# bibtab

bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2007:NAA
author: Jonathan M. Borwein and Warren B. Moors
title: Nonsmooth Analysis, Approximation Theory and Banach Space Theory
crossref: Pearl:2007:OPT
pages: 557--566
year: 2007
bibdate: Sat Aug 13 17:04:44 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 17:04:44 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Warren B. Moors
rawtitle: Nonsmooth Analysis, Approximation Theory and {Banach} Space Theory
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2007:NAA,
  author =       "Jonathan M. Borwein and Warren B. Moors",
  title =        "Nonsmooth Analysis, Approximation Theory and {Banach}
                 Space Theory",
  crossref =     "Pearl:2007:OPT",
  pages =        "557--566",
  year =         "2007",
  bibdate =      "Sat Aug 13 17:04:44 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2007:PCS
author: Jonathan M. Borwein
title: Proximality and Chebyshev sets
journal: j-OPTIM-LETT
volume: 1
number: 1
pages: 21--32
year: 2007
DOI: https://doi.org/10.1007/s11590-006-0014-5
ISSN: 1862-4472 (print), 1862-4480 (electronic) OR 18624472 (print), 18624480 (electronic)
ISSNL: 1862-4472 OR 18624472
MRclass: 41A50 (46A55 46N10 47J20 49J53)
MRnumber: 2357605
MRreviewer: John R. Giles
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/323/
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
rawtitle: Proximality and {Chebyshev} sets
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
This paper is a companion to a lecture given at the Prague Spring School in Analysis in April 2006. It highlights four distinct variational methods of proving that a finite dimensional Chebyshev set is convex and hopes to inspire renewed work on the open question of whether every Chebyshev set in Hilbert space is convex.

rawabstract:
This paper is a companion to a lecture given at the Prague Spring School in Analysis in April 2006. It highlights four distinct variational methods of proving that a finite dimensional Chebyshev set is convex and hopes to inspire renewed work on the open question of whether every Chebyshev set in Hilbert space is convex.

entry:
@Article{Borwein:2007:PCS,
  author =       "Jonathan M. Borwein",
  title =        "Proximality and {Chebyshev} sets",
  journal =      j-OPTIM-LETT,
  volume =       "1",
  number =       "1",
  pages =        "21--32",
  year =         "2007",
  DOI =          "https://doi.org/10.1007/s11590-006-0014-5",
  ISSN =         "1862-4472 (print), 1862-4480 (electronic)",
  ISSN-L =       "1862-4472",
  MRclass =      "41A50 (46A55 46N10 47J20 49J53)",
  MRnumber =     "2357605",
  MRreviewer =   "John R. Giles",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/323/",
  abstract =     "This paper is a companion to a lecture given at the
                 Prague Spring School in Analysis in April 2006. It
                 highlights four distinct variational methods of proving
                 that a finite dimensional Chebyshev set is convex and
                 hopes to inspire renewed work on the open question of
                 whether every Chebyshev set in Hilbert space is
                 convex.",
  acknowledgement = ack-nhfb,
  ajournal =     "Optim. Lett.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Optimization Letters",
  journal-URL =  "http://link.springer.com/journal/11590",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2007:PCS",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2007:PRB
author: J. M. Borwein and B. Salvy
title: A Proof of a Recursion for Bessel Moments
journal: ArXiv e-prints
pages: 21--32
month: jun
monthnumber: 6
year: 2007
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/2007arXiv0706.1409B; http://docserver.carma.newcastle.edu.au/346/
keywords: Computer Science - Symbolic Computation, Mathematics - Classical Analysis and ODEs
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and B. Salvy
rawtitle: A Proof of a Recursion for {Bessel} Moments
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Salvy, Bruno/0000-0002-4313-0679
abstract:
We provide a proof of a conjecture in (Bailey, Borwein, Borwein, Crandall 2007) on the existence and form of linear recursions for moments of powers of the Bessel function $ K_0 $.

rawabstract:
We provide a proof of a conjecture in (Bailey, Borwein, Borwein, Crandall 2007) on the existence and form of linear recursions for moments of powers of the Bessel function $ K_0 $.

entry:
@Article{Borwein:2007:PRB,
  author =       "J. M. Borwein and B. Salvy",
  title =        "A Proof of a Recursion for {Bessel} Moments",
  journal =      "ArXiv e-prints",
  month =        jun,
  year =         "2007",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2007arXiv0706.1409B;
                 http://docserver.carma.newcastle.edu.au/346/",
  abstract =     "We provide a proof of a conjecture in (Bailey,
                 Borwein, Borwein, Crandall 2007) on the existence and
                 form of linear recursions for moments of powers of the
                 Bessel function $ K_0 $.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "0706.1409",
  keywords =     "Computer Science - Symbolic Computation, Mathematics -
                 Classical Analysis and ODEs",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Salvy,
                 Bruno/0000-0002-4313-0679",
  primaryclass = "cs.SC",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:2007:REM
author: J. M. Borwein and Mason Macklem
title: Retro-enhancement of Mathematical Literature
pages: 21--32
month: mar
monthnumber: 3
year: 2007
bibdate: Tue Aug 16 10:05:13 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:05:13 ???
note: Preprint.
URL: http://docserver.carma.newcastle.edu.au/339/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and Mason Macklem
rawnote: Preprint.
rawtitle: Retro-enhancement of Mathematical Literature
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Unpublished{Borwein:2007:REM,
  author =       "J. M. Borwein and Mason Macklem",
  title =        "Retro-enhancement of Mathematical Literature",
  month =        mar,
  year =         "2007",
  bibdate =      "Tue Aug 16 10:05:13 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Preprint.",
  URL =          "http://docserver.carma.newcastle.edu.au/339/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2007:VPE
author: David Borwein and Jonathan Borwein
title: van der Pol Expansions of $L$-Series
journal: j-CAN-MATH-BULL
volume: 50
number: 1
pages: 11--23
month: mar
monthnumber: 3
year: 2007
CODEN: CMBUA3
DOI: https://doi.org/10.4153/CMB-2007-002-0
ISSN: 0008-4395 (print), 1496-4287 (electronic) OR 00084395 (print), 14964287 (electronic)
ISSNL: 0008-4395 OR 00084395
MRclass: 11M35 (11M41)
MRnumber: 2296621
MRreviewer: Saulius Zamarys
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/283/
fjournal: Canadian Mathematical Bulletin. Bulletin Canadien de Mathematiques
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://cms.math.ca/cmb/
rawauthor: David Borwein and Jonathan Borwein
rawtitle: {van der Pol} Expansions of {$L$}-Series
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
http://cms.math.ca/cmb/v50/; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib

abstract:
We provide concise series representations for various L-series integrals. Different techniques are needed below and above the abscissa of absolute convergence of the underlying L-series.

rawabstract:
We provide concise series representations for various L-series integrals. Different techniques are needed below and above the abscissa of absolute convergence of the underlying L-series.

entry:
@Article{Borwein:2007:VPE,
  author =       "David Borwein and Jonathan Borwein",
  title =        "{van der Pol} Expansions of {$L$}-Series",
  journal =      j-CAN-MATH-BULL,
  volume =       "50",
  number =       "1",
  pages =        "11--23",
  month =        mar,
  year =         "2007",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-2007-002-0",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  MRclass =      "11M35 (11M41)",
  MRnumber =     "2296621",
  MRreviewer =   "Saulius Zamarys",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://cms.math.ca/cmb/v50/;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/canmathbull.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/283/",
  abstract =     "We provide concise series representations for various
                 L-series integrals. Different techniques are needed
                 below and above the abscissa of absolute convergence of
                 the underlying L-series.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Canadian Mathematical Bulletin. Bulletin Canadien de
                 Math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cmb/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2007:VPE",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Bailey:2008:CAD
author: David H. Bailey and Jonathan M. Borwein
booktitle: Tapas in experimental mathematics
title: Computer-assisted discovery and proof
volume: 457
publisher: pub-AMS
address: pub-AMS:adr
pages: 21--52
year: 2008
DOI: https://doi.org/10.1090/conm/457/08901
MRclass: 11Y99 (68T15 68U35 68W30)
MRnumber: 2427663
MRreviewer: Jeffrey O. Shallit
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: Contemp. Math.
URL: http://docserver.carma.newcastle.edu.au/338/; http://www.ams.org/books/conm/457/8901
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawbooktitle: Tapas in experimental mathematics
rawtitle: Computer-assisted discovery and proof
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Bailey:2008:CAD,
  author =       "David H. Bailey and Jonathan M. Borwein",
  booktitle =    "Tapas in experimental mathematics",
  title =        "Computer-assisted discovery and proof",
  volume =       "457",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "21--52",
  year =         "2008",
  DOI =          "https://doi.org/10.1090/conm/457/08901",
  MRclass =      "11Y99 (68T15 68U35 68W30)",
  MRnumber =     "2427663",
  MRreviewer =   "Jeffrey O. Shallit",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Contemp. Math.",
  URL =          "http://docserver.carma.newcastle.edu.au/338/;
                 http://www.ams.org/books/conm/457/8901",
  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: inproceedings
filename: borwein-jonathan-m.bib
label: Bailey:2008:EEB
author: David H. Bailey and Jonathan M. Borwein
title: Effective Error Bounds for Euler--Maclaurin-Based Quadrature Schemes
crossref: IEEE:2008:HIS
pages: 1--7
year: 2008
DOI: https://doi.org/10.1109/HPCS.2006.22
ISBN: 0-7695-2582-2 OR 0769525822
ISBN13: 978-0-7695-2582-2 OR 9780769525822
ISSN: 1550-5243 (print), 2378-2099 (electronic) OR 15505243 (print), 23782099 (electronic)
ISSNL: 1550-5243 OR 15505243
bibdate: Sat Aug 13 17:20:17 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 17:20:17 ???
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Effective Error Bounds for {Euler--Maclaurin}-Based Quadrature Schemes
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
abstract:
We analyze the behavior of Euler--Maclaurin-based integration schemes with the intention of deriving accurate and economic estimations of the error. These schemes typically provide very high-precision results (hundreds or thousands of digits), in reasonable run time, even in cases where the integrand function has a blow-up singularity or infinite derivative at an endpoint. Heretofore, researchers using these schemes have relied mostly on ad hoc error estimation schemes to project the estimated error of the present iteration. In this paper, we seek to develop some more rigorous, yet highly usable schemes to estimate these errors.

rawabstract:
We analyze the behavior of Euler--Maclaurin-based integration schemes with the intention of deriving accurate and economic estimations of the error. These schemes typically provide very high-precision results (hundreds or thousands of digits), in reasonable run time, even in cases where the integrand function has a blow-up singularity or infinite derivative at an endpoint. Heretofore, researchers using these schemes have relied mostly on ad hoc error estimation schemes to project the estimated error of the present iteration. In this paper, we seek to develop some more rigorous, yet highly usable schemes to estimate these errors.

entry:
@InProceedings{Bailey:2008:EEB,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Effective Error Bounds for {Euler--Maclaurin}-Based
                 Quadrature Schemes",
  crossref =     "IEEE:2008:HIS",
  pages =        "1--7",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/HPCS.2006.22",
  ISBN =         "0-7695-2582-2",
  ISBN-13 =      "978-0-7695-2582-2",
  ISSN =         "1550-5243 (print), 2378-2099 (electronic)",
  ISSN-L =       "1550-5243",
  bibdate =      "Sat Aug 13 17:20:17 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  abstract =     "We analyze the behavior of Euler--Maclaurin-based
                 integration schemes with the intention of deriving
                 accurate and economic estimations of the error. These
                 schemes typically provide very high-precision results
                 (hundreds or thousands of digits), in reasonable run
                 time, even in cases where the integrand function has a
                 blow-up singularity or infinite derivative at an
                 endpoint. Heretofore, researchers using these schemes
                 have relied mostly on ad hoc error estimation schemes
                 to project the estimated error of the present
                 iteration. In this paper, we seek to develop some more
                 rigorous, yet highly usable schemes to estimate these
                 errors.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  pagecount =    "7",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2008:EIE
author: David H. Bailey and Jonathan M. Borwein and David Broadhurst and M. L. Glasser
title: Elliptic integral evaluations of Bessel moments and applications
journal: j-J-PHYS-A-MATH-THEOR
volume: 41
number: 20
pages: 205203
month: may
monthnumber: 5
year: 2008
CODEN: JPAMB5
DOI: https://doi.org/10.1088/1751-8113/41/20/205203
ISSN: 1751-8113 (print), 1751-8121 (electronic) OR 17518113 (print), 17518121 (electronic)
ISSNL: 1751-8113 OR 17518113
MRclass: 33C10 (33E05 33F05)
MRnumber: 2450513
MRreviewer: Subuhi Khan
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: 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
rawauthor: David H. Bailey and Jonathan M. Borwein and David Broadhurst and M. L. Glasser
rawtitle: Elliptic integral evaluations of {Bessel} moments and applications
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://adsabs.harvard.edu/abs/2008JPhA...41t5203B; http://arxiv.org/abs/0801.0891; http://iopscience.iop.org/article/10.1088/1751-8113/41/20/205203; http://stacks.iop.org/1751-8121/41/i=20/a=205203

abstract:
We record and substantially extend what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical physics. In particular, we develop formulae for integrals of products of six or fewer Bessel functions. In consequence, we are able to discover and prove closed forms for $ c_n, k coloneq int ^infty _0 t^k K^n_0 (t) d t $ with integers $ n = 1, 2, 3, 4 $ and $ k geq 0 $, obtaining new results for the even moments $ c_3, 2k $ and $ c_4, 2k $. We also derive new closed forms for the odd moments $ s_n, 2k + 1 coloneq int ^infty _0 t^2k + 1 I_0 (t) K^n - 1_0 (t) d t $ with $ n = 3, 4 $ and for $ t_n, 2k + 1 coloneq int ^infty _0 t^2k + 1 I^2_0 (t) K^n - 2_0 (t) d t $ with $ n = 5 $, relating the latter to Green functions on hexagonal, diamond and cubic lattices. We conjecture the values of $ s_5, 2k + 1 $, make substantial progress on the evaluation of $ c_5, 2k + 1 $, $ s_6, 2k + 1 $ and $ t_6, 2k + 1 $ and report more limited progress regarding $ c_5, 2k $, $ c_6, 2k + 1 $ and $ c_6, 2k $. In the process, we obtain eight conjectural evaluations, each of which has been checked to 1200 decimal places. One of these lies deep in four-dimensional quantum field theory and two are probably provable by delicate combinatorics. There remains a hard core of five conjectures whose proofs would be most instructive, to mathematicians and physicists alike.

