368",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2013:LSW
author: D. Borwein and J. M. Borwein and A. Straub
title: On lattice sums and Wigner limits
journal: ArXiv e-prints
pages: xx + 368
month: oct
monthnumber: 10
year: 2013
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/2013arXiv1310.1423B; http://docserver.carma.newcastle.edu.au/1509/
keywords: Mathematical Physics, Mathematics - Classical Analysis and ODEs, Mathematics - Number Theory
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. Borwein and J. M. Borwein and A. Straub
rawtitle: On lattice sums and {Wigner} limits
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053
abstract:
Wigner limits are given formally as the difference between a lattice sum, associated to a positive definite quadratic form, and a corresponding multiple integral. To define these limits, which arose in work of Wigner on the energy of static electron lattices, in a mathematically rigorous way one commonly truncates the lattice sum and the corresponding integral and takes the limit along expanding hypercubes or other regular geometric shapes. We generalize the known mathematically rigorous two and three dimensional results regarding Wigner limits, as laid down in [Analysis of certain lattice sums, D. Borwein, J. M. Borwein, and R. Shail, 1989], to integer lattices of arbitrary dimension. In doing so, we also resolve a problem posed in Chapter 7 of [Lattice Sums: Then and Now, J. M. Borwein, L. Glasser, R. McPhedran, J. G. Wan, and I. J. Zucker, 2013]. For the sake of clarity, we begin by considering the simpler case of cubic lattice sums first, before treating the case of arbitrary quadratic forms. We also consider limits taken along expanding hyperballs with respect to general norms, and connect with classical topics such as Gauss's circle problem. An appendix is included to recall certain properties of Epstein zeta functions that are either used in the paper or serve to provide perspective.

rawabstract:
Wigner limits are given formally as the difference between a lattice sum, associated to a positive definite quadratic form, and a corresponding multiple integral. To define these limits, which arose in work of Wigner on the energy of static electron lattices, in a mathematically rigorous way one commonly truncates the lattice sum and the corresponding integral and takes the limit along expanding hypercubes or other regular geometric shapes. We generalize the known mathematically rigorous two and three dimensional results regarding Wigner limits, as laid down in [Analysis of certain lattice sums, D. Borwein, J. M. Borwein, and R. Shail, 1989], to integer lattices of arbitrary dimension. In doing so, we also resolve a problem posed in Chapter 7 of [Lattice Sums: Then and Now, J. M. Borwein, L. Glasser, R. McPhedran, J. G. Wan, and I. J. Zucker, 2013]. For the sake of clarity, we begin by considering the simpler case of cubic lattice sums first, before treating the case of arbitrary quadratic forms. We also consider limits taken along expanding hyperballs with respect to general norms, and connect with classical topics such as Gauss's circle problem. An appendix is included to recall certain properties of Epstein zeta functions that are either used in the paper or serve to provide perspective.

entry:
@Article{Borwein:2013:LSW,
  author =       "D. Borwein and J. M. Borwein and A. Straub",
  title =        "On lattice sums and {Wigner} limits",
  journal =      "ArXiv e-prints",
  month =        oct,
  year =         "2013",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2013arXiv1310.1423B;
                 http://docserver.carma.newcastle.edu.au/1509/",
  abstract =     "Wigner limits are given formally as the difference
                 between a lattice sum, associated to a positive
                 definite quadratic form, and a corresponding multiple
                 integral. To define these limits, which arose in work
                 of Wigner on the energy of static electron lattices, in
                 a mathematically rigorous way one commonly truncates
                 the lattice sum and the corresponding integral and
                 takes the limit along expanding hypercubes or other
                 regular geometric shapes. We generalize the known
                 mathematically rigorous two and three dimensional
                 results regarding Wigner limits, as laid down in
                 [Analysis of certain lattice sums, D. Borwein, J. M.
                 Borwein, and R. Shail, 1989], to integer lattices of
                 arbitrary dimension. In doing so, we also resolve a
                 problem posed in Chapter 7 of [Lattice Sums: Then and
                 Now, J. M. Borwein, L. Glasser, R. McPhedran, J. G.
                 Wan, and I. J. Zucker, 2013]. For the sake of clarity,
                 we begin by considering the simpler case of cubic
                 lattice sums first, before treating the case of
                 arbitrary quadratic forms. We also consider limits
                 taken along expanding hyperballs with respect to
                 general norms, and connect with classical topics such
                 as Gauss's circle problem. An appendix is included to
                 recall certain properties of Epstein zeta functions
                 that are either used in the paper or serve to provide
                 perspective.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1310.1423",
  keywords =     "Mathematical Physics, Mathematics - Classical Analysis
                 and ODEs, Mathematics - Number Theory",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053",
  primaryclass = "math-ph",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2013:MMS
author: Jonathan M. Borwein and Armin Straub
title: Mahler measures, short walks and log-sine integrals
journal: j-THEOR-COMP-SCI
volume: 479
pages: 4--21
year: 2013
CODEN: TCSCDI
DOI: https://doi.org/10.1016/j.tcs.2012.10.025
ISSN: 0304-3975 (print), 1879-2294 (electronic) OR 03043975 (print), 18792294 (electronic)
ISSNL: 0304-3975 OR 03043975
MRclass: 11R06 (11M32 33E20 60G50 68W30)
MRnumber: 3034554
MRreviewer: Kevin G. Hare
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 ???
note: Symbolic-Numerical Algorithms.
fjournal: Theoretical Computer Science
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/03043975
rawauthor: Jonathan M. Borwein and Armin Straub
rawnote: Symbolic-Numerical Algorithms.
rawtitle: {Mahler} measures, short walks and log-sine integrals
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053
URL:
http://docserver.carma.newcastle.edu.au/1383/; http://www.sciencedirect.com/science/article/pii/S0304397512009462

abstract:
The Mahler measure of a polynomial in several variables has been a subject of much study over the past thirty years --- very few closed forms are proven but more are conjectured. In the case of multiple Mahler measures more tractable but interesting families exist. Using values of log-sine integrals we provide systematic evaluations of various higher and multiple Mahler measures. The evaluations in terms of log-sine integrals become particularly useful in light of the fact that log-sine integrals may be automatically reexpressed as polylogarithmic values. We present this correspondence along with related generating functions for log-sine integrals. Our initial interest in considering Mahler measures stems from a study of uniform random walks in the plane as first introduced by Pearson. The main results on the moments of the distance traveled by an n -step walk, as well as the corresponding probability density functions, are reviewed. It is the derivative values of the moments that are Mahler measures. This work would be impossible without very extensive symbolic and numeric computations. It also makes frequent use of the new NIST Handbook of Mathematical Functions and similar tools. Our intention is to show off the interplay between numeric and symbolic computing while exploring the three mathematical topics in the title.

rawabstract:
The Mahler measure of a polynomial in several variables has been a subject of much study over the past thirty years --- very few closed forms are proven but more are conjectured. In the case of multiple Mahler measures more tractable but interesting families exist. Using values of log-sine integrals we provide systematic evaluations of various higher and multiple Mahler measures. The evaluations in terms of log-sine integrals become particularly useful in light of the fact that log-sine integrals may be automatically reexpressed as polylogarithmic values. We present this correspondence along with related generating functions for log-sine integrals. Our initial interest in considering Mahler measures stems from a study of uniform random walks in the plane as first introduced by Pearson. The main results on the moments of the distance traveled by an n -step walk, as well as the corresponding probability density functions, are reviewed. It is the derivative values of the moments that are Mahler measures. This work would be impossible without very extensive symbolic and numeric computations. It also makes frequent use of the new NIST Handbook of Mathematical Functions and similar tools. Our intention is to show off the interplay between numeric and symbolic computing while exploring the three mathematical topics in the title.

entry:
@Article{Borwein:2013:MMS,
  author =       "Jonathan M. Borwein and Armin Straub",
  title =        "{Mahler} measures, short walks and log-sine
                 integrals",
  journal =      j-THEOR-COMP-SCI,
  volume =       "479",
  pages =        "4--21",
  year =         "2013",
  CODEN =        "TCSCDI",
  DOI =          "https://doi.org/10.1016/j.tcs.2012.10.025",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  MRclass =      "11R06 (11M32 33E20 60G50 68W30)",
  MRnumber =     "3034554",
  MRreviewer =   "Kevin G. Hare",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Symbolic-Numerical Algorithms.",
  URL =          "http://docserver.carma.newcastle.edu.au/1383/;
                 http://www.sciencedirect.com/science/article/pii/S0304397512009462",
  abstract =     "The Mahler measure of a polynomial in several
                 variables has been a subject of much study over the
                 past thirty years --- very few closed forms are proven
                 but more are conjectured. In the case of multiple
                 Mahler measures more tractable but interesting families
                 exist. Using values of log-sine integrals we provide
                 systematic evaluations of various higher and multiple
                 Mahler measures. The evaluations in terms of log-sine
                 integrals become particularly useful in light of the
                 fact that log-sine integrals may be automatically
                 reexpressed as polylogarithmic values. We present this
                 correspondence along with related generating functions
                 for log-sine integrals. Our initial interest in
                 considering Mahler measures stems from a study of
                 uniform random walks in the plane as first introduced
                 by Pearson. The main results on the moments of the
                 distance traveled by an n -step walk, as well as the
                 corresponding probability density functions, are
                 reviewed. It is the derivative values of the moments
                 that are Mahler measures. This work would be impossible
                 without very extensive symbolic and numeric
                 computations. It also makes frequent use of the new
                 NIST Handbook of Mathematical Functions and similar
                 tools. Our intention is to show off the interplay
                 between numeric and symbolic computing while exploring
                 the three mathematical topics in the title.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2013:MOE
author: Jonathan M. Borwein and Regina S. Burachik and Liangjin Yao
title: Monotone operators without enlargements
crossref: Bailey:2013:CAM
volume: 50
pages: 79--103
year: 2013
DOI: https://doi.org/10.1007/978-1-4614-7621-4_5
MRclass: 47H05
MRnumber: 3108423
MRreviewer: Heinz H. Bauschke
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: Springer Proc. Math. Stat.
URL: http://docserver.carma.newcastle.edu.au/1447/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Regina S. Burachik and Liangjin Yao
rawtitle: Monotone operators without enlargements
ORCID: Burachik, Regina/0000-0003-1332-6213; Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2013:MOE,
  author =       "Jonathan M. Borwein and Regina S. Burachik and
                 Liangjin Yao",
  title =        "Monotone operators without enlargements",
  crossref =     "Bailey:2013:CAM",
  volume =       "50",
  pages =        "79--103",
  year =         "2013",
  DOI =          "https://doi.org/10.1007/978-1-4614-7621-4_5",
  MRclass =      "47H05",
  MRnumber =     "3108423",
  MRreviewer =   "Heinz H. Bauschke",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Springer Proc. Math. Stat.",
  URL =          "http://docserver.carma.newcastle.edu.au/1447/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Burachik, Regina/0000-0003-1332-6213; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2013:MSM
author: Jonathan M. Borwein and Liangjin Yao
title: Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator
journal: j-SET-VALUED-VAR-ANAL
volume: 21
number: 4
pages: 603--616
year: 2013
DOI: https://doi.org/10.1007/s11228-013-0259-y
ISSN: 1877-0533 (print), 1877-0541 (electronic) OR 18770533 (print), 18770541 (electronic)
ISSNL: 1877-0533 OR 18770533
MRclass: 47H05 (47A05 47B65 90C25)
MRnumber: 3134450
MRreviewer: Radu Ioan Bo{\c{t}}
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://arxiv.org/abs/1212.4266; http://docserver.carma.newcastle.edu.au/1483/
fjournal: Set-Valued and Variational Analysis
acknowledgement: ack-nhfb
ajournal: Set-Valued Var. Anal.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11228
rawauthor: Jonathan M. Borwein and Liangjin Yao
rawtitle: Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal monotonicity of A + B provided that A, B are maximally monotone and A is a linear relation, as soon as Rockafellar's constraint qualification holds: . Moreover, A + B is of type (FPV).

rawabstract:
The most famous open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal monotonicity of A + B provided that A, B are maximally monotone and A is a linear relation, as soon as Rockafellar's constraint qualification holds: . Moreover, A + B is of type (FPV).

entry:
@Article{Borwein:2013:MSM,
  author =       "Jonathan M. Borwein and Liangjin Yao",
  title =        "Maximality of the sum of a maximally monotone linear
                 relation and a maximally monotone operator",
  journal =      j-SET-VALUED-VAR-ANAL,
  volume =       "21",
  number =       "4",
  pages =        "603--616",
  year =         "2013",
  DOI =          "https://doi.org/10.1007/s11228-013-0259-y",
  ISSN =         "1877-0533 (print), 1877-0541 (electronic)",
  ISSN-L =       "1877-0533",
  MRclass =      "47H05 (47A05 47B65 90C25)",
  MRnumber =     "3134450",
  MRreviewer =   "Radu Ioan Bo{\c{t}}",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/1212.4266;
                 http://docserver.carma.newcastle.edu.au/1483/",
  abstract =     "The most famous open problem in Monotone Operator
                 Theory concerns the maximal monotonicity of the sum of
                 two maximally monotone operators provided that
                 Rockafellar's constraint qualification holds. In this
                 paper, we prove the maximal monotonicity of A + B
                 provided that A, B are maximally monotone and A is a
                 linear relation, as soon as Rockafellar's constraint
                 qualification holds: . Moreover, A + B is of type
                 (FPV).",
  acknowledgement = ack-nhfb,
  ajournal =     "Set-Valued Var. Anal.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Set-Valued and Variational Analysis",
  journal-URL =  "http://link.springer.com/journal/11228",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  unique-id =    "Borwein:2013:MSM",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2013:NCR
author: J. M. Borwein and B. Sims and M. K. Tam
title: Norm Convergence of Realistic Projection and Reflection Methods
journal: ArXiv e-prints
pages: 603--616
month: dec
monthnumber: 12
year: 2013
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/2013arXiv1312.7323B; http://docserver.carma.newcastle.edu.au/1493/
keywords: Mathematics - Optimization and Control
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and B. Sims and M. K. Tam
rawtitle: Norm Convergence of Realistic Projection and Reflection Methods
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We provide sufficient conditions for norm convergence of various projection and reflection methods, as well as giving limiting examples regarding convergence rates.

rawabstract:
We provide sufficient conditions for norm convergence of various projection and reflection methods, as well as giving limiting examples regarding convergence rates.

entry:
@Article{Borwein:2013:NCR,
  author =       "J. M. Borwein and B. Sims and M. K. Tam",
  title =        "Norm Convergence of Realistic Projection and
                 Reflection Methods",
  journal =      "ArXiv e-prints",
  month =        dec,
  year =         "2013",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2013arXiv1312.7323B;
                 http://docserver.carma.newcastle.edu.au/1493/",
  abstract =     "We provide sufficient conditions for norm convergence
                 of various projection and reflection methods, as well
                 as giving limiting examples regarding convergence
                 rates.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1312.7323",
  keywords =     "Mathematics - Optimization and Control",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.OC",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2013:STMa
author: J. M. Borwein and L. Yao
title: Sum theorems for maximally monotone operators of type (FPV)
journal: ArXiv e-prints
pages: 603--616
month: may
monthnumber: 5
year: 2013
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/2013arXiv1305.6691B; http://docserver.carma.newcastle.edu.au/1503/
keywords: Mathematics - Functional Analysis, Primary 47H05, Secondary 49N15, 52A41, 90C25
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and L. Yao
rawtitle: Sum theorems for maximally monotone operators of type ({FPV})
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar's constraint qualification holds. In this paper, we establish the maximal monotonicity of $ A + B $ provided that $A$ and $B$ are maximally monotone operators such that $ sta (dom A) cap inte dom B neq varnothing $, and $A$ is of type (FPV). We show that when also $ dom A$ is convex, the sum operator: $ A + B$ is also of type (FPV). Our result generalizes and unifies several recent sum theorems.

rawabstract:
The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar's constraint qualification holds. In this paper, we establish the maximal monotonicity of $ A + B $ provided that $A$ and $B$ are maximally monotone operators such that $ \sta (\dom A) \cap \inte \dom B \neq \varnothing $, and $A$ is of type (FPV). We show that when also $ \dom A$ is convex, the sum operator: $ A + B$ is also of type (FPV). Our result generalizes and unifies several recent sum theorems.

entry:
@Article{Borwein:2013:STMa,
  author =       "J. M. Borwein and L. Yao",
  title =        "Sum theorems for maximally monotone operators of type
                 ({FPV})",
  journal =      "ArXiv e-prints",
  month =        may,
  year =         "2013",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2013arXiv1305.6691B;
                 http://docserver.carma.newcastle.edu.au/1503/",
  abstract =     "The most important open problem in Monotone Operator
                 Theory concerns the maximal monotonicity of the sum of
                 two maximally monotone operators provided that the
                 classical Rockafellar's constraint qualification holds.
                 In this paper, we establish the maximal monotonicity of
                 $ A + B $ provided that $A$ and $B$ are maximally
                 monotone operators such that $ \sta (\dom A) \cap \inte
                 \dom B \neq \varnothing $, and $A$ is of type (FPV). We
                 show that when also $ \dom A$ is convex, the sum
                 operator: $ A + B$ is also of type (FPV). Our result
                 generalizes and unifies several recent sum theorems.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1305.6691",
  keywords =     "Mathematics - Functional Analysis, Primary 47H05,
                 Secondary 49N15, 52A41, 90C25",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2013:STMb
author: Jonathan M. Borwein and Liangjin Yao
title: Structure theory for maximally monotone operators with points of continuity
journal: j-J-OPT-THEORY-APPL
volume: 157
number: 1
pages: 1--24
year: 2013
CODEN: JOTABN
DOI: https://doi.org/10.1007/s10957-012-0162-y
ISSN: 0022-3239 (print), 1573-2878 (electronic) OR 00223239 (print), 15732878 (electronic)
ISSNL: 0022-3239 OR 00223239
MRclass: 47H05 (46N10)
MRnumber: 3034040
MRreviewer: Radu Ioan Bo{\c{t}}
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://arxiv.org/abs/1203.1101; http://docserver.carma.newcastle.edu.au/1375/
fjournal: Journal of Optimization Theory and Applications
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/volumesAndIssues/10957
rawauthor: Jonathan M. Borwein and Liangjin Yao
rawtitle: Structure theory for maximally monotone operators with points of continuity
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2013:STMb,
  author =       "Jonathan M. Borwein and Liangjin Yao",
  title =        "Structure theory for maximally monotone operators with
                 points of continuity",
  journal =      j-J-OPT-THEORY-APPL,
  volume =       "157",
  number =       "1",
  pages =        "1--24",
  year =         "2013",
  CODEN =        "JOTABN",
  DOI =          "https://doi.org/10.1007/s10957-012-0162-y",
  ISSN =         "0022-3239 (print), 1573-2878 (electronic)",
  ISSN-L =       "0022-3239",
  MRclass =      "47H05 (46N10)",
  MRnumber =     "3034040",
  MRreviewer =   "Radu Ioan Bo{\c{t}}",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/1203.1101;
                 http://docserver.carma.newcastle.edu.au/1375/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Optimization Theory and Applications",
  journal-URL =  "http://link.springer.com/journal/volumesAndIssues/10957",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2013:TSF
author: Jonathan M. Borwein and Armin Straub and James Wan
title: Three-Step and Four-Step Random Walk Integrals
journal: j-EXP-MATH
volume: 22
number: 1
pages: 1--14
year: 2013
DOI: https://doi.org/10.1080/10586458.2013.748379
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 60G50 (33C20 33E05)
MRnumber: 3038778
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/763/
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 M. Borwein and Armin Straub and James Wan
rawtitle: Three-Step and Four-Step Random Walk Integrals
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/expmath.bib

abstract:
We investigate the moments of 3-step and 4-step uniform random walks in the plane. In particular, we further analyze a formula conjectured in [Borwein etal. 11] expressing 4-step moments in terms of 3-step moments. Diverse related results including hypergeometric and elliptic closed forms for W-4(+/- 1) are given, and two new conjectures are recorded.

rawabstract:
We investigate the moments of 3-step and 4-step uniform random walks in the plane. In particular, we further analyze a formula conjectured in [Borwein etal. 11] expressing 4-step moments in terms of 3-step moments. Diverse related results including hypergeometric and elliptic closed forms for W-4(+/- 1) are given, and two new conjectures are recorded.

entry:
@Article{Borwein:2013:TSF,
  author =       "Jonathan M. Borwein and Armin Straub and James Wan",
  title =        "Three-Step and Four-Step Random Walk Integrals",
  journal =      j-EXP-MATH,
  volume =       "22",
  number =       "1",
  pages =        "1--14",
  year =         "2013",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2013.748379",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "60G50 (33C20 33E05)",
  MRnumber =     "3038778",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "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/763/",
  abstract =     "We investigate the moments of 3-step and 4-step
                 uniform random walks in the plane. In particular, we
                 further analyze a formula conjectured in [Borwein etal.
                 11] expressing 4-step moments in terms of 3-step
                 moments. Diverse related results including
                 hypergeometric and elliptic closed forms for W-4(+/- 1)
                 are given, and two new conjectures are recorded.",
  acknowledgement = ack-nhfb,
  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; Straub,
                 Armin/0000-0001-6802-6053",
  unique-id =    "Borwein:2013:TSF",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2013:VMP
author: Jonathan M. Borwein and Qiji J. Zhu
title: Variational methods in the presence of symmetry
journal: j-ADV-NONLINEAR-ANAL
volume: 2
number: 3
pages: 271--307
year: 2013
DOI: https://doi.org/10.1515/anona-2013-1001
ISSN: 2191-9496 (print), 2191-950X (electronic) OR 21919496 (print), 2191950X (electronic)
ISSNL: 2191-9496 OR 21919496
MRclass: 49J53 (58E30)
MRnumber: 3089743
MRreviewer: Nicolas Hadjisavvas
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/1514/
fjournal: Advances in Nonlinear Analysis
acknowledgement: ack-nhfb
ajournal: Adv. Nonlinear Anal.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.degruyter.com/view/j/anona
rawauthor: Jonathan M. Borwein and Qiji J. Zhu
rawtitle: Variational methods in the presence of symmetry
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
The purpose of this paper is to survey and to provide a unified framework to connect a diverse group of results, currently scattered in the literature, that can be usefully viewed as consequences of applying variational methods to problems involving symmetry. Here, variational methods refer to mathematical treatment by way of constructing an appropriate action function whose critical points-or saddle points-correspond to or contain the desired solutions.

rawabstract:
The purpose of this paper is to survey and to provide a unified framework to connect a diverse group of results, currently scattered in the literature, that can be usefully viewed as consequences of applying variational methods to problems involving symmetry. Here, variational methods refer to mathematical treatment by way of constructing an appropriate action function whose critical points-or saddle points-correspond to or contain the desired solutions.