rawabstract:
We record and substantially extend what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical physics. In particular, we develop formulae for integrals of products of six or fewer Bessel functions. In consequence, we are able to discover and prove closed forms for $ c_{n, k} \coloneq {\int }^\infty_0 t^k K^n_0 (t) d t $ with integers $ n = 1, 2, 3, 4 $ and $ k \geq 0 $, obtaining new results for the even moments $ c_{3, 2k} $ and $ c_{4, 2k} $. We also derive new closed forms for the odd moments $ s_{n, 2k + 1} \coloneq \int^\infty_0 t^{2k + 1} I_0 (t) K^{n - 1}_0 (t) \, d t $ with $ n = 3, 4 $ and for $ t_{n, 2k + 1} \coloneq \int^\infty_0 t^{2k + 1} I^2_0 (t) K^{n - 2}_0 (t) \, d t $ with $ n = 5 $, relating the latter to Green functions on hexagonal, diamond and cubic lattices. We conjecture the values of $ s_{5, 2k + 1} $, make substantial progress on the evaluation of $ c_{5, 2k + 1} $, $ s_{6, 2k + 1} $ and $ t_{6, 2k + 1} $ and report more limited progress regarding $ c_{5, 2k} $, $ c_{6, 2k + 1} $ and $ c_{6, 2k} $. In the process, we obtain eight conjectural evaluations, each of which has been checked to 1200 decimal places. One of these lies deep in four-dimensional quantum field theory and two are probably provable by delicate combinatorics. There remains a hard core of five conjectures whose proofs would be most instructive, to mathematicians and physicists alike.

entry:
@Article{Bailey:2008:EIE,
  author =       "David H. Bailey and Jonathan M. Borwein and David
                 Broadhurst and M. L. Glasser",
  title =        "Elliptic integral evaluations of {Bessel} moments and
                 applications",
  journal =      j-J-PHYS-A-MATH-THEOR,
  volume =       "41",
  number =       "20",
  pages =        "205203",
  month =        may,
  year =         "2008",
  CODEN =        "JPAMB5",
  DOI =          "https://doi.org/10.1088/1751-8113/41/20/205203",
  ISSN =         "1751-8113 (print), 1751-8121 (electronic)",
  ISSN-L =       "1751-8113",
  MRclass =      "33C10 (33E05 33F05)",
  MRnumber =     "2450513",
  MRreviewer =   "Subuhi Khan",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2008JPhA...41t5203B;
                 http://arxiv.org/abs/0801.0891;
                 http://iopscience.iop.org/article/10.1088/1751-8113/41/20/205203;
                 http://stacks.iop.org/1751-8121/41/i=20/a=205203",
  abstract =     "We record and substantially extend what is known about
                 the closed forms for various Bessel function moments
                 arising in quantum field theory, condensed matter
                 theory and other parts of mathematical physics. In
                 particular, we develop formulae for integrals of
                 products of six or fewer Bessel functions. In
                 consequence, we are able to discover and prove closed
                 forms for $ c_{n, k} \coloneq {\int }^\infty_0 t^k
                 K^n_0 (t) d t $ with integers $ n = 1, 2, 3, 4 $ and $
                 k \geq 0 $, obtaining new results for the even moments
                 $ c_{3, 2k} $ and $ c_{4, 2k} $. We also derive new
                 closed forms for the odd moments $ s_{n, 2k + 1}
                 \coloneq \int^\infty_0 t^{2k + 1} I_0 (t) K^{n - 1}_0
                 (t) \, d t $ with $ n = 3, 4 $ and for $ t_{n, 2k + 1}
                 \coloneq \int^\infty_0 t^{2k + 1} I^2_0 (t) K^{n - 2}_0
                 (t) \, d t $ with $ n = 5 $, relating the latter to
                 Green functions on hexagonal, diamond and cubic
                 lattices. We conjecture the values of $ s_{5, 2k + 1}
                 $, make substantial progress on the evaluation of $
                 c_{5, 2k + 1} $, $ s_{6, 2k + 1} $ and $ t_{6, 2k + 1}
                 $ and report more limited progress regarding $ c_{5,
                 2k} $, $ c_{6, 2k + 1} $ and $ c_{6, 2k} $. In the
                 process, we obtain eight conjectural evaluations, each
                 of which has been checked to 1200 decimal places. One
                 of these lies deep in four-dimensional quantum field
                 theory and two are probably provable by delicate
                 combinatorics. There remains a hard core of five
                 conjectures whose proofs would be most instructive, to
                 mathematicians and physicists alike.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eid =          "205203",
  eprint =       "0801.0891",
  fjournal =     "Journal of Physics. A. Mathematical and Theoretical",
  journal-URL =  "http://iopscience.iop.org/1751-8121",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  pagecount =    "46",
  primaryclass = "hep-th",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Bailey:2008:HPC
author: D. H. Bailey and J. M. Borwein
booktitle: Proceedings of XII Advanced Computing and Analysis Techniques in Physics Research
title: High-Precision Computation and Mathematical Physics
pages: 14
year: 2008
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/2008acat.confE..14B; http://docserver.carma.newcastle.edu.au/386/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. H. Bailey and J. M. Borwein
rawbooktitle: Proceedings of {XII} Advanced Computing and Analysis Techniques in Physics Research
rawtitle: High-Precision Computation and Mathematical Physics
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
abstract:
At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion effort. This paper presents a survey of recent applications of these tech niques and provides some analysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb $n$-body atomic systems, scattering amplitudes of quarks, gluons and bosons, nonlinear oscillator theory, Ising theory, quantum field theory and experimental mathematics. We conclude that high-precision arithmetic facilities are now an indispensable component of a modern large-scale scientific computing environment.

rawabstract:
At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion effort. This paper presents a survey of recent applications of these tech niques and provides some analysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb $n$-body atomic systems, scattering amplitudes of quarks, gluons and bosons, nonlinear oscillator theory, Ising theory, quantum field theory and experimental mathematics. We conclude that high-precision arithmetic facilities are now an indispensable component of a modern large-scale scientific computing environment.

entry:
@InProceedings{Bailey:2008:HPC,
  author =       "D. H. Bailey and J. M. Borwein",
  booktitle =    "Proceedings of {XII} Advanced Computing and Analysis
                 Techniques in Physics Research",
  title =        "High-Precision Computation and Mathematical Physics",
  publisher =    "????",
  address =      "????",
  pages =        "14",
  year =         "2008",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2008acat.confE..14B;
                 http://docserver.carma.newcastle.edu.au/386/",
  abstract =     "At the present time, IEEE 64-bit floating-point
                 arithmetic is sufficiently accurate for most scientific
                 applications. However, for a rapidly growing body of
                 important scientific computing applications, a higher
                 level of numeric precision is required. Such
                 calculations are facilitated by high-precision software
                 packages that include high-level language translation
                 modules to minimize the conversion effort. This paper
                 presents a survey of recent applications of these tech
                 niques and provides some analysis of their numerical
                 requirements. These applications include supernova
                 simulations, climate modeling, planetary orbit
                 calculations, Coulomb $n$-body atomic systems,
                 scattering amplitudes of quarks, gluons and bosons,
                 nonlinear oscillator theory, Ising theory, quantum
                 field theory and experimental mathematics. We conclude
                 that high-precision arithmetic facilities are now an
                 indispensable component of a modern large-scale
                 scientific computing environment.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:2008:HPH
author: David H. Bailey and Jonathan M. Borwein
title: Highly Parallel, High-Precision Numerical Integration
type: Report
institution: Lawrence Berkeley National Laboratory and Faculty of Computer Science, Dalhousie University
address: Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5, Canada
pages: 18
day: 1
month: apr
monthnumber: 4
year: 2008
bibdate: Fri Sep 30 08:30:39 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 08:30:39 ???
URL: http://www.davidhbailey.com/dhbpapers/quadparallel.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Highly Parallel, High-Precision Numerical Integration
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
abstract:
This paper describes schemes for rapidly computing numerical values of definite integrals to very high accuracy (hundreds to thousands of digits) on highly parallel computer systems. Such schemes are of interest not only in computational physics and computational chemistry, but also in experimental mathematics, where high-precision numerical values of definite integrals can be used to numerically discover new identities. This paper presents performance results for 1-D and 2-D integral test suites on highly parallel computer systems. Results are also given for certain problems that derive from mathematical physics. One of these results confirms a conjecture to 20,000 digit accuracy. The performance rate for this calculation is 690 Gflop/s on 1024 CPUs of a state-of-the-art parallel system. Other results, which range in precision from 120 to 500 digits, and for 1-D, 2-D, 3-D and 4-D integrals, derive from Ising theory. The largest of these calculations required 28 hours on 256 CPUs. We believe that these are the first instances of evaluations of nontrivial 3-D and 4-D integrals to multi-hundred-digit accuracy.

rawabstract:
This paper describes schemes for rapidly computing numerical values of definite integrals to very high accuracy (hundreds to thousands of digits) on highly parallel computer systems. Such schemes are of interest not only in computational physics and computational chemistry, but also in experimental mathematics, where high-precision numerical values of definite integrals can be used to numerically discover new identities. This paper presents performance results for 1-D and 2-D integral test suites on highly parallel computer systems. Results are also given for certain problems that derive from mathematical physics. One of these results confirms a conjecture to 20,000 digit accuracy. The performance rate for this calculation is 690 Gflop/s on 1024 CPUs of a state-of-the-art parallel system. Other results, which range in precision from 120 to 500 digits, and for 1-D, 2-D, 3-D and 4-D integrals, derive from Ising theory. The largest of these calculations required 28 hours on 256 CPUs. We believe that these are the first instances of evaluations of nontrivial 3-D and 4-D integrals to multi-hundred-digit accuracy.

entry:
@TechReport{Bailey:2008:HPH,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Highly Parallel, High-Precision Numerical
                 Integration",
  type =         "Report",
  institution =  "Lawrence Berkeley National Laboratory and Faculty of
                 Computer Science, Dalhousie University",
  address =      "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5,
                 Canada",
  pages =        "18",
  day =          "1",
  month =        apr,
  year =         "2008",
  bibdate =      "Fri Sep 30 08:30:39 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/quadparallel.pdf",
  abstract =     "This paper describes schemes for rapidly computing
                 numerical values of definite integrals to very high
                 accuracy (hundreds to thousands of digits) on highly
                 parallel computer systems. Such schemes are of interest
                 not only in computational physics and computational
                 chemistry, but also in experimental mathematics, where
                 high-precision numerical values of definite integrals
                 can be used to numerically discover new identities.
                 This paper presents performance results for 1-D and 2-D
                 integral test suites on highly parallel computer
                 systems. Results are also given for certain problems
                 that derive from mathematical physics. One of these
                 results confirms a conjecture to 20,000 digit accuracy.
                 The performance rate for this calculation is 690
                 Gflop/s on 1024 CPUs of a state-of-the-art parallel
                 system. Other results, which range in precision from
                 120 to 500 digits, and for 1-D, 2-D, 3-D and 4-D
                 integrals, derive from Ising theory. The largest of
                 these calculations required 28 hours on 256 CPUs. We
                 believe that these are the first instances of
                 evaluations of nontrivial 3-D and 4-D integrals to
                 multi-hundred-digit accuracy.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Bailey:2008:HPN
author: D. H. Bailey and J. M. Borwein
booktitle: MICA conference May 2008
title: High-Precision Numerical Integration: Progress and Challenges
pages: 1--19
year: 2008
bibdate: Sat Aug 13 16:39:19 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 16:39:19 ???
URL: http://docserver.carma.newcastle.edu.au/1444/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. H. Bailey and J. M. Borwein
rawbooktitle: MICA conference May 2008
rawtitle: High-Precision Numerical Integration: Progress and Challenges
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
abstract:
One of the most fruitful advances in the field of experimental mathematics has been the development of practical methods for very high-precision numerical integration, a quest initiated by Keith Geddes and other researchers in the 1980s and 1990s. These techniques, when coupled with equally powerful integer relation detection methods, have resulted in the analytic evaluation of many integrals that previously were beyond the realm of symbolic techniques. This paper presents a survey of the current state-of-the-art in this area (including results by the present authors and others), mentions some new results, and then sketches what challenges lie ahead.

rawabstract:
One of the most fruitful advances in the field of experimental mathematics has been the development of practical methods for very high-precision numerical integration, a quest initiated by Keith Geddes and other researchers in the 1980s and 1990s. These techniques, when coupled with equally powerful integer relation detection methods, have resulted in the analytic evaluation of many integrals that previously were beyond the realm of symbolic techniques. This paper presents a survey of the current state-of-the-art in this area (including results by the present authors and others), mentions some new results, and then sketches what challenges lie ahead.

entry:
@InCollection{Bailey:2008:HPN,
  author =       "D. H. Bailey and J. M. Borwein",
  booktitle =    "MICA conference May 2008",
  title =        "High-Precision Numerical Integration: Progress and
                 Challenges",
  publisher =    "????",
  address =      "????",
  pages =        "1--19",
  year =         "2008",
  bibdate =      "Sat Aug 13 16:39:19 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1444/",
  abstract =     "One of the most fruitful advances in the field of
                 experimental mathematics has been the development of
                 practical methods for very high-precision numerical
                 integration, a quest initiated by Keith Geddes and
                 other researchers in the 1980s and 1990s. These
                 techniques, when coupled with equally powerful integer
                 relation detection methods, have resulted in the
                 analytic evaluation of many integrals that previously
                 were beyond the realm of symbolic techniques. This
                 paper presents a survey of the current state-of-the-art
                 in this area (including results by the present authors
                 and others), mentions some new results, and then
                 sketches what challenges lie ahead.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:2008:PSP
author: David H. Bailey and Jonathan M. Borwein
title: Proposed SIAM Problem
type: Report
institution: Lawrence Berkeley National Laboratory and Faculty of Computer Science, Dalhousie University
address: Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5, Canada
pages: 1--2
day: 12
month: aug
monthnumber: 8
year: 2008
bibdate: Fri Sep 30 08:36:07 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 08:36:07 ???
URL: http://www.davidhbailey.com/dhbpapers/siam-bessel.pdf
keywords: Bessel moment integrals
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Proposed {SIAM} Problem
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
abstract:
[From the introduction:] A recent paper by the present authors, together with mathematical physicists David Broadhurst and M. Larry Glasser, explored Bessel moment integrals, namely definite integrals of the general form $ int _0^infty t^m f^n(t) d t $, where the function $ f(t) $ is one of the classical Bessel functions [2]. In that paper, numerous previously unknown analytic evaluations were obtained, using a combination of analytic methods together with some fairly high-powered numerical computations, often performed on highly parallel computers.

rawabstract:
[From the introduction:] A recent paper by the present authors, together with mathematical physicists David Broadhurst and M. Larry Glasser, explored Bessel moment integrals, namely definite integrals of the general form $ \int_0^\infty t^m f^n(t) \, d t $, where the function $ f(t) $ is one of the classical Bessel functions [2]. In that paper, numerous previously unknown analytic evaluations were obtained, using a combination of analytic methods together with some fairly high-powered numerical computations, often performed on highly parallel computers.