entry:
@Article{Borwein:2013:VMP,
  author =       "Jonathan M. Borwein and Qiji J. Zhu",
  title =        "Variational methods in the presence of symmetry",
  journal =      j-ADV-NONLINEAR-ANAL,
  volume =       "2",
  number =       "3",
  pages =        "271--307",
  year =         "2013",
  DOI =          "https://doi.org/10.1515/anona-2013-1001",
  ISSN =         "2191-9496 (print), 2191-950X (electronic)",
  ISSN-L =       "2191-9496",
  MRclass =      "49J53 (58E30)",
  MRnumber =     "3089743",
  MRreviewer =   "Nicolas Hadjisavvas",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1514/",
  abstract =     "The purpose of this paper is to survey and to provide
                 a unified framework to connect a diverse group of
                 results, currently scattered in the literature, that
                 can be usefully viewed as consequences of applying
                 variational methods to problems involving symmetry.
                 Here, variational methods refer to mathematical
                 treatment by way of constructing an appropriate action
                 function whose critical points-or saddle
                 points-correspond to or contain the desired
                 solutions.",
  acknowledgement = ack-nhfb,
  ajournal =     "Adv. Nonlinear Anal.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Advances in Nonlinear Analysis",
  journal-URL =  "http://www.degruyter.com/view/j/anona",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  unique-id =    "Borwein:2013:VMP",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Piantadosi:2013:GSR
author: Julia Piantadosi and Phil Howlett and Jonathan Borwein and John Henstridge
title: Generation of simulated rainfall data at different time-scales
crossref: Bean:2013:MDM
pages: ??--??
year: 2013
bibdate: Sat Aug 13 15:52:53 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 15:52:53 ???
URL: http://docserver.carma.newcastle.edu.au/1381/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Julia Piantadosi and Phil Howlett and Jonathan Borwein and John Henstridge
rawtitle: Generation of simulated rainfall data at different time-scales
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Howlett, Phil/0000-0003-2382-8137
entry:
@InProceedings{Piantadosi:2013:GSR,
  author =       "Julia Piantadosi and Phil Howlett and Jonathan Borwein
                 and John Henstridge",
  title =        "Generation of simulated rainfall data at different
                 time-scales",
  crossref =     "Bean:2013:MDM",
  pages =        "??--??",
  year =         "2013",
  bibdate =      "Sat Aug 13 15:52:53 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1381/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Howlett,
                 Phil/0000-0003-2382-8137",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Piantadosi:2013:MSS
author: Julia Piantadosi and Phil Howlett and Jonathan Borwein
title: Modelling and simulation of seasonal rainfall
type: Report
institution: MODSIM/ASOR
address: Adelaide, SA, Australia
month: dec
monthnumber: 12
year: 2013
bibdate: Sat Aug 13 15:15:53 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 15:15:53 ???
URL: http://docserver.carma.newcastle.edu.au/1453/
keywords: Australian Society for Operations Research (ASOR)
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Julia Piantadosi and Phil Howlett and Jonathan Borwein
rawtitle: Modelling and simulation of seasonal rainfall
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Howlett, Phil/0000-0003-2382-8137
entry:
@TechReport{Piantadosi:2013:MSS,
  author =       "Julia Piantadosi and Phil Howlett and Jonathan
                 Borwein",
  title =        "Modelling and simulation of seasonal rainfall",
  type =         "Report",
  institution =  "MODSIM/ASOR",
  address =      "Adelaide, SA, Australia",
  pages =        "??",
  month =        dec,
  year =         "2013",
  bibdate =      "Sat Aug 13 15:15:53 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1453/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Australian Society for Operations Research (ASOR)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Howlett,
                 Phil/0000-0003-2382-8137",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Stodden:2013:SDR
author: Victoria Stodden and Jonathan Borwein and David H. Bailey
title: ``Setting the Default to Reproducible'' in Computational Science Research
journal: j-SIAM-NEWS
volume: 46
number: 5
pages: 4--6
month: jun
monthnumber: 6
year: 2013
ISSN: 0036-1437 OR 00361437
ISSNL: 0036-1437 OR 00361437
bibdate: Fri Sep 02 07:29:13 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.02 07:29:13 ???
fjournal: SIAM News
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.siam.org/news/
rawauthor: Victoria Stodden and Jonathan Borwein and David H. Bailey
rawtitle: ``{Setting} the Default to Reproducible'' in Computational Science Research
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
https://sinews2.siam.org/DetailsPage/tabid/607/ArticleID/351/%E2%80%9CSetting-the-Default-to-Reproducible%E2%80%9D-in-Computational-Science-Research.aspx

entry:
@Article{Stodden:2013:SDR,
  author =       "Victoria Stodden and Jonathan Borwein and David H.
                 Bailey",
  title =        "``{Setting} the Default to Reproducible'' in
                 Computational Science Research",
  journal =      j-SIAM-NEWS,
  volume =       "46",
  number =       "5",
  pages =        "4--6",
  month =        jun,
  year =         "2013",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Fri Sep 02 07:29:13 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "https://sinews2.siam.org/DetailsPage/tabid/607/ArticleID/351/%E2%80%9CSetting-the-Default-to-Reproducible%E2%80%9D-in-Computational-Science-Research.aspx",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: AragonArtacho:2014:ACA
author: Francisco J. Aragon Artacho and Jonathan M. Borwein and Victoria Martin-Marquez and Liangjin Yao
title: Applications of convex analysis within mathematics
journal: j-MATH-PROG
volume: 148
number: 1--2
pages: 49--88
month: dec
monthnumber: 12
year: 2014
CODEN: MHPGA4
DOI: https://doi.org/10.1007/s10107-013-0707-3
ISSN: 0025-5610 (print), 1436-4646 (electronic) OR 00255610 (print), 14364646 (electronic)
ISSNL: 0025-5610 OR 00255610
MRclass: 47N10 (47A06 47B65 47H05 90C25)
MRnumber: 3274845
MRreviewer: Aris Daniilidis
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 volume of Serdica Mathematical Journal in honour of Asen Dontchev.
URL: http://arxiv.org/abs/1302.1978; http://docserver.carma.newcastle.edu.au/1513/
fjournal: Mathematical Programming. A Publication of the Mathematical Optimization Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/10107
rawnote: Special volume of Serdica Mathematical Journal in honour of Asen Dontchev.
rawtitle: Applications of convex analysis within mathematics
abstract:
In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal convolution in Monotone Operator Theory. Among other things, we recapture the Minty surjectivity theorem in Hilbert space, and present a new proof of the sum theorem in reflexive spaces. More technically, we also discuss autoconjugate representers for maximally monotone operators. Finally, we consider various other applications in mathematical analysis.

rawauthor:
Francisco J. {Arag{\'o}n Artacho} and Jonathan M. Borwein and Victoria Mart{\'{\i}}n-M{\'a}rquez and Liangjin Yao

ORCID:
Aragon Artacho, Francisco Javier/0000-0002-2445-8011; Borwein, Jonathan/0000-0002-1263-0646; Martin Marquez, Victoria/0000-0002-8963-9825

entry:
@Article{AragonArtacho:2014:ACA,
  author =       "Francisco J. {Arag{\'o}n Artacho} and Jonathan M.
                 Borwein and Victoria Mart{\'{\i}}n-M{\'a}rquez and
                 Liangjin Yao",
  title =        "Applications of convex analysis within mathematics",
  journal =      j-MATH-PROG,
  volume =       "148",
  number =       "1--2",
  pages =        "49--88",
  month =        dec,
  year =         "2014",
  CODEN =        "MHPGA4",
  DOI =          "https://doi.org/10.1007/s10107-013-0707-3",
  ISSN =         "0025-5610 (print), 1436-4646 (electronic)",
  ISSN-L =       "0025-5610",
  MRclass =      "47N10 (47A06 47B65 47H05 90C25)",
  MRnumber =     "3274845",
  MRreviewer =   "Aris Daniilidis",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Special volume of Serdica Mathematical Journal in
                 honour of Asen Dontchev.",
  URL =          "http://arxiv.org/abs/1302.1978;
                 http://docserver.carma.newcastle.edu.au/1513/",
  abstract =     "In this paper, we study convex analysis and its
                 theoretical applications. We first apply important
                 tools of convex analysis to Optimization and to
                 Analysis. We then show various deep applications of
                 convex analysis and especially infimal convolution in
                 Monotone Operator Theory. Among other things, we
                 recapture the Minty surjectivity theorem in Hilbert
                 space, and present a new proof of the sum theorem in
                 reflexive spaces. More technically, we also discuss
                 autoconjugate representers for maximally monotone
                 operators. Finally, we consider various other
                 applications in mathematical analysis.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematical Programming. A Publication of the
                 Mathematical Optimization Society",
  journal-URL =  "http://link.springer.com/journal/10107",
  ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
                 Borwein, Jonathan/0000-0002-1263-0646; Martin Marquez,
                 Victoria/0000-0002-8963-9825",
  researcherid-numbers = "Martin-Marquez, Victoria/H-1047-2015; Aragon
                 Artacho, Francisco Javier/C-2531-2012",
  unique-id =    "ISI:000344809700003",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: AragonArtacho:2014:DRF
author: Francisco J. Aragon Artacho and Jonathan M. Borwein and Matthew K. Tam
title: Douglas--Rachford Feasibility Methods for Matrix Completion Problems
journal: j-ANZIAM-J
volume: 55
number: 4
pages: 299--326
month: apr
monthnumber: 4
year: 2014
CODEN: AJNOA2
DOI: https://doi.org/10.1017/S1446181114000145
ISSN: 1446-1811 (print), 1446-8735 (electronic) OR 14461811 (print), 14468735 (electronic)
ISSNL: 1446-1811 OR 14461811
MRclass: 47J25 (15A83 65K05 90C59)
MRnumber: 3257300
MRreviewer: Heinz H. Bauschke
bibdate: Fri Sep 30 10:50:24 2016
bibtimestamp: 2016.09.30 10:50:24 ???
fjournal: The ANZIAM Journal. The Australian & New Zealand Industrial and Applied Mathematics Journal
acknowledgement: ack-nhfb
ajournal: ANZIAM J.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://journals.cambridge.org/action/displayJournal?jid=ANZ
onlinedate: 25 July 2014
rawauthor: Francisco J. {Arag{\'o}n Artacho} and Jonathan M. Borwein and Matthew K. Tam
rawtitle: {Douglas--Rachford} Feasibility Methods for Matrix Completion Problems
ORCID: Aragon Artacho, Francisco Javier/0000-0002-2445-8011; 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/anziamj.bib

URL:
http://arxiv.org/abs/1308.4243; http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9347336; https://www.cambridge.org/core/journals/anziam-journal/article/douglasrachford-feasibility-methods-for-matrix-completion-problems/0DCB430BF7CF1187A7A1DB5B9C3C2BCC

abstract:
In this paper, we give general recommendations for successful application of the Douglas--Rachford reflection method to convex and nonconvex real matrix completion problems. These guidelines are demonstrated by various illustrative examples.

rawabstract:
In this paper, we give general recommendations for successful application of the Douglas--Rachford reflection method to convex and nonconvex real matrix completion problems. These guidelines are demonstrated by various illustrative examples.

entry:
@Article{AragonArtacho:2014:DRF,
  author =       "Francisco J. {Arag{\'o}n Artacho} and Jonathan M.
                 Borwein and Matthew K. Tam",
  title =        "{Douglas--Rachford} Feasibility Methods for Matrix
                 Completion Problems",
  journal =      j-ANZIAM-J,
  volume =       "55",
  number =       "4",
  pages =        "299--326",
  month =        apr,
  year =         "2014",
  CODEN =        "AJNOA2",
  DOI =          "https://doi.org/10.1017/S1446181114000145",
  ISSN =         "1446-1811 (print), 1446-8735 (electronic)",
  ISSN-L =       "1446-1811",
  MRclass =      "47J25 (15A83 65K05 90C59)",
  MRnumber =     "3257300",
  MRreviewer =   "Heinz H. Bauschke",
  bibdate =      "Fri Sep 30 10:50:24 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/anziamj.bib",
  URL =          "http://arxiv.org/abs/1308.4243;
                 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9347336;
                 https://www.cambridge.org/core/journals/anziam-journal/article/douglasrachford-feasibility-methods-for-matrix-completion-problems/0DCB430BF7CF1187A7A1DB5B9C3C2BCC",
  abstract =     "In this paper, we give general recommendations for
                 successful application of the Douglas--Rachford
                 reflection method to convex and nonconvex real matrix
                 completion problems. These guidelines are demonstrated
                 by various illustrative examples.",
  acknowledgement = ack-nhfb,
  ajournal =     "ANZIAM J.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The ANZIAM Journal. The Australian \& New Zealand
                 Industrial and Applied Mathematics Journal",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
  onlinedate =   "25 July 2014",
  ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
                 Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Aragon Artacho, Francisco Javier/C-2531-2012;
                 Tam, Matthew/G-8127-2013",
  unique-id =    "ISI:000343750400001",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: AragonArtacho:2014:RRD
author: Francisco J. Aragon Artacho and Jonathan M. Borwein and Matthew K. Tam
title: Recent Results on Douglas--Rachford Methods for Combinatorial Optimization Problems
journal: j-J-OPT-THEORY-APPL
volume: 163
number: 1
pages: 1--30
month: oct
monthnumber: 10
year: 2014
CODEN: JOTABN
DOI: https://doi.org/10.1007/s10957-013-0488-0
ISSN: 0022-3239 (print), 1573-2878 (electronic) OR 00223239 (print), 15732878 (electronic)
ISSNL: 0022-3239 OR 00223239
MRclass: 47J25 (90C27)
MRnumber: 3260973
MRreviewer: Heinz H. Bauschke
bibdate: Fri Aug 12 08:22:52 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 08:22:52 ???
URL: http://arxiv.org/abs/1305.2657; http://docserver.carma.newcastle.edu.au/1510/
fjournal: Journal of Optimization Theory and Applications
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/volumesAndIssues/10957
rawauthor: Francisco J. {Arag{\'o}n Artacho} and Jonathan M. Borwein and Matthew K. Tam
rawtitle: Recent Results on {Douglas--Rachford} Methods for Combinatorial Optimization Problems
ORCID: Aragon Artacho, Francisco Javier/0000-0002-2445-8011; Borwein, Jonathan/0000-0002-1263-0646
abstract:
We discuss recent positive experiences applying convex feasibility algorithms of Douglas--Rachford type to highly combinatorial and far from convex problems.

entry:
@Article{AragonArtacho:2014:RRD,
  author =       "Francisco J. {Arag{\'o}n Artacho} and Jonathan M.
                 Borwein and Matthew K. Tam",
  title =        "Recent Results on {Douglas--Rachford} Methods for
                 Combinatorial Optimization Problems",
  journal =      j-J-OPT-THEORY-APPL,
  volume =       "163",
  number =       "1",
  pages =        "1--30",
  month =        oct,
  year =         "2014",
  CODEN =        "JOTABN",
  DOI =          "https://doi.org/10.1007/s10957-013-0488-0",
  ISSN =         "0022-3239 (print), 1573-2878 (electronic)",
  ISSN-L =       "0022-3239",
  MRclass =      "47J25 (90C27)",
  MRnumber =     "3260973",
  MRreviewer =   "Heinz H. Bauschke",
  bibdate =      "Fri Aug 12 08:22:52 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/1305.2657;
                 http://docserver.carma.newcastle.edu.au/1510/",
  abstract =     "We discuss recent positive experiences applying convex
                 feasibility algorithms of Douglas--Rachford type to
                 highly combinatorial and far from convex problems.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Optimization Theory and Applications",
  journal-URL =  "http://link.springer.com/journal/volumesAndIssues/10957",
  ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
                 Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Aragon Artacho, Francisco Javier/C-2531-2012;
                 Tam, Matthew/G-8127-2013",
  unique-id =    "ISI:000342442600001",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2014:ASL
author: David H. Bailey and Jonathan M. Borwein and Alexander D. Kaiser
title: Automated simplification of large symbolic expressions
journal: j-J-SYMBOLIC-COMP
volume: 60
pages: 120--136
year: 2014
CODEN: JSYCEH
DOI: https://doi.org/10.1016/j.jsc.2013.09.001
ISSN: 0747-7171 (print), 1095-855x (electronic) OR 07477171 (print), 1095855x (electronic)
ISSNL: 0747-7171 OR 07477171
MRclass: 68W30
MRnumber: 3131383
bibdate: Thu Aug 11 10:27:38 2016
bibtimestamp: 2016.08.11 10:27:38 ???
fjournal: Journal of Symbolic Computation
keywords: Computer algebra systems; Error correction; Experimental mathematics; Simplification
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/07477171
rawauthor: David H. Bailey and Jonathan M. Borwein and Alexander D. Kaiser
rawtitle: Automated simplification of large symbolic expressions
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/mathematica.bib

URL:
http://docserver.carma.newcastle.edu.au/1456/; http://www.sciencedirect.com/science/article/pii/S074771711300117X

abstract:
We present a set of algorithms for automated simplification of symbolic constants of the form $ sum _i alpha _i x_i $ with $ alpha _i $ rational and $ x_i $ complex. The included algorithms, called SimplifySum (available from url https://github.com/alexkaiser/SimplifySum), and implemented in Mathematica, remove redundant terms, attempt to make terms and the full expression real, and remove terms using repeated application of the multipair PSLQ integer relation detection algorithm. Also included are facilities for making substitutions according to user-specified identities. We illustrate this toolset by giving some real-world examples of its usage, including one, for instance, where the tool reduced a symbolic expression of approximately 100000 characters in size enough to enable manual manipulation to one with just four simple terms.

rawabstract:
We present a set of algorithms for automated simplification of symbolic constants of the form $ \sum_i \alpha_i x_i $ with $ \alpha_i $ rational and $ x_i $ complex. The included algorithms, called SimplifySum (available from \url{https://github.com/alexkaiser/SimplifySum}), and implemented in Mathematica, remove redundant terms, attempt to make terms and the full expression real, and remove terms using repeated application of the multipair PSLQ integer relation detection algorithm. Also included are facilities for making substitutions according to user-specified identities. We illustrate this toolset by giving some real-world examples of its usage, including one, for instance, where the tool reduced a symbolic expression of approximately 100\,000 characters in size enough to enable manual manipulation to one with just four simple terms.

entry:
@Article{Bailey:2014:ASL,
  author =       "David H. Bailey and Jonathan M. Borwein and Alexander
                 D. Kaiser",
  title =        "Automated simplification of large symbolic
                 expressions",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "60",
  number =       "??",
  pages =        "120--136",
  year =         "2014",
  CODEN =        "JSYCEH",
  DOI =          "https://doi.org/10.1016/j.jsc.2013.09.001",
  ISSN =         "0747-7171 (print), 1095-855x (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "68W30",
  MRnumber =     "3131383",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1456/;
                 http://www.sciencedirect.com/science/article/pii/S074771711300117X",
  abstract =     "We present a set of algorithms for automated
                 simplification of symbolic constants of the form $
                 \sum_i \alpha_i x_i $ with $ \alpha_i $ rational and $
                 x_i $ complex. The included algorithms, called
                 SimplifySum (available from
                 \url{https://github.com/alexkaiser/SimplifySum}), and
                 implemented in Mathematica, remove redundant terms,
                 attempt to make terms and the full expression real, and
                 remove terms using repeated application of the
                 multipair PSLQ integer relation detection algorithm.
                 Also included are facilities for making substitutions
                 according to user-specified identities. We illustrate
                 this toolset by giving some real-world examples of its
                 usage, including one, for instance, where the tool
                 reduced a symbolic expression of approximately 100\,000
                 characters in size enough to enable manual manipulation
                 to one with just four simple terms.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
  keywords =     "Computer algebra systems; Error correction;
                 Experimental mathematics; Simplification",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  unique-id =    "ISI:000328661000009",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2014:CTE
author: David H. Bailey and Jonathan M. Borwein and Richard E. Crandall
title: Computation and theory of extended Mordell--Tornheim--Witten sums
journal: j-MATH-COMPUT
volume: 83
number: 288
pages: 1795--1821
month: jul
monthnumber: 7
year: 2014
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-2014-02768-3
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33B15 (11M32 33F05 65D20 65D30)
MRnumber: 3194130
MRreviewer: Mehdi Hassani
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/mcom/
rawauthor: David H. Bailey and Jonathan M. Borwein and Richard E. Crandall
rawtitle: Computation and theory of extended {Mordell--Tornheim--Witten} sums
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
http://www.ams.org/mcom/2014-83-288; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib

URL:
http://docserver.carma.newcastle.edu.au/1459/; http://www.ams.org/journals/mcom/2014-83-288/S0025-5718-2014-02768-3; http://www.ams.org/journals/mcom/2014-83-288/S0025-5718-2014-02768-3/S0025-5718-2014-02768-3.pdf

abstract:
We consider some fundamental generalized Mordell--Tornheim--Witten (MTW) zeta-function values along with their derivatives, and explore connections with multiple-zeta values (MZVs). To achieve this, we make use of symbolic integration, high precision numerical integration, and some interesting combinatorics and special-function theory. Our original motivation was to represent unresolved constructs such as Eulerian log-gamma integrals. We are able to resolve all such integrals in terms of an MTW basis. We also present, for a substantial subset of MTW values, explicit closed-form expressions. In the process, we significantly extend methods for high-precision numerical computation of polylogarithms and their derivatives with respect to order.

rawabstract:
We consider some fundamental generalized Mordell--Tornheim--Witten (MTW) zeta-function values along with their derivatives, and explore connections with multiple-zeta values (MZVs). To achieve this, we make use of symbolic integration, high precision numerical integration, and some interesting combinatorics and special-function theory. Our original motivation was to represent unresolved constructs such as Eulerian log-gamma integrals. We are able to resolve all such integrals in terms of an MTW basis. We also present, for a substantial subset of MTW values, explicit closed-form expressions. In the process, we significantly extend methods for high-precision numerical computation of polylogarithms and their derivatives with respect to order.

entry:
@Article{Bailey:2014:CTE,
  author =       "David H. Bailey and Jonathan M. Borwein and Richard E.
                 Crandall",
  title =        "Computation and theory of extended
                 {Mordell--Tornheim--Witten} sums",
  journal =      j-MATH-COMPUT,
  volume =       "83",
  number =       "288",
  pages =        "1795--1821",
  month =        jul,
  year =         "2014",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-2014-02768-3",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B15 (11M32 33F05 65D20 65D30)",
  MRnumber =     "3194130",
  MRreviewer =   "Mehdi Hassani",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://www.ams.org/mcom/2014-83-288;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1459/;
                 http://www.ams.org/journals/mcom/2014-83-288/S0025-5718-2014-02768-3;
                 http://www.ams.org/journals/mcom/2014-83-288/S0025-5718-2014-02768-3/S0025-5718-2014-02768-3.pdf",
  abstract =     "We consider some fundamental generalized
                 Mordell--Tornheim--Witten (MTW) zeta-function values
                 along with their derivatives, and explore connections
                 with multiple-zeta values (MZVs). To achieve this, we
                 make use of symbolic integration, high precision
                 numerical integration, and some interesting
                 combinatorics and special-function theory. Our original
                 motivation was to represent unresolved constructs such
                 as Eulerian log-gamma integrals. We are able to resolve
                 all such integrals in terms of an MTW basis. We also
                 present, for a substantial subset of MTW values,
                 explicit closed-form expressions. In the process, we
                 significantly extend methods for high-precision
                 numerical computation of polylogarithms and their
                 derivatives with respect to order.",
  acknowledgement = ack-nhfb,
  article-number = "PII S 0025-5718(2014)02768-3",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  unique-id =    "ISI:000337230000010",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2014:IWS
author: D. H. Bailey and J. M. Borwein
title: ICERM Workshop Sets Out Opportunities and Challenges in Experimental Mathematics
journal: j-SIAM-NEWS
volume: 47
number: 9
pages: 4, 8
year: 2014
ISSN: 0036-1437 OR 00361437
ISSNL: 0036-1437 OR 00361437
bibdate: Sat Aug 13 13:56:34 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 13:56:34 ???
fjournal: SIAM News
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.siam.org/news/
rawauthor: D. H. Bailey and J. M. Borwein
rawtitle: {ICERM Workshop} Sets Out Opportunities and Challenges in Experimental Mathematics
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://www.davidhbailey.com/dhbpapers/icerm-summ.pdf; https://sinews.siam.org/Portals/Sinews2/Issue%20Pdfs/sn_November2014.pdf

entry:
@Article{Bailey:2014:IWS,
  author =       "D. H. Bailey and J. M. Borwein",
  title =        "{ICERM Workshop} Sets Out Opportunities and Challenges
                 in Experimental Mathematics",
  journal =      j-SIAM-NEWS,
  volume =       "47",
  number =       "9",
  pages =        "4, 8",
  month =        "????",
  year =         "2014",
  DOI =          "",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Sat Aug 13 13:56:34 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/icerm-summ.pdf;
                 https://sinews.siam.org/Portals/Sinews2/Issue%20Pdfs/sn_November2014.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:2014:OCC
pages: 18
day: 28
month: aug
monthnumber: 8
year: 2014
bibdate: Tue Aug 16 09:53:29 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:53:29 ???
note: Preprint in collaboration with the workshop participants.
URL: http://www.davidhbailey.com/dhbpapers/ICERM-2014.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawnote: Preprint in collaboration with the workshop participants.
author:
David H. Bailey and Jonathan M. Borwein and Olga Caprotti and Ursula Martin and Bruno Salvy and Michela Taufer

title:
Opportunities and Challenges in 21st Century Mathematical Computation: ICERM Workshop Report, July 10--14, 2014

abstract:
``Experimental mathematics'' has emerged in the past 25 years or so to become a competitive paradigm for research in the mathematical sciences. A workshop held at the Institute for Computational and Experimental Research in Mathematics (ICERM), July 21--25, 2014, explored emerging challenges of experimental mathematics in the rapidly changing era of modern computer technology. This report summarizes the workshop findings

rawabstract:
``Experimental mathematics'' has emerged in the past 25 years or so to become a competitive paradigm for research in the mathematical sciences. A workshop held at the Institute for Computational and Experimental Research in Mathematics (ICERM), July 21--25, 2014, explored emerging challenges of experimental mathematics in the rapidly changing era of modern computer technology. This report summarizes the workshop findings

rawauthor:
David H. Bailey and Jonathan M. Borwein and Olga Caprotti and Ursula Martin and Bruno Salvy and Michela Taufer

rawtitle:
Opportunities and Challenges in 21st Century Mathematical Computation: {ICERM} Workshop Report, {July 10--14, 2014}

ORCID:
Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646; Salvy, Bruno/0000-0002-4313-0679

entry:
@TechReport{Bailey:2014:OCC,
  author =       "David H. Bailey and Jonathan M. Borwein and Olga
                 Caprotti and Ursula Martin and Bruno Salvy and Michela
                 Taufer",
  title =        "Opportunities and Challenges in 21st Century
                 Mathematical Computation: {ICERM} Workshop Report,
                 {July 10--14, 2014}",
  institution =  "????",
  address =      "????",
  pages =        "18",
  day =          "28",
  month =        aug,
  year =         "2014",
  bibdate =      "Tue Aug 16 09:53:29 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Preprint in collaboration with the workshop
                 participants.",
  URL =          "http://www.davidhbailey.com/dhbpapers/ICERM-2014.pdf",
  abstract =     "``Experimental mathematics'' has emerged in the past
                 25 years or so to become a competitive paradigm for
                 research in the mathematical sciences. A workshop held
                 at the Institute for Computational and Experimental
                 Research in Mathematics (ICERM), July 21--25, 2014,
                 explored emerging challenges of experimental
                 mathematics in the rapidly changing era of modern
                 computer technology. This report summarizes the
                 workshop findings",
  acknowledgement = ack-nhfb,
  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; Salvy,
                 Bruno/0000-0002-4313-0679",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2014:PDUa
author: David H. Bailey and Jonathan Borwein
title: Pi Day Is Upon Us Again and We Still Do Not Know if Pi Is Normal
journal: j-AMER-MATH-MONTHLY
volume: 121
number: 3
pages: 191--206
month: mar
monthnumber: 3
year: 2014
CODEN: AMMYAE
DOI: https://doi.org/10.4169/amer.math.monthly.121.03.191
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 11K16 (11A63)
MRnumber: 3168990
MRreviewer: Manfred G. Madritsch
bibdate: Tue Mar 4 06:16:50 MST 2014
bibtimestamp: 2014.03.04 06:16:50 MST
URL: https://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.121.03.191.pdf
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: David H. Bailey and Jonathan Borwein
rawtitle: {Pi Day} Is Upon Us Again and We Still Do Not Know if Pi Is Normal
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.jstor.org/journals/00029890.html; https://www.jstor.org/stable/10.4169/amermathmont.121.issue-03; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib

note:
Chinese translation in Mathematical Advances in Translation (Chinese Academy of Science) [metadata unknown].

abstract:
The digits of pi have intrigued both the public and research mathematicians from the beginning of time. This article briefly reviews the history of this venerable constant, and then describes some recent research on the question of whether pi is normal, or, in other words,. whether its digits are statistically random in a specific sense.

rawabstract:
The digits of pi have intrigued both the public and research mathematicians from the beginning of time. This article briefly reviews the history of this venerable constant, and then describes some recent research on the question of whether pi is normal, or, in other words,. whether its digits are statistically random in a specific sense.

rawnote:
Chinese translation in Mathematical Advances in Translation (Chinese Academy of Science) [metadata unknown].

entry:
@Article{Bailey:2014:PDUa,
  author =       "David H. Bailey and Jonathan Borwein",
  title =        "{Pi Day} Is Upon Us Again and We Still Do Not Know if
                 Pi Is Normal",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "121",
  number =       "3",
  pages =        "191--206",
  month =        mar,
  year =         "2014",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.121.03.191",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11K16 (11A63)",
  MRnumber =     "3168990",
  MRreviewer =   "Manfred G. Madritsch",
  bibdate =      "Tue Mar 4 06:16:50 MST 2014",
  bibsource =    "https://www.jstor.org/journals/00029890.html;
                 https://www.jstor.org/stable/10.4169/amermathmont.121.issue-03;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  note =         "Chinese translation in Mathematical Advances in
                 Translation (Chinese Academy of Science) [metadata
                 unknown].",
  URL =          "https://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.121.03.191.pdf",
  abstract =     "The digits of pi have intrigued both the public and
                 research mathematicians from the beginning of time.
                 This article briefly reviews the history of this
                 venerable constant, and then describes some recent
                 research on the question of whether pi is normal, or,
                 in other words,. whether its digits are statistically
                 random in a specific sense.",
  acknowledgement = ack-nhfb,
  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",
  unique-id =    "ISI:000332922000001",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2014:PDUb
author: David H. Bailey and Jonathan M. Borwein
title: Pi Day is upon us again, and we still do not know if pi is normal
journal: Mathematical Advances of Translation
volume: 33
pages: 222--235
year: 2014
bibdate: Fri Sep 30 08:59:40 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 08:59:40 ???
note: Chinese translation of cite Bailey:2014:PDUa.
language: Chinese
remark: TO DO: Find ISSN of this journal; it is not found in major library catalogs.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawnote: Chinese translation of \cite{Bailey:2014:PDUa}.
rawtitle: {Pi Day} is upon us again, and we still do not know if pi is normal
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bailey:2014:PDUb,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "{Pi Day} is upon us again, and we still do not know if
                 pi is normal",
  journal =      "Mathematical Advances of Translation",
  volume =       "33",
  number =       "??",
  pages =        "222--235",
  month =        "????",
  year =         "2014",
  bibdate =      "Fri Sep 30 08:59:40 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Chinese translation of \cite{Bailey:2014:PDUa}.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  language =     "Chinese",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "TO DO: Find ISSN of this journal; it is not found in
                 major library catalogs.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2014:PMFb
author: David H. Bailey and Jonathan M. Borwein and Marcos Lopez de Prado and Qiji Jim Zhu
journal: j-NAMS
volume: 61
number: 5
pages: 458--471
month: may
monthnumber: 5
year: 2014
CODEN: AMNOAN
DOI: https://doi.org/10.1090/noti1105
ISSN: 0002-9920 (print), 1088-9477 (electronic) OR 00029920 (print), 10889477 (electronic)
ISSNL: 0002-9920 OR 00029920
MRclass: 91G70 (62P05 91G80)
MRnumber: 3203237
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/1506/; http://www.ams.org/notices/201405/rnoti-p458.pdf
fjournal: Notices of the American Mathematical Society
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 and Marcos {L{\'o}pez de Prado} and Qiji Jim Zhu
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
title:
Pseudo-mathematics and financial charlatanism: the effects of backtest overfitting on out-of-sample performance

rawtitle:
Pseudo-mathematics and financial charlatanism: the effects of backtest overfitting on out-of-sample performance

entry:
@Article{Bailey:2014:PMFb,
  author =       "David H. Bailey and Jonathan M. Borwein and Marcos
                 {L{\'o}pez de Prado} and Qiji Jim Zhu",
  title =        "Pseudo-mathematics and financial charlatanism: the
                 effects of backtest overfitting on out-of-sample
                 performance",
  journal =      j-NAMS,
  volume =       "61",
  number =       "5",
  pages =        "458--471",
  month =        may,
  year =         "2014",
  CODEN =        "AMNOAN",
  DOI =          "https://doi.org/10.1090/noti1105",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  MRclass =      "91G70 (62P05 91G80)",
  MRnumber =     "3203237",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1506/;
                 http://www.ams.org/notices/201405/rnoti-p458.pdf",
  acknowledgement = ack-nhfb,
  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",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2014:RTP
author: D. H. Bailey and J. M. Borwein
title: The recent trademarking of Pi: a troubling precedent
journal: j-NAMS
volume: 61
number: 10
pages: 121--124
month: nov
monthnumber: 11
year: 2014
CODEN: AMNOAN
DOI: https://doi.org/10.1090/noti1172
ISSN: 0002-9920 (print), 1088-9477 (electronic) OR 00029920 (print), 10889477 (electronic)
ISSNL: 0002-9920 OR 00029920
bibdate: Fri Aug 12 07:48:44 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 07:48:44 ???
fjournal: Notices of the American Mathematical Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/notices/
rawauthor: D. H. Bailey and J. M. Borwein
rawtitle: The recent trademarking of Pi: a troubling precedent
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/id/eprint/1501; http://www.ams.org/notices/201410/rnoti-p1224.pdf

entry:
@Article{Bailey:2014:RTP,
  author =       "D. H. Bailey and J. M. Borwein",
  title =        "The recent trademarking of Pi: a troubling precedent",
  journal =      j-NAMS,
  volume =       "61",
  number =       "10",
  pages =        "121--124",
  month =        nov,
  year =         "2014",
  CODEN =        "AMNOAN",
  DOI =          "https://doi.org/10.1090/noti1172",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibdate =      "Fri Aug 12 07:48:44 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/id/eprint/1501;
                 http://www.ams.org/notices/201410/rnoti-p1224.pdf",
  acknowledgement = ack-nhfb,
  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",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2014:ACR
author: Jonathan M. Borwein and Guoyin Li and Liangjin Yao
journal: j-SIAM-J-OPT
volume: 24
number: 1
pages: 498--527
year: 2014
CODEN: SJOPE8
DOI: https://doi.org/10.1137/130919052
ISSN: 1052-6234 (print), 1095-7189 (electronic) OR 10526234 (print), 10957189 (electronic)
ISSNL: 1052-6234 OR 10526234
MRclass: 47J25 (90C25 90C31)
MRnumber: 3180867
MRreviewer: Francisco J. Arag{\'o}n Artacho
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://arxiv.org/abs/1304.7965; http://docserver.carma.newcastle.edu.au/1508/
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 M. Borwein and Guoyin Li and Liangjin Yao
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Li, Guoyin/0000-0002-2099-7974
title:
Analysis of the convergence rate for the cyclic projection algorithm applied to basic semialgebraic convex sets

abstract:
In this paper, we study the rate of convergence of the cyclic projection algorithm applied to finitely many basic semialgebraic convex sets. We establish an explicit convergence rate estimate which relies on the maximum degree of the polynomials that generate the basic semialgebraic convex sets and the dimension of the underlying space. We achieve our results by exploiting the algebraic structure of the basic semialgebraic convex sets.

rawabstract:
In this paper, we study the rate of convergence of the cyclic projection algorithm applied to finitely many basic semialgebraic convex sets. We establish an explicit convergence rate estimate which relies on the maximum degree of the polynomials that generate the basic semialgebraic convex sets and the dimension of the underlying space. We achieve our results by exploiting the algebraic structure of the basic semialgebraic convex sets.

rawtitle:
Analysis of the convergence rate for the cyclic projection algorithm applied to basic semialgebraic convex sets

entry:
@Article{Borwein:2014:ACR,
  author =       "Jonathan M. Borwein and Guoyin Li and Liangjin Yao",
  title =        "Analysis of the convergence rate for the cyclic
                 projection algorithm applied to basic semialgebraic
                 convex sets",
  journal =      j-SIAM-J-OPT,
  volume =       "24",
  number =       "1",
  pages =        "498--527",
  year =         "2014",
  CODEN =        "SJOPE8",
  DOI =          "https://doi.org/10.1137/130919052",
  ISSN =         "1052-6234 (print), 1095-7189 (electronic)",
  ISSN-L =       "1052-6234",
  MRclass =      "47J25 (90C25 90C31)",
  MRnumber =     "3180867",
  MRreviewer =   "Francisco J. Arag{\'o}n Artacho",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/1304.7965;
                 http://docserver.carma.newcastle.edu.au/1508/",
  abstract =     "In this paper, we study the rate of convergence of the
                 cyclic projection algorithm applied to finitely many
                 basic semialgebraic convex sets. We establish an
                 explicit convergence rate estimate which relies on the
                 maximum degree of the polynomials that generate the
                 basic semialgebraic convex sets and the dimension of
                 the underlying space. We achieve our results by
                 exploiting the algebraic structure of the basic
                 semialgebraic convex sets.",
  acknowledgement = ack-nhfb,
  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; Li,
                 Guoyin/0000-0002-2099-7974",
  researcherid-numbers = "Li, Guoyin/B-7866-2009",
  unique-id =    "ISI:000333761700020",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2014:CDR
author: Jonathan M. Borwein and Matthew K. Tam
title: A cyclic Douglas--Rachford iteration scheme
journal: j-J-OPT-THEORY-APPL
volume: 160
number: 1
pages: 1--29
year: 2014
CODEN: JOTABN
DOI: https://doi.org/10.1007/s10957-013-0381-x
ISSN: 0022-3239 (print), 1573-2878 (electronic) OR 00223239 (print), 15732878 (electronic)
ISSNL: 0022-3239 OR 00223239
MRclass: 47J25 (90C25 90C48)
MRnumber: 3149115
MRreviewer: Francisco J. Arag{\'o}n Artacho
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://arxiv.org/abs/1303.1859; http://docserver.carma.newcastle.edu.au/1469/
fjournal: Journal of Optimization Theory and Applications
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/volumesAndIssues/10957
rawauthor: Jonathan M. Borwein and Matthew K. Tam
rawtitle: A cyclic {Douglas--Rachford} iteration scheme
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper, we present two Douglas--Rachford inspired iteration schemes which can be applied directly to N-set convex feasibility problems in Hilbert space. Our main results are weak convergence of the methods to a point whose nearest point projections onto each of the N sets coincide. For affine subspaces, convergence is in norm. Initial results from numerical experiments, comparing our methods to the classical (product-space) Douglas--Rachford scheme, are promising.

rawabstract:
In this paper, we present two Douglas--Rachford inspired iteration schemes which can be applied directly to N-set convex feasibility problems in Hilbert space. Our main results are weak convergence of the methods to a point whose nearest point projections onto each of the N sets coincide. For affine subspaces, convergence is in norm. Initial results from numerical experiments, comparing our methods to the classical (product-space) Douglas--Rachford scheme, are promising.

entry:
@Article{Borwein:2014:CDR,
  author =       "Jonathan M. Borwein and Matthew K. Tam",
  title =        "A cyclic {Douglas--Rachford} iteration scheme",
  journal =      j-J-OPT-THEORY-APPL,
  volume =       "160",
  number =       "1",
  pages =        "1--29",
  year =         "2014",
  CODEN =        "JOTABN",
  DOI =          "https://doi.org/10.1007/s10957-013-0381-x",
  ISSN =         "0022-3239 (print), 1573-2878 (electronic)",
  ISSN-L =       "0022-3239",
  MRclass =      "47J25 (90C25 90C48)",
  MRnumber =     "3149115",
  MRreviewer =   "Francisco J. Arag{\'o}n Artacho",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/1303.1859;
                 http://docserver.carma.newcastle.edu.au/1469/",
  abstract =     "In this paper, we present two Douglas--Rachford
                 inspired iteration schemes which can be applied
                 directly to N-set convex feasibility problems in
                 Hilbert space. Our main results are weak convergence of
                 the methods to a point whose nearest point projections
                 onto each of the N sets coincide. For affine subspaces,
                 convergence is in norm. Initial results from numerical
                 experiments, comparing our methods to the classical
                 (product-space) Douglas--Rachford scheme, are
                 promising.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Optimization Theory and Applications",
  journal-URL =  "http://link.springer.com/journal/volumesAndIssues/10957",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Tam, Matthew/G-8127-2013",
  unique-id =    "ISI:000330586300001",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2014:CZD
author: Jonathan M. Borwein and Regina S. Burachik and Liangjin Yao
title: Conditions for zero duality gap in convex programming
journal: j-J-NONLINEAR-CONVEX-ANAL
volume: 15
number: 1
pages: 167--190
year: 2014
ISSN: 1345-4773 (print), 1880-5221 (electronic) OR 13454773 (print), 18805221 (electronic)
ISSNL: 1345-4773 OR 13454773
MRclass: 49J52 (49N15 90C25 90C46)
MRnumber: 3184756
MRreviewer: Rafa{\l} K. Goebel
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://arxiv.org/abs/1211.49533; http://docserver.carma.newcastle.edu.au/1465/
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: Jonathan M. Borwein and Regina S. Burachik and Liangjin Yao
rawtitle: Conditions for zero duality gap in convex programming
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Burachik, Regina/0000-0003-1332-6213
abstract:
We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is less restrictive than all existing constraint qualifications, including the closed epigraph condition. Our dual condition was inspired by, and is less restrictive than, the so-called Bertsekas' condition for monotropic programming problems. We give several corollaries of our result and special cases as applications. We pay special attention to the polyhedral and sublinear cases, and their implications in convex optimization.

rawabstract:
We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is less restrictive than all existing constraint qualifications, including the closed epigraph condition. Our dual condition was inspired by, and is less restrictive than, the so-called Bertsekas' condition for monotropic programming problems. We give several corollaries of our result and special cases as applications. We pay special attention to the polyhedral and sublinear cases, and their implications in convex optimization.

entry:
@Article{Borwein:2014:CZD,
  author =       "Jonathan M. Borwein and Regina S. Burachik and
                 Liangjin Yao",
  title =        "Conditions for zero duality gap in convex
                 programming",
  journal =      j-J-NONLINEAR-CONVEX-ANAL,
  volume =       "15",
  number =       "1",
  pages =        "167--190",
  year =         "2014",
  ISSN =         "1345-4773 (print), 1880-5221 (electronic)",
  ISSN-L =       "1345-4773",
  MRclass =      "49J52 (49N15 90C25 90C46)",
  MRnumber =     "3184756",
  MRreviewer =   "Rafa{\l} K. Goebel",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/1211.49533;
                 http://docserver.carma.newcastle.edu.au/1465/",
  abstract =     "We introduce and study a new dual condition which
                 characterizes zero duality gap in nonsmooth convex
                 optimization. We prove that our condition is less
                 restrictive than all existing constraint
                 qualifications, including the closed epigraph
                 condition. Our dual condition was inspired by, and is
                 less restrictive than, the so-called Bertsekas'
                 condition for monotropic programming problems. We give
                 several corollaries of our result and special cases as
                 applications. We pay special attention to the
                 polyhedral and sublinear cases, and their implications
                 in convex optimization.",
  acknowledgement = ack-nhfb,
  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; Burachik,
                 Regina/0000-0003-1332-6213",
  researcherid-numbers = "Burachik, Regina/A-9859-2008",
  unique-id =    "ISI:000331342600012",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2014:DNS
author: David Borwein and Jonathan Borwein
title: Deriving New Sinc Results from Old
journal: j-AMER-MATH-MONTHLY
volume: 121
number: 8
pages: 700--705
month: oct
monthnumber: 10
year: 2014
CODEN: AMMYAE
DOI: https://doi.org/10.4169/amer.math.monthly.121.08.700
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 52A38 (33B10 42A99 51M25)
MRnumber: 3318479
MRreviewer: Victor V. Pambuccian
bibdate: Fri Feb 13 16:59:49 MST 2015
bibtimestamp: 2015.02.13 16:59:49 MST
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: David Borwein and Jonathan Borwein
rawtitle: Deriving New Sinc Results from Old
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.jstor.org/stable/10.4169/amermathmont.121.issue-08; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib

URL:
http://docserver.carma.newcastle.edu.au/1502/; https://www.jstor.org/stable/10.4169/amer.math.monthly.121.08.700

abstract:
From previously established results in [2], we develop a simple proof of Keith Ball's expression in [1] for the volume of the intersection of an (n - 1)-dimensional hyperplane with an n-dimensional cube, as well as a simple proof of the formula given by Frank and Riede in [5] for that volume.

rawabstract:
From previously established results in [2], we develop a simple proof of Keith Ball's expression in [1] for the volume of the intersection of an (n - 1)-dimensional hyperplane with an n-dimensional cube, as well as a simple proof of the formula given by Frank and Riede in [5] for that volume.

entry:
@Article{Borwein:2014:DNS,
  author =       "David Borwein and Jonathan Borwein",
  title =        "Deriving New Sinc Results from Old",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "121",
  number =       "8",
  pages =        "700--705",
  month =        oct,
  year =         "2014",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.121.08.700",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "52A38 (33B10 42A99 51M25)",
  MRnumber =     "3318479",
  MRreviewer =   "Victor V. Pambuccian",
  bibdate =      "Fri Feb 13 16:59:49 MST 2015",
  bibsource =    "https://www.jstor.org/stable/10.4169/amermathmont.121.issue-08;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1502/;
                 https://www.jstor.org/stable/10.4169/amer.math.monthly.121.08.700",
  abstract =     "From previously established results in [2], we develop
                 a simple proof of Keith Ball's expression in [1] for
                 the volume of the intersection of an (n -
                 1)-dimensional hyperplane with an n-dimensional cube,
                 as well as a simple proof of the formula given by Frank
                 and Riede in [5] for that volume.",
  acknowledgement = ack-nhfb,
  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",
  unique-id =    "ISI:000343376800004",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2014:ECVa
author: Jonathan M. Borwein
title: Experimental Computation and Visual Theorems
crossref: Hong:2014:MSI
pages: 1--8
year: 2014
DOI: https://doi.org/10.1007/978-3-662-44199-2_1
MRclass: 46-02 (65-02 68U01)
MRnumber: 3334735
MRreviewer: Matti Vuorinen
bibdate: Sat Aug 13 13:54:11 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 13:54:11 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawtitle: Experimental Computation and Visual Theorems
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InProceedings{Borwein:2014:ECVa,
  author =       "Jonathan M. Borwein",
  title =        "Experimental Computation and Visual Theorems",
  crossref =     "Hong:2014:MSI",
  pages =        "1--8",
  year =         "2014",
  DOI =          "https://doi.org/10.1007/978-3-662-44199-2_1",
  MRclass =      "46-02 (65-02 68U01)",
  MRnumber =     "3334735",
  MRreviewer =   "Matti Vuorinen",
  bibdate =      "Sat Aug 13 13:54:11 2016",
  bibsource =    "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: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2014:LAE
author: Jonathan M. Borwein
title: The Life of $ pi $: From Archimedes to ENIAC and Beyond
crossref: Sidoli:2014:ATB
pages: 531--561
year: 2014
DOI: https://doi.org/10.1007/978-3-642-36736-6_24
MRclass: 01A20 (11Y60)
MRnumber: 3203895
MRreviewer: Leo Corry
bibdate: Sat Aug 13 15:11:22 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 15:11:22 ???
note: Extended and updated version of cite Borwein:2008:VPG.
URL: http://www.carma.newcastle.edu.au/~jb616/pi-2010.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawnote: Extended and updated version of \cite{Borwein:2008:VPG}.
rawtitle: The Life of $ \pi $: From {Archimedes} to {ENIAC} and Beyond
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2014:LAE,
  author =       "Jonathan M. Borwein",
  title =        "The Life of $ \pi $: From {Archimedes} to {ENIAC} and
                 Beyond",
  crossref =     "Sidoli:2014:ATB",
  pages =        "531--561",
  year =         "2014",
  DOI =          "https://doi.org/10.1007/978-3-642-36736-6_24",
  MRclass =      "01A20 (11Y60)",
  MRnumber =     "3203895",
  MRreviewer =   "Leo Corry",
  bibdate =      "Sat Aug 13 15:11:22 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Extended and updated version of
                 \cite{Borwein:2008:VPG}.",
  URL =          "http://www.carma.newcastle.edu.au/~jb616/pi-2010.pdf",
  acknowledgement = ack-nhfb,
  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:2014:LKMa
author: Jonathan M. Borwein and Yann Bugeaud and Michael Coons
title: The legacy of Kurt Mahler
journal: j-EUR-MATH-SOC-NEWSL
volume: 91
pages: 19--23
month: mar
monthnumber: 3
year: 2014
ISSN: 1027-488X OR 1027488X
ISSNL: 1027-488X OR 1027488X
MRclass: 01A70
MRnumber: 3202400
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://www.ems-ph.org/journals/journal.php?jrn=news
fjournal: European Mathematical Society. Newsletter
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Yann Bugeaud and Michael Coons
rawtitle: The legacy of {Kurt Mahler}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2014:LKMa,
  author =       "Jonathan M. Borwein and Yann Bugeaud and Michael
                 Coons",
  title =        "The legacy of {Kurt Mahler}",
  journal =      j-EUR-MATH-SOC-NEWSL,
  volume =       "91",
  pages =        "19--23",
  month =        mar,
  year =         "2014",
  ISSN =         "1027-488X",
  ISSN-L =       "1027-488X",
  MRclass =      "01A70",
  MRnumber =     "3202400",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.ems-ph.org/journals/journal.php?jrn=news",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "European Mathematical Society. Newsletter",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  xxpages =      "12--16",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2014:LKMb
author: Jonathan M. Borwein and Yann Bugeaud and Michael Coons
title: The legacy of Kurt Mahler
journal: j-AUSTRALIAN-MATH-SOC-GAZ
volume: 41
number: 1
pages: 11--21
month: mar
monthnumber: 3
year: 2014
ISSN: 0311-0729 (print), 1326-2297 (electronic) OR 03110729 (print), 13262297 (electronic)
ISSNL: 0311-0729 OR 03110729
MRclass: 01A70
MRnumber: 3221622
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://www.austms.org.au/Publ/Gazette/2014/Mar14/Mahler.pdf
fjournal: The Australian Mathematical Society. Gazette
ZMnumber: 1308.01014
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 Yann Bugeaud and Michael Coons
rawtitle: The legacy of {Kurt Mahler}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2014:LKMb,
  author =       "Jonathan M. Borwein and Yann Bugeaud and Michael
                 Coons",
  title =        "The legacy of {Kurt Mahler}",
  journal =      j-AUSTRALIAN-MATH-SOC-GAZ,
  volume =       "41",
  number =       "1",
  pages =        "11--21",
  month =        mar,
  year =         "2014",
  ISSN =         "0311-0729 (print), 1326-2297 (electronic)",
  ISSN-L =       "0311-0729",
  MRclass =      "01A70",
  MRnumber =     "3221622",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.austms.org.au/Publ/Gazette/2014/Mar14/Mahler.pdf",
  ZMnumber =     "1308.01014",
  acknowledgement = ack-nhfb,
  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: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2014:LPA
author: Jonathan M. Borwein
title: The Life of Pi: From Archimedes to ENIAC and Beyond
crossref: Sidoli:2014:ATB
pages: 531--561
year: 2014
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/265/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawtitle: The Life of Pi: From {Archimedes} to {ENIAC} and Beyond
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2014:LPA,
  author =       "Jonathan M. Borwein",
  title =        "The Life of Pi: From {Archimedes} to {ENIAC} and
                 Beyond",
  crossref =     "Sidoli:2014:ATB",
  pages =        "531--561",
  year =         "2014",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/265/",
  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:2014:LSW
author: David Borwein and Jonathan M. Borwein and Armin Straub
title: On lattice sums and Wigner limits
journal: j-J-MATH-ANAL-APPL
volume: 414
number: 2
pages: 489--513
year: 2014
CODEN: JMANAK
DOI: https://doi.org/10.1016/j.jmaa.2014.01.008
ISSN: 0022-247X (print), 1096-0813 (electronic) OR 0022247X (print), 10960813 (electronic)
ISSNL: 0022-247X OR 0022247X
MRclass: 11D09 (11H06 11L03)
MRnumber: 3167976
MRreviewer: Ross C. McPhedran
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: Analytic continuation; Lattice sums; Wigner electron sums
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 Armin Straub
rawtitle: On lattice sums and {Wigner} limits
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053
URL:
http://arxiv.org/abs/1310.1423; http://docserver.carma.newcastle.edu.au/1509/; http://www.sciencedirect.com/science/article/pii/S0022247X14000134

abstract:
Wigner limits are given formally as the difference between a lattice sum, associated to a positive definite quadratic form, and a corresponding multiple integral. To define these limits, which arose in work of Wigner on the energy of static electron lattices, in a mathematically rigorous way one commonly truncates the lattice sum and the corresponding integral and takes the limit along expanding hypercubes or other regular geometric shapes. We generalize the known mathematically rigorous two- and three-dimensional results regarding Wigner limits, as laid down in [3], to integer lattices of arbitrary dimension. In doing so, we also resolve a problem posed in [6, Chapter 7]. For the sake of clarity, we begin by considering the simpler case of cubic lattice sums first, before treating the case of arbitrary quadratic forms. We also consider limits taken along expanding hyperballs with respect to general norms, and connect with classical topics such as Gauss's circle problem. Appendix A is included to recall certain properties of Epstein zeta functions that are either used in the paper or serve to provide perspective.