entry:
@TechReport{Bailey:2008:PSP,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Proposed {SIAM} Problem",
  type =         "Report",
  institution =  "Lawrence Berkeley National Laboratory and Faculty of
                 Computer Science, Dalhousie University",
  address =      "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5,
                 Canada",
  pages =        "1--2",
  day =          "12",
  month =        aug,
  year =         "2008",
  bibdate =      "Fri Sep 30 08:36:07 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/siam-bessel.pdf",
  abstract =     "[From the introduction:] A recent paper by the present
                 authors, together with mathematical physicists David
                 Broadhurst and M. Larry Glasser, explored Bessel moment
                 integrals, namely definite integrals of the general
                 form $ \int_0^\infty t^m f^n(t) \, d t $, where the
                 function $ f(t) $ is one of the classical Bessel
                 functions [2]. In that paper, numerous previously
                 unknown analytic evaluations were obtained, using a
                 combination of analytic methods together with some
                 fairly high-powered numerical computations, often
                 performed on highly parallel computers.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Bessel moment integrals",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Baillie:2008:SSS
author: Robert Baillie and David Borwein and Jonathan M. Borwein
title: Surprising sinc sums and integrals
journal: j-AMER-MATH-MONTHLY
volume: 115
number: 10
pages: 888--901
month: dec
monthnumber: 12
year: 2008
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 33B10 (26D05 40A25 42A05)
MRnumber: 2468551
MRreviewer: Valery V. Karachik
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/332/; http://www.jstor.org/stable/27642636
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.jstor.org/journals/00029890.html
rawauthor: Robert Baillie and David Borwein and Jonathan M. Borwein
rawtitle: Surprising sinc sums and integrals
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Baillie:2008:SSS,
  author =       "Robert Baillie and David Borwein and Jonathan M.
                 Borwein",
  title =        "Surprising sinc sums and integrals",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "115",
  number =       "10",
  pages =        "888--901",
  month =        dec,
  year =         "2008",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "33B10 (26D05 40A25 42A05)",
  MRnumber =     "2468551",
  MRreviewer =   "Valery V. Karachik",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/332/;
                 http://www.jstor.org/stable/27642636",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:2008:BST
author: J. M. Borwein and A. C. Eberhard
title: Banach spaces of type (NI) and monotone operators on non-reflexive spaces
pages: 888--901
month: jun
monthnumber: 6
year: 2008
bibdate: Tue Aug 16 10:02:34 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:02:34 ???
note: Preprint.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and A. C. Eberhard
rawnote: Preprint.
rawtitle: {Banach} spaces of type ({NI}) and monotone operators on non-reflexive spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Eberhard, Andrew/0000-0003-2977-3456
entry:
@Unpublished{Borwein:2008:BST,
  author =       "J. M. Borwein and A. C. Eberhard",
  title =        "{Banach} spaces of type ({NI}) and monotone operators
                 on non-reflexive spaces",
  month =        jun,
  year =         "2008",
  bibdate =      "Tue Aug 16 10:02:34 2016",
  bibsource =    "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; Eberhard,
                 Andrew/0000-0003-2977-3456",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2008:CCC
author: J. Borwein and V. Jungic and D. Langstroth and M. Macklem and S. Wilson
title: Coast-to-Coast (C2C) Seminar: Background, History, and Practice
crossref: Borwein:2008:CMD
chapter: 9
pages: 127--140
year: 2008
DOI: https://doi.org/10.1201/b10587-12
bibdate: Sat Aug 13 16:51:32 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 16:51:32 ???
URL: http://www.crcnetbase.com/doi/pdfplus/10.1201/b10587-12
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. Borwein and V. Jungi{\'c} and D. Langstroth and M. Macklem and S. Wilson
rawtitle: Coast-to-Coast ({C2C}) Seminar: Background, History, and Practice
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2008:CCC,
  author =       "J. Borwein and V. Jungi{\'c} and D. Langstroth and M.
                 Macklem and S. Wilson",
  title =        "Coast-to-Coast ({C2C}) Seminar: Background, History,
                 and Practice",
  crossref =     "Borwein:2008:CMD",
  chapter =      "9",
  pages =        "127--140",
  year =         "2008",
  DOI =          "https://doi.org/10.1201/b10587-12",
  bibdate =      "Sat Aug 13 16:51:32 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.crcnetbase.com/doi/pdfplus/10.1201/b10587-12",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2008:DRT
author: Jonathan M. Borwein and D. Russell Luke
title: Dynamics of a Ramanujan-type continued fraction with cyclic coefficients
journal: j-RAMANUJAN-J
volume: 16
number: 3
pages: 285--304
year: 2008
CODEN: RAJOF9
DOI: https://doi.org/10.1007/s11139-007-9096-7
ISSN: 1382-4090 (print), 1572-9303 (electronic) OR 13824090 (print), 15729303 (electronic)
ISSNL: 1382-4090 OR 13824090
MRclass: 40A15 (11J70)
MRnumber: 2429902
MRreviewer: Haakon S. Waadeland
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/1480/
fjournal: The Ramanujan Journal
remark: CoLab Preprint 261.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11139
rawauthor: Jonathan M. Borwein and D. Russell Luke
rawtitle: Dynamics of a {Ramanujan}-type continued fraction with cyclic coefficients
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We study several generalizations of the AGM continued fraction of Ramanujan inspired by a series of recent articles in which the validity of the AGM relation and the domain of convergence of the continued fraction were determined for certain complex parameters (Borwein et al., Exp. Math. 13, 275-286, 2004, Ramanujan J., in press, 2004; Borwein and Crandall, Exp. Math. 12, 287-296, 2004). A study of the AGM continued fraction is equivalent to an analysis of the convergence of certain difference equations and the stability of dynamical systems. Using the matrix analytical tools developed in 2004, we determine the convergence properties of deterministic difference equations and so divergence of their corresponding continued fractions.

rawabstract:
We study several generalizations of the AGM continued fraction of Ramanujan inspired by a series of recent articles in which the validity of the AGM relation and the domain of convergence of the continued fraction were determined for certain complex parameters (Borwein et al., Exp. Math. 13, 275-286, 2004, Ramanujan J., in press, 2004; Borwein and Crandall, Exp. Math. 12, 287-296, 2004). A study of the AGM continued fraction is equivalent to an analysis of the convergence of certain difference equations and the stability of dynamical systems. Using the matrix analytical tools developed in 2004, we determine the convergence properties of deterministic difference equations and so divergence of their corresponding continued fractions.

entry:
@Article{Borwein:2008:DRT,
  author =       "Jonathan M. Borwein and D. Russell Luke",
  title =        "Dynamics of a {Ramanujan}-type continued fraction with
                 cyclic coefficients",
  journal =      j-RAMANUJAN-J,
  volume =       "16",
  number =       "3",
  pages =        "285--304",
  year =         "2008",
  CODEN =        "RAJOF9",
  DOI =          "https://doi.org/10.1007/s11139-007-9096-7",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  MRclass =      "40A15 (11J70)",
  MRnumber =     "2429902",
  MRreviewer =   "Haakon S. Waadeland",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1480/",
  abstract =     "We study several generalizations of the AGM continued
                 fraction of Ramanujan inspired by a series of recent
                 articles in which the validity of the AGM relation and
                 the domain of convergence of the continued fraction
                 were determined for certain complex parameters (Borwein
                 et al., Exp. Math. 13, 275-286, 2004, Ramanujan J., in
                 press, 2004; Borwein and Crandall, Exp. Math. 12,
                 287-296, 2004). A study of the AGM continued fraction
                 is equivalent to an analysis of the convergence of
                 certain difference equations and the stability of
                 dynamical systems. Using the matrix analytical tools
                 developed in 2004, we determine the convergence
                 properties of deterministic difference equations and so
                 divergence of their corresponding continued
                 fractions.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The {Ramanujan} Journal",
  journal-URL =  "http://link.springer.com/journal/11139",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CoLab Preprint 261.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2008:DRT",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2008:EBF
author: David Borwein and Jonathan M. Borwein and O-Yeat Chan
title: The evaluation of Bessel functions via exp--arc integrals
journal: j-J-MATH-ANAL-APPL
volume: 341
number: 1
pages: 478--500
month: may
monthnumber: 5
year: 2008
CODEN: JMANAK
DOI: https://doi.org/10.1016/j.jmaa.2007.10.003
ISSN: 0022-247X (print), 1096-0813 (electronic) OR 0022247X (print), 10960813 (electronic)
ISSNL: 0022-247X OR 0022247X
MRclass: 33C10 (33F05 65D20)
MRnumber: 2394100
MRreviewer: Richard B. Paris
bibdate: Thu Aug 11 10:27:38 2016
bibtimestamp: 2016.08.11 10:27:38 ???
fjournal: Journal of Mathematical Analysis and Applications
keywords: Bessel function; Exponential-hyperbolic expansions; Uniform series expansion
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 O-Yeat Chan
rawtitle: The evaluation of {Bessel} functions via exp--arc integrals
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/elefunt.bib

URL:
http://adsabs.harvard.edu/abs/2008JMAA..341..478B; http://docserver.carma.newcastle.edu.au/1231/; http://www.sciencedirect.com/science/article/pii/S0022247X07012346

abstract:
A standard method for computing values of Bessel functions has been to use the well-known ascending series for small argument, and to use an asymptotic series for large argument; with the choice of the series changing at some appropriate argument magnitude, depending on the number of digits required. In a recent paper, D. Borwein, J. Borwein, and R. Crandall [D. Borwein, J. M. Borwein, R. Crandall, Effective Laguerre asymptotics, preprint at http://locutus.cs.dal.ca:8088/archive/00000334/] derived a series for an ``exp-arc'' integral which gave rise to an absolutely convergent series for the J and I Bessel functions with integral order. Such series can be rapidly evaluated via recursion and elementary operations, and provide a viable alternative to the conventional ascending-asymptotic switching. In the present work, we extend the method to deal with Bessel functions of general (non-integral) order, as well as to deal with the Y and K Bessel functions.

rawabstract:
A standard method for computing values of Bessel functions has been to use the well-known ascending series for small argument, and to use an asymptotic series for large argument; with the choice of the series changing at some appropriate argument magnitude, depending on the number of digits required. In a recent paper, D. Borwein, J. Borwein, and R. Crandall [D. Borwein, J. M. Borwein, R. Crandall, Effective Laguerre asymptotics, preprint at http://locutus.cs.dal.ca:8088/archive/00000334/] derived a series for an ``exp-arc'' integral which gave rise to an absolutely convergent series for the J and I Bessel functions with integral order. Such series can be rapidly evaluated via recursion and elementary operations, and provide a viable alternative to the conventional ascending-asymptotic switching. In the present work, we extend the method to deal with Bessel functions of general (non-integral) order, as well as to deal with the Y and K Bessel functions.

entry:
@Article{Borwein:2008:EBF,
  author =       "David Borwein and Jonathan M. Borwein and O-Yeat
                 Chan",
  title =        "The evaluation of {Bessel} functions via exp--arc
                 integrals",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "341",
  number =       "1",
  pages =        "478--500",
  month =        may,
  year =         "2008",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/j.jmaa.2007.10.003",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "33C10 (33F05 65D20)",
  MRnumber =     "2394100",
  MRreviewer =   "Richard B. Paris",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://adsabs.harvard.edu/abs/2008JMAA..341..478B;
                 http://docserver.carma.newcastle.edu.au/1231/;
                 http://www.sciencedirect.com/science/article/pii/S0022247X07012346",
  abstract =     "A standard method for computing values of Bessel
                 functions has been to use the well-known ascending
                 series for small argument, and to use an asymptotic
                 series for large argument; with the choice of the
                 series changing at some appropriate argument magnitude,
                 depending on the number of digits required. In a recent
                 paper, D. Borwein, J. Borwein, and R. Crandall [D.
                 Borwein, J. M. Borwein, R. Crandall, Effective Laguerre
                 asymptotics, preprint at
                 http://locutus.cs.dal.ca:8088/archive/00000334/]
                 derived a series for an ``exp-arc'' integral which gave
                 rise to an absolutely convergent series for the J and I
                 Bessel functions with integral order. Such series can
                 be rapidly evaluated via recursion and elementary
                 operations, and provide a viable alternative to the
                 conventional ascending-asymptotic switching. In the
                 present work, we extend the method to deal with Bessel
                 functions of general (non-integral) order, as well as
                 to deal with the Y and K Bessel functions.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "Bessel function; Exponential-hyperbolic expansions;
                 Uniform series expansion",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2008:ECE
author: J. M. Borwein and I. J. Zucker and J. Boersma
title: The evaluation of character Euler double sums
journal: j-RAMANUJAN-J
volume: 15
number: 3
pages: 377--405
year: 2008
CODEN: RAJOF9
DOI: https://doi.org/10.1007/s11139-007-9083-z
ISSN: 1382-4090 (print), 1572-9303 (electronic) OR 13824090 (print), 15729303 (electronic)
ISSNL: 1382-4090 OR 13824090
MRclass: 11M41 (11M06)
MRnumber: 2390277
MRreviewer: Stamatis Koumandos
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: The Ramanujan Journal
remark: CoLab Preprint 260.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11139
rawauthor: J. M. Borwein and I. J. Zucker and J. Boersma
rawtitle: The evaluation of character {Euler} double sums
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/255/; http://link.springer.com/article/10.1007/s11139-007-9083-z

abstract:
Euler considered sums of the form [GRAPHICS] Here natural generalizations of these sums namely [complex equation] are investigated, where chi(p) and chi(q) are characters, and s and t are positive integers. The cases when p and q are either 1, 2a, 2b or -4 are examined in detail, and closed-form expressions are found for t = 1 and general s in terms of the Riemann zeta function and the Catalan zeta function-the Dirichlet series L(-4)(s) = 1(-s) - 3(-s) + 5(-s) - 7(-s) + center dot center dot center dot. Some results for arbitrary p and q are obtained as well.

rawabstract:
Euler considered sums of the form [GRAPHICS] Here natural generalizations of these sums namely [complex equation] are investigated, where chi(p) and chi(q) are characters, and s and t are positive integers. The cases when p and q are either 1, 2a, 2b or -4 are examined in detail, and closed-form expressions are found for t = 1 and general s in terms of the Riemann zeta function and the Catalan zeta function-the Dirichlet series L(-4)(s) = 1(-s) - 3(-s) + 5(-s) - 7(-s) + center dot center dot center dot. Some results for arbitrary p and q are obtained as well.