rawabstract:
Wigner limits are given formally as the difference between a lattice sum, associated to a positive definite quadratic form, and a corresponding multiple integral. To define these limits, which arose in work of Wigner on the energy of static electron lattices, in a mathematically rigorous way one commonly truncates the lattice sum and the corresponding integral and takes the limit along expanding hypercubes or other regular geometric shapes. We generalize the known mathematically rigorous two- and three-dimensional results regarding Wigner limits, as laid down in [3], to integer lattices of arbitrary dimension. In doing so, we also resolve a problem posed in [6, Chapter 7]. For the sake of clarity, we begin by considering the simpler case of cubic lattice sums first, before treating the case of arbitrary quadratic forms. We also consider limits taken along expanding hyperballs with respect to general norms, and connect with classical topics such as Gauss's circle problem. Appendix A is included to recall certain properties of Epstein zeta functions that are either used in the paper or serve to provide perspective.

entry:
@Article{Borwein:2014:LSW,
  author =       "David Borwein and Jonathan M. Borwein and Armin
                 Straub",
  title =        "On lattice sums and {Wigner} limits",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "414",
  number =       "2",
  pages =        "489--513",
  year =         "2014",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/j.jmaa.2014.01.008",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "11D09 (11H06 11L03)",
  MRnumber =     "3167976",
  MRreviewer =   "Ross C. McPhedran",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/1310.1423;
                 http://docserver.carma.newcastle.edu.au/1509/;
                 http://www.sciencedirect.com/science/article/pii/S0022247X14000134",
  abstract =     "Wigner limits are given formally as the difference
                 between a lattice sum, associated to a positive
                 definite quadratic form, and a corresponding multiple
                 integral. To define these limits, which arose in work
                 of Wigner on the energy of static electron lattices, in
                 a mathematically rigorous way one commonly truncates
                 the lattice sum and the corresponding integral and
                 takes the limit along expanding hypercubes or other
                 regular geometric shapes. We generalize the known
                 mathematically rigorous two- and three-dimensional
                 results regarding Wigner limits, as laid down in [3],
                 to integer lattices of arbitrary dimension. In doing
                 so, we also resolve a problem posed in [6, Chapter 7].
                 For the sake of clarity, we begin by considering the
                 simpler case of cubic lattice sums first, before
                 treating the case of arbitrary quadratic forms. We also
                 consider limits taken along expanding hyperballs with
                 respect to general norms, and connect with classical
                 topics such as Gauss's circle problem. Appendix A is
                 included to recall certain properties of Epstein zeta
                 functions that are either used in the paper or serve to
                 provide perspective.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "Analytic continuation; Lattice sums; Wigner electron
                 sums",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053",
  unique-id =    "ISI:000334651500001",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2014:LTI
author: Jonathan M. Borwein and Liangjin Yao
title: Legendre-type integrands and convex integral functions
journal: j-J-CONVEX-ANAL
volume: 21
number: 1
pages: 261--288
year: 2014
ISSN: 0944-6532 (print), 2363-6394 (electronic) OR 09446532 (print), 23636394 (electronic)
MRclass: 46B20 (47H05 49K10)
MRnumber: 3235316
MRreviewer: Jes{\'u}s Ferrer
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 and Liangjin Yao
rawtitle: {Legendre}-type integrands and convex integral functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://arxiv.org/abs/1208.5217; http://docserver.carma.newcastle.edu.au/1455/; http://www.heldermann.de/JCA/JCA21/JCA211/jca21015.htm

abstract:
In this paper, we study the properties of integral functionals induced on L-E(1)(S, mu) by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann-Shannon entropy and the Fermi-Dirac entropy are strongly rotund. We also study convergence in measure and give various limiting counterexamples.

rawabstract:
In this paper, we study the properties of integral functionals induced on L-E(1)(S, mu) by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann-Shannon entropy and the Fermi-Dirac entropy are strongly rotund. We also study convergence in measure and give various limiting counterexamples.

entry:
@Article{Borwein:2014:LTI,
  author =       "Jonathan M. Borwein and Liangjin Yao",
  title =        "{Legendre}-type integrands and convex integral
                 functions",
  journal =      j-J-CONVEX-ANAL,
  volume =       "21",
  number =       "1",
  pages =        "261--288",
  year =         "2014",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "46B20 (47H05 49K10)",
  MRnumber =     "3235316",
  MRreviewer =   "Jes{\'u}s Ferrer",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/1208.5217;
                 http://docserver.carma.newcastle.edu.au/1455/;
                 http://www.heldermann.de/JCA/JCA21/JCA211/jca21015.htm",
  abstract =     "In this paper, we study the properties of integral
                 functionals induced on L-E(1)(S, mu) by closed convex
                 functions on a Euclidean space E. We give sufficient
                 conditions for such integral functions to be strongly
                 rotund (well-posed). We show that in this generality
                 functions such as the Boltzmann-Shannon entropy and the
                 Fermi-Dirac entropy are strongly rotund. We also study
                 convergence in measure and give various limiting
                 counterexamples.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Convex Analysis",
  journal-URL =  "http://www.heldermann.de/JCA/jcacon.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  unique-id =    "ISI:000337215600015",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2014:MSS
author: Jonathan Borwein and Phil Howlett and Julia Piantadosi
title: Modelling and Simulation of Seasonal Rainfall Using the Principle of Maximum Entropy
journal: j-ENTROPY
volume: 16
number: 2
pages: 747--769
month: feb
monthnumber: 2
year: 2014
CODEN: ENTRFG
DOI: https://doi.org/10.3390/e16020747
ISSN: 1099-4300 OR 10994300
ISSNL: 1099-4300 OR 10994300
MRclass: 62P12 (62H05)
MRnumber: 3177597
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 ???
fjournal: Entropy
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein and Phil Howlett and Julia Piantadosi
rawtitle: Modelling and Simulation of Seasonal Rainfall Using the Principle of Maximum Entropy
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Howlett, Phil/0000-0003-2382-8137
URL:
http://adsabs.harvard.edu/abs/2014Entrp..16..747B; http://docserver.carma.newcastle.edu.au/1507/; http://www.mdpi.com/1099-4300/16/

abstract:
We use the principle of maximum entropy to propose a parsimonious model for the generation of simulated rainfall during the wettest three-month season at a typical location on the east coast of Australia. The model uses a checkerboard copula of maximum entropy to model the joint probability distribution for total seasonal rainfall and a set of two-parameter gamma distributions to model each of the marginal monthly rainfall totals. The model allows us to match the grade correlation coefficients for the checkerboard copula to the observed Spearman rank correlation coefficients for the monthly rainfalls and, hence, provides a model that correctly describes the mean and variance for each of the monthly totals and also for the overall seasonal total. Thus, we avoid the need for a posteriori adjustment of simulated monthly totals in order to correctly simulate the observed seasonal statistics. Detailed results are presented for the modelling and simulation of seasonal rainfall in the town of Kempsey on the mid-north coast of New South Wales. Empirical evidence from extensive simulations is used to validate this application of the model. A similar analysis for Sydney is also described.

rawabstract:
We use the principle of maximum entropy to propose a parsimonious model for the generation of simulated rainfall during the wettest three-month season at a typical location on the east coast of Australia. The model uses a checkerboard copula of maximum entropy to model the joint probability distribution for total seasonal rainfall and a set of two-parameter gamma distributions to model each of the marginal monthly rainfall totals. The model allows us to match the grade correlation coefficients for the checkerboard copula to the observed Spearman rank correlation coefficients for the monthly rainfalls and, hence, provides a model that correctly describes the mean and variance for each of the monthly totals and also for the overall seasonal total. Thus, we avoid the need for a posteriori adjustment of simulated monthly totals in order to correctly simulate the observed seasonal statistics. Detailed results are presented for the modelling and simulation of seasonal rainfall in the town of Kempsey on the mid-north coast of New South Wales. Empirical evidence from extensive simulations is used to validate this application of the model. A similar analysis for Sydney is also described.

entry:
@Article{Borwein:2014:MSS,
  author =       "Jonathan Borwein and Phil Howlett and Julia
                 Piantadosi",
  title =        "Modelling and Simulation of Seasonal Rainfall Using
                 the Principle of Maximum Entropy",
  journal =      j-ENTROPY,
  volume =       "16",
  number =       "2",
  pages =        "747--769",
  month =        feb,
  year =         "2014",
  CODEN =        "ENTRFG",
  DOI =          "https://doi.org/10.3390/e16020747",
  ISSN =         "1099-4300",
  ISSN-L =       "1099-4300",
  MRclass =      "62P12 (62H05)",
  MRnumber =     "3177597",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2014Entrp..16..747B;
                 http://docserver.carma.newcastle.edu.au/1507/;
                 http://www.mdpi.com/1099-4300/16/",
  abstract =     "We use the principle of maximum entropy to propose a
                 parsimonious model for the generation of simulated
                 rainfall during the wettest three-month season at a
                 typical location on the east coast of Australia. The
                 model uses a checkerboard copula of maximum entropy to
                 model the joint probability distribution for total
                 seasonal rainfall and a set of two-parameter gamma
                 distributions to model each of the marginal monthly
                 rainfall totals. The model allows us to match the grade
                 correlation coefficients for the checkerboard copula to
                 the observed Spearman rank correlation coefficients for
                 the monthly rainfalls and, hence, provides a model that
                 correctly describes the mean and variance for each of
                 the monthly totals and also for the overall seasonal
                 total. Thus, we avoid the need for a posteriori
                 adjustment of simulated monthly totals in order to
                 correctly simulate the observed seasonal statistics.
                 Detailed results are presented for the modelling and
                 simulation of seasonal rainfall in the town of Kempsey
                 on the mid-north coast of New South Wales. Empirical
                 evidence from extensive simulations is used to validate
                 this application of the model. A similar analysis for
                 Sydney is also described.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Entropy",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Howlett,
                 Phil/0000-0003-2382-8137",
  unique-id =    "ISI:000334246400007",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borwein:2014:NFI
author: Jonathan M. Borwein and Alfred Jacobus van der Poorten and Jeffrey Outlaw Shallit and Wadim Zudilin
title: Neverending Fractions: an Introduction to Continued Fractions
volume: 23
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: x + 212
year: 2014
DOI: https://doi.org/10.1017/CBO9780511902659
ISBN: 0-521-18649-8 OR 0521186498
ISBN13: 978-0-521-18649-0 OR 9780521186490
LCCN: QA295 .B667 2014
MRclass: 11A55 (11J70 40-01 40A15)
MRnumber: 3468515
bibdate: Thu Jun 12 08:53:05 MDT 2014
bibtimestamp: 2014.06.12 08:53:05 MDT
series: Australian Mathematical Society lecture series
subject: Continued fractions; Processes, Infinite; Fractions
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Alfred Jacobus van der Poorten and Jeffrey Outlaw Shallit and Wadim Zudilin
rawtitle: Neverending Fractions: an Introduction to Continued Fractions
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Zudilin, Wadim/0000-0001-9551-2903
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/1722/; http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511902659

TOC:
Preface 1. Some preliminaries from number theory 2. Continued fractions, as they are 3. Metric theory of continued fractions 4. Quadratic irrationals through a magnifier 5. Hyperelliptic curves and Somos sequences 6. From folding to Fibonacci 7. The integer part of $q alpha + beta $ 8. The Erdos--Moser equation 9. Irregular continued fractions Appendix. Selected continued fractions Bibliography Index

rawTOC:
Preface \\ 1. Some preliminaries from number theory \\ 2. Continued fractions, as they are \\ 3. Metric theory of continued fractions \\ 4. Quadratic irrationals through a magnifier \\ 5. Hyperelliptic curves and Somos sequences \\ 6. From folding to Fibonacci \\ 7. The integer part of $q \alpha + \beta$ \\ 8. The Erd{\H{o}}s--Moser equation \\ 9. Irregular continued fractions \\ Appendix. Selected continued fractions \\ Bibliography \\ Index

entry:
@Book{Borwein:2014:NFI,
  author =       "Jonathan M. Borwein and Alfred Jacobus van der Poorten
                 and Jeffrey Outlaw Shallit and Wadim Zudilin",
  title =        "Neverending Fractions: an Introduction to Continued
                 Fractions",
  volume =       "23",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "x + 212",
  year =         "2014",
  DOI =          "https://doi.org/10.1017/CBO9780511902659",
  ISBN =         "0-521-18649-8",
  ISBN-13 =      "978-0-521-18649-0",
  LCCN =         "QA295 .B667 2014",
  MRclass =      "11A55 (11J70 40-01 40A15)",
  MRnumber =     "3468515",
  bibdate =      "Thu Jun 12 08:53:05 MDT 2014",
  bibsource =    "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",
  series =       "Australian Mathematical Society lecture series",
  URL =          "http://docserver.carma.newcastle.edu.au/1722/;
                 http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511902659",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Zudilin,
                 Wadim/0000-0001-9551-2903",
  subject =      "Continued fractions; Processes, Infinite; Fractions",
  tableofcontents = "Preface \\
                 1. Some preliminaries from number theory \\
                 2. Continued fractions, as they are \\
                 3. Metric theory of continued fractions \\
                 4. Quadratic irrationals through a magnifier \\
                 5. Hyperelliptic curves and Somos sequences \\
                 6. From folding to Fibonacci \\
                 7. The integer part of $q \alpha + \beta$ \\
                 8. The Erd{\H{o}}s--Moser equation \\
                 9. Irregular continued fractions \\
                 Appendix. Selected continued fractions \\
                 Bibliography \\
                 Index",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2014:RMIa
author: J. M. Borwein and M. K. Tam
title: Reflection methods for inverse problems with applications to protein conformation determination
pages: ??--??
year: 2014
bibdate: Fri Aug 12 18:37:52 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 18:37:52 ???
URL: http://docserver.carma.newcastle.edu.au/1678/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and M. K. Tam
rawtitle: Reflection methods for inverse problems with applications to protein conformation determination
ORCID: Borwein, Jonathan/0000-0002-1263-0646
booktitle:
CIMPA school Generalized Nash Equilibrium Problems, Bilevel programming and MPEC New Delhi, India, December 2012

rawbooktitle:
{CIMPA school Generalized Nash Equilibrium Problems, Bilevel programming and MPEC New Delhi, India, December 2012}

entry:
@InProceedings{Borwein:2014:RMIa,
  author =       "J. M. Borwein and M. K. Tam",
  booktitle =    "{CIMPA school Generalized Nash Equilibrium Problems,
                 Bilevel programming and MPEC New Delhi, India, December
                 2012}",
  title =        "Reflection methods for inverse problems with
                 applications to protein conformation determination",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2014",
  DOI =          "",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "",
  bibdate =      "Fri Aug 12 18:37:52 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1678/",
  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:2014:RMIb
author: J. M. Borwein and M. K. Tam
title: Reflection methods for inverse problems with application to protein conformation determination
journal: ArXiv e-prints
pages: ??--??
month: aug
monthnumber: 8
year: 2014
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/2014arXiv1408.4213B; http://docserver.carma.newcastle.edu.au/1678/
keywords: Mathematics - Optimization and Control
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and M. K. Tam
rawtitle: Reflection methods for inverse problems with application to protein conformation determination
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
The Douglas--Rachford reflection method is a general purpose algorithm useful for solving the feasibility problem of finding a point in the intersection of finitely many sets. In this chapter we demonstrate that applied to a specific problem, the method can benefit from heuristics specific to said problem which exploit its special structure. In particular, we focus on the problem of protein conformation determination formulated within the framework of matrix completion, as was considered in a recent paper of the present authors.

rawabstract:
The Douglas--Rachford reflection method is a general purpose algorithm useful for solving the feasibility problem of finding a point in the intersection of finitely many sets. In this chapter we demonstrate that applied to a specific problem, the method can benefit from heuristics specific to said problem which exploit its special structure. In particular, we focus on the problem of protein conformation determination formulated within the framework of matrix completion, as was considered in a recent paper of the present authors.

entry:
@Article{Borwein:2014:RMIb,
  author =       "J. M. Borwein and M. K. Tam",
  title =        "Reflection methods for inverse problems with
                 application to protein conformation determination",
  journal =      "ArXiv e-prints",
  month =        aug,
  year =         "2014",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2014arXiv1408.4213B;
                 http://docserver.carma.newcastle.edu.au/1678/",
  abstract =     "The Douglas--Rachford reflection method is a general
                 purpose algorithm useful for solving the feasibility
                 problem of finding a point in the intersection of
                 finitely many sets. In this chapter we demonstrate that
                 applied to a specific problem, the method can benefit
                 from heuristics specific to said problem which exploit
                 its special structure. In particular, we focus on the
                 problem of protein conformation determination
                 formulated within the framework of matrix completion,
                 as was considered in a recent paper of the present
                 authors.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1408.4213",
  keywords =     "Mathematics - Optimization and Control",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.OC",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2014:ROM
author: J. M. Borwein and Brailey Sims
journal: j-AUSTRALIAN-MATH-SOC-GAZ
volume: 41
number: 2
pages: 116--118
month: may
monthnumber: 5
year: 2014
ISSN: 0311-0729 (print), 1326-2297 (electronic) OR 03110729 (print), 13262297 (electronic)
ISSNL: 0311-0729 OR 03110729
bibdate: Tue Aug 16 09:16:30 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:16:30 ???
URL: http://www.austms.org.au/Publ/Gazette/2014/May14/BkRev.pdf
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: J. M. Borwein and Brailey Sims
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Review of booktitle Origins of Mathematical Words: A Comprehensive Dictionary of Latin, Greek and Arabic Roots by Anthony lo Bello. The John Hopkins University Press, 2013

rawtitle:
Review of {{\booktitle{Origins of Mathematical Words: A Comprehensive Dictionary of Latin, Greek and Arabic Roots}} by Anthony lo Bello. The John Hopkins University Press, 2013}

entry:
@Article{Borwein:2014:ROM,
  author =       "J. M. Borwein and Brailey Sims",
  title =        "Review of {{\booktitle{Origins of Mathematical Words:
                 A Comprehensive Dictionary of Latin, Greek and Arabic
                 Roots}} by Anthony lo Bello. The John Hopkins
                 University Press, 2013}",
  journal =      j-AUSTRALIAN-MATH-SOC-GAZ,
  volume =       "41",
  number =       "2",
  pages =        "116--118",
  month =        may,
  year =         "2014",
  ISSN =         "0311-0729 (print), 1326-2297 (electronic)",
  ISSN-L =       "0311-0729",
  bibdate =      "Tue Aug 16 09:16:30 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.austms.org.au/Publ/Gazette/2014/May14/BkRev.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Aust. Math. Soc. Gaz.",
  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",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2014:SLM
author: David Borwein and Jonathan M. Borwein and Brailey Sims
title: On the Solution of Linear Mean Recurrences
journal: j-AMER-MATH-MONTHLY
volume: 121
number: 6
pages: 486--498
month: jun
monthnumber: 6
year: 2014
CODEN: AMMYAE
DOI: https://doi.org/10.4169/amer.math.monthly.121.06.486
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 39B12 (15B51 65Q30)
MRnumber: 3225456
bibdate: Wed Sep 10 09:38:03 MDT 2014
bibtimestamp: 2014.09.10 09:38:03 MDT
URL: http://docserver.carma.newcastle.edu.au/1505/; https://www.jstor.org/stable/10.4169
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: David Borwein and Jonathan M. Borwein and Brailey Sims
rawtitle: On the Solution of Linear Mean Recurrences
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.jstor.org/stable/10.4169/amermathmont.121.issue-06; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib

abstract:
Motivated by questions of algorithm analysis, we provide several distinct approaches to determining convergence and limit values for a class of linear iterations.

rawabstract:
Motivated by questions of algorithm analysis, we provide several distinct approaches to determining convergence and limit values for a class of linear iterations.

entry:
@Article{Borwein:2014:SLM,
  author =       "David Borwein and Jonathan M. Borwein and Brailey
                 Sims",
  title =        "On the Solution of Linear Mean Recurrences",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "121",
  number =       "6",
  pages =        "486--498",
  month =        jun # "\slash " # jul,
  year =         "2014",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.121.06.486",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "39B12 (15B51 65Q30)",
  MRnumber =     "3225456",
  bibdate =      "Wed Sep 10 09:38:03 MDT 2014",
  bibsource =    "https://www.jstor.org/stable/10.4169/amermathmont.121.issue-06;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1505/;
                 https://www.jstor.org/stable/10.4169",
  abstract =     "Motivated by questions of algorithm analysis, we
                 provide several distinct approaches to determining
                 convergence and limit values for a class of linear
                 iterations.",
  acknowledgement = ack-nhfb,
  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",
  unique-id =    "ISI:000337330700002",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2014:SRC
author: Jonathan M. Borwein and Liangjin Yao
title: Some results on the convexity of the closure of the domain of a maximally monotone operator
journal: j-OPTIM-LETT
volume: 8
number: 1
pages: 237--246
year: 2014
DOI: https://doi.org/10.1007/s11590-012-0564-7
ISSN: 1862-4472 (print), 1862-4480 (electronic) OR 18624472 (print), 18624480 (electronic)
ISSNL: 1862-4472 OR 18624472
MRclass: 47H05 (26B25 47B65)
MRnumber: 3152913
MRreviewer: Aris Daniilidis
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://arxiv.org/abs/1205.4482; http://docserver.carma.newcastle.edu.au/1373/
fjournal: Optimization Letters
acknowledgement: ack-nhfb
ajournal: Optim. Lett.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11590
rawauthor: Jonathan M. Borwein and Liangjin Yao
rawtitle: Some results on the convexity of the closure of the domain of a maximally monotone operator
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We provide a concise analysis about what is known regarding when the closure of the domain of a maximally monotone operator on an arbitrary real Banach space is convex. In doing so, we also provide an affirmative answer to a problem posed by Simons.