entry:
@Article{Borwein:2008:ECE,
  author =       "J. M. Borwein and I. J. Zucker and J. Boersma",
  title =        "The evaluation of character {Euler} double sums",
  journal =      j-RAMANUJAN-J,
  volume =       "15",
  number =       "3",
  pages =        "377--405",
  year =         "2008",
  CODEN =        "RAJOF9",
  DOI =          "https://doi.org/10.1007/s11139-007-9083-z",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  MRclass =      "11M41 (11M06)",
  MRnumber =     "2390277",
  MRreviewer =   "Stamatis Koumandos",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/255/;
                 http://link.springer.com/article/10.1007/s11139-007-9083-z",
  abstract =     "Euler considered sums of the form [GRAPHICS] Here
                 natural generalizations of these sums namely [complex
                 equation] are investigated, where chi(p) and chi(q) are
                 characters, and s and t are positive integers. The
                 cases when p and q are either 1, 2a, 2b or -4 are
                 examined in detail, and closed-form expressions are
                 found for t = 1 and general s in terms of the Riemann
                 zeta function and the Catalan zeta function-the
                 Dirichlet series L(-4)(s) = 1(-s) - 3(-s) + 5(-s) -
                 7(-s) + center dot center dot center dot. Some results
                 for arbitrary p and q are obtained as well.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The {Ramanujan} Journal",
  journal-URL =  "http://link.springer.com/journal/11139",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CoLab Preprint 260.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2008:ECE",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2008:ELA
author: David Borwein and Jonathan M. Borwein and Richard E. Crandall
title: Effective Laguerre asymptotics
journal: j-SIAM-J-NUMER-ANAL
volume: 46
number: 6
pages: 3285--3312
year: 2008
CODEN: SJNAAM
DOI: https://doi.org/10.1137/07068031X
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
MRclass: 33C65 (30E20 34E05)
MRnumber: 2448665
MRreviewer: Yu-Qiu Zhao
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/334/
fjournal: SIAM Journal on Numerical Analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://epubs.siam.org/sinum
rawauthor: David Borwein and Jonathan M. Borwein and Richard E. Crandall
rawtitle: Effective {Laguerre} asymptotics
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/elefunt.bib

abstract:
It is known that the generalized Laguerre polynomials can enjoy subexponential growth for large primary index. In particular, for certain fixed parameter pairs (a, z) one has the large-n asymptotic behavior L-n((-a)) (-z) similar to C(a, z)(n)(-a)/2-1/ (4)e(2) root nz. We introduce a computationally motivated contour integral that allows efficient numerical Laguerre evaluations yet also leads to the complete asymptotic series over the full parameter domain of subexponential behavior. We present a fast algorithm for symbolic generation of the rather formidable expansion coefficients. Along the way we address the difficult problem of establishing effective (i. e., rigorous and explicit) error bounds on the general expansion. A primary tool for these developments is an ``exp-arc'' method giving a natural bridge between converging series and effective asymptotics.

rawabstract:
It is known that the generalized Laguerre polynomials can enjoy subexponential growth for large primary index. In particular, for certain fixed parameter pairs (a, z) one has the large-n asymptotic behavior L-n((-a)) (-z) similar to C(a, z)(n)(-a)/2-1/ (4)e(2) root nz. We introduce a computationally motivated contour integral that allows efficient numerical Laguerre evaluations yet also leads to the complete asymptotic series over the full parameter domain of subexponential behavior. We present a fast algorithm for symbolic generation of the rather formidable expansion coefficients. Along the way we address the difficult problem of establishing effective (i. e., rigorous and explicit) error bounds on the general expansion. A primary tool for these developments is an ``exp-arc'' method giving a natural bridge between converging series and effective asymptotics.

entry:
@Article{Borwein:2008:ELA,
  author =       "David Borwein and Jonathan M. Borwein and Richard E.
                 Crandall",
  title =        "Effective {Laguerre} asymptotics",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "46",
  number =       "6",
  pages =        "3285--3312",
  year =         "2008",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/07068031X",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "33C65 (30E20 34E05)",
  MRnumber =     "2448665",
  MRreviewer =   "Yu-Qiu Zhao",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/334/",
  abstract =     "It is known that the generalized Laguerre polynomials
                 can enjoy subexponential growth for large primary
                 index. In particular, for certain fixed parameter pairs
                 (a, z) one has the large-n asymptotic behavior
                 L-n((-a)) (-z) similar to C(a, z)(n)(-a)/2-1/ (4)e(2)
                 root nz. We introduce a computationally motivated
                 contour integral that allows efficient numerical
                 Laguerre evaluations yet also leads to the complete
                 asymptotic series over the full parameter domain of
                 subexponential behavior. We present a fast algorithm
                 for symbolic generation of the rather formidable
                 expansion coefficients. Along the way we address the
                 difficult problem of establishing effective (i. e.,
                 rigorous and explicit) error bounds on the general
                 expansion. A primary tool for these developments is an
                 ``exp-arc'' method giving a natural bridge between
                 converging series and effective asymptotics.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2008:ELA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2008:HIW
author: Jonathan M. Borwein
title: Hilbert's Inequality and Witten's Zeta-Function
journal: j-AMER-MATH-MONTHLY
volume: 115
number: 2
pages: 125--137
month: feb
monthnumber: 2
year: 2008
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jan 30 12:00:30 MST 2012
bibtimestamp: 2012.01.30 12:00:30 MST
URL: http://www.jstor.org/stable/27642418
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Jonathan M. Borwein
rawtitle: {Hilbert}'s Inequality and {Witten}'s Zeta-Function
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
http://www.jstor.org/journals/00029890.html; http://www.jstor.org/stable/i27642413; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib

entry:
@Article{Borwein:2008:HIW,
  author =       "Jonathan M. Borwein",
  title =        "{Hilbert}'s Inequality and {Witten}'s Zeta-Function",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "115",
  number =       "2",
  pages =        "125--137",
  month =        feb,
  year =         "2008",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jan 30 12:00:30 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/i27642413;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib",
  URL =          "http://www.jstor.org/stable/27642418",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2008:IEM
author: Jonathan Borwein
title: Implications of experimental mathematics for the philosophy of mathematics
crossref: Gold:2008:POD
chapter: 2
pages: 33--59
year: 2008
MRclass: 00A30 (03A05)
MRnumber: 2452073
bibdate: Sat Aug 13 16:37:59 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 16:37:59 ???
series: MAA Spectrum
URL: http://docserver.carma.newcastle.edu.au/280/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein
rawtitle: Implications of experimental mathematics for the philosophy of mathematics
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2008:IEM,
  author =       "Jonathan Borwein",
  title =        "Implications of experimental mathematics for the
                 philosophy of mathematics",
  crossref =     "Gold:2008:POD",
  chapter =      "2",
  pages =        "33--59",
  year =         "2008",
  MRclass =      "00A30 (03A05)",
  MRnumber =     "2452073",
  bibdate =      "Sat Aug 13 16:37:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "MAA Spectrum",
  URL =          "http://docserver.carma.newcastle.edu.au/280/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  xxpages =      "33--59",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borwein:2008:ME
author: Jonathan Borwein and David Bailey
title: Mathematics by Experiment
publisher: pub-A-K-PETERS
address: pub-A-K-PETERS:adr
edition: Second
pages: xii + 377
year: 2008
DOI: https://doi.org/10.1201/b10704
ISBN: 1-56881-442-9, 1-4398-6536-1 (PDF e-book) OR 1568814429, 1439865361 (PDF ebook)
ISBN13: 978-1-56881-442-1, 978-1-4398-6536-1 (PDF e-book) OR 9781568814421, 9781439865361 (PDF ebook)
LCCN: QA76.95 .B67 2008
MRclass: 00A35 (37-04)
MRnumber: 2473161
MRreviewer: Michael Otte
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: Plausible reasoning in the 21st Century.
URL: http://docserver.carma.newcastle.edu.au/272/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein and David Bailey
rawnote: Plausible reasoning in the 21st Century.
rawtitle: Mathematics by Experiment
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
TOC:
Front matter / i 1. What is experimental mathematics? / 1 2. Experimental mathematics in action / 47 3. Pi and its friends / 103 4. Normality of numbers / 143 5. The power of constructive proofs / 175 6. Numerical techniques / 215 7. Recent experiences / 243 Bibliography / 349

rawTOC:
Front matter / i \\ 1. What is experimental mathematics? / 1 \\ 2. Experimental mathematics in action / 47 \\ 3. Pi and its friends / 103 \\ 4. Normality of numbers / 143 \\ 5. The power of constructive proofs / 175 \\ 6. Numerical techniques / 215 \\ 7. Recent experiences / 243 \\ Bibliography / 349

entry:
@Book{Borwein:2008:ME,
  author =       "Jonathan Borwein and David Bailey",
  title =        "Mathematics by Experiment",
  publisher =    pub-A-K-PETERS,
  address =      pub-A-K-PETERS:adr,
  edition =      "Second",
  pages =        "xii + 377",
  year =         "2008",
  DOI =          "https://doi.org/10.1201/b10704",
  ISBN =         "1-56881-442-9, 1-4398-6536-1 (PDF e-book)",
  ISBN-13 =      "978-1-56881-442-1, 978-1-4398-6536-1 (PDF e-book)",
  LCCN =         "QA76.95 .B67 2008",
  MRclass =      "00A35 (37-04)",
  MRnumber =     "2473161",
  MRreviewer =   "Michael Otte",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Plausible reasoning in the 21st Century.",
  URL =          "http://docserver.carma.newcastle.edu.au/272/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  tableofcontents = "Front matter / i \\
                 1. What is experimental mathematics? / 1 \\
                 2. Experimental mathematics in action / 47 \\
                 3. Pi and its friends / 103 \\
                 4. Normality of numbers / 143 \\
                 5. The power of constructive proofs / 175 \\
                 6. Numerical techniques / 215 \\
                 7. Recent experiences / 243 \\
                 Bibliography / 349",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2008:PRB
author: Jonathan M. Borwein and Bruno Salvy
title: A Proof of a Recurrence for Bessel Moments
journal: j-EXP-MATH
volume: 17
number: 2
pages: 223--230
year: 2008
DOI: https://doi.org/10.1080/10586458.2008.10129032
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 68W30 (33C10 33E30 33F10)
MRnumber: 2433887
MRreviewer: Carsten Schneider
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/346/; http://projecteuclid.org/euclid.em/1227118973
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 Bruno Salvy
rawtitle: A Proof of a Recurrence for {Bessel} Moments
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Salvy, Bruno/0000-0002-4313-0679
bibsource:
http://projecteuclid.org/euclid.em; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/expmath.bib; http://www.tandfonline.com/toc/uexm20/17/2

abstract:
We provide a proof of a conjecture in [Bailey et al. 07a] on the existence and form of linear recurrences for moments of powers of the Bessel function K-0.

rawabstract:
We provide a proof of a conjecture in [Bailey et al. 07a] on the existence and form of linear recurrences for moments of powers of the Bessel function K-0.

entry:
@Article{Borwein:2008:PRB,
  author =       "Jonathan M. Borwein and Bruno Salvy",
  title =        "A Proof of a Recurrence for {Bessel} Moments",
  journal =      j-EXP-MATH,
  volume =       "17",
  number =       "2",
  pages =        "223--230",
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2008.10129032",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "68W30 (33C10 33E30 33F10)",
  MRnumber =     "2433887",
  MRreviewer =   "Carsten Schneider",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib;
                 http://www.tandfonline.com/toc/uexm20/17/2",
  URL =          "http://docserver.carma.newcastle.edu.au/346/;
                 http://projecteuclid.org/euclid.em/1227118973",
  abstract =     "We provide a proof of a conjecture in [Bailey et al.
                 07a] on the existence and form of linear recurrences
                 for moments of powers of the Bessel function K-0.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Salvy,
                 Bruno/0000-0002-4313-0679",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2008:PRB",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2008:VPG
author: J. M. Borwein
booktitle: Mathematics and Culture, La matematica: Problemi e teoremi
title: La vita di pi greco. (Italian) [The life of Greek pi]
publisher: Guilio Einaudi Editori
address: Turino, Italy
pages: ??--??
year: 2008
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://www.carma.newcastle.edu.au/~jb616/pi-2010.pdf
language: Italian
remark: CoLab Preprint 265
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein
rawbooktitle: Mathematics and Culture, La matematica: Problemi e teoremi
rawtitle: La vita di pi greco. ({Italian}) [{The} life of {Greek} pi]
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InProceedings{Borwein:2008:VPG,
  author =       "J. M. Borwein",
  editor =       "????",
  booktitle =    "Mathematics and Culture, La matematica: Problemi e
                 teoremi",
  title =        "La vita di pi greco. ({Italian}) [{The} life of
                 {Greek} pi]",
  publisher =    "Guilio Einaudi Editori",
  address =      "Turino, Italy",
  pages =        "??--??",
  year =         "2008",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "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/~jb616/pi-2010.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  language =     "Italian",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CoLab Preprint 265",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2008:WEM
author: J. M. Borwein and D. H. Bailey
editor: Giovanni Treccani
booktitle: Enciclopedia della Scienza e della Tecnica
title: What is Experimental Mathematics
address: Roma, Italia
pages: ??--??
year: 2008
bibdate: Sat Aug 13 16:32:55 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 16:32:55 ???
note: Reprint of cite [Chapter 1]Borwein:2004:MEP.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and D. H. Bailey
rawbooktitle: Enciclopedia della Scienza e della Tecnica
raweditor: Giovanni Treccani
rawnote: Reprint of \cite[Chapter 1]{Borwein:2004:MEP}.
rawtitle: What is Experimental Mathematics
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2008:WEM,
  author =       "J. M. Borwein and D. H. Bailey",
  editor =       "Giovanni Treccani",
  booktitle =    "Enciclopedia della Scienza e della Tecnica",
  title =        "What is Experimental Mathematics",
  publisher =    "????",
  address =      "Roma, Italia",
  pages =        "??--??",
  year =         "2008",
  bibdate =      "Sat Aug 13 16:32:55 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Reprint of \cite[Chapter 1]{Borwein:2004:MEP}.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  xxnote =       "Check: is Treccani the editor or publisher?? I cannot
                 find this book in library catalogs or large
                 booksellers.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Eberhard:2008:SOC
author: A. C. Eberhard and J. M. Borwein
title: Second Order Cones for Maximal Monotone Operators via Representative Functions
journal: j-SET-VALUED-ANAL
volume: 16
number: 2--3
pages: 157--184
year: 2008
CODEN: SVANEG
DOI: https://doi.org/10.1007/s11228-008-0075-y
ISSN: 0927-6947 (print), 1572-932X (electronic) OR 09276947 (print), 1572932X (electronic)
ISSNL: 0927-6947 OR 09276947
MRclass: 49J53 (46N10 47H04 47H05 47N10)
MRnumber: 2399200
MRreviewer: Nicolas Hadjisavvas
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:36:22 MDT
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11228
rawauthor: A. C. Eberhard and J. M. Borwein
rawtitle: Second Order Cones for Maximal Monotone Operators via Representative Functions
ORCID: Eberhard, Andrew/0000-0003-2977-3456; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/348/; http://link.springer.com/article/10.1007/s11228-008-0075-y

abstract:
It is shown that various first and second order derivatives of the Fitzpatrick and Penot representative functions for a maximal monotone operator T, in a reflexive Banach space, can be used to represent differential information associated with the tangent and normal cones to the Graph T. In particular we obtain formula for the proto-derivative, as well as its polar, the normal cone to the graph of T. First order derivatives are shown to be useful in recognising points of single-valuedness of T. We show that a strong form of proto-differentiability to the graph of T, is often associated with single-valuedness of T.

rawabstract:
It is shown that various first and second order derivatives of the Fitzpatrick and Penot representative functions for a maximal monotone operator T, in a reflexive Banach space, can be used to represent differential information associated with the tangent and normal cones to the Graph T. In particular we obtain formula for the proto-derivative, as well as its polar, the normal cone to the graph of T. First order derivatives are shown to be useful in recognising points of single-valuedness of T. We show that a strong form of proto-differentiability to the graph of T, is often associated with single-valuedness of T.

entry:
@Article{Eberhard:2008:SOC,
  author =       "A. C. Eberhard and J. M. Borwein",
  title =        "Second Order Cones for Maximal Monotone Operators via
                 Representative Functions",
  journal =      j-SET-VALUED-ANAL,
  volume =       "16",
  number =       "2--3",
  pages =        "157--184",
  year =         "2008",
  CODEN =        "SVANEG",
  DOI =          "https://doi.org/10.1007/s11228-008-0075-y",
  ISSN =         "0927-6947 (print), 1572-932X (electronic)",
  ISSN-L =       "0927-6947",
  MRclass =      "49J53 (46N10 47H04 47H05 47N10)",
  MRnumber =     "2399200",
  MRreviewer =   "Nicolas Hadjisavvas",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/348/;
                 http://link.springer.com/article/10.1007/s11228-008-0075-y",
  abstract =     "It is shown that various first and second order
                 derivatives of the Fitzpatrick and Penot representative
                 functions for a maximal monotone operator T, in a
                 reflexive Banach space, can be used to represent
                 differential information associated with the tangent
                 and normal cones to the Graph T. In particular we
                 obtain formula for the proto-derivative, as well as its
                 polar, the normal cone to the graph of T. First order
                 derivatives are shown to be useful in recognising
                 points of single-valuedness of T. We show that a strong
                 form of proto-differentiability to the graph of T, is
                 often associated with single-valuedness of T.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Set-Valued Analysis. An International Journal Devoted
                 to the Theory of Multifunctions and its Applications",
  journal-URL =  "http://link.springer.com/journal/11228",
  ORCID-numbers = "Eberhard, Andrew/0000-0003-2977-3456; Borwein,
                 Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009; Eberhard,
                 Andrew/B-5576-2013",
  unique-id =    "Eberhard:2008:SOC",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2009:EMCa
author: David H. Bailey and Jonathan M. Borwein
title: Experimental mathematics and computational statistics
journal: Wiley Interdisciplinary Reviews: Computational Statistics
volume: 1
number: 1
pages: 12--24
month: jul
monthnumber: 7
year: 2009
DOI: https://doi.org/10.1002/wics.1
ISSN: 1939-0068 (print), 1939-5108 (electronic) OR 19390068 (print), 19395108 (electronic)
ISSNL: 1939-0068 OR 19390068
bibdate: Thu Aug 11 11:01:49 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 11:01:49 ???
URL: http://docserver.carma.newcastle.edu.au/1227/
fjournal: WIREs Computational Statistics
keywords: experimental mathematics, numerical integration, numerical analysis, computational statistics
acknowledgement: ack-nhfb
ajournal: WIREs
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://onlinelibrary.wiley.com/journal/19390068
onlinedate: 13 July 2009
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Experimental mathematics and computational statistics
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
abstract:
The field of statistics has long been noted for techniques to detect patterns and regularities in numerical data. In this article, we explore connections between statistics and the emerging field of experimental mathematics. These include both applications of experimental mathematics in statistics as well as statistical methods applied to computational mathematics.

rawabstract:
The field of statistics has long been noted for techniques to detect patterns and regularities in numerical data. In this article, we explore connections between statistics and the emerging field of experimental mathematics. These include both applications of experimental mathematics in statistics as well as statistical methods applied to computational mathematics.

entry:
@Article{Bailey:2009:EMCa,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Experimental mathematics and computational
                 statistics",
  journal =      "Wiley Interdisciplinary Reviews: Computational
                 Statistics",
  volume =       "1",
  number =       "1",
  pages =        "12--24",
  month =        jul # "--" # aug,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1002/wics.1",
  ISSN =         "1939-0068 (print), 1939-5108 (electronic)",
  ISSN-L =       "1939-0068",
  bibdate =      "Thu Aug 11 11:01:49 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1227/",
  abstract =     "The field of statistics has long been noted for
                 techniques to detect patterns and regularities in
                 numerical data. In this article, we explore connections
                 between statistics and the emerging field of
                 experimental mathematics. These include both
                 applications of experimental mathematics in statistics
                 as well as statistical methods applied to computational
                 mathematics.",
  acknowledgement = ack-nhfb,
  ajournal =     "WIREs",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "WIREs Computational Statistics",
  journal-URL =  "https://onlinelibrary.wiley.com/journal/19390068",
  keywords =     "experimental mathematics, numerical integration,
                 numerical analysis, computational statistics",
  onlinedate =   "13 July 2009",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Bailey:2009:EMCb
author: D. H. Bailey and J. M. Borwein
booktitle: Online Encyclopedia of Computational Statistics. A Wiley Interdisciplinary Review
title: Experimental Mathematics and Computational Statistics
publisher: pub-WILEY
address: pub-WILEY:adr
pages: ??--??
month: jul
monthnumber: 7
year: 2009
ISBN: 0-470-97388-9 (hardcover) OR 0470973889 (hardcover)
ISBN13: 978-0-470-97388-2 (hardcover) OR 9780470973882 (hardcover)
LCCN: GE45.S73 E56 2012
bibdate: Fri Aug 12 09:29:41 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 09:29:41 ???
note: Six volumes (lix + 3150 pages).
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. H. Bailey and J. M. Borwein
rawbooktitle: Online Encyclopedia of Computational Statistics. {A} {Wiley} Interdisciplinary Review
rawnote: Six volumes (lix + 3150 pages).
rawtitle: Experimental Mathematics and Computational Statistics
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://ca.wiley.com/WileyCDA/Section/id-390445.html; http://docserver.carma.newcastle.edu.au/1227/; http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470973889.html

remark:
Probably identical to cite Bailey:2009:EMCa. Appears to be first edition, but not available at publisher site.

entry:
@InCollection{Bailey:2009:EMCb,
  author =       "D. H. Bailey and J. M. Borwein",
  booktitle =    "Online Encyclopedia of Computational Statistics. {A}
                 {Wiley} Interdisciplinary Review",
  title =        "Experimental Mathematics and Computational
                 Statistics",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "??--??",
  month =        jul,
  year =         "2009",
  DOI =          "",
  ISBN =         "0-470-97388-9 (hardcover)",
  ISBN-13 =      "978-0-470-97388-2 (hardcover)",
  LCCN =         "GE45.S73 E56 2012",
  bibdate =      "Fri Aug 12 09:29:41 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Six volumes (lix + 3150 pages).",
  URL =          "http://ca.wiley.com/WileyCDA/Section/id-390445.html;
                 http://docserver.carma.newcastle.edu.au/1227/;
                 http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470973889.html",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "Probably identical to \cite{Bailey:2009:EMCa}. Appears
                 to be first edition, but not available at publisher
                 site.",
  xxISBN =       "0-470-97388-9 (second edition) (2012?)",
  xxisbn-13 =    "978-0-470-97388-2 (second edition) (2012?)",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2009:HPH
author: David Bailey and Jonathan Borwein
title: Highly parallel, high precision integration
journal: International Journal of Computational Science and Engineering
volume: 4
pages: ??--??
year: 2009
ISSN: 1742-7185 (print), 1742-7193 (electronic) OR 17427185 (print), 17427193 (electronic)
ISSNL: 1742-7185 OR 17427185
bibdate: Fri Aug 12 09:16:29 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 09:16:29 ???
URL: http://docserver.carma.newcastle.edu.au/294/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.inderscience.com/jhome.php?jcode=ijcse
rawauthor: David Bailey and Jonathan Borwein
rawtitle: Highly parallel, high precision integration
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
remark:
I cannot find this article at the publisher site, which lacks metadata by volume, and fails to find author or title values. Not in tables of contents of volume 4, numbers 1, 2, 3, and 4.

entry:
@Article{Bailey:2009:HPH,
  author =       "David Bailey and Jonathan Borwein",
  title =        "Highly parallel, high precision integration",
  journal =      "International Journal of Computational Science and
                 Engineering",
  volume =       "4",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2009",
  ISSN =         "1742-7185 (print), 1742-7193 (electronic)",
  ISSN-L =       "1742-7185",
  bibdate =      "Fri Aug 12 09:16:29 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/294/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  journal-URL =  "http://www.inderscience.com/jhome.php?jcode=ijcse",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "I cannot find this article at the publisher site,
                 which lacks metadata by volume, and fails to find
                 author or title values. Not in tables of contents of
                 volume 4, numbers 1, 2, 3, and 4.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2009:PAD
author: David H. Bailey and Jonathan M. Borwein
title: PSLQ: an Algorithm to Discover to Integer Relations
journal: Computeralgebra Rundbrief
volume: 45
pages: 8--11
month: oct
monthnumber: 10
year: 2009
ISSN: 0933-5994 OR 09335994
ISSNL: 0933-5994 OR 09335994
bibdate: Sat Aug 13 16:11:51 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 16:11:51 ???
URL: http://www.fachgruppe-computeralgebra.de/cms/tiki-index.php?page=Rundbrief
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.fachgruppe-computeralgebra.de/rundbrief/
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: {PSLQ}: an Algorithm to Discover to Integer Relations
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bailey:2009:PAD,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "{PSLQ}: an Algorithm to Discover to Integer
                 Relations",
  journal =      "Computeralgebra Rundbrief",
  volume =       "45",
  number =       "??",
  pages =        "8--11",
  month =        oct,
  year =         "2009",
  ISSN =         "0933-5994",
  ISSN-L =       "0933-5994",
  bibdate =      "Sat Aug 13 16:11:51 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.fachgruppe-computeralgebra.de/cms/tiki-index.php?page=Rundbrief",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  journal-URL =  "http://www.fachgruppe-computeralgebra.de/rundbrief/",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2009:RQR
author: D. H. Bailey and J. M. Borwein and R. E. Crandall
title: Resolution of the Quinn--Rand--Strogatz Constant of Nonlinear Physics
journal: j-EXP-MATH
volume: 18
number: 1
pages: 107--116
year: 2009
DOI: https://doi.org/10.1080/10586458.2009.10128885
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 11Y60 (11M35 11Z05)
MRnumber: 2548991
MRreviewer: Herman J. J. te Riele
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/345/; http://projecteuclid.org/euclid.em/1243430534
fjournal: Experimental Mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.tandfonline.com/loi/uexm20
rawauthor: D. H. Bailey and J. M. Borwein and R. E. Crandall
rawtitle: Resolution of the {Quinn--Rand--Strogatz} Constant of Nonlinear Physics
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
http://projecteuclid.org/euclid.em; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/expmath.bib; http://www.tandfonline.com/toc/uexm20/18/1

abstract:
Herein we develop connections between zeta functions and some recent ``mysterious'' constants of nonlinear physics. In an important analysis of coupled Winfree oscillators, Quinn, Rand, and Strogatz [Quinn et al. 07] developed a certain N-oscillator scenario whose bifurcation phase offset small phi is implicitly defined, with a conjectured asymptotic behavior sin phi similar to 1 - c(1)/N, with experimental estimate c(1) = 0.605443657.... We are able to derive the exact theoretical value of this ``QRS constant'' c(1) as a real zero of a particular Hurwitz zeta function. This discovery enables, for example, the rapid resolution of cl to extreme precision. Results and conjectures are provided in regard to higher-order terms of the sin phi asymptotic, and to yet more physics constants emerging from the original QRS work.

rawabstract:
Herein we develop connections between zeta functions and some recent ``mysterious'' constants of nonlinear physics. In an important analysis of coupled Winfree oscillators, Quinn, Rand, and Strogatz [Quinn et al. 07] developed a certain N-oscillator scenario whose bifurcation phase offset small phi is implicitly defined, with a conjectured asymptotic behavior sin phi similar to 1 - c(1)/N, with experimental estimate c(1) = 0.605443657.... We are able to derive the exact theoretical value of this ``QRS constant'' c(1) as a real zero of a particular Hurwitz zeta function. This discovery enables, for example, the rapid resolution of cl to extreme precision. Results and conjectures are provided in regard to higher-order terms of the sin phi asymptotic, and to yet more physics constants emerging from the original QRS work.

entry:
@Article{Bailey:2009:RQR,
  author =       "D. H. Bailey and J. M. Borwein and R. E. Crandall",
  title =        "Resolution of the {Quinn--Rand--Strogatz} Constant of
                 Nonlinear Physics",
  journal =      j-EXP-MATH,
  volume =       "18",
  number =       "1",
  pages =        "107--116",
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2009.10128885",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11Y60 (11M35 11Z05)",
  MRnumber =     "2548991",
  MRreviewer =   "Herman J. J. te Riele",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib;
                 http://www.tandfonline.com/toc/uexm20/18/1",
  URL =          "http://docserver.carma.newcastle.edu.au/345/;
                 http://projecteuclid.org/euclid.em/1243430534",
  abstract =     "Herein we develop connections between zeta functions
                 and some recent ``mysterious'' constants of nonlinear
                 physics. In an important analysis of coupled Winfree
                 oscillators, Quinn, Rand, and Strogatz [Quinn et al.
                 07] developed a certain N-oscillator scenario whose
                 bifurcation phase offset small phi is implicitly
                 defined, with a conjectured asymptotic behavior sin phi
                 similar to 1 - c(1)/N, with experimental estimate c(1)
                 = 0.605443657.... We are able to derive the exact
                 theoretical value of this ``QRS constant'' c(1) as a
                 real zero of a particular Hurwitz zeta function. This
                 discovery enables, for example, the rapid resolution of
                 cl to extreme precision. Results and conjectures are
                 provided in regard to higher-order terms of the sin phi
                 asymptotic, and to yet more physics constants emerging
                 from the original QRS work.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Bailey:2009:RQR",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:2009:SMPa
author: David H. Bailey and Jonathan M. Borwein
title: Solution to booktitle Monthly Problem #11418
type: Report
address: Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5, Canada and Callaghan, NSW 2308, Australia
pages: 107--116
day: 6
month: jul
monthnumber: 7
year: 2009
bibdate: Fri Sep 30 08:40:15 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 08:40:15 ???
URL: http://www.davidhbailey.com/dhbpapers/amm-11418.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Solution to {{\booktitle{Monthly}}} Problem \#11418
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
institution:
Lawrence Berkeley National Laboratory and Faculty of Computer Science, Dalhousie University and School of Mathematical and Physical Sciences, University of Newcastle

remark:
The report evaluates the integral $ J = int _infty ^infty frac t^2 sech ^2(t)a - tanh (t) d t $ for complex $ |a| > 1 $.