entry:
@Article{Borwein:2014:SRC,
  author =       "Jonathan M. Borwein and Liangjin Yao",
  title =        "Some results on the convexity of the closure of the
                 domain of a maximally monotone operator",
  journal =      j-OPTIM-LETT,
  volume =       "8",
  number =       "1",
  pages =        "237--246",
  year =         "2014",
  DOI =          "https://doi.org/10.1007/s11590-012-0564-7",
  ISSN =         "1862-4472 (print), 1862-4480 (electronic)",
  ISSN-L =       "1862-4472",
  MRclass =      "47H05 (26B25 47B65)",
  MRnumber =     "3152913",
  MRreviewer =   "Aris Daniilidis",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/1205.4482;
                 http://docserver.carma.newcastle.edu.au/1373/",
  abstract =     "We provide a concise analysis about what is known
                 regarding when the closure of the domain of a maximally
                 monotone operator on an arbitrary real Banach space is
                 convex. In doing so, we also provide an affirmative
                 answer to a problem posed by Simons.",
  acknowledgement = ack-nhfb,
  ajournal =     "Optim. Lett.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Optimization Letters",
  journal-URL =  "http://link.springer.com/journal/11590",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  unique-id =    "ISI:000330434600019",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2014:STMa
author: Jonathan M. Borwein and Liangjin Yao
title: Sum theorems for maximally monotone operators of type (FPV)
journal: j-J-AUSTRAL-MATH-SOC
volume: 97
number: 1
pages: 1--26
year: 2014
CODEN: JAUMAX
DOI: https://doi.org/10.1017/S1446788714000056
ISSN: 1446-7887 (print), 1446-8107 (electronic) OR 14467887 (print), 14468107 (electronic)
ISSNL: 1446-7887 OR 14467887
MRclass: 47H05 (49J53 90C25 90C48)
MRnumber: 3233391
MRreviewer: Radu Ioan Bo{\c{t}}
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 the Australian Mathematical Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Liangjin Yao
rawtitle: Sum theorems for maximally monotone operators of type ({FPV})
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://arxiv.org/abs/1305.6691; http://docserver.carma.newcastle.edu.au/1503/; http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9306990

abstract:
The most important open problem in monotone operator theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar's constraint qualification holds. In this paper, we establish the maximal monotonicity of A + B provided that A and B are maximally monotone operators such that star(dom A) boolean AND int dom B not equal phi, and A is of type (FPV). We show that when also dom A is convex, the sum operator A + B is also of type (FPV). Our result generalizes and unifies several recent sum theorems.

rawabstract:
The most important open problem in monotone operator theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar's constraint qualification holds. In this paper, we establish the maximal monotonicity of A + B provided that A and B are maximally monotone operators such that star(dom A) boolean AND int dom B not equal phi, and A is of type (FPV). We show that when also dom A is convex, the sum operator A + B is also of type (FPV). Our result generalizes and unifies several recent sum theorems.

entry:
@Article{Borwein:2014:STMa,
  author =       "Jonathan M. Borwein and Liangjin Yao",
  title =        "Sum theorems for maximally monotone operators of type
                 ({FPV})",
  journal =      j-J-AUSTRAL-MATH-SOC,
  volume =       "97",
  number =       "1",
  pages =        "1--26",
  year =         "2014",
  CODEN =        "JAUMAX",
  DOI =          "https://doi.org/10.1017/S1446788714000056",
  ISSN =         "1446-7887 (print), 1446-8107 (electronic)",
  ISSN-L =       "1446-7887",
  MRclass =      "47H05 (49J53 90C25 90C48)",
  MRnumber =     "3233391",
  MRreviewer =   "Radu Ioan Bo{\c{t}}",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/1305.6691;
                 http://docserver.carma.newcastle.edu.au/1503/;
                 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9306990",
  abstract =     "The most important open problem in monotone operator
                 theory concerns the maximal monotonicity of the sum of
                 two maximally monotone operators provided that the
                 classical Rockafellar's constraint qualification holds.
                 In this paper, we establish the maximal monotonicity of
                 A + B provided that A and B are maximally monotone
                 operators such that star(dom A) boolean AND int dom B
                 not equal phi, and A is of type (FPV). We show that
                 when also dom A is convex, the sum operator A + B is
                 also of type (FPV). Our result generalizes and unifies
                 several recent sum theorems.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of the Australian Mathematical Society",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  unique-id =    "ISI:000343185700001",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: James:2014:STR
title: Standing Together for Reproducibility in Large-Scale Computing: Report on reproducibility@XSEDE
journal: ArXiv e-prints
pages: 1--26
month: dec
monthnumber: 12
year: 2014
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/2014arXiv1412.5557J
keywords: Computer Science - Distributed, Parallel, and Cluster Computing, 68N01, D.2.9
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawtitle: Standing Together for Reproducibility in Large-Scale Computing: Report on {reproducibility@XSEDE}
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
author:
D. James and N. Wilkins-Diehr and V. Stodden and D. Colbry and C. Rosales and M. Fahey and J. Shi and R. F. Silva and K. Lee and R. Roskies and L. Loewe and S. Lindsey and R. Kooper and L. Barba and D. Bailey and J. Borwein and O. Corcho and E. Deelman and M. Dietze and B. Gilbert and J. Harkes and S. Keele and P. Kumar and J. Lee and E. Linke and R. Marciano and L. Marini and C. Mattman and D. Mattson and K. McHenry and R. McLay and S. Miguez and B. Minsker and M. Perez-Hernandez and D. Ryan and M. Rynge and I. Santana-Perez and M. Satyanarayanan and G. St.Clair and K. Webster and E. Hovig and D. S. Katz and S. Kay and G. Sandve and D. Skinner and G. Allen and J. Cazes and K. W. Cho and J. Fonseca and L. Hwang and L. Koesterke and P. Patel and L. Pouchard and E. Seidel and I. Suriarachchi

abstract:
This is the final report on reproducibility@XSEDE, a one-day workshop held in conjunction with XSEDE14, the annual conference of the Extreme Science and Engineering Discovery Environment (XSEDE). The workshop's discussion-oriented agenda focused on reproducibility in large-scale computational research. Two important themes capture the spirit of the workshop submissions and discussions: (1) organizational stakeholders, especially supercomputer centers, are in a unique position to promote, enable, and support reproducible research; and (2) individual researchers should conduct each experiment as though someone will replicate that experiment. Participants documented numerous issues, questions, technologies, practices, and potentially promising initiatives emerging from the discussion, but also highlighted four areas of particular interest to XSEDE: (1) documentation and training that promotes reproducible research; (2) system-level tools that provide build- and run-time information at the level of the individual job; (3) the need to model best practices in research collaborations involving XSEDE staff; and (4) continued work on gateways and related technologies. In addition, an intriguing question emerged from the day's interactions: would there be value in establishing an annual award for excellence in reproducible research?

rawabstract:
This is the final report on reproducibility@XSEDE, a one-day workshop held in conjunction with XSEDE14, the annual conference of the Extreme Science and Engineering Discovery Environment (XSEDE). The workshop's discussion-oriented agenda focused on reproducibility in large-scale computational research. Two important themes capture the spirit of the workshop submissions and discussions: (1) organizational stakeholders, especially supercomputer centers, are in a unique position to promote, enable, and support reproducible research; and (2) individual researchers should conduct each experiment as though someone will replicate that experiment. Participants documented numerous issues, questions, technologies, practices, and potentially promising initiatives emerging from the discussion, but also highlighted four areas of particular interest to XSEDE: (1) documentation and training that promotes reproducible research; (2) system-level tools that provide build- and run-time information at the level of the individual job; (3) the need to model best practices in research collaborations involving XSEDE staff; and (4) continued work on gateways and related technologies. In addition, an intriguing question emerged from the day's interactions: would there be value in establishing an annual award for excellence in reproducible research?

rawauthor:
D. James and N. Wilkins-Diehr and V. Stodden and D. Colbry and C. Rosales and M. Fahey and J. Shi and R. F. Silva and K. Lee and R. Roskies and L. Loewe and S. Lindsey and R. Kooper and L. Barba and D. Bailey and J. Borwein and O. Corcho and E. Deelman and M. Dietze and B. Gilbert and J. Harkes and S. Keele and P. Kumar and J. Lee and E. Linke and R. Marciano and L. Marini and C. Mattman and D. Mattson and K. McHenry and R. McLay and S. Miguez and B. Minsker and M. Perez-Hernandez and D. Ryan and M. Rynge and I. Santana-Perez and M. Satyanarayanan and G. {St.Clair} and K. Webster and E. Hovig and D. S. Katz and S. Kay and G. Sandve and D. Skinner and G. Allen and J. Cazes and K. W. Cho and J. Fonseca and L. Hwang and L. Koesterke and P. Patel and L. Pouchard and E. Seidel and I. Suriarachchi

entry:
@Article{James:2014:STR,
  author =       "D. James and N. Wilkins-Diehr and V. Stodden and D.
                 Colbry and C. Rosales and M. Fahey and J. Shi and R. F.
                 Silva and K. Lee and R. Roskies and L. Loewe and S.
                 Lindsey and R. Kooper and L. Barba and D. Bailey and J.
                 Borwein and O. Corcho and E. Deelman and M. Dietze and
                 B. Gilbert and J. Harkes and S. Keele and P. Kumar and
                 J. Lee and E. Linke and R. Marciano and L. Marini and
                 C. Mattman and D. Mattson and K. McHenry and R. McLay
                 and S. Miguez and B. Minsker and M. Perez-Hernandez and
                 D. Ryan and M. Rynge and I. Santana-Perez and M.
                 Satyanarayanan and G. {St.Clair} and K. Webster and E.
                 Hovig and D. S. Katz and S. Kay and G. Sandve and D.
                 Skinner and G. Allen and J. Cazes and K. W. Cho and J.
                 Fonseca and L. Hwang and L. Koesterke and P. Patel and
                 L. Pouchard and E. Seidel and I. Suriarachchi",
  title =        "Standing Together for Reproducibility in Large-Scale
                 Computing: Report on {reproducibility@XSEDE}",
  journal =      "ArXiv e-prints",
  month =        dec,
  year =         "2014",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2014arXiv1412.5557J",
  abstract =     "This is the final report on reproducibility@XSEDE, a
                 one-day workshop held in conjunction with XSEDE14, the
                 annual conference of the Extreme Science and
                 Engineering Discovery Environment (XSEDE). The
                 workshop's discussion-oriented agenda focused on
                 reproducibility in large-scale computational research.
                 Two important themes capture the spirit of the workshop
                 submissions and discussions: (1) organizational
                 stakeholders, especially supercomputer centers, are in
                 a unique position to promote, enable, and support
                 reproducible research; and (2) individual researchers
                 should conduct each experiment as though someone will
                 replicate that experiment. Participants documented
                 numerous issues, questions, technologies, practices,
                 and potentially promising initiatives emerging from the
                 discussion, but also highlighted four areas of
                 particular interest to XSEDE: (1) documentation and
                 training that promotes reproducible research; (2)
                 system-level tools that provide build- and run-time
                 information at the level of the individual job; (3) the
                 need to model best practices in research collaborations
                 involving XSEDE staff; and (4) continued work on
                 gateways and related technologies. In addition, an
                 intriguing question emerged from the day's
                 interactions: would there be value in establishing an
                 annual award for excellence in reproducible research?",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1412.5557",
  keywords =     "Computer Science - Distributed, Parallel, and Cluster
                 Computing, 68N01, D.2.9",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  primaryclass = "cs.DC",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Piantadosi:2014:MSS
author: Julia Piantadosi and Phil Howlett and Jonathan Borwein
title: Modelling and simulation of seasonal rainfall using checkerboard copulas of maximum entropy
pages: 1--26
year: 2014
bibdate: Tue Aug 16 09:36:53 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:36:53 ???
note: Submitted eMathematics and Computers in Simulation MATCOM, May 2014.
URL: http://docserver.carma.newcastle.edu.au/1694/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Julia Piantadosi and Phil Howlett and Jonathan Borwein
rawnote: Submitted eMathematics and Computers in Simulation MATCOM, May 2014.
rawtitle: Modelling and simulation of seasonal rainfall using checkerboard copulas of maximum entropy
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Howlett, Phil/0000-0003-2382-8137
entry:
@Unpublished{Piantadosi:2014:MSS,
  author =       "Julia Piantadosi and Phil Howlett and Jonathan
                 Borwein",
  title =        "Modelling and simulation of seasonal rainfall using
                 checkerboard copulas of maximum entropy",
  year =         "2014",
  bibdate =      "Tue Aug 16 09:36:53 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Submitted eMathematics and Computers in Simulation
                 MATCOM, May 2014.",
  URL =          "http://docserver.carma.newcastle.edu.au/1694/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Howlett,
                 Phil/0000-0003-2382-8137",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: AragonArtacho:2015:GBD
author: F. J. Aragon Artacho and J. M. Borwein and M. K. Tam
title: Global Behavior of the Douglas--Rachford Method for a Nonconvex Feasibility Problem
journal: ArXiv e-prints
pages: 1--26
month: jun
monthnumber: 6
year: 2015
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/2015arXiv150609026A; http://docserver.carma.newcastle.edu.au/1701/
keywords: Mathematics - Optimization and Control, 90C26, 65K05
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: F. J. {Arag{\'o}n Artacho} and J. M. Borwein and M. K. Tam
rawtitle: Global Behavior of the {Douglas--Rachford} Method for a Nonconvex Feasibility Problem
ORCID: Aragon Artacho, Francisco Javier/0000-0002-2445-8011; Borwein, Jonathan/0000-0002-1263-0646
abstract:
In recent times the Douglas--Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.

rawabstract:
In recent times the Douglas--Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.

entry:
@Article{AragonArtacho:2015:GBD,
  author =       "F. J. {Arag{\'o}n Artacho} and J. M. Borwein and M. K.
                 Tam",
  title =        "Global Behavior of the {Douglas--Rachford} Method for
                 a Nonconvex Feasibility Problem",
  journal =      "ArXiv e-prints",
  month =        jun,
  year =         "2015",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2015arXiv150609026A;
                 http://docserver.carma.newcastle.edu.au/1701/",
  abstract =     "In recent times the Douglas--Rachford algorithm has
                 been observed empirically to solve a variety of
                 nonconvex feasibility problems including those of a
                 combinatorial nature. For many of these problems
                 current theory is not sufficient to explain this
                 observed success and is mainly concerned with questions
                 of local convergence. In this paper we analyze global
                 behavior of the method for finding a point in the
                 intersection of a half-space and a potentially
                 non-convex set which is assumed to satisfy a
                 well-quasi-ordering property or a property weaker than
                 compactness. In particular, the special case in which
                 the second set is finite is covered by our framework
                 and provides a prototypical setting for combinatorial
                 optimization problems.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1506.09026",
  keywords =     "Mathematics - Optimization and Control, 90C26, 65K05",
  ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
                 Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.OC",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2015:CCI
author: D. H. Bailey and J. M. Borwein
journal: j-APPL-MATH-COMP
volume: 268
pages: 462--477
day: 1
month: oct
monthnumber: 10
year: 2015
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/j.amc.2015.06.048
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
MRclass: 33B30 (11M41 40A25)
MRnumber: 3399433
bibdate: Thu Aug 11 10:27:38 2016
bibtimestamp: 2016.08.11 10:27:38 ???
URL: http://www.sciencedirect.com/science/article/pii/S0096300315008292
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: D. H. Bailey and J. M. Borwein
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
title:
Crandall's computation of the incomplete Gamma function and the Hurwitz zeta function, with applications to Dirichlet $L$-series

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib; https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
This paper extends tools developed by Crandall (2012) [16] to provide robust, high-precision methods for computation of the incomplete Gamma function and the Lerch transcendent. We then apply these to the corresponding computation of the Hurwitz zeta function and so of Dirichlet $L$-series and character polylogarithms.

keywords:
Character polylogarithms; Dirichlet L-series; Hurwitz zeta function; Incomplete gamma function; Lerch transcendent function; Polylogarithms

rawabstract:
This paper extends tools developed by Crandall (2012) [16] to provide robust, high-precision methods for computation of the incomplete Gamma function and the Lerch transcendent. We then apply these to the corresponding computation of the Hurwitz zeta function and so of Dirichlet $L$-series and character polylogarithms.

rawtitle:
{Crandall}'s computation of the incomplete {Gamma} function and the {Hurwitz} zeta function, with applications to {Dirichlet} {$L$}-series

entry:
@Article{Bailey:2015:CCI,
  author =       "D. H. Bailey and J. M. Borwein",
  title =        "{Crandall}'s computation of the incomplete {Gamma}
                 function and the {Hurwitz} zeta function, with
                 applications to {Dirichlet} {$L$}-series",
  journal =      j-APPL-MATH-COMP,
  volume =       "268",
  number =       "??",
  pages =        "462--477",
  day =          "1",
  month =        oct,
  year =         "2015",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2015.06.048",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "33B30 (11M41 40A25)",
  MRnumber =     "3399433",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315008292",
  abstract =     "This paper extends tools developed by Crandall (2012)
                 [16] to provide robust, high-precision methods for
                 computation of the incomplete Gamma function and the
                 Lerch transcendent. We then apply these to the
                 corresponding computation of the Hurwitz zeta function
                 and so of Dirichlet $L$-series and character
                 polylogarithms.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "Character polylogarithms; Dirichlet L-series; Hurwitz
                 zeta function; Incomplete gamma function; Lerch
                 transcendent function; Polylogarithms",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  unique-id =    "ISI:000361769000039",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Bailey:2015:COG
author: D. H. Bailey and J. M. Borwein
crossref: Davis:2015:MSS
pages: 25--67
year: 2015
DOI: https://doi.org/10.1007/978-3-319-21473-3_3
bibdate: Fri Aug 12 18:52:16 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 18:52:16 ???
URL: http://link.springer.com/chapter/10.1007/978-3-319-21473-3_3
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. H. Bailey and J. M. Borwein
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
title:
Computation as an ontological game changer: The impact of modern mathematical computation tools on the ontology of mathematics

rawtitle:
Computation as an ontological game changer: The impact of modern mathematical computation tools on the ontology of mathematics

entry:
@InCollection{Bailey:2015:COG,
  author =       "D. H. Bailey and J. M. Borwein",
  title =        "Computation as an ontological game changer: The impact
                 of modern mathematical computation tools on the
                 ontology of mathematics",
  crossref =     "Davis:2015:MSS",
  pages =        "25--67",
  year =         "2015",
  DOI =          "https://doi.org/10.1007/978-3-319-21473-3_3",
  bibdate =      "Fri Aug 12 18:52:16 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-319-21473-3_3",
  acknowledgement = ack-nhfb,
  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:2015:CTM
author: D. H. Bailey and J. M. Borwein
title: Computation and theory of Mordell--Tornheim--Witten sums II
journal: j-J-APPROX-THEORY
volume: 197
pages: 115--140
month: sep
monthnumber: 9
year: 2015
CODEN: JAXTAZ
DOI: https://doi.org/10.1016/j.jat.2014.10.004
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
MRclass: 11M41 (33B30 33F05 65D20)
MRnumber: 3351543
MRreviewer: Mehdi Hassani
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 ???
note: Special Issue Dedicated to Dick Askey on the occasion of his 80th birthday.
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: D. H. Bailey and J. M. Borwein
rawnote: Special Issue Dedicated to Dick Askey on the occasion of his 80th birthday.
rawtitle: Computation and theory of {Mordell--Tornheim--Witten} sums {II}
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1494/; http://www.carma.newcastle.edu.au/jon/MTW2.pdf; http://www.sciencedirect.com/science/article/pii/S0021904514001841

abstract:
In Bailey et al. [8] the current authors, along with the late and much-missed Richard Crandall (1947--2012), considered generalized Mordell--Tornheim--Witten (MTW) zeta-function values along with their derivatives, and explored connections with multiple-zeta values (MZVs). This entailed use of symbolic integration, high precision numerical integration, and some interesting combinatorics and special-function theory. The original motivation was to represent objects such as Eulerian log-gamma integrals; and all such integrals were expressed in terms of a MTW basis. Herein, we extend the research envisaged in Bailey et al. [8] by analyzing the relations between a significantly more general class of MTW sums. This has required significantly more subtle scientific computation and concomitant special function theory.

rawabstract:
In Bailey et al. [8] the current authors, along with the late and much-missed Richard Crandall (1947--2012), considered generalized Mordell--Tornheim--Witten (MTW) zeta-function values along with their derivatives, and explored connections with multiple-zeta values (MZVs). This entailed use of symbolic integration, high precision numerical integration, and some interesting combinatorics and special-function theory. The original motivation was to represent objects such as Eulerian log-gamma integrals; and all such integrals were expressed in terms of a MTW basis. Herein, we extend the research envisaged in Bailey et al. [8] by analyzing the relations between a significantly more general class of MTW sums. This has required significantly more subtle scientific computation and concomitant special function theory.

entry:
@Article{Bailey:2015:CTM,
  author =       "D. H. Bailey and J. M. Borwein",
  title =        "Computation and theory of {Mordell--Tornheim--Witten}
                 sums {II}",
  journal =      j-J-APPROX-THEORY,
  volume =       "197",
  number =       "??",
  pages =        "115--140",
  month =        sep,
  year =         "2015",
  CODEN =        "JAXTAZ",
  DOI =          "https://doi.org/10.1016/j.jat.2014.10.004",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  MRclass =      "11M41 (33B30 33F05 65D20)",
  MRnumber =     "3351543",
  MRreviewer =   "Mehdi Hassani",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Special Issue Dedicated to Dick Askey on the occasion
                 of his 80th birthday.",
  URL =          "http://docserver.carma.newcastle.edu.au/1494/;
                 http://www.carma.newcastle.edu.au/jon/MTW2.pdf;
                 http://www.sciencedirect.com/science/article/pii/S0021904514001841",
  abstract =     "In Bailey et al. [8] the current authors, along with
                 the late and much-missed Richard Crandall (1947--2012),
                 considered generalized Mordell--Tornheim--Witten (MTW)
                 zeta-function values along with their derivatives, and
                 explored connections with multiple-zeta values (MZVs).
                 This entailed use of symbolic integration, high
                 precision numerical integration, and some interesting
                 combinatorics and special-function theory. The original
                 motivation was to represent objects such as Eulerian
                 log-gamma integrals; and all such integrals were
                 expressed in terms of a MTW basis. Herein, we extend
                 the research envisaged in Bailey et al. [8] by
                 analyzing the relations between a significantly more
                 general class of MTW sums. This has required
                 significantly more subtle scientific computation and
                 concomitant special function theory.",
  acknowledgement = ack-nhfb,
  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 = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  unique-id =    "ISI:000356633800008",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Bailey:2015:EAM
author: David H. Bailey and Jonathan M. Borwein
title: Experimental Applied Mathematics
crossref: Higham:2015:PCA
pages: 925--933
year: 2015
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
note: Entry VIII.6.
URL: http://docserver.carma.newcastle.edu.au/1460/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawnote: Entry VIII.6.
rawtitle: Experimental Applied Mathematics
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/subjects/companion-applied-mathematics.bib

entry:
@InCollection{Bailey:2015:EAM,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Experimental Applied Mathematics",
  crossref =     "Higham:2015:PCA",
  pages =        "925--933",
  year =         "2015",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/companion-applied-mathematics.bib",
  note =         "Entry VIII.6.",
  URL =          "http://docserver.carma.newcastle.edu.au/1460/",
  acknowledgement = ack-nhfb # " and " # ack-njh,
  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: incollection
filename: borwein-jonathan-m.bib
label: Bailey:2015:ECO
author: David H. Bailey and Jonathan M. Borwein
booktitle: Mathematics, substance and surmise
publisher: pub-SV
address: pub-SV:adr
pages: 25--67
year: 2015
MRclass: 00A35 (03B35 68W30)
MRnumber: 3467267
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://www.davidhbailey.com/dhbpapers/ontology.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawbooktitle: Mathematics, substance and surmise
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
title:
Experimental computation as an ontological game changer: the impact of modern mathematical computation tools on the ontology of mathematics

rawtitle:
Experimental computation as an ontological game changer: the impact of modern mathematical computation tools on the ontology of mathematics

entry:
@InCollection{Bailey:2015:ECO,
  author =       "David H. Bailey and Jonathan M. Borwein",
  booktitle =    "Mathematics, substance and surmise",
  title =        "Experimental computation as an ontological game
                 changer: the impact of modern mathematical computation
                 tools on the ontology of mathematics",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "25--67",
  year =         "2015",
  MRclass =      "00A35 (03B35 68W30)",
  MRnumber =     "3467267",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/ontology.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: Bailey:2015:ELG
author: David H. Bailey and David Borwein and Jonathan M. Borwein
title: On Eulerian log-gamma integrals and Tornheim--Witten zeta functions
journal: j-RAMANUJAN-J
volume: 36
number: 1--2
pages: 43--68
month: feb
monthnumber: 2
year: 2015
DOI: https://doi.org/10.1007/s11139-012-9427-1
ISSN: 1382-4090 (print), 1572-9303 (electronic) OR 13824090 (print), 15729303 (electronic)
ISSNL: 1382-4090 OR 13824090
MRclass: 11M35 (11M32 33B15 33F05)
MRnumber: 3296709
MRreviewer: Renata Macaitien{\.e}
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/1377/
fjournal: The Ramanujan Journal
ZMnumber: 06398825
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11139
rawauthor: David H. Bailey and David Borwein and Jonathan M. Borwein
rawtitle: On {Eulerian} log-gamma integrals and {Tornheim--Witten} zeta functions
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
abstract:
Stimulated by earlier work by Moll and his coworkers (Amdeberhan et al., Proc. Am. Math. Soc., bf 139(2): 535--545, 2010), we evaluate various basic log Gamma integrals in terms of partial derivatives of Tornheim--Witten zeta functions and their extensions arising from evaluations of Fourier series. In particular, we fully evaluate $ mathcal LG(n) = int _0^1 log ^n Gamma (x) d x $ for $ 1 leq n leq 4 $ and make some comments regarding the general case. The subsidiary computational challenges are substantial, interesting and significant in their own right.