entry:
@TechReport{Bailey:2009:SMPa,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Solution to {{\booktitle{Monthly}}} Problem \#11418",
  type =         "Report",
  institution =  "Lawrence Berkeley National Laboratory and Faculty of
                 Computer Science, Dalhousie University and School of
                 Mathematical and Physical Sciences, University of
                 Newcastle",
  address =      "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5,
                 Canada and Callaghan, NSW 2308, Australia",
  day =          "6",
  month =        jul,
  year =         "2009",
  bibdate =      "Fri Sep 30 08:40:15 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/amm-11418.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "The report evaluates the integral $ J =
                 \int_\infty^\infty \frac {t^2 \sech^2(t)}{a - \tanh
                 (t)} \, d t $ for complex $ |a| > 1 $.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:2009:SMPb
author: David H. Bailey and Jonathan M. Borwein
title: Solutions to booktitle Monthly Problems 11456 and 11457
type: Report
institution: Lawrence Berkeley National Laboratory and Faculty of Computer Science, Dalhousie University
address: Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5, Canada
pages: 2
day: 10
month: oct
monthnumber: 10
year: 2009
bibdate: Fri Sep 30 08:34:31 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 08:34:31 ???
URL: http://www.davidhbailey.com/dhbpapers/amm-11456.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Solutions to {{\booktitle{Monthly}}} Problems 11456 and 11457
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@TechReport{Bailey:2009:SMPb,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Solutions to {{\booktitle{Monthly}}} Problems 11456
                 and 11457",
  type =         "Report",
  institution =  "Lawrence Berkeley National Laboratory and Faculty of
                 Computer Science, Dalhousie University",
  address =      "Berkeley, CA 94720, USA and Halifax, NS, B3H 2W5,
                 Canada",
  pages =        "2",
  day =          "10",
  month =        oct,
  year =         "2009",
  bibdate =      "Fri Sep 30 08:34:31 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/amm-11456.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borwein:2009:CCI
author: Jonathan M. Borwein and Keith J. Devlin
title: The computer as crucible: an introduction to experimental mathematics
publisher: pub-A-K-PETERS
address: pub-A-K-PETERS:adr
pages: xi + 158
year: 2009
ISBN: 1-56881-343-0 OR 1568813430
ISBN13: 978-1-56881-343-1 OR 9781568813431
LCCN: QA8.7 .B67 2009
MRclass: 00A35 (11-04 11Y16 11Y60)
MRnumber: 2464847
MRreviewer: Samuel S. Wagstaff, Jr.
bibdate: Tue Nov 10 17:48:24 MST 2009
bibtimestamp: 2009.11.10 17:48:24 MST
URL: http://docserver.carma.newcastle.edu.au/1730/; http://www.loc.gov/catdir/toc/fy0904/2008022180.html
subject: Experimental mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Keith J. Devlin
rawtitle: The computer as crucible: an introduction to experimental mathematics
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/master.bib; z3950.loc.gov:7090/Voyager

TOC:
What is experimental mathematics? What is the quadrillionth decimal place of $pi$? What is that number? The most important function in mathematics Evaluate the following integral Serendipity Calculating [pi] The computer knows more math than you do Take it to the limit Danger! Always exercise caution when using the computer Stuff we left out (until now)

rawTOC:
What is experimental mathematics? \\ What is the quadrillionth decimal place of $pi$? \\ What is that number? \\ The most important function in mathematics \\ Evaluate the following integral \\ Serendipity \\ Calculating [pi] \\ The computer knows more math than you do \\ Take it to the limit \\ Danger! Always exercise caution when using the computer \\ Stuff we left out (until now)

entry:
@Book{Borwein:2009:CCI,
  author =       "Jonathan M. Borwein and Keith J. Devlin",
  title =        "The computer as crucible: an introduction to
                 experimental mathematics",
  publisher =    pub-A-K-PETERS,
  address =      pub-A-K-PETERS:adr,
  pages =        "xi + 158",
  year =         "2009",
  ISBN =         "1-56881-343-0",
  ISBN-13 =      "978-1-56881-343-1",
  LCCN =         "QA8.7 .B67 2009",
  MRclass =      "00A35 (11-04 11Y16 11Y60)",
  MRnumber =     "2464847",
  MRreviewer =   "Samuel S. Wagstaff, Jr.",
  bibdate =      "Tue Nov 10 17:48:24 MST 2009",
  bibsource =    "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/1730/;
                 http://www.loc.gov/catdir/toc/fy0904/2008022180.html",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  libnote =      "Not in my library.",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject =      "Experimental mathematics",
  tableofcontents = "What is experimental mathematics? \\
                 What is the quadrillionth decimal place of $pi$? \\
                 What is that number? \\
                 The most important function in mathematics \\
                 Evaluate the following integral \\
                 Serendipity \\
                 Calculating [pi] \\
                 The computer knows more math than you do \\
                 Take it to the limit \\
                 Danger! Always exercise caution when using the computer
                 \\
                 Stuff we left out (until now)",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2009:DAD
author: J. M. Borwein
title: Digitally-assisted discovery and proof
crossref: Lin:2009:PPM
pages: I.3--I.11
year: 2009
bibdate: Sat Aug 13 16:21:36 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 16:21:36 ???
note: Plenary address.
URL: http://docserver.carma.newcastle.edu.au/390/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein
rawnote: Plenary address.
rawtitle: Digitally-assisted discovery and proof
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InProceedings{Borwein:2009:DAD,
  author =       "J. M. Borwein",
  title =        "Digitally-assisted discovery and proof",
  crossref =     "Lin:2009:PPM",
  pages =        "I.3--I.11",
  year =         "2009",
  bibdate =      "Sat Aug 13 16:21:36 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Plenary address.",
  URL =          "http://docserver.carma.newcastle.edu.au/390/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2009:DCF
author: Jonathan Borwein and Jon Vanderwerff
title: Differentiability of conjugate functions and perturbed minimization principles
journal: j-J-CONVEX-ANAL
volume: 16
number: 3--4
pages: 707--711
year: 2009
ISSN: 0944-6532 (print), 2363-6394 (electronic) OR 09446532 (print), 23636394 (electronic)
MRclass: 49K40 (46G05 46N10 49J50 52A41 58E30 90C46)
MRnumber: 2583890
MRreviewer: Philip D. Loewen
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Journal of Convex Analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.heldermann.de/JCA/jcacon.htm
rawauthor: Jonathan Borwein and Jon Vanderwerff
rawtitle: Differentiability of conjugate functions and perturbed minimization principles
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/383/; http://www.heldermann.de/JCA/JCA16/JCA163/jca16042.htm

abstract:
We survey the tight connection between differentiability of conjugate functions and perturbed optimization principles

rawabstract:
We survey the tight connection between differentiability of conjugate functions and perturbed optimization principles

entry:
@Article{Borwein:2009:DCF,
  author =       "Jonathan Borwein and Jon Vanderwerff",
  title =        "Differentiability of conjugate functions and perturbed
                 minimization principles",
  journal =      j-J-CONVEX-ANAL,
  volume =       "16",
  number =       "3--4",
  pages =        "707--711",
  year =         "2009",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "49K40 (46G05 46N10 49J50 52A41 58E30 90C46)",
  MRnumber =     "2583890",
  MRreviewer =   "Philip D. Loewen",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/383/;
                 http://www.heldermann.de/JCA/JCA16/JCA163/jca16042.htm",
  abstract =     "We survey the tight connection between
                 differentiability of conjugate functions and perturbed
                 optimization principles",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Convex Analysis",
  journal-URL =  "http://www.heldermann.de/JCA/jcacon.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2009:DCF",
  xxpages =      "699--706",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2009:EBS
author: Jonathan M. Borwein and Neil J. Calkin and Dante Manna
title: Euler--Boole summation revisited
journal: j-AMER-MATH-MONTHLY
volume: 116
number: 5
pages: 387--412
year: 2009
CODEN: AMMYAE
DOI: https://doi.org/10.4169/193009709X470290
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 11B68 (11B73 26A06)
MRnumber: 2510837
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 ???
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.jstor.org/journals/00029890.html
rawauthor: Jonathan M. Borwein and Neil J. Calkin and Dante Manna
rawtitle: {Euler--Boole} summation revisited
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2009:EBS,
  author =       "Jonathan M. Borwein and Neil J. Calkin and Dante
                 Manna",
  title =        "{Euler--Boole} summation revisited",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "116",
  number =       "5",
  pages =        "387--412",
  year =         "2009",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/193009709X470290",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11B68 (11B73 26A06)",
  MRnumber =     "2510837",
  MRreviewer =   "Samuel S. Wagstaff, Jr.",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2009:MME
author: Jonathan M. Borwein
title: Maths Matters: Exploratory experimentation: digitally-assisted discovery and proof
journal: j-AUSTRALIAN-MATH-SOC-GAZ
volume: 36
number: 3
pages: 166--175
month: jul
monthnumber: 7
year: 2009
ISSN: 0311-0729 (print), 1326-2297 (electronic) OR 03110729 (print), 13262297 (electronic)
ISSNL: 0311-0729 OR 03110729
MRclass: 00A35 68W30 97U50 00A30
MRnumber: 2543725
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: The Australian Mathematical Society. Gazette
ZMnumber: 1175.00028
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.austms.org.au/gazette
rawauthor: Jonathan M. Borwein
rawtitle: Maths Matters: Exploratory experimentation: digitally-assisted discovery and proof
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2009:MME,
  author =       "Jonathan M. Borwein",
  title =        "Maths Matters: Exploratory experimentation:
                 digitally-assisted discovery and proof",
  journal =      j-AUSTRALIAN-MATH-SOC-GAZ,
  volume =       "36",
  number =       "3",
  pages =        "166--175",
  month =        jul,
  year =         "2009",
  ISSN =         "0311-0729 (print), 1326-2297 (electronic)",
  ISSN-L =       "0311-0729",
  MRclass =      "00A35 68W30 97U50 00A30",
  MRnumber =     "2543725",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  ZMnumber =     "1175.00028",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The Australian Mathematical Society. Gazette",
  journal-URL =  "http://www.austms.org.au/gazette",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark-1 =     "This material is largely excerpted from a longer paper
                 written for ICMI Study 19 `On Proof and Proving in
                 Mathematics Education', and a plenary talk given in May
                 2009 at the corresponding Workshop at National Taiwan
                 Normal University. [NHFB remarks: It appears that the
                 longer paper did not appear in ICMI [International
                 Commission on Mathematical Instruction] Study 19, which
                 is published in \booktitle{ZDM Mathematics Education}
                 {\bf 40}(2) May 2008,
                 \url{http://link.springer.com/journal/11858/40/2/page/1},
                 and in the Chinese\slash English proceedings with ISBN
                 986-01-8210-8.]",
  remark-2 =     "From page 166: ``The computer offers to provide
                 scaffolding both to enhance mathematical reasoning and
                 to restrain mathematical error.''",
  remark-3 =     "From page 174: ``We live in an information-rich,
                 judgement-poor world and the explosion of information
                 and tools is not going to diminish.''",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2009:NCM
author: Jonathan Borwein and Rafal Goebel
booktitle: Optimization
title: On the nondifferentiability of cone-monotone functions in Banach spaces
volume: 32
publisher: pub-SV
address: pub-SV:adr
pages: 3--14
year: 2009
DOI: https://doi.org/10.1007/978-0-387-98096-6_1
MRclass: 49J50 (47G10 47N10)
MRnumber: 2599222
MRreviewer: John R. Giles
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: Springer Optim. Appl.
remark: CECM Preprint 02:179.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein and Rafal Goebel
rawbooktitle: Optimization
rawtitle: On the nondifferentiability of cone-monotone functions in {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2009:NCM,
  author =       "Jonathan Borwein and Rafal Goebel",
  booktitle =    "Optimization",
  title =        "On the nondifferentiability of cone-monotone functions
                 in {Banach} spaces",
  volume =       "32",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "3--14",
  year =         "2009",
  DOI =          "https://doi.org/10.1007/978-0-387-98096-6_1",
  MRclass =      "49J50 (47G10 47N10)",
  MRnumber =     "2599222",
  MRreviewer =   "John R. Giles",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Springer Optim. Appl.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 02:179.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2009:PCM
author: Jonathan M. Borwein
journal: j-SIAM-REVIEW
volume: 51
number: 4
pages: 790--794
month: dec
monthnumber: 12
year: 2009
CODEN: SIREAD
DOI: https://doi.org/10.1137/SIREAD000051000004000785000001
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
MRclass: 00A17
MRnumber: 2573944
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1228/; http://www.jstor.org/stable/25662346
fjournal: SIAM Review
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://epubs.siam.org/sirev
rawauthor: Jonathan M. Borwein
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
booktitle The Princeton companion to mathematics. Timothy Gowers, with June Barrow Green and Imre Leader. Princeton University Press, Princeton, NJ, 2008. $99.00. xxii + 1034 pp., hardcover. ISBN 978-0-691-1 1880-2. [book review of refcno 2467561]

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

rawtitle:
{{\booktitle{The Princeton companion to mathematics}}. Timothy Gowers, with June Barrow Green and Imre Leader. Princeton University Press, Princeton, NJ, 2008. \$99.00. xxii + 1034 pp., hardcover. ISBN 978-0-691-1 1880-2. [book review of \refcno 2467561]}

entry:
@Article{Borwein:2009:PCM,
  author =       "Jonathan M. Borwein",
  title =        "{{\booktitle{The Princeton companion to mathematics}}.
                 Timothy Gowers, with June Barrow Green and Imre Leader.
                 Princeton University Press, Princeton, NJ, 2008.
                 \$99.00. xxii + 1034 pp., hardcover. ISBN 978-0-691-1
                 1880-2. [book review of \refcno 2467561]}",
  journal =      j-SIAM-REVIEW,
  volume =       "51",
  number =       "4",
  pages =        "790--794",
  month =        dec,
  year =         "2009",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/SIREAD000051000004000785000001",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "00A17",
  MRnumber =     "2573944",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1228/;
                 http://www.jstor.org/stable/25662346",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2009:SCC
author: Jonathan M. Borwein and Warren B. Moors
title: Stability of closedness of convex cones under linear mappings
journal: j-J-CONVEX-ANAL
volume: 16
number: 3--4
pages: 699--705
year: 2009
ISSN: 0944-6532 (print), 2363-6394 (electronic) OR 09446532 (print), 23636394 (electronic)
MRclass: 47N10 (90C25 90C31)
MRnumber: 2583889
MRreviewer: John R. Giles
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
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 Warren B. Moors
rawtitle: Stability of closedness of convex cones under linear mappings
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1229/; http://www.heldermann.de/JCA/JCA16/JCA163/jca16041.htm

abstract:
In this paper we reconsider the question of when the continuous linear image of a closed convex cone is closed in Euclidean space. In particular, we show that although it is not true that the closedness of the image is preserved under small perturbations of the linear mappings it is ``almost'' true that the closedness of the image is preserved under small perturbations, in the sense that, for ``almost all'' linear mappings from R(n) into R(m) if the image of the cone is closed then there is a small neighbourhood around it whose members also preserve the closedness of the cone.

rawabstract:
In this paper we reconsider the question of when the continuous linear image of a closed convex cone is closed in Euclidean space. In particular, we show that although it is not true that the closedness of the image is preserved under small perturbations of the linear mappings it is ``almost'' true that the closedness of the image is preserved under small perturbations, in the sense that, for ``almost all'' linear mappings from R(n) into R(m) if the image of the cone is closed then there is a small neighbourhood around it whose members also preserve the closedness of the cone.