rawabstract:
Stimulated by earlier work by Moll and his coworkers (Amdeberhan et al., Proc. Am. Math. Soc., {\bf 139}(2): 535--545, 2010), we evaluate various basic log Gamma integrals in terms of partial derivatives of Tornheim--Witten zeta functions and their extensions arising from evaluations of Fourier series. In particular, we fully evaluate $ \mathcal {LG}(n) = \int_0^1 \log^n \Gamma (x) \, d x $ for $ 1 \leq n \leq 4 $ and make some comments regarding the general case. The subsidiary computational challenges are substantial, interesting and significant in their own right.

entry:
@Article{Bailey:2015:ELG,
  author =       "David H. Bailey and David Borwein and Jonathan M.
                 Borwein",
  title =        "On {Eulerian} log-gamma integrals and
                 {Tornheim--Witten} zeta functions",
  journal =      j-RAMANUJAN-J,
  volume =       "36",
  number =       "1--2",
  pages =        "43--68",
  month =        feb,
  year =         "2015",
  DOI =          "https://doi.org/10.1007/s11139-012-9427-1",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  MRclass =      "11M35 (11M32 33B15 33F05)",
  MRnumber =     "3296709",
  MRreviewer =   "Renata Macaitien{\.e}",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1377/",
  ZMnumber =     "06398825",
  abstract =     "Stimulated by earlier work by Moll and his coworkers
                 (Amdeberhan et al., Proc. Am. Math. Soc., {\bf 139}(2):
                 535--545, 2010), we evaluate various basic log Gamma
                 integrals in terms of partial derivatives of
                 Tornheim--Witten zeta functions and their extensions
                 arising from evaluations of Fourier series. In
                 particular, we fully evaluate $ \mathcal {LG}(n) =
                 \int_0^1 \log^n \Gamma (x) \, d x $ for $ 1 \leq n \leq
                 4 $ and make some comments regarding the general case.
                 The subsidiary computational challenges are
                 substantial, interesting and significant in their own
                 right.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The {Ramanujan} Journal",
  journal-URL =  "http://link.springer.com/journal/11139",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  unique-id =    "ISI:000347701700003",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2015:HPA
author: David H. Bailey and Jonathan M. Borwein
title: High-precision arithmetic in mathematical physics
journal: Mathematics
volume: 3
number: 2
pages: 337--367
month: jun
monthnumber: 6
year: 2015
DOI: https://doi.org/10.3390/math3020337
ISSN: 2227-7390 OR 22277390
ISSNL: 2227-7390 OR 22277390
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://www.mdpi.com/2227-7390/3/2/337
remark: See improvements in cite Dolgov:2020:PCI.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.mdpi.com/journal/mathematics
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: High-precision arithmetic in mathematical physics
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/fparith.bib

abstract:
For many scientific calculations, particularly those involving empirical data, IEEE 32-bit floating-point arithmetic produces results of sufficient accuracy, while for other applications IEEE 64-bit floating-point is more appropriate. But for some very demanding applications, even higher levels of precision are often required. This article discusses the challenge of high-precision computation, in the context of mathematical physics, and highlights what facilities are required to support future computation, in light of emerging developments in computer architecture.

rawabstract:
For many scientific calculations, particularly those involving empirical data, IEEE 32-bit floating-point arithmetic produces results of sufficient accuracy, while for other applications IEEE 64-bit floating-point is more appropriate. But for some very demanding applications, even higher levels of precision are often required. This article discusses the challenge of high-precision computation, in the context of mathematical physics, and highlights what facilities are required to support future computation, in light of emerging developments in computer architecture.

entry:
@Article{Bailey:2015:HPA,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "High-precision arithmetic in mathematical physics",
  journal =      "Mathematics",
  volume =       "3",
  number =       "2",
  pages =        "337--367",
  month =        jun,
  year =         "2015",
  DOI =          "https://doi.org/10.3390/math3020337",
  ISSN =         "2227-7390",
  ISSN-L =       "2227-7390",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mdpi.com/2227-7390/3/2/337",
  abstract =     "For many scientific calculations, particularly those
                 involving empirical data, IEEE 32-bit floating-point
                 arithmetic produces results of sufficient accuracy,
                 while for other applications IEEE 64-bit floating-point
                 is more appropriate. But for some very demanding
                 applications, even higher levels of precision are often
                 required. This article discusses the challenge of
                 high-precision computation, in the context of
                 mathematical physics, and highlights what facilities
                 are required to support future computation, in light of
                 emerging developments in computer architecture.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  journal-URL =  "http://www.mdpi.com/journal/mathematics",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "See improvements in \cite{Dolgov:2020:PCI}.",
  unique-id =    "ISI:000364229100010",
  xxpublisher =  "Multidisciplinary Digital Publishing Institute",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:2015:OTD
author: David H. Bailey and Jonathan M. Borwein and Amir Salehipour and Marcos Lopez de Prado and Qiji Zhu
title: Online tools for demonstration of backtest overfitting
institution: Lawrence Berkeley National Laboratory and four others
address: Berkeley, CA 94720, USA and others
pages: 13
day: 29
month: nov
monthnumber: 11
year: 2015
MRclass: 60E, 62C, 91G10, 91G60, 91G70
bibdate: Fri Sep 30 09:04:44 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 09:04:44 ???
URL: http://ssrn.com/abstract=2597421
keywords: Backtest overfitting, multiple testing, Sharpe Ratio, Deflated Sharpe Ratio, investment strategy
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawtitle: Online tools for demonstration of backtest overfitting
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
abstract:
In mathematical finance, backtest overfitting relates to the usage of historical market data (a backtest) to develop an investment strategy, where the strategy profits from random patterns rather than variables signals. Backtest overfitting is now thought to be a primary reason why quantitative investment models and strategies that look good on paper often disappoint in practice.par In this study we introduce two online tools, the Backtest Overfitting Demonstration Tool, or BODT for short, and the Tenure Maker Simulation Tool, or TMST, which illustrate the impact of backtest overfitting on investment models and strategies. We describe BODT and TSMT, the experiments they perform, together with technical details such as the evaluation metrics and parameters used.

rawabstract:
In mathematical finance, backtest overfitting relates to the usage of historical market data (a backtest) to develop an investment strategy, where the strategy profits from random patterns rather than variables signals. Backtest overfitting is now thought to be a primary reason why quantitative investment models and strategies that look good on paper often disappoint in practice.\par In this study we introduce two online tools, the Backtest Overfitting Demonstration Tool, or BODT for short, and the Tenure Maker Simulation Tool, or TMST, which illustrate the impact of backtest overfitting on investment models and strategies. We describe BODT and TSMT, the experiments they perform, together with technical details such as the evaluation metrics and parameters used.

rawauthor:
David H. Bailey and Jonathan M. Borwein and Amir Salehipour and Marcos {L{\'o}pez de Prado} and Qiji Zhu

entry:
@TechReport{Bailey:2015:OTD,
  author =       "David H. Bailey and Jonathan M. Borwein and Amir
                 Salehipour and Marcos {L{\'o}pez de Prado} and Qiji
                 Zhu",
  title =        "Online tools for demonstration of backtest
                 overfitting",
  institution =  "Lawrence Berkeley National Laboratory and four
                 others",
  address =      "Berkeley, CA 94720, USA and others",
  pages =        "13",
  day =          "29",
  month =        nov,
  year =         "2015",
  MRclass =      "60E, 62C, 91G10, 91G60, 91G70",
  bibdate =      "Fri Sep 30 09:04:44 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://ssrn.com/abstract=2597421",
  abstract =     "In mathematical finance, backtest overfitting relates
                 to the usage of historical market data (a backtest) to
                 develop an investment strategy, where the strategy
                 profits from random patterns rather than variables
                 signals. Backtest overfitting is now thought to be a
                 primary reason why quantitative investment models and
                 strategies that look good on paper often disappoint in
                 practice.\par

                 In this study we introduce two online tools, the
                 Backtest Overfitting Demonstration Tool, or BODT for
                 short, and the Tenure Maker Simulation Tool, or TMST,
                 which illustrate the impact of backtest overfitting on
                 investment models and strategies. We describe BODT and
                 TSMT, the experiments they perform, together with
                 technical details such as the evaluation metrics and
                 parameters used.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Backtest overfitting, multiple testing, Sharpe Ratio,
                 Deflated Sharpe Ratio, investment strategy",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2015:CAGa
author: J. M. Borwein and O. Giladi
title: Convex analysis in groups and semigroups: a sampler
journal: ArXiv e-prints
pages: 13
month: oct
monthnumber: 10
year: 2015
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/2015arXiv151004480B; http://docserver.carma.newcastle.edu.au/1693/
keywords: Mathematics - Optimization and Control
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and O. Giladi
rawtitle: Convex analysis in groups and semigroups: a sampler
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We define convexity canonically in the setting of monoids. We show that many classical results from convex analysis hold for functions defined on such groups and semigroups, rather than only on vector spaces. Some examples and counter-examples are also discussed.

rawabstract:
We define convexity canonically in the setting of monoids. We show that many classical results from convex analysis hold for functions defined on such groups and semigroups, rather than only on vector spaces. Some examples and counter-examples are also discussed.

entry:
@Article{Borwein:2015:CAGa,
  author =       "J. M. Borwein and O. Giladi",
  title =        "Convex analysis in groups and semigroups: a sampler",
  journal =      "ArXiv e-prints",
  month =        oct,
  year =         "2015",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2015arXiv151004480B;
                 http://docserver.carma.newcastle.edu.au/1693/",
  abstract =     "We define convexity canonically in the setting of
                 monoids. We show that many classical results from
                 convex analysis hold for functions defined on such
                 groups and semigroups, rather than only on vector
                 spaces. Some examples and counter-examples are also
                 discussed.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1510.04480",
  keywords =     "Mathematics - Optimization and Control",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.OC",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2015:CDR
author: Jonathan M. Borwein and Matthew K. Tam
title: The cyclic Douglas--Rachford method for inconsistent feasibility problems
journal: j-J-NONLINEAR-CONVEX-ANAL
volume: 16
number: 4
pages: 573--584
month: apr
monthnumber: 4
year: 2015
ISSN: 1345-4773 (print), 1880-5221 (electronic) OR 13454773 (print), 18805221 (electronic)
ISSNL: 1345-4773 OR 13454773
MRclass: 47J25 (47H09 47H10)
MRnumber: 3343161
MRreviewer: Jean Mawhin
bibdate: Fri Sep 30 09:55:02 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 09:55:02 ???
URL: http://docserver.carma.newcastle.edu.au/1496/; http://www.ybook.co.jp/online2/jncav16-4.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: Jonathan M. Borwein and Matthew K. Tam
rawtitle: The cyclic {Douglas--Rachford} method for inconsistent feasibility problems
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We analyse the behaviour of the newly introduced cyclic Douglas--Rachford algorithm for finding a point in the intersection of a finite number of closed convex sets. This work considers the case in which the target intersection set is possibly empty.

affiliation:
Borwein, JM (Reprint Author), Univ Newcastle, CARMA Ctr, Callaghan, NSW 2308, Australia. Borwein, Jonathan M.; Tam, Matthew K., Univ Newcastle, CARMA Ctr, Callaghan, NSW 2308, Australia.

entry:
@Article{Borwein:2015:CDR,
  author =       "Jonathan M. Borwein and Matthew K. Tam",
  title =        "The cyclic {Douglas--Rachford} method for inconsistent
                 feasibility problems",
  journal =      j-J-NONLINEAR-CONVEX-ANAL,
  volume =       "16",
  number =       "4",
  pages =        "573--584",
  month =        apr,
  year =         "2015",
  DOI =          "",
  ISSN =         "1345-4773 (print), 1880-5221 (electronic)",
  ISSN-L =       "1345-4773",
  MRclass =      "47J25 (47H09 47H10)",
  MRnumber =     "3343161",
  MRreviewer =   "Jean Mawhin",
  bibdate =      "Fri Sep 30 09:55:02 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1496/;
                 http://www.ybook.co.jp/online2/jncav16-4.html",
  abstract =     "We analyse the behaviour of the newly introduced
                 cyclic Douglas--Rachford algorithm for finding a point
                 in the intersection of a finite number of closed convex
                 sets. This work considers the case in which the target
                 intersection set is possibly empty.",
  acknowledgement = ack-nhfb,
  affiliation =  "Borwein, JM (Reprint Author), Univ Newcastle, CARMA
                 Ctr, Callaghan, NSW 2308, Australia. Borwein, Jonathan
                 M.; Tam, Matthew K., Univ Newcastle, CARMA Ctr,
                 Callaghan, NSW 2308, Australia.",
  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",
  unique-id =    "ISI:000355240900001",
  xxpages =      "537--584",
  xxtitle =      "The cyclic {Douglas--Rachford} feasibility method:
                 behaviour on infeasible problems",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2015:CRA
author: J. M. Borwein and G. Li and M. K. Tam
title: Convergence rate analysis for averaged fixed point iterations in the presence of Holder regularity
journal: ArXiv e-prints
pages: 573--584
month: oct
monthnumber: 10
year: 2015
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/2015arXiv151006823B; http://docserver.carma.newcastle.edu.au/1690/
keywords: Mathematics - Optimization and Control
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and G. Li and M. K. Tam
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper, we establish sublinear and linear convergence of fixed point iterations generated by averaged operators in a Hilbert space. Our results are achieved under a bounded Holder regularity assumption which generalizes the well-known notion of bounded linear regularity. As an application of our results, we provide a convergence rate analysis for Krasnoselskii--Mann iterations, the cyclic projection algorithm, and the Douglas--Rachford feasibility algorithm along with some variants. In the important case in which the underlying sets are convex sets described by convex polynomials in a finite dimensional space, we show that the Holder regularity properties are automatically satisfied, from which sublinear convergence follows.

rawabstract:
In this paper, we establish sublinear and linear convergence of fixed point iterations generated by averaged operators in a Hilbert space. Our results are achieved under a bounded H{\"o}lder regularity assumption which generalizes the well-known notion of bounded linear regularity. As an application of our results, we provide a convergence rate analysis for Krasnoselskii--Mann iterations, the cyclic projection algorithm, and the Douglas--Rachford feasibility algorithm along with some variants. In the important case in which the underlying sets are convex sets described by convex polynomials in a finite dimensional space, we show that the H{\"o}lder regularity properties are automatically satisfied, from which sublinear convergence follows.

rawtitle:
Convergence rate analysis for averaged fixed point iterations in the presence of H{\"o}lder regularity

entry:
@Article{Borwein:2015:CRA,
  author =       "J. M. Borwein and G. Li and M. K. Tam",
  title =        "Convergence rate analysis for averaged fixed point
                 iterations in the presence of H{\"o}lder regularity",
  journal =      "ArXiv e-prints",
  month =        oct,
  year =         "2015",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2015arXiv151006823B;
                 http://docserver.carma.newcastle.edu.au/1690/",
  abstract =     "In this paper, we establish sublinear and linear
                 convergence of fixed point iterations generated by
                 averaged operators in a Hilbert space. Our results are
                 achieved under a bounded H{\"o}lder regularity
                 assumption which generalizes the well-known notion of
                 bounded linear regularity. As an application of our
                 results, we provide a convergence rate analysis for
                 Krasnoselskii--Mann iterations, the cyclic projection
                 algorithm, and the Douglas--Rachford feasibility
                 algorithm along with some variants. In the important
                 case in which the underlying sets are convex sets
                 described by convex polynomials in a finite dimensional
                 space, we show that the H{\"o}lder regularity
                 properties are automatically satisfied, from which
                 sublinear convergence follows.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1510.06823",
  keywords =     "Mathematics - Optimization and Control",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.OC",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:2015:CU
author: Jonathan M. Borwein and Brailey Sims
title: Convexity in ultraproducts
pages: 573--584
month: aug
monthnumber: 8
year: 2015
bibdate: Tue Aug 16 09:40:17 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:40:17 ???
note: Preprint.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Brailey Sims
rawnote: Preprint.
rawtitle: Convexity in ultraproducts
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Unpublished{Borwein:2015:CU,
  author =       "Jonathan M. Borwein and Brailey Sims",
  title =        "Convexity in ultraproducts",
  month =        aug,
  year =         "2015",
  bibdate =      "Tue Aug 16 09:40:17 2016",
  bibsource =    "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: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2015:DCP
author: Jonathan M. Borwein and D. Russell Luke
title: Duality and Convex Programming
crossref: Scherzer:2015:HMM
volume: 1
pages: 257--304
year: 2015
DOI: https://doi.org/10.1007/978-1-4939-0790-8_7
MRclass: 94A08
MRnumber: 3560070
MRreviewer: Nicolas Hadjisavvas
bibdate: Sat Aug 13 16:07:59 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 16:07:59 ???
URL: http://docserver.carma.newcastle.edu.au/1217/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and D. Russell Luke
rawtitle: Duality and Convex Programming
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2015:DCP,
  author =       "Jonathan M. Borwein and D. Russell Luke",
  title =        "Duality and Convex Programming",
  crossref =     "Scherzer:2015:HMM",
  volume =       "1",
  pages =        "257--304",
  year =         "2015",
  DOI =          "https://doi.org/10.1007/978-1-4939-0790-8_7",
  MRclass =      "94A08",
  MRnumber =     "3560070",
  MRreviewer =   "Nicolas Hadjisavvas",
  bibdate =      "Sat Aug 13 16:07:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1217/",
  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:2015:DSU
author: J. M. Borwein and A. Straub and C. Vignat
title: Densities of short uniform random walks in higher dimensions
journal: ArXiv e-prints
pages: 257--304
month: aug
monthnumber: 8
year: 2015
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/2015arXiv150804729B; http://docserver.carma.newcastle.edu.au/1699/
keywords: Mathematics - Classical Analysis and ODEs, Mathematics - Number Theory
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and A. Straub and C. Vignat
rawtitle: Densities of short uniform random walks in higher dimensions
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053
abstract:
We study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus on explicit (hypergeometric) evaluations of the moment functions and probability densities in the case of up to five steps. Somewhat to our surprise, we are able to provide complete extensions to arbitrary dimensions for most of the central results known in the two-dimensional case.

rawabstract:
We study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus on explicit (hypergeometric) evaluations of the moment functions and probability densities in the case of up to five steps. Somewhat to our surprise, we are able to provide complete extensions to arbitrary dimensions for most of the central results known in the two-dimensional case.

entry:
@Article{Borwein:2015:DSU,
  author =       "J. M. Borwein and A. Straub and C. Vignat",
  title =        "Densities of short uniform random walks in higher
                 dimensions",
  journal =      "ArXiv e-prints",
  month =        aug,
  year =         "2015",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2015arXiv150804729B;
                 http://docserver.carma.newcastle.edu.au/1699/",
  abstract =     "We study arithmetic properties of short uniform random
                 walks in arbitrary dimensions, with a focus on explicit
                 (hypergeometric) evaluations of the moment functions
                 and probability densities in the case of up to five
                 steps. Somewhat to our surprise, we are able to provide
                 complete extensions to arbitrary dimensions for most of
                 the central results known in the two-dimensional
                 case.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1508.04729",
  keywords =     "Mathematics - Classical Analysis and ODEs, Mathematics
                 - Number Theory",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053",
  primaryclass = "math.CA",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2015:FM
author: Jonathan M. Borwein
title: The Future of Mathematics: 1965 to 2065
crossref: Kennedy:2015:CAM
pages: 313--329
year: 2015
MRclass: 00A35
MRnumber: 3408151
bibdate: Fri Aug 12 19:11:45 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 19:11:45 ???
URL: http://docserver.carma.newcastle.edu.au/1720/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawtitle: The Future of Mathematics: 1965 to 2065
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2015:FM,
  author =       "Jonathan M. Borwein",
  title =        "The Future of Mathematics: 1965 to 2065",
  crossref =     "Kennedy:2015:CAM",
  pages =        "313--329",
  year =         "2015",
  MRclass =      "00A35",
  MRnumber =     "3408151",
  bibdate =      "Fri Aug 12 19:11:45 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1720/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  xxpages =      "313--330",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2015:LKM
author: Jonathan M. Borwein and Yann Bugeaud and Michael Coons
title: The legacy of Kurt Mahler
journal: j-NAMS
volume: 62
number: 5
pages: 526--531
month: may
monthnumber: 5
year: 2015
CODEN: AMNOAN
DOI: https://doi.org/10.1090/noti1241
ISSN: 0002-9920 (print), 1088-9477 (electronic) OR 00029920 (print), 10889477 (electronic)
ISSNL: 0002-9920 OR 00029920
MRclass: 01A70, 01A75 (Collected or selected works), 11-03
MRnumber: 3328921
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://www.ams.org/notices/201505/rnoti-p526.pdf
fjournal: Notices of the American Mathematical Society
ZMnumber: 1338.01030
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/notices/
rawauthor: Jonathan M. Borwein and Yann Bugeaud and Michael Coons
rawtitle: The legacy of {Kurt Mahler}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2015:LKM,
  author =       "Jonathan M. Borwein and Yann Bugeaud and Michael
                 Coons",
  title =        "The legacy of {Kurt Mahler}",
  journal =      j-NAMS,
  volume =       "62",
  number =       "5",
  pages =        "526--531",
  month =        may,
  year =         "2015",
  CODEN =        "AMNOAN",
  DOI =          "https://doi.org/10.1090/noti1241",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  MRclass =      "01A70, 01A75 (Collected or selected works), 11-03",
  MRnumber =     "3328921",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.ams.org/notices/201505/rnoti-p526.pdf",
  ZMnumber =     "1338.01030",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:2015:MCR
author: D. Borwein and J. M. Borwein and B. Sims
title: Monotonicity of certain Riemann sums
pages: 526--531
year: 2015
bibdate: Tue Aug 16 09:36:05 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:36:05 ???
note: Submitted, Mathematics Magazine, January 2015.
URL: http://docserver.carma.newcastle.edu.au/1692/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. Borwein and J. M. Borwein and B. Sims
rawnote: Submitted, Mathematics Magazine, January 2015.
rawtitle: Monotonicity of certain {Riemann} sums
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Unpublished{Borwein:2015:MCR,
  author =       "D. Borwein and J. M. Borwein and B. Sims",
  title =        "Monotonicity of certain {Riemann} sums",
  year =         "2015",
  bibdate =      "Tue Aug 16 09:36:05 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Submitted, Mathematics Magazine, January 2015.",
  URL =          "http://docserver.carma.newcastle.edu.au/1692/",
  acknowledgement = ack-nhfb,
  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:2015:MMI
author: Jonathan M. Borwein and Joydeep Dutta
title: Maximal Monotone Inclusions and Fitzpatrick Functions
journal: j-J-OPT-THEORY-APPL
pages: 1--28
year: 2015
CODEN: JOTABN
DOI: https://doi.org/10.1007/s10957-015-0813-x
ISSN: 0022-3239 (print), 1573-2878 (electronic) OR 00223239 (print), 15732878 (electronic)
ISSNL: 0022-3239 OR 00223239
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
fjournal: Journal of Optimization Theory and Applications
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/volumesAndIssues/10957
rawauthor: Jonathan M. Borwein and Joydeep Dutta
rawtitle: Maximal Monotone Inclusions and {Fitzpatrick} Functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
note:
Special issue of JOTA on Nondifferentiable Optimization and Nonsmooth Analysis, dedicated to Vladimir Demyanov.