entry:
@Article{Borwein:2009:SCC,
  author =       "Jonathan M. Borwein and Warren B. Moors",
  title =        "Stability of closedness of convex cones under linear
                 mappings",
  journal =      j-J-CONVEX-ANAL,
  volume =       "16",
  number =       "3--4",
  pages =        "699--705",
  year =         "2009",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "47N10 (90C25 90C31)",
  MRnumber =     "2583889",
  MRreviewer =   "John R. Giles",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1229/;
                 http://www.heldermann.de/JCA/JCA16/JCA163/jca16041.htm",
  abstract =     "In this paper we reconsider the question of when the
                 continuous linear image of a closed convex cone is
                 closed in Euclidean space. In particular, we show that
                 although it is not true that the closedness of the
                 image is preserved under small perturbations of the
                 linear mappings it is ``almost'' true that the
                 closedness of the image is preserved under small
                 perturbations, in the sense that, for ``almost all''
                 linear mappings from R(n) into R(m) if the image of the
                 cone is closed then there is a small neighbourhood
                 around it whose members also preserve the closedness of
                 the cone.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Convex Analysis",
  journal-URL =  "http://www.heldermann.de/JCA/jcacon.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2009:SCC",
  xxpages =      "707--713",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2009:SFC
author: Jonathan M. Borwein and Chris H. Hamilton
title: Symbolic Fenchel conjugation
journal: j-MATH-PROG
volume: 116
number: 1--2
pages: 17--35
year: 2009
CODEN: MHPGA4
DOI: https://doi.org/10.1007/s10107-007-0134-4
ISSN: 0025-5610 (print), 1436-4646 (electronic) OR 00255610 (print), 14364646 (electronic)
ISSNL: 0025-5610 OR 00255610
MRclass: 90-04 (44A15 49J52 65K10 90C25 90C46)
MRnumber: 2421271
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: Special issue in honor of Alfred Auslender.
URL: http://docserver.carma.newcastle.edu.au/1479/
fjournal: Mathematical Programming
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/10107
rawauthor: Jonathan M. Borwein and Chris H. Hamilton
rawnote: Special issue in honor of Alfred Auslender.
rawtitle: Symbolic {Fenchel} conjugation
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Of key importance in convex analysis and optimization is the notion of duality, and in particular that of Fenchel duality. This work explores improvements to existing algorithms for the symbolic calculation of subdifferentials and Fenchel conjugates of convex functions defined on the real line. More importantly, these algorithms are extended to enable the symbolic calculation of Fenchel conjugates on a class of real-valued functions defined on the real line. More importantly, these algorithms are extended to enable the symbolic calculation of Fenchel conjugates on a class of real-valued functions defined on R(n). These algorithms are realized in the form of the Maple package SCAT.

rawabstract:
Of key importance in convex analysis and optimization is the notion of duality, and in particular that of Fenchel duality. This work explores improvements to existing algorithms for the symbolic calculation of subdifferentials and Fenchel conjugates of convex functions defined on the real line. More importantly, these algorithms are extended to enable the symbolic calculation of Fenchel conjugates on a class of real-valued functions defined on the real line. More importantly, these algorithms are extended to enable the symbolic calculation of Fenchel conjugates on a class of real-valued functions defined on R(n). These algorithms are realized in the form of the Maple package SCAT.

entry:
@Article{Borwein:2009:SFC,
  author =       "Jonathan M. Borwein and Chris H. Hamilton",
  title =        "Symbolic {Fenchel} conjugation",
  journal =      j-MATH-PROG,
  volume =       "116",
  number =       "1--2",
  pages =        "17--35",
  year =         "2009",
  CODEN =        "MHPGA4",
  DOI =          "https://doi.org/10.1007/s10107-007-0134-4",
  ISSN =         "0025-5610 (print), 1436-4646 (electronic)",
  ISSN-L =       "0025-5610",
  MRclass =      "90-04 (44A15 49J52 65K10 90C25 90C46)",
  MRnumber =     "2421271",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Special issue in honor of Alfred Auslender.",
  URL =          "http://docserver.carma.newcastle.edu.au/1479/",
  abstract =     "Of key importance in convex analysis and optimization
                 is the notion of duality, and in particular that of
                 Fenchel duality. This work explores improvements to
                 existing algorithms for the symbolic calculation of
                 subdifferentials and Fenchel conjugates of convex
                 functions defined on the real line. More importantly,
                 these algorithms are extended to enable the symbolic
                 calculation of Fenchel conjugates on a class of
                 real-valued functions defined on the real line. More
                 importantly, these algorithms are extended to enable
                 the symbolic calculation of Fenchel conjugates on a
                 class of real-valued functions defined on R(n). These
                 algorithms are realized in the form of the Maple
                 package SCAT.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematical Programming",
  journal-URL =  "http://link.springer.com/journal/10107",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2009:SFC",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2009:UBC
author: Jonathan M. Borwein and O-Yeat Chan
title: Uniform bounds for the complementary incomplete gamma function
journal: j-MATH-INEQUAL-APPL
volume: 12
number: 1
pages: 115--121
year: 2009
DOI: https://doi.org/10.7153/mia-12-10
ISSN: 1331-4343 (print), 1848-9966 (electronic) OR 13314343 (print), 18489966 (electronic)
ISSNL: 1331-4343 OR 13314343
MRclass: 33B20
MRnumber: 2489355
MRreviewer: Necdet Batir
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/335/
fjournal: Mathematical Inequalities & Applications
acknowledgement: ack-nhfb
ajournal: Math. Inequal. Appl.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://mia.ele-math.com/
rawauthor: Jonathan M. Borwein and O-Yeat Chan
rawtitle: Uniform bounds for the complementary incomplete gamma function
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We prove upper and lower bounds for the complementary incomplete gamma function Gamma(a, z) with complex parameters a and z. Our bounds are refined within the circular hyperboloid of one sheet (a, z) : vertical bar z vertical bar > c vertical bar a - 1 vertical bar with a real and z complex. Our results show that within the hyperboloid, vertical bar Gamma(a, z)vertical bar is of order vertical bar Z vertical bar(a-1)e(-Re(z)), and extends an upper estimate of Natalini and Palumbo to complex values of z.

rawabstract:
We prove upper and lower bounds for the complementary incomplete gamma function Gamma(a, z) with complex parameters a and z. Our bounds are refined within the circular hyperboloid of one sheet \{(a, z) : vertical bar z vertical bar > c vertical bar a - 1 vertical bar\} with a real and z complex. Our results show that within the hyperboloid, vertical bar Gamma(a, z)vertical bar is of order vertical bar Z vertical bar(a-1)e(-Re(z)), and extends an upper estimate of Natalini and Palumbo to complex values of z.

entry:
@Article{Borwein:2009:UBC,
  author =       "Jonathan M. Borwein and O-Yeat Chan",
  title =        "Uniform bounds for the complementary incomplete gamma
                 function",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "12",
  number =       "1",
  pages =        "115--121",
  year =         "2009",
  DOI =          "https://doi.org/10.7153/mia-12-10",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  ISSN-L =       "1331-4343",
  MRclass =      "33B20",
  MRnumber =     "2489355",
  MRreviewer =   "Necdet Batir",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/335/",
  abstract =     "We prove upper and lower bounds for the complementary
                 incomplete gamma function Gamma(a, z) with complex
                 parameters a and z. Our bounds are refined within the
                 circular hyperboloid of one sheet \{(a, z) : vertical
                 bar z vertical bar > c vertical bar a - 1 vertical
                 bar\} with a real and z complex. Our results show that
                 within the hyperboloid, vertical bar Gamma(a,
                 z)vertical bar is of order vertical bar Z vertical
                 bar(a-1)e(-Re(z)), and extends an upper estimate of
                 Natalini and Palumbo to complex values of z.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Inequal. Appl.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2009:UBC",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2009:UCF
author: J. Borwein and A. J. Guirao and P. Hajek and J. Vanderwerff
title: Uniformly convex functions on Banach spaces
journal: j-PROC-AM-MATH-SOC
volume: 137
number: 3
pages: 1081--1091
year: 2009
CODEN: PAMYAR
DOI: https://doi.org/10.1090/S0002-9939-08-09630-5
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 46B20 (46G05 46N10 49J50 52A41 90C48)
MRnumber: 2457450
MRreviewer: Doug Ward
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/340/
fjournal: Proceedings of the American Mathematical Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/journals/proc
rawauthor: J. Borwein and A. J. Guirao and P. H{\'a}jek and J. Vanderwerff
rawtitle: Uniformly convex functions on {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Given a Banach space $ (X, || cdot ||) $, we study the connection between uniformly convex functions $ f colon X to R $ bounded above by $ || cdot ||^p $ and the existence of norms on $X$ with moduli of convexity of power type. In particular, we show that there exists a uniformly convex function $ f colon X to R$ bounded above $ || cdot ||^2$ if and only if $X$ admits an equivalent norm with modulus of convexity of power type 2

rawabstract:
Given a Banach space $ (X, || \cdot ||) $, we study the connection between uniformly convex functions $ f \colon X \to R $ bounded above by $ || \cdot ||^p $ and the existence of norms on $X$ with moduli of convexity of power type. In particular, we show that there exists a uniformly convex function $ f \colon X \to R$ bounded above $ || \cdot ||^2$ if and only if $X$ admits an equivalent norm with modulus of convexity of power type 2

entry:
@Article{Borwein:2009:UCF,
  author =       "J. Borwein and A. J. Guirao and P. H{\'a}jek and J.
                 Vanderwerff",
  title =        "Uniformly convex functions on {Banach} spaces",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "137",
  number =       "3",
  pages =        "1081--1091",
  year =         "2009",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/S0002-9939-08-09630-5",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "46B20 (46G05 46N10 49J50 52A41 90C48)",
  MRnumber =     "2457450",
  MRreviewer =   "Doug Ward",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/340/",
  abstract =     "Given a Banach space $ (X, || \cdot ||) $, we study
                 the connection between uniformly convex functions $ f
                 \colon X \to R $ bounded above by $ || \cdot ||^p $ and
                 the existence of norms on $X$ with moduli of convexity
                 of power type. In particular, we show that there exists
                 a uniformly convex function $ f \colon X \to R$ bounded
                 above $ || \cdot ||^2$ if and only if $X$ admits an
                 equivalent norm with modulus of convexity of power type
                 2",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Hajek,
                 Petr/D-5429-2014",
  unique-id =    "Borwein:2009:UCF",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Jackson:2009:JER
author: Allyn Jackson
title: John Ewing retires from the AMS
journal: j-NAMS
volume: 56
number: 1
pages: 48--51
month: jan
monthnumber: 1
year: 2009
CODEN: AMNOAN
ISSN: 0002-9920 (print), 1088-9477 (electronic) OR 00029920 (print), 10889477 (electronic)
ISSNL: 0002-9920 OR 00029920
bibdate: Tue Aug 16 09:18:13 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:18:13 ???
URL: https://www.ams.org/journals/notices/200901/200901-full-issue.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: Allyn Jackson
rawtitle: {John Ewing} retires from the {AMS}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
note:
With contributions by Jonathan Borwein and Jane Kister. Borwein's is a sidebar on page 49, with the title booktitle Some Reflections on John Ewing.

rawnote:
With contributions by Jonathan Borwein and Jane Kister. Borwein's is a sidebar on page 49, with the title \booktitle{Some Reflections on John Ewing}.

entry:
@Article{Jackson:2009:JER,
  author =       "Allyn Jackson",
  title =        "{John Ewing} retires from the {AMS}",
  journal =      j-NAMS,
  volume =       "56",
  number =       "1",
  pages =        "48--51",
  month =        jan,
  year =         "2009",
  CODEN =        "AMNOAN",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibdate =      "Tue Aug 16 09:18:13 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "With contributions by Jonathan Borwein and Jane
                 Kister. Borwein's is a sidebar on page 49, with the
                 title \booktitle{Some Reflections on John Ewing}.",
  URL =          "https://www.ams.org/journals/notices/200901/200901-full-issue.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Bacak:2010:DCF
author: M. Bacak and J. Borwein and B. Sims
title: Differentiability of convex functions in CAT(0) spaces
pages: 48--51
month: aug
monthnumber: 8
year: 2010
bibdate: Tue Aug 16 10:01:41 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:01:41 ???
note: Preprint.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: M. Bac{\'a}k and J. Borwein and B. Sims
rawnote: Preprint.
rawtitle: Differentiability of convex functions in {CAT(0)} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Unpublished{Bacak:2010:DCF,
  author =       "M. Bac{\'a}k and J. Borwein and B. Sims",
  title =        "Differentiability of convex functions in {CAT(0)}
                 spaces",
  month =        aug,
  year =         "2010",
  bibdate =      "Tue Aug 16 10:01:41 2016",
  bibsource =    "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: Bacak:2010:ICL
author: Miroslav Bacak and Jonathan M. Borwein and Andrew Eberhard and Boris S. Mordukhovich
journal: j-J-CONVEX-ANAL
volume: 17
number: 3--4
pages: 737--763
year: 2010
ISSN: 0944-6532 (print), 2363-6394 (electronic) OR 09446532 (print), 23636394 (electronic)
MRclass: 49J52 (46G05)
MRnumber: 2731276
MRreviewer: Shawn Xianfu Wang
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 Hedi Attouch.
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: Miroslav Ba{\v{c}}{\'a}k and Jonathan M. Borwein and Andrew Eberhard and Boris S. Mordukhovich
rawnote: Special volume in honour of Hedi Attouch.
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Eberhard, Andrew/0000-0003-2977-3456
title:
Infimal convolutions and Lipschitzian properties of subdifferentials for prox-regular functions in Hilbert spaces

URL:
http://docserver.carma.newcastle.edu.au/1224/; http://www.heldermann.de/JCA/JCA17/JCA173/jca17049.htm

abstract:
In this paper we study infimal convolutions of extended-real-valued functions in Hilbert spaces paying a special attention to the rather broad and remarkable class of prox-regular functions. Such functions have been well recognized as highly important in many aspects of variational analysis and its applications in both finite-dimensional and infinite-dimensional settings. Based on advanced variational techniques, we discover some new subdifferential properties of infimal convolutions and apply them to the study of Lipschitzian behavior of subdifferentials for prox-regular functions in Hilbert spaces. It is shown, in particular, that the fulfillment of a natural Lipschitz-like property for (set-valued) subdifferentials of prox-regular functions forces such functions, under weak assumptions, actually to be locally smooth with single-valued subdifferentials reduced to Lipschitz continuous gradient mappings.

rawabstract:
In this paper we study infimal convolutions of extended-real-valued functions in Hilbert spaces paying a special attention to the rather broad and remarkable class of prox-regular functions. Such functions have been well recognized as highly important in many aspects of variational analysis and its applications in both finite-dimensional and infinite-dimensional settings. Based on advanced variational techniques, we discover some new subdifferential properties of infimal convolutions and apply them to the study of Lipschitzian behavior of subdifferentials for prox-regular functions in Hilbert spaces. It is shown, in particular, that the fulfillment of a natural Lipschitz-like property for (set-valued) subdifferentials of prox-regular functions forces such functions, under weak assumptions, actually to be locally smooth with single-valued subdifferentials reduced to Lipschitz continuous gradient mappings.