URL:
http://docserver.carma.newcastle.edu.au/1715/; http://link.springer.com/article/10.1007/s10957-015-0813-x

rawnote:
Special issue of JOTA on Nondifferentiable Optimization and Nonsmooth Analysis, dedicated to Vladimir Demyanov.

entry:
@Article{Borwein:2015:MMI,
  author =       "Jonathan M. Borwein and Joydeep Dutta",
  title =        "Maximal Monotone Inclusions and {Fitzpatrick}
                 Functions",
  journal =      j-J-OPT-THEORY-APPL,
  volume =       "??",
  number =       "??",
  pages =        "1--28",
  year =         "2015",
  CODEN =        "JOTABN",
  DOI =          "https://doi.org/10.1007/s10957-015-0813-x",
  ISSN =         "0022-3239 (print), 1573-2878 (electronic)",
  ISSN-L =       "0022-3239",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Special issue of JOTA on Nondifferentiable
                 Optimization and Nonsmooth Analysis, dedicated to
                 Vladimir Demyanov.",
  URL =          "http://docserver.carma.newcastle.edu.au/1715/;
                 http://link.springer.com/article/10.1007/s10957-015-0813-x",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Optimization Theory and Applications",
  journal-URL =  "http://link.springer.com/journal/volumesAndIssues/10957",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2015:NCR
author: Jonathan M. Borwein and Brailey Sims and Matthew K. Tam
title: Norm convergence of realistic projection and reflection methods
journal: j-OPTIMIZATION
volume: 64
number: 1
pages: 161--178
month: jan
monthnumber: 1
year: 2015
CODEN: OPTZDQ
DOI: https://doi.org/10.1080/02331934.2014.947499
ISSN: 0233-1934, 0323-3898 OR 02331934, 03233898
ISSNL: 0233-1934 OR 02331934
MRclass: 47J25 (47H09 47H10 90C25 90C48)
MRnumber: 3293546
MRreviewer: Patrick L. Combettes
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/1493/
fjournal: Optimization
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.tandfonline.com/loi/gopt20
rawauthor: Jonathan M. Borwein and Brailey Sims and Matthew K. Tam
rawtitle: Norm convergence of realistic projection and reflection methods
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We provide sufficient conditions for norm convergence of various projection and reflection methods, as well as giving limiting examples regarding convergence rates.

entry:
@Article{Borwein:2015:NCR,
  author =       "Jonathan M. Borwein and Brailey Sims and Matthew K.
                 Tam",
  title =        "Norm convergence of realistic projection and
                 reflection methods",
  journal =      j-OPTIMIZATION,
  volume =       "64",
  number =       "1",
  pages =        "161--178",
  month =        jan,
  year =         "2015",
  CODEN =        "OPTZDQ",
  DOI =          "https://doi.org/10.1080/02331934.2014.947499",
  ISSN =         "0233-1934, 0323-3898",
  ISSN-L =       "0233-1934",
  MRclass =      "47J25 (47H09 47H10 90C25 90C48)",
  MRnumber =     "3293546",
  MRreviewer =   "Patrick L. Combettes",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1493/",
  abstract =     "We provide sufficient conditions for norm convergence
                 of various projection and reflection methods, as well
                 as giving limiting examples regarding convergence
                 rates.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Optimization",
  journal-URL =  "http://www.tandfonline.com/loi/gopt20",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Tam, Matthew/G-8127-2013",
  unique-id =    "ISI:000346849000011",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2015:NPD
author: J. M. Borwein and O. Giladi
title: Nearest points and delta convex functions in Banach spaces
journal: ArXiv e-prints
pages: 161--178
month: oct
monthnumber: 10
year: 2015
bibdate: Fri Sep 30 09:28:29 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 09:28:29 ???
note: Preprint of cite Borwein:2016:NPD.
URL: http://adsabs.harvard.edu/abs/2015arXiv151004471B
fjournal: Bulletin of the Australian Mathematical Society
keywords: Mathematics - Functional Analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://journals.cambridge.org/action/displayJournal?jid=BAZ
rawauthor: J. M. Borwein and O. Giladi
rawnote: Preprint of \cite{Borwein:2016:NPD}.
rawtitle: Nearest points and delta convex functions in {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Given a closed set $C$ in a Banach space $ (X, || cdot ||)$, a point $ x in X$ is said to have a nearest point in $C$ if there exists $ z in C$ such that $ d_C(x) = || x - z || $, where $ d_C$ is the distance of $x$ from $C$. We shortly survey the problem of studying how large is the set of points in $X$ which have nearest points in $C$. We then discuss the topic of delta-convex functions and how it is related to finding nearest points.

rawabstract:
Given a closed set $C$ in a Banach space $ (X, || \cdot ||)$, a point $ x \in X$ is said to have a nearest point in $C$ if there exists $ z \in C$ such that $ d_C(x) = || x - z || $, where $ d_C$ is the distance of $x$ from $C$. We shortly survey the problem of studying how large is the set of points in $X$ which have nearest points in $C$. We then discuss the topic of delta-convex functions and how it is related to finding nearest points.

entry:
@Article{Borwein:2015:NPD,
  author =       "J. M. Borwein and O. Giladi",
  title =        "Nearest points and delta convex functions in {Banach}
                 spaces",
  journal =      "ArXiv e-prints",
  month =        oct,
  year =         "2015",
  bibdate =      "Fri Sep 30 09:28:29 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Preprint of \cite{Borwein:2016:NPD}.",
  URL =          "http://adsabs.harvard.edu/abs/2015arXiv151004471B",
  abstract =     "Given a closed set $C$ in a Banach space $ (X, ||
                 \cdot ||)$, a point $ x \in X$ is said to have a
                 nearest point in $C$ if there exists $ z \in C$ such
                 that $ d_C(x) = || x - z || $, where $ d_C$ is the
                 distance of $x$ from $C$. We shortly survey the problem
                 of studying how large is the set of points in $X$ which
                 have nearest points in $C$. We then discuss the topic
                 of delta-convex functions and how it is related to
                 finding nearest points.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1510.04471",
  fjournal =     "Bulletin of the Australian Mathematical Society",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=BAZ",
  keywords =     "Mathematics - Functional Analysis",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
  unique-id =    "ISI:000372529100012",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2015:PPA
author: Jonathan M. Borwein and Scott T. Chapman
title: I Prefer Pi: Addenda
journal: j-AMER-MATH-MONTHLY
volume: 122
number: 8
pages: 800--800
month: oct
monthnumber: 10
year: 2015
CODEN: AMMYAE
DOI: https://doi.org/10.4169/amer.math.monthly.122.8.800
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 11A05 (11Z05)
MRnumber: 3399115
bibdate: Tue Oct 20 06:20:38 MDT 2015
bibtimestamp: 2015.10.20 06:20:38 MDT
URL: https://www.jstor.org/stable/10.4169/amer.math.monthly.122.8.800
fjournal: American Mathematical Monthly
ZMnumber: 1328.01077
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 and Scott T. Chapman
rawtitle: {I} Prefer Pi: Addenda
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/amermathmonthly2010.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib

note:
See cite Borwein:2015:PPB. The addenda correct formulas (4) and (12), references [34] and [74], and add a new reference.

abstract:
In the rush to prepare our March 2015 article on Pi [1], several infelicities escaped our eye. Herein we repair the damage.

rawabstract:
In the rush to prepare our March 2015 article on Pi [1], several infelicities escaped our eye. Herein we repair the damage.

rawnote:
See \cite{Borwein:2015:PPB}. The addenda correct formulas (4) and (12), references [34] and [74], and add a new reference.

entry:
@Article{Borwein:2015:PPA,
  author =       "Jonathan M. Borwein and Scott T. Chapman",
  title =        "{I} Prefer Pi: Addenda",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "122",
  number =       "8",
  pages =        "800--800",
  month =        oct,
  year =         "2015",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.122.8.800",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11A05 (11Z05)",
  MRnumber =     "3399115",
  bibdate =      "Tue Oct 20 06:20:38 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  note =         "See \cite{Borwein:2015:PPB}. The addenda correct
                 formulas (4) and (12), references [34] and [74], and
                 add a new reference.",
  URL =          "https://www.jstor.org/stable/10.4169/amer.math.monthly.122.8.800",
  ZMnumber =     "1328.01077",
  abstract =     "In the rush to prepare our March 2015 article on Pi
                 [1], several infelicities escaped our eye. Herein we
                 repair the damage.",
  acknowledgement = ack-nhfb,
  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",
  unique-id =    "ISI:000363911100013",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2015:PPB
author: Jonathan M. Borwein and Scott T. Chapman
journal: j-AMER-MATH-MONTHLY
volume: 122
number: 3
pages: 195--216
month: mar
monthnumber: 3
year: 2015
CODEN: AMMYAE
DOI: https://doi.org/10.4169/amer.math.monthly.122.03.195
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 01A05 (11Z05)
MRnumber: 3327710
bibdate: Wed Jun 10 09:05:28 MDT 2015
bibtimestamp: 2015.06.10 09:05:28 MDT
note: See addenda cite Borwein:2015:PPA.
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: Jonathan M. Borwein and Scott T. Chapman
rawnote: See addenda \cite{Borwein:2015:PPA}.
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
I Prefer Pi: a Brief History and Anthology of Articles in the booktitle American Mathematical Monthly

bibsource:
https://www.jstor.org/stable/10.4169/amermathmont.122.issue-03; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib

URL:
http://docserver.carma.newcastle.edu.au/1615/; https://www.jstor.org/stable/10.4169; https://www.jstor.org/stable/10.4169/amer.math.monthly.122.03.195

abstract:
In celebration of both a special ``big'' $ pi $ Day (3/14/15) and the 2015 centennial of the Mathematical Association of America, we review the illustrious history of the constant $ pi $ in the pages of the American Mathematical Monthly.

rawabstract:
In celebration of both a special ``big'' $ \pi $ Day (3/14/15) and the 2015 centennial of the Mathematical Association of America, we review the illustrious history of the constant $ \pi $ in the pages of the American Mathematical Monthly.

rawtitle:
{I} Prefer Pi: a Brief History and Anthology of Articles in the {{\booktitle{American Mathematical Monthly}}}

entry:
@Article{Borwein:2015:PPB,
  author =       "Jonathan M. Borwein and Scott T. Chapman",
  title =        "{I} Prefer Pi: a Brief History and Anthology of
                 Articles in the {{\booktitle{American Mathematical
                 Monthly}}}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "122",
  number =       "3",
  pages =        "195--216",
  month =        mar,
  year =         "2015",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.122.03.195",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "01A05 (11Z05)",
  MRnumber =     "3327710",
  bibdate =      "Wed Jun 10 09:05:28 MDT 2015",
  bibsource =    "https://www.jstor.org/stable/10.4169/amermathmont.122.issue-03;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  note =         "See addenda \cite{Borwein:2015:PPA}.",
  URL =          "http://docserver.carma.newcastle.edu.au/1615/;
                 https://www.jstor.org/stable/10.4169;
                 https://www.jstor.org/stable/10.4169/amer.math.monthly.122.03.195",
  abstract =     "In celebration of both a special ``big'' $ \pi $ Day
                 (3/14/15) and the 2015 centennial of the Mathematical
                 Association of America, we review the illustrious
                 history of the constant $ \pi $ in the pages of the
                 American Mathematical Monthly.",
  acknowledgement = ack-nhfb,
  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",
  unique-id =    "ISI:000369889300002",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2015:RNP
author: Jonathan M. Borwein and Armin Straub
title: Relations for Nielsen polylogarithms
journal: j-J-APPROX-THEORY
volume: 193
pages: 74--88
month: may
monthnumber: 5
year: 2015
CODEN: JAXTAZ
DOI: https://doi.org/10.1016/j.jat.2013.07.003
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
MRclass: 33B30
MRnumber: 3324564
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 ???
note: Special Issue Dedicated to Dick Askey on the occasion of his 80th birthday.
fjournal: Journal of Approximation Theory
keywords: Clausen functions; Log-sine integrals; Multiple polylogarithms; Multiple zeta values
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: Jonathan M. Borwein and Armin Straub
rawnote: Special Issue Dedicated to Dick Askey on the occasion of his 80th birthday.
rawtitle: Relations for {Nielsen} polylogarithms
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053
URL:
http://docserver.carma.newcastle.edu.au/1500/; http://www.sciencedirect.com/science/article/pii/S0021904513001202

abstract:
Polylogarithms appear in many diverse fields of mathematics. Herein, we investigate relations amongst the restricted class of Nielsen-type (essentially, height one) polylogarithms, both generic and at special arguments including the sixth roots of unity. Numerical computations suggest that the collected relations, partially motivated by a previous study of the authors on log-sine integrals, are complete except in the case when the argument is the fundamental sixth root of unity. For use in other applications, all our results are implemented and accessible for use in symbolic computation or to facilitate numeric computation. In particular, the relations are explicitly exhibited in the case of low weights.

rawabstract:
Polylogarithms appear in many diverse fields of mathematics. Herein, we investigate relations amongst the restricted class of Nielsen-type (essentially, height one) polylogarithms, both generic and at special arguments including the sixth roots of unity. Numerical computations suggest that the collected relations, partially motivated by a previous study of the authors on log-sine integrals, are complete except in the case when the argument is the fundamental sixth root of unity. For use in other applications, all our results are implemented and accessible for use in symbolic computation or to facilitate numeric computation. In particular, the relations are explicitly exhibited in the case of low weights.

entry:
@Article{Borwein:2015:RNP,
  author =       "Jonathan M. Borwein and Armin Straub",
  title =        "Relations for {Nielsen} polylogarithms",
  journal =      j-J-APPROX-THEORY,
  volume =       "193",
  number =       "??",
  pages =        "74--88",
  month =        may,
  year =         "2015",
  CODEN =        "JAXTAZ",
  DOI =          "https://doi.org/10.1016/j.jat.2013.07.003",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  MRclass =      "33B30",
  MRnumber =     "3324564",
  MRreviewer =   "Junesang Choi",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Special Issue Dedicated to Dick Askey on the occasion
                 of his 80th birthday.",
  URL =          "http://docserver.carma.newcastle.edu.au/1500/;
                 http://www.sciencedirect.com/science/article/pii/S0021904513001202",
  abstract =     "Polylogarithms appear in many diverse fields of
                 mathematics. Herein, we investigate relations amongst
                 the restricted class of Nielsen-type (essentially,
                 height one) polylogarithms, both generic and at special
                 arguments including the sixth roots of unity. Numerical
                 computations suggest that the collected relations,
                 partially motivated by a previous study of the authors
                 on log-sine integrals, are complete except in the case
                 when the argument is the fundamental sixth root of
                 unity. For use in other applications, all our results
                 are implemented and accessible for use in symbolic
                 computation or to facilitate numeric computation. In
                 particular, the relations are explicitly exhibited in
                 the case of low weights.",
  acknowledgement = ack-nhfb,
  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",
  keywords =     "Clausen functions; Log-sine integrals; Multiple
                 polylogarithms; Multiple zeta values",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053",
  unique-id =    "ISI:000352676400006",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2015:RPM
author: Jonathan M. Borwein and Liangjin Yao
title: Recent progress on monotone operator theory
crossref: Reich:2015:IPO
pages: 51--81
year: 2015
DOI: https://doi.org/10.1090/conm/636/12728
MRclass: 47H05 (46B10 47-02)
MRnumber: 3155360
MRreviewer: Behzad Djafari-Rouhani
bibdate: Wed Aug 10 11:09:47 2016
bibsource: 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/1457/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Liangjin Yao
rawtitle: Recent progress on monotone operator theory
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InProceedings{Borwein:2015:RPM,
  author =       "Jonathan M. Borwein and Liangjin Yao",
  title =        "Recent progress on monotone operator theory",
  crossref =     "Reich:2015:IPO",
  pages =        "51--81",
  year =         "2015",
  DOI =          "https://doi.org/10.1090/conm/636/12728",
  MRclass =      "47H05 (46B10 47-02)",
  MRnumber =     "3155360",
  MRreviewer =   "Behzad Djafari-Rouhani",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1457/",
  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:2015:SRC
author: Jonathan M. Borwein and Ohad Giladi
title: Some remarks on convex analysis in topological groups
journal: ArXiv e-prints
pages: 51--81
month: oct
monthnumber: 10
year: 2015
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/2015arXiv151004487B; http://docserver.carma.newcastle.edu.au/1697/
keywords: Mathematics - Optimization and Control, Mathematics - Functional Analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Ohad Giladi
rawtitle: Some remarks on convex analysis in topological groups
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We discuss some key results from convex analysis in the setting of topological groups and monoids. These include separation theorems, Krein--Milman type theorems, and minimax theorems.

rawabstract:
We discuss some key results from convex analysis in the setting of topological groups and monoids. These include separation theorems, Krein--Milman type theorems, and minimax theorems.

entry:
@Article{Borwein:2015:SRC,
  author =       "Jonathan M. Borwein and Ohad Giladi",
  title =        "Some remarks on convex analysis in topological
                 groups",
  journal =      "ArXiv e-prints",
  month =        oct,
  year =         "2015",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2015arXiv151004487B;
                 http://docserver.carma.newcastle.edu.au/1697/",
  abstract =     "We discuss some key results from convex analysis in
                 the setting of topological groups and monoids. These
                 include separation theorems, Krein--Milman type
                 theorems, and minimax theorems.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1510.04487",
  keywords =     "Mathematics - Optimization and Control, Mathematics -
                 Functional Analysis",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.OC",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2015:WWH
author: Jonathan M. Borwein
title: Who We Are and How We Got That Way?
crossref: Casazza:2015:M
pages: 140--156
year: 2015
bibdate: Sat Aug 13 13:47:19 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 13:47:19 ???
URL: http://docserver.carma.newcastle.edu.au/777/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawtitle: Who We Are and How We Got That Way?
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2015:WWH,
  author =       "Jonathan M. Borwein",
  title =        "Who We Are and How We Got That Way?",
  crossref =     "Casazza:2015:M",
  pages =        "140--156",
  year =         "2015",
  bibdate =      "Sat Aug 13 13:47:19 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/777/",
  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: AragonArtacho:2016:GBD
author: Francisco J. Aragon Artacho and Jonathan M. Borwein and Matthew K. Tam
title: Global behavior of the Douglas--Rachford method for a nonconvex feasibility problem
journal: j-J-GLOBAL-OPT
volume: 65
number: 2
pages: 309--327
month: jun
monthnumber: 6
year: 2016
CODEN: JGOPEO
DOI: https://doi.org/10.1007/s10898-015-0380-6
ISSN: 0925-5001 (print), 1573-2916 (electronic) OR 09255001 (print), 15732916 (electronic)
ISSNL: 0925-5001 OR 09255001
MRclass: 90C26 (65K05)
MRnumber: 3498569
MRreviewer: Zhili Ge
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/1701/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/10898
rawauthor: Francisco J. {Arag{\'o}n Artacho} and Jonathan M. Borwein and Matthew K. Tam
rawtitle: Global behavior of the {Douglas--Rachford} method for a nonconvex feasibility problem
ORCID: Aragon Artacho, Francisco Javier/0000-0002-2445-8011; Borwein, Jonathan/0000-0002-1263-0646
abstract:
In recent times the Douglas--Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.

fjournal:
Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering

entry:
@Article{AragonArtacho:2016:GBD,
  author =       "Francisco J. {Arag{\'o}n Artacho} and Jonathan M.
                 Borwein and Matthew K. Tam",
  title =        "Global behavior of the {Douglas--Rachford} method for
                 a nonconvex feasibility problem",
  journal =      j-J-GLOBAL-OPT,
  volume =       "65",
  number =       "2",
  pages =        "309--327",
  month =        jun,
  year =         "2016",
  CODEN =        "JGOPEO",
  DOI =          "https://doi.org/10.1007/s10898-015-0380-6",
  ISSN =         "0925-5001 (print), 1573-2916 (electronic)",
  ISSN-L =       "0925-5001",
  MRclass =      "90C26 (65K05)",
  MRnumber =     "3498569",
  MRreviewer =   "Zhili Ge",
  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/1701/",
  abstract =     "In recent times the Douglas--Rachford algorithm has
                 been observed empirically to solve a variety of
                 nonconvex feasibility problems including those of a
                 combinatorial nature. For many of these problems
                 current theory is not sufficient to explain this
                 observed success and is mainly concerned with questions
                 of local convergence. In this paper we analyze global
                 behavior of the method for finding a point in the
                 intersection of a half-space and a potentially
                 non-convex set which is assumed to satisfy a
                 well-quasi-ordering property or a property weaker than
                 compactness. In particular, the special case in which
                 the second set is finite is covered by our framework
                 and provides a prototypical setting for combinatorial
                 optimization problems.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Global Optimization. An International
                 Journal Dealing with Theoretical and Computational
                 Aspects of Seeking Global Optima and Their Applications
                 in Science, Management and Engineering",
  journal-URL =  "http://link.springer.com/journal/10898",
  ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
                 Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Aragon Artacho, Francisco Javier/C-2531-2012",
  unique-id =    "ISI:000377611500007",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Bailey:2016:AIS
author: David H. Bailey and Jonathan M. Borwein
title: Ancient Indian Square Roots: An Exercise in Forensic Paleo-Mathematics
crossref: Selin:2016:EHS
pages: 305--310
year: 2016
DOI: https://doi.org/10.1007/978-94-007-7747-7_10265
bibdate: Fri Aug 12 18:58:22 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 18:58:22 ???
note: Redacted from cite Bailey:2012:AIS.
URL: http://docserver.carma.newcastle.edu.au/1385/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawnote: Redacted from \cite{Bailey:2012:AIS}.
rawtitle: Ancient {Indian} Square Roots: An Exercise in Forensic Paleo-Mathematics
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Bailey:2016:AIS,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Ancient {Indian} Square Roots: An Exercise in Forensic
                 Paleo-Mathematics",
  crossref =     "Selin:2016:EHS",
  pages =        "305--310",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-94-007-7747-7_10265",
  bibdate =      "Fri Aug 12 18:58:22 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Redacted from \cite{Bailey:2012:AIS}.",
  URL =          "http://docserver.carma.newcastle.edu.au/1385/",
  acknowledgement = ack-nhfb,
  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:2016:BOF
author: David H. Bailey and Jonathan M. Borwein and Amir Salehipour and Marcos Lopez de Prado and Qiji Zhu
title: Backtest Overfitting in Financial Markets
journal: Automated Trader Magazine
volume: 39
number: Q1
pages: 52--57
year: 2016
bibdate: Fri Aug 12 07:28:28 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 07:28:28 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.automatedtrader.net/home.xhtm
rawtitle: Backtest Overfitting in Financial Markets
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1713/; http://www.automatedtrader.net/articles/strategies/155469/backtest-overfitting-in-financial-markets

rawauthor:
David H. Bailey and Jonathan M. Borwein and Amir Salehipour and Marcos {L{\'o}pez de Prado} and Qiji Zhu

entry:
@Article{Bailey:2016:BOF,
  author =       "David H. Bailey and Jonathan M. Borwein and Amir
                 Salehipour and Marcos {L{\'o}pez de Prado} and Qiji
                 Zhu",
  title =        "Backtest Overfitting in Financial Markets",
  journal =      "Automated Trader Magazine",
  volume =       "39",
  number =       "Q1",
  pages =        "52--57",
  month =        "????",
  year =         "2016",
  bibdate =      "Fri Aug 12 07:28:28 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1713/;
                 http://www.automatedtrader.net/articles/strategies/155469/backtest-overfitting-in-financial-markets",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  journal-URL =  "http://www.automatedtrader.net/home.xhtm",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2016:CDA
author: David H. Bailey and Jonathan M. Borwein and Jason Kimberley and Watson Ladd
title: Computer Discovery and Analysis of Large Poisson Polynomials
journal: j-EXP-MATH
pages: ??--??
year: 2016
DOI: https://doi.org/10.1080/10586458.2016.1180565
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
bibdate: Fri Aug 12 07:21:56 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 07:21:56 ???
fjournal: Experimental Mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.tandfonline.com/loi/uexm20
onlinedate: 24 August 2016
rawauthor: David H. Bailey and Jonathan M. Borwein and Jason Kimberley and Watson Ladd
rawtitle: Computer Discovery and Analysis of Large {Poisson} Polynomials
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1689/; http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1180565

entry:
@Article{Bailey:2016:CDA,
  author =       "David H. Bailey and Jonathan M. Borwein and Jason
                 Kimberley and Watson Ladd",
  title =        "Computer Discovery and Analysis of Large {Poisson}
                 Polynomials",
  journal =      j-EXP-MATH,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        "",
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2016.1180565",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  bibdate =      "Fri Aug 12 07:21:56 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1689/;
                 http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1180565",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  onlinedate =   "24 August 2016",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  xxtitle =      "Discovery and Analysis of Large {Poisson} Polynomials
                 Using the {MPFUN--MPFR} Arbitrary Precision Software",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:2016:CEE
author: D. H. Bailey and J. M. Borwein
title: Computation and experimental evaluation of Mordell--Tornheim--Witten sum derivatives
address: Davis, CA, USA and Callaghan, NSW 2308, Australia
pages: 9
day: 16
month: aug
monthnumber: 8
year: 2016
bibdate: Tue Aug 16 09:37:31 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:37:31 ???
URL: http://www.davidhbailey.com/dhbpapers/omega-numerics.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. H. Bailey and J. M. Borwein
rawtitle: Computation and experimental evaluation of {Mordell--Tornheim--Witten} sum derivatives
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
institution:
University of California at Davis and Centre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle

abstract:
In previous studies the present authors and others have studied in have studied Mordell--Tornheim--Witten sums and their connections with multiple-zeta values. In this note we describe the numerical computation of derivatives at zero of a specialization originating in [14] and studied further in [10, 15, 11], and the experimental evaluation of these numerical values in terms of well-known constants.

rawabstract:
In previous studies the present authors and others have studied in have studied Mordell--Tornheim--Witten sums and their connections with multiple-zeta values. In this note we describe the numerical computation of derivatives at zero of a specialization originating in [14] and studied further in [10, 15, 11], and the experimental evaluation of these numerical values in terms of well-known constants.

entry:
@TechReport{Bailey:2016:CEE,
  author =       "D. H. Bailey and J. M. Borwein",
  title =        "Computation and experimental evaluation of
                 {Mordell--Tornheim--Witten} sum derivatives",
  institution =  "University of California at Davis and Centre for
                 Computer Assisted Research Mathematics and its
                 Applications (CARMA), University of Newcastle",
  address =      "Davis, CA, USA and Callaghan, NSW 2308, Australia",
  pages =        "9",
  day =          "16",
  month =        aug,
  year =         "2016",
  bibdate =      "Tue Aug 16 09:37:31 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/omega-numerics.pdf",
  abstract =     "In previous studies the present authors and others
                 have studied in have studied Mordell--Tornheim--Witten
                 sums and their connections with multiple-zeta values.
                 In this note we describe the numerical computation of
                 derivatives at zero of a specialization originating in
                 [14] and studied further in [10, 15, 11], and the
                 experimental evaluation of these numerical values in
                 terms of well-known constants.",
  acknowledgement = ack-nhfb,
  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: incollection
filename: borwein-jonathan-m.bib
label: Bailey:2016:CPI
author: David H. Bailey and Jonathan M. Borwein and Andrew Mattingly and Glenn Wightwick
title: The computation of previously inaccessible digits of $ pi $
crossref: Bailey:2016:PNG
pages: 327--339
year: 2016
DOI: https://doi.org/10.1007/978-3-319-32377-0_20
bibdate: Tue Mar 14 11:34:57 2017
bibtimestamp: 2017.03.14 11:34:57 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein and Andrew Mattingly and Glenn Wightwick
rawtitle: The computation of previously inaccessible digits of $ \pi $
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/agm.bib

entry:
@InCollection{Bailey:2016:CPI,
  author =       "David H. Bailey and Jonathan M. Borwein and Andrew
                 Mattingly and Glenn Wightwick",
  title =        "The computation of previously inaccessible digits of $
                 \pi $",
  crossref =     "Bailey:2016:PNG",
  pages =        "327--339",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0_20",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.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",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2016:CSC
author: D. H. Bailey and J. M. Borwein
journal: j-MATH-COMPUT
volume: 85
number: 297
pages: 295--324
year: 2016
CODEN: MCMPAF
DOI: https://doi.org/10.1090/mcom/2974
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11L40 (33F05)
MRnumber: 3404451
MRreviewer: Karin Halupczok
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/mcom/
rawauthor: D. H. Bailey and J. M. Borwein
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
title:
Computation and structure of character polylogarithms with applications to character Mordell--Tornheim--Witten sums

bibsource:
http://www.ams.org/mcom/2016-85-297; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib

URL:
http://docserver.carma.newcastle.edu.au/1492/; http://www.ams.org/journals/mcom/2016-85-297/S0025-5718-2015-02974-3; http://www.ams.org/journals/mcom/2016-85-297/S0025-5718-2015-02974-3/S0025-5718-2015-02974-3.pdf; http://www.ams.org/mathscinet/search/author.html?authorName=Borwein%2C%20J.%20M.; http://www.ams.org/mathscinet/search/author.html?mrauthid=29355; http://www.carma.newcastle.edu.au/jon/MTWIII.pdf

abstract:
This paper extends tools developed to study character polylogarithms. These objects are used to compute Mordell--Tornheim--Witten character sums and to explore their connections with multiple-zeta values (MZVs) and with their character analogues.

rawabstract:
This paper extends tools developed to study character polylogarithms. These objects are used to compute Mordell--Tornheim--Witten character sums and to explore their connections with multiple-zeta values (MZVs) and with their character analogues.

rawtitle:
Computation and structure of character polylogarithms with applications to character {Mordell--Tornheim--Witten} sums

entry:
@Article{Bailey:2016:CSC,
  author =       "D. H. Bailey and J. M. Borwein",
  title =        "Computation and structure of character polylogarithms
                 with applications to character
                 {Mordell--Tornheim--Witten} sums",
  journal =      j-MATH-COMPUT,
  volume =       "85",
  number =       "297",
  pages =        "295--324",
  year =         "2016",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/mcom/2974",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11L40 (33F05)",
  MRnumber =     "3404451",
  MRreviewer =   "Karin Halupczok",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://www.ams.org/mcom/2016-85-297;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1492/;
                 http://www.ams.org/journals/mcom/2016-85-297/S0025-5718-2015-02974-3;
                 http://www.ams.org/journals/mcom/2016-85-297/S0025-5718-2015-02974-3/S0025-5718-2015-02974-3.pdf;
                 http://www.ams.org/mathscinet/search/author.html?authorName=Borwein%2C%20J.%20M.;
                 http://www.ams.org/mathscinet/search/author.html?mrauthid=29355;
                 http://www.carma.newcastle.edu.au/jon/MTWIII.pdf",
  abstract =     "This paper extends tools developed to study character
                 polylogarithms. These objects are used to compute
                 Mordell--Tornheim--Witten character sums and to explore
                 their connections with multiple-zeta values (MZVs) and
                 with their character analogues.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  unique-id =    "ISI:000362848100011",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Bailey:2016:EMS
author: D. H. Bailey and J. M. Borwein
booktitle: 7th European Mathematics Congress (EMC) on Mathematics in the Society of the Future
title: Experimental Mathematics in the Society of the Future
publisher: European Mathematical Society
address: Zurich, Switzerland
pages: 7--25
year: 2016
DOI: https://doi.org/10.4171/164-1/2
MRclass: 00A35
MRnumber: 3497586
bibdate: Fri Aug 12 18:35:05 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 18:35:05 ???
URL: http://docserver.carma.newcastle.edu.au/1675/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. H. Bailey and J. M. Borwein
rawbooktitle: 7th European Mathematics Congress (EMC) on Mathematics in the Society of the Future
rawtitle: Experimental Mathematics in the Society of the Future
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Bailey:2016:EMS,
  author =       "D. H. Bailey and J. M. Borwein",
  booktitle =    "7th European Mathematics Congress (EMC) on Mathematics
                 in the Society of the Future",
  title =        "Experimental Mathematics in the Society of the
                 Future",
  publisher =    "European Mathematical Society",
  address =      "Z{\"u}rich, Switzerland",
  pages =        "7--25",
  year =         "2016",
  DOI =          "https://doi.org/10.4171/164-1/2",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "",
  MRclass =      "00A35",
  MRnumber =     "3497586",
  bibdate =      "Fri Aug 12 18:35:05 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1675/",
  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: incollection
filename: borwein-jonathan-m.bib
label: Bailey:2016:FRS
author: David H. Bailey and Jonathan M. Borwein and Victoria Stodden
editor: Harald Atmanspacher and Sabine Maasen
booktitle: Reproducibility: Principles, Problems, Practices, and Prospects
title: Facilitating Reproducibility in Scientific Computing: Principles and Practice
publisher: pub-WILEY
address: pub-WILEY:adr
pages: 205--231
year: 2016
DOI: https://doi.org/10.1002/9781118865064.ch9
ISBN: 1-118-86506-5 OR 1118865065
ISBN13: 978-1-118-86506-4 OR 9781118865064
bibdate: Thu Aug 11 11:01:49 2016
bibtimestamp: 2016.08.11 11:01:49 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein and Victoria Stodden
rawbooktitle: Reproducibility: Principles, Problems, Practices, and Prospects
raweditor: Harald Atmanspacher and Sabine Maasen
rawtitle: Facilitating Reproducibility in Scientific Computing: Principles and Practice
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/fparith.bib

note:
This book was awarded the 2017 Prose Award (``Honorable Mention'') in the category ``Textbook / Best in Physical Sciences and Mathematics''; see url https://proseawards.com/winners/2017-award-winners/ and url http://experimentalmath.org/2017/02/reproducibility-principles-problems-practices-and-prospects/.

abstract:
This chapter discusses the roots of the reproducibility problem in scientific computing, and summarizes some possible solutions that have been suggested in the community. Statistical overfitting can be thought of as an instance of ``selection bias'', wherein one presents the results of only those tests that support well one's hypothesis. The problem of statistical overfitting in computational science is perhaps best illustrated in the field of mathematical finance. Present-day researchers are not as fully aware of the potential pitfalls of performance reporting. In any event, various high-performance computing researchers have noted a resurrection of some of these questionable practices. Using high-precision arithmetic (higher than the standard IEEE 64-bit arithmetic) is often quite useful in ameliorating numerical difficulties and enhancing reproducibility. Very high-precision floating-point arithmetic is essential to obtain reproducible results in experimental mathematics and in related mathematical physics applications. The chapter also discusses reproducibility in symbolic computing.

keywords:
high-performance computing; high-precision arithmetic; mathematical physics; numerical reproducibility; performance reporting; scientific computing; statistical overfitting; symbolic computing

rawabstract:
This chapter discusses the roots of the reproducibility problem in scientific computing, and summarizes some possible solutions that have been suggested in the community. Statistical overfitting can be thought of as an instance of ``selection bias'', wherein one presents the results of only those tests that support well one's hypothesis. The problem of statistical overfitting in computational science is perhaps best illustrated in the field of mathematical finance. Present-day researchers are not as fully aware of the potential pitfalls of performance reporting. In any event, various high-performance computing researchers have noted a resurrection of some of these questionable practices. Using high-precision arithmetic (higher than the standard IEEE 64-bit arithmetic) is often quite useful in ameliorating numerical difficulties and enhancing reproducibility. Very high-precision floating-point arithmetic is essential to obtain reproducible results in experimental mathematics and in related mathematical physics applications. The chapter also discusses reproducibility in symbolic computing.

rawnote:
This book was awarded the 2017 Prose Award (``Honorable Mention'') in the category ``Textbook / Best in Physical Sciences and Mathematics''; see \url{https://proseawards.com/winners/2017-award-winners/} and \url{http://experimentalmath.org/2017/02/reproducibility-principles-problems-practices-and-prospects/}.

entry:
@InCollection{Bailey:2016:FRS,
  author =       "David H. Bailey and Jonathan M. Borwein and Victoria
                 Stodden",
  editor =       "Harald Atmanspacher and Sabine Maasen",
  booktitle =    "Reproducibility: Principles, Problems, Practices, and
                 Prospects",
  title =        "Facilitating Reproducibility in Scientific Computing:
                 Principles and Practice",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "205--231",
  year =         "2016",
  DOI =          "https://doi.org/10.1002/9781118865064.ch9",
  ISBN =         "1-118-86506-5",
  ISBN-13 =      "978-1-118-86506-4",
  bibdate =      "Thu Aug 11 11:01:49 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This book was awarded the 2017 Prose Award
                 (``Honorable Mention'') in the category ``Textbook /
                 Best in Physical Sciences and Mathematics''; see
                 \url{https://proseawards.com/winners/2017-award-winners/}
                 and
                 \url{http://experimentalmath.org/2017/02/reproducibility-principles-problems-practices-and-prospects/}.",
  abstract =     "This chapter discusses the roots of the
                 reproducibility problem in scientific computing, and
                 summarizes some possible solutions that have been
                 suggested in the community. Statistical overfitting can
                 be thought of as an instance of ``selection bias'',
                 wherein one presents the results of only those tests
                 that support well one's hypothesis. The problem of
                 statistical overfitting in computational science is
                 perhaps best illustrated in the field of mathematical
                 finance. Present-day researchers are not as fully aware
                 of the potential pitfalls of performance reporting. In
                 any event, various high-performance computing
                 researchers have noted a resurrection of some of these
                 questionable practices. Using high-precision arithmetic
                 (higher than the standard IEEE 64-bit arithmetic) is
                 often quite useful in ameliorating numerical
                 difficulties and enhancing reproducibility. Very
                 high-precision floating-point arithmetic is essential
                 to obtain reproducible results in experimental
                 mathematics and in related mathematical physics
                 applications. The chapter also discusses
                 reproducibility in symbolic computing.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "high-performance computing; high-precision arithmetic;
                 mathematical physics; numerical reproducibility;
                 performance reporting; scientific computing;
                 statistical overfitting; symbolic computing",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Bailey:2016:HHI
author: D. Bailey and J. Borwein and M. Lopez de Prado and A. Salehipour and Qiji Zhu
title: How hard is it to avoid backtest overfitting?
pages: 205--231
year: 2016
bibdate: Tue Aug 16 09:31:54 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:31:54 ???
note: Submitted to Applied Mathematical Finance, July 2016.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. Bailey and J. Borwein and M. {L{\'o}pez de Prado} and A. Salehipour and Qiji Zhu
rawnote: Submitted to Applied Mathematical Finance, July 2016.
rawtitle: How hard is it to avoid backtest overfitting?
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Unpublished{Bailey:2016:HHI,
  author =       "D. Bailey and J. Borwein and M. {L{\'o}pez de Prado}
                 and A. Salehipour and Qiji Zhu",
  title =        "How hard is it to avoid backtest overfitting?",
  year =         "2016",
  bibdate =      "Tue Aug 16 09:31:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Submitted to Applied Mathematical Finance, July
                 2016.",
  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:2016:RCS
author: David H. Bailey and Jonathan M. Borwein and Richard P. Brent and Mohsen Reisi
title: Reproducibility in Computational Science: A Case Study: Randomness of the Digits of Pi
journal: j-EXP-MATH
volume: 22
pages: 1--8
year: 2016
DOI: https://doi.org/10.1080/10586458.2016.1163755
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
bibdate: Fri Aug 12 07:22:53 2016
bibtimestamp: 2016.08.12 07:22:53 ???
note: See cite Ganz:2014:DES.
fjournal: Experimental Mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.tandfonline.com/loi/uexm20
onlinedate: 24 August 2016
rawauthor: David H. Bailey and Jonathan M. Borwein and Richard P. Brent and Mohsen Reisi
rawnote: See \cite{Ganz:2014:DES}.
rawtitle: Reproducibility in Computational Science: A Case Study: Randomness of the Digits of Pi
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1695/; http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1163755

remark:
This paper reproduces work in cite Ganz:2014:DES, and then shows that the report in that paper of nonrandomness of digits of $ pi $ is an artifact of an unlucky choice of sample block sizes. Statistics from several different block sizes support the widely-held, but still unproven, belief that $ pi $ is a normal number (where all digits occur with equal probability).

entry:
@Article{Bailey:2016:RCS,
  author =       "David H. Bailey and Jonathan M. Borwein and Richard P.
                 Brent and Mohsen Reisi",
  title =        "Reproducibility in Computational Science: A Case
                 Study: Randomness of the Digits of Pi",
  journal =      j-EXP-MATH,
  volume =       "22",
  number =       "??",
  pages =        "1--8",
  month =        "",
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2016.1163755",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  bibdate =      "Fri Aug 12 07:22:53 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  note =         "See \cite{Ganz:2014:DES}.",
  URL =          "http://docserver.carma.newcastle.edu.au/1695/;
                 http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1163755",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  onlinedate =   "24 August 2016",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "This paper reproduces work in \cite{Ganz:2014:DES},
                 and then shows that the report in that paper of
                 nonrandomness of digits of $ \pi $ is an artifact of an
                 unlucky choice of sample block sizes. Statistics from
                 several different block sizes support the widely-held,
                 but still unproven, belief that $ \pi $ is a normal
                 number (where all digits occur with equal
                 probability).",
  xxauthor =     "David H. Bailey and Jonathan M. Borwein and Richard P.
                 Brent and Mohsen Reisi Ardali",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2016:SPDa
author: D. Bailey and J. Borwein and M. Lopez de Prado
title: Stock portfolio design and backtest overfitting
journal: j-J-INVESTMENT-MANAGE
pages: ??--??
year: 2016
ISSN: 1545-9144 (print), 1545-9152 (electronic) OR 15459144 (print), 15459152 (electronic)
ISSNL: 1545-9144 OR 15459144
bibdate: Fri Aug 12 07:17:41 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 07:17:41 ???
URL: http://docserver.carma.newcastle.edu.au/1684/; http://www.davidhbailey.com/dhbpapers/stockfund.pdf
fjournal: Journal of Investment Management
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.joim.com/library-archives/
rawauthor: D. Bailey and J. Borwein and M. {L{\'o}pez de Prado}
rawtitle: Stock portfolio design and backtest overfitting
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bailey:2016:SPDa,
  author =       "D. Bailey and J. Borwein and M. {L{\'o}pez de Prado}",
  title =        "Stock portfolio design and backtest overfitting",
  journal =      j-J-INVESTMENT-MANAGE,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2016",
  DOI =          "",
  ISSN =         "1545-9144 (print), 1545-9152 (electronic)",
  ISSN-L =       "1545-9144",
  bibdate =      "Fri Aug 12 07:17:41 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1684/;
                 http://www.davidhbailey.com/dhbpapers/stockfund.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Investment Management",
  journal-URL =  "https://www.joim.com/library-archives/",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  pagecount =    "16",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2016:SPDb
author: David H. Bailey and Jonathan M. Borwein and Marcos Lopez de Prado
title: Stock portfolio design and backtest overfitting
journal: SSRN Electronic Journal
pages: ??--??
year: 2016
DOI: https://doi.org/10.2139/ssrn.2739335
bibdate: Fri Feb 9 09:23:54 2018
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2018.02.09 09:23:54 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein and Marcos {L{\'o}pez de Prado}
rawtitle: Stock portfolio design and backtest overfitting
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bailey:2016:SPDb,
  author =       "David H. Bailey and Jonathan M. Borwein and Marcos
                 {L{\'o}pez de Prado}",
  title =        "Stock portfolio design and backtest overfitting",
  journal =      "{SSRN} Electronic Journal",
  year =         "2016",
  DOI =          "https://doi.org/10.2139/ssrn.2739335",
  bibdate =      "Fri Feb 9 09:23:54 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2016:AGM
author: J. M. Borwein and P. B. Borwein
title: The arithmetic--geometric mean and fast computation of elementary functions (1984)
crossref: Bailey:2016:PNG
pages: 79--96
year: 2016
DOI: https://doi.org/10.1007/978-3-319-32377-0_4
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibsource: 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/chapter/10.1007/978-3-319-32377-0_4
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein
rawtitle: The arithmetic--geometric mean and fast computation of elementary functions (1984)
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2016:AGM,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The arithmetic--geometric mean and fast computation of
                 elementary functions (1984)",
  crossref =     "Bailey:2016:PNG",
  pages =        "79--96",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-32377-0_4",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-319-32377-0_4",
  acknowledgement = ack-nhfb,
  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:2016:AO
author: J. M. Borwein
title: Adventures with the OEIS
journal: j-RAMANUJAN-J
pages: ??--??
year: 2016
ISSN: 1382-4090 (print), 1572-9303 (electronic) OR 13824090 (print), 15729303 (electronic)
ISSNL: 1382-4090 OR 13824090
bibdate: Fri Aug 12 07:16:30 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 07:16:30 ???
URL: http://docserver.carma.newcastle.edu.au/1686/
fjournal: The Ramanujan Journal
keywords: Neil J. A. Sloane; OEIS (Online Encyclopedia of Integer Sequences)
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11139
rawauthor: J. M. Borwein
rawtitle: Adventures with the {OEIS}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2016:AO,
  author =       "J. M. Borwein",
  title =        "Adventures with the {OEIS}",
  journal =      j-RAMANUJAN-J,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2016",
  DOI =          "",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  bibdate =      "Fri Aug 12 07:16:30 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1686/",
  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",
  keywords =     "Neil J. A. Sloane; OEIS (Online Encyclopedia of
                 Integer Sequences)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:2016:BOM
author: J. M. Borwein and K. Dilcher and H. Tomkins
title: The behaviour at the origin of multiple Witten zeta functions
pages: ??--??
month: jul
monthnumber: 7
year: 2016
bibdate: Tue Aug 16 09:38:11 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:38:11 ???
note: In preparation.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and K. Dilcher and H. Tomkins
rawnote: In preparation.
rawtitle: The behaviour at the origin of multiple {Witten} zeta functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Unpublished{Borwein:2016:BOM,
  author =       "J. M. Borwein and K. Dilcher and H. Tomkins",
  title =        "The behaviour at the origin of multiple {Witten} zeta
                 functions",
  month =        jul,
  year =         "2016",
  bibdate =      "Tue Aug 16 09:38:11 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "In preparation.",
  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:2016:CFD
author: Jonathan M. Borwein and Corwin W. Sinnamon
title: A closed form for the density functions of random walks in odd dimensions
journal: j-BULL-AUSTRAL-MATH-SOC
volume: 93
number: 2
pages: 330--339
month: apr
monthnumber: 4
year: 2016
CODEN: ALNBAB
DOI: https://doi.org/10.1017/S0004972715001112
ISSN: 0004-9727 (print), 1755-1633 (electronic) OR 00049727 (print), 17551633 (electronic)
ISSNL: 0004-9727 OR 00049727
MRclass: 60G50 (33C20)
MRnumber: 3480942
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 Corwin W. Sinnamon
rawtitle: A closed form for the density functions of random walks in odd dimensions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1702/; http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=10230818

abstract:
We derive an explicit piecewise-polynomial closed form for the probability density function of the distance travelled by a uniform random walk in an odd-dimensional space.

rawabstract:
We derive an explicit piecewise-polynomial closed form for the probability density function of the distance travelled by a uniform random walk in an odd-dimensional space.

entry:
@Article{Borwein:2016:CFD,
  author =       "Jonathan M. Borwein and Corwin W. Sinnamon",
  title =        "A closed form for the density functions of random
                 walks in odd dimensions",
  journal =      j-BULL-AUSTRAL-MATH-SOC,
  volume =       "93",
  number =       "2",
  pages =        "330--339",
  month =        apr,
  year =         "2016",
  CODEN =        "ALNBAB",
  DOI =          "https://doi.org/10.1017/S0004972715001112",
  ISSN =         "0004-9727 (print), 1755-1633 (electronic)",
  ISSN-L =       "0004-9727",
  MRclass =      "60G50 (33C20)",
  MRnumber =     "3480942",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1702/;
                 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=10230818",
  abstract =     "We derive an explicit piecewise-polynomial closed form
                 for the probability density function of the distance
                 travelled by a uniform random walk in an
                 odd-dimensional space.",
  acknowledgement = ack-nhfb,
  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",
  unique-id =    "ISI:000372529100017",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2016:CLA
author: Jonathan M. Borwein and Neil J. Calkin and Scott B. Lindstrom and Andrew Mattingly
title: Continued Logarithms and Associated Continued Fractions
journal: j-EXP-MATH
volume: 26
number: 4
pages: 412--429
month: sep
monthnumber: 9
year: 2016
DOI: https://doi.org/10.1080/10586458.2016.1195307
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 11J70 (11Y65, 11A55)
MRnumber: 3480942
bibdate: Sat Oct 21 17:29:42 2017
bibtimestamp: 2017.10.21 17:29:42 ???
URL: http://docserver.carma.newcastle.edu.au/1687/
fjournal: Experimental Mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.tandfonline.com/loi/uexm20
onlinedate: 16 September 2016
rawauthor: Jonathan M. Borwein and Neil J. Calkin and Scott B. Lindstrom and Andrew Mattingly
rawtitle: Continued Logarithms and Associated Continued Fractions
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/expmath.bib

keywords:
continued fractions; continued logarithms; Gauss-Kuzmin distribution; Khintchine's constant; logarithmic Khintchine numbers

remark:
Presented as a colloquium at the University of Western Ontario, London, ON, Canada prior to publication.

entry:
@Article{Borwein:2016:CLA,
  author =       "Jonathan M. Borwein and Neil J. Calkin and Scott B.
                 Lindstrom and Andrew Mattingly",
  title =        "Continued Logarithms and Associated Continued
                 Fractions",
  journal =      j-EXP-MATH,
  volume =       "26",
  number =       "4",
  pages =        "412--429",
  month =        sep,
  year =         "2016",
  DOI =          "https://doi.org/10.1080/10586458.2016.1195307",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11J70 (11Y65, 11A55)",
  MRnumber =     "3480942",
  bibdate =      "Sat Oct 21 17:29:42 2017",
  bibsource =    "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/1687/",
  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",
  keywords =     "continued fractions; continued logarithms;
                 Gauss-Kuzmin distribution; Khintchine's constant;
                 logarithmic Khintchine numbers",
  onlinedate =   "16 September 2016",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Presented as a colloquium at the University of Western
                 Ontario, London, ON, Canada prior to publication.",
}