rawtitle:
Infimal convolutions and {Lipschitzian} properties of subdifferentials for prox-regular functions in {Hilbert} spaces

entry:
@Article{Bacak:2010:ICL,
  author =       "Miroslav Ba{\v{c}}{\'a}k and Jonathan M. Borwein and
                 Andrew Eberhard and Boris S. Mordukhovich",
  title =        "Infimal convolutions and {Lipschitzian} properties of
                 subdifferentials for prox-regular functions in
                 {Hilbert} spaces",
  journal =      j-J-CONVEX-ANAL,
  volume =       "17",
  number =       "3--4",
  pages =        "737--763",
  year =         "2010",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "49J52 (46G05)",
  MRnumber =     "2731276",
  MRreviewer =   "Shawn Xianfu Wang",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Special volume in honour of Hedi Attouch.",
  URL =          "http://docserver.carma.newcastle.edu.au/1224/;
                 http://www.heldermann.de/JCA/JCA17/JCA173/jca17049.htm",
  abstract =     "In this paper we study infimal convolutions of
                 extended-real-valued functions in Hilbert spaces paying
                 a special attention to the rather broad and remarkable
                 class of prox-regular functions. Such functions have
                 been well recognized as highly important in many
                 aspects of variational analysis and its applications in
                 both finite-dimensional and infinite-dimensional
                 settings. Based on advanced variational techniques, we
                 discover some new subdifferential properties of infimal
                 convolutions and apply them to the study of
                 Lipschitzian behavior of subdifferentials for
                 prox-regular functions in Hilbert spaces. It is shown,
                 in particular, that the fulfillment of a natural
                 Lipschitz-like property for (set-valued)
                 subdifferentials of prox-regular functions forces such
                 functions, under weak assumptions, actually to be
                 locally smooth with single-valued subdifferentials
                 reduced to Lipschitz continuous gradient mappings.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Convex Analysis",
  journal-URL =  "http://www.heldermann.de/JCA/jcacon.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Eberhard,
                 Andrew/0000-0003-2977-3456",
  researcherid-numbers = "Eberhard, Andrew/B-5576-2013",
  unique-id =    "Bacak:2010:ICL",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2010:ATB
author: D. H. Bailey and J. M. Borwein and R. E. Crandall
title: Advances in the theory of box integrals
journal: j-MATH-COMPUT
volume: 79
number: 271
pages: 1839--1866
month: jul
monthnumber: 7
year: 2010
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-10-02338-0
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11Y60 (65D30)
MRnumber: 2630017
MRreviewer: Michael J. Evans
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/389/; http://www.jstor.org/stable/20779125
fjournal: Mathematics of Computation
remark: D-drive preprint 389 (March 2009).
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 and R. E. Crandall
rawtitle: Advances in the theory of box integrals
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
abstract:
Box integrals--expectations $ langle vert vec r vert ^s rangle $ or $ langle vert vec r - vec q vert ^s rangle $ over the unit $ n$-cube--have over three decades been occasionally given closed forms for isolated $ n, s$. By employing experimental mathematics together with a new, global analytic strategy, we prove that for each of $ n = 1, 2, 3, 4$ dimensions the box integrals are for any integer $ s$ hypergeometrically closed (hyperclosed'') in an explicit sense we clarify herein. For $ n = 5$ dimensions, such a complete hyperclosure proof is blocked by a single, unresolved integral we call $ mathcal K_5$; although we do prove that all but a finite set of ($ n = 5$) cases enjoy hyperclosure. We supply a compendium of exemplary closed forms that arise naturally from the theory.

rawabstract:
Box integrals--expectations $ \langle \vert \vec r \vert^s \rangle $ or $ \langle \vert \vec r - \vec q \vert^s \rangle $ over the unit $ n$-cube--have over three decades been occasionally given closed forms for isolated $ n, s$. By employing experimental mathematics together with a new, global analytic strategy, we prove that for each of $ n = 1, 2, 3, 4$ dimensions the box integrals are for any integer $ s$ hypergeometrically closed (hyperclosed'') in an explicit sense we clarify herein. For $ n = 5$ dimensions, such a complete hyperclosure proof is blocked by a single, unresolved integral we call $ {\mathcal K}_5$; although we do prove that all but a finite set of ($ n = 5$) cases enjoy hyperclosure. We supply a compendium of exemplary closed forms that arise naturally from the theory.

entry:
@Article{Bailey:2010:ATB,
  author =       "D. H. Bailey and J. M. Borwein and R. E. Crandall",
  title =        "Advances in the theory of box integrals",
  journal =      j-MATH-COMPUT,
  volume =       "79",
  number =       "271",
  pages =        "1839--1866",
  month =        jul,
  year =         "2010",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-10-02338-0",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y60 (65D30)",
  MRnumber =     "2630017",
  MRreviewer =   "Michael J. Evans",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/389/;
                 http://www.jstor.org/stable/20779125",
  abstract =     "Box integrals--expectations $ \langle \vert \vec r
                 \vert^s \rangle $ or $ \langle \vert \vec r - \vec q
                 \vert^s \rangle $ over the unit $ n$-cube--have over
                 three decades been occasionally given closed forms for
                 isolated $ n, s$. By employing experimental mathematics
                 together with a new, global analytic strategy, we prove
                 that for each of $ n = 1, 2, 3, 4$ dimensions the box
                 integrals are for any integer $ s$ hypergeometrically
                 closed (hyperclosed'') in an explicit sense we clarify
                 herein. For $ n = 5$ dimensions, such a complete
                 hyperclosure proof is blocked by a single, unresolved
                 integral we call $ {\mathcal K}_5$; although we do
                 prove that all but a finite set of ($ n = 5$) cases
                 enjoy hyperclosure. We supply a compendium of exemplary
                 closed forms that arise naturally from the theory.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "D-drive preprint 389 (March 2009).",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Bailey:2010:ATB",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Bailey:2010:ECO
author: David H. Bailey and Jonathan M. Borwein
title: Experimental computation with oscillatory integrals
crossref: Amdeberhan:2010:GEM
pages: 25--40
year: 2010
DOI: https://doi.org/10.1090/conm/517/10131
MRclass: 11Y35 (42B20)
MRnumber: 2731059
bibdate: Wed Aug 10 11:09:47 2016
bibsource: 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/391/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Experimental computation with oscillatory integrals
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@InProceedings{Bailey:2010:ECO,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Experimental computation with oscillatory integrals",
  crossref =     "Amdeberhan:2010:GEM",
  pages =        "25--40",
  year =         "2010",
  DOI =          "https://doi.org/10.1090/conm/517/10131",
  MRclass =      "11Y35 (42B20)",
  MRnumber =     "2731059",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/391/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2010:EMMa
author: David H. Bailey and Jonathan M. Borwein and David J. Broadhurst and Wadim Zudilin
title: Experimental Mathematics and Mathematical Physics
journal: ArXiv e-prints
pages: 25--40
month: may
monthnumber: 5
year: 2010
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/2010arXiv1005.0414B; http://docserver.carma.newcastle.edu.au/1215/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein and David J. Broadhurst and Wadim Zudilin
rawtitle: Experimental Mathematics and Mathematical Physics
abstract:
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.

keywords:
Mathematical Physics, High Energy Physics - Phenomenology, Mathematics - Classical Analysis and ODEs, Mathematics - Number Theory

rawabstract:
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.

ORCID:
Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646; Zudilin, Wadim/0000-0001-9551-2903

entry:
@Article{Bailey:2010:EMMa,
  author =       "David H. Bailey and Jonathan M. Borwein and David J.
                 Broadhurst and Wadim Zudilin",
  title =        "Experimental Mathematics and Mathematical Physics",
  journal =      "ArXiv e-prints",
  month =        may,
  year =         "2010",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010arXiv1005.0414B;
                 http://docserver.carma.newcastle.edu.au/1215/",
  abstract =     "One of the most effective techniques of experimental
                 mathematics is to compute mathematical entities such as
                 integrals, series or limits to high precision, then
                 attempt to recognize the resulting numerical values.
                 Recently these techniques have been applied with great
                 success to problems in mathematical physics. Notable
                 among these applications are the identification of some
                 key multi-dimensional integrals that arise in Ising
                 theory, quantum field theory and in magnetic spin
                 theory.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1005.0414",
  keywords =     "Mathematical Physics, High Energy Physics -
                 Phenomenology, Mathematics - Classical Analysis and
                 ODEs, Mathematics - Number Theory",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646; Zudilin,
                 Wadim/0000-0001-9551-2903",
  primaryclass = "math-ph",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Bailey:2010:EMMb
author: David H. Bailey and Jonathan M. Borwein and David Broadhurst and Wadim Zudilin
booktitle: Gems in experimental mathematics
title: Experimental mathematics and mathematical physics
volume: 517
publisher: pub-AMS
address: pub-AMS:adr
pages: 41--58
year: 2010
DOI: https://doi.org/10.1090/conm/517/10132
MRclass: 33F05 (11Y60 33F10 65D30)
MRnumber: 2731060
MRreviewer: Zhonghua Li
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: Contemp. Math.
URL: http://docserver.carma.newcastle.edu.au/1215/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein and David Broadhurst and Wadim Zudilin
rawbooktitle: Gems in experimental mathematics
rawtitle: Experimental mathematics and mathematical physics
ORCID:
Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646; Zudilin, Wadim/0000-0001-9551-2903

entry:
@InCollection{Bailey:2010:EMMb,
  author =       "David H. Bailey and Jonathan M. Borwein and David
                 Broadhurst and Wadim Zudilin",
  booktitle =    "Gems in experimental mathematics",
  title =        "Experimental mathematics and mathematical physics",
  volume =       "517",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "41--58",
  year =         "2010",
  DOI =          "https://doi.org/10.1090/conm/517/10132",
  MRclass =      "33F05 (11Y60 33F10 65D30)",
  MRnumber =     "2731060",
  MRreviewer =   "Zhonghua Li",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Contemp. Math.",
  URL =          "http://docserver.carma.newcastle.edu.au/1215/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646; Zudilin,
                 Wadim/0000-0001-9551-2903",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:2010:SMP
author: David H. Bailey and Jonathan M. Borwein
title: Solution to booktitle Monthly Problem 11515
type: Report
address: Berkeley, CA 94720, USA and Callaghan, NSW 2308, Australia
pages: 2
day: 15
month: jun
monthnumber: 6
year: 2010
bibdate: Fri Sep 30 08:23:00 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 08:23:00 ???
URL: http://www.davidhbailey.com/dhbpapers/amm-11515.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Solution to {{\booktitle{Monthly}}} Problem 11515
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
institution:
Lawrence Berkeley National Laboratory and School of Mathematical and Physical Sciences, University of Newcastle

remark:
The problem of evaluating $ S(t) = sum _n = 1^infty 4^n sin ^4 (t / 2^n) $ is shown to be equal to the simple closed form $ T(t) = t^2 - sin ^2 (t) $.

entry:
@TechReport{Bailey:2010:SMP,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Solution to {{\booktitle{Monthly}}} Problem 11515",
  type =         "Report",
  institution =  "Lawrence Berkeley National Laboratory and School of
                 Mathematical and Physical Sciences, University of
                 Newcastle",
  address =      "Berkeley, CA 94720, USA and Callaghan, NSW 2308,
                 Australia",
  pages =        "2",
  day =          "15",
  month =        jun,
  year =         "2010",
  bibdate =      "Fri Sep 30 08:23:00 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/amm-11515.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "The problem of evaluating $ S(t) = \sum_{n = 1}^\infty
                 4^n \sin^4 (t / 2^n) $ is shown to be equal to the
                 simple closed form $ T(t) = t^2 - \sin^2 (t) $.",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borwein:2010:CFC
author: Jonathan M. Borwein and Jon D. Vanderwerff
title: Convex functions: constructions, characterizations and counterexamples
volume: 109
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: x + 521
year: 2010
DOI: https://doi.org/10.1017/CBO9781139087322
ISBN: 0-521-85005-3 OR 0521850053
ISBN13: 978-0-521-85005-6 OR 9780521850056
MRclass: 49-02 (46B20 46N10 49J53 52A41 90C25)
MRnumber: 2596822
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: Encyclopedia of Mathematics and its Applications
URL: http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139087322
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Jon D. Vanderwerff
rawtitle: Convex functions: constructions, characterizations and counterexamples
ORCID: Borwein, Jonathan/0000-0002-1263-0646
TOC:
Frontmatter / i--vi Contents / vii--viii Preface / ix--x 1: Why convex? / 1--17 2: Convex functions on Euclidean spaces / 18--93 3: Finer structure of Euclidean spaces / 94--125 4: Convex functions on Banach spaces / 126--208 5: Duality between smoothness and strict convexity / 209--275 6: Further analytic topics / 276--337 7: Barriers and Legendre functions / 338--376 8: Convex functions and classifications of Banach spaces / 377--402 9: Monotone operators and the Fitzpatrick function / 403--459 10: Further remarks and notes / 460--482 List of symbols / 483--484 References / 485--507

rawTOC:
Frontmatter / i--vi \\ Contents / vii--viii \\ Preface / ix--x \\ 1: Why convex? / 1--17 \\ 2: Convex functions on Euclidean spaces / 18--93 \\ 3: Finer structure of Euclidean spaces / 94--125 \\ 4: Convex functions on Banach spaces / 126--208 \\ 5: Duality between smoothness and strict convexity / 209--275 \\ 6: Further analytic topics / 276--337 \\ 7: Barriers and Legendre functions / 338--376 \\ 8: Convex functions and classifications of Banach spaces / 377--402 \\ 9: Monotone operators and the Fitzpatrick function / 403--459 \\ 10: Further remarks and notes / 460--482 \\ List of symbols / 483--484 \\ References / 485--507

entry:
@Book{Borwein:2010:CFC,
  author =       "Jonathan M. Borwein and Jon D. Vanderwerff",
  title =        "Convex functions: constructions, characterizations and
                 counterexamples",
  volume =       "109",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "x + 521",
  year =         "2010",
  DOI =          "https://doi.org/10.1017/CBO9781139087322",
  ISBN =         "0-521-85005-3",
  ISBN-13 =      "978-0-521-85005-6",
  MRclass =      "49-02 (46B20 46N10 49J53 52A41 90C25)",
  MRnumber =     "2596822",
  MRreviewer =   "Heinz H. Bauschke",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Encyclopedia of Mathematics and its Applications",
  URL =          "http://ebooks.cambridge.org/ebook.jsf?bid=CBO9781139087322",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  tableofcontents = "Frontmatter / i--vi \\
                 Contents / vii--viii \\
                 Preface / ix--x \\
                 1: Why convex? / 1--17 \\
                 2: Convex functions on Euclidean spaces / 18--93 \\
                 3: Finer structure of Euclidean spaces / 94--125 \\
                 4: Convex functions on Banach spaces / 126--208 \\
                 5: Duality between smoothness and strict convexity /
                 209--275 \\
                 6: Further analytic topics / 276--337 \\
                 7: Barriers and Legendre functions / 338--376 \\
                 8: Convex functions and classifications of Banach
                 spaces / 377--402 \\
                 9: Monotone operators and the Fitzpatrick function /
                 403--459 \\
                 10: Further remarks and notes / 460--482 \\
                 List of symbols / 483--484 \\
                 References / 485--507",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2010:DTM
author: Jonathan M. Borwein and O-Yeat Chan
title: Duality in tails of multiple-zeta values
journal: j-INT-J-NUMBER-THEORY
volume: 6
number: 3
pages: 501--514
month: may
monthnumber: 5
year: 2010
DOI: https://doi.org/10.1142/S1793042110003058
ISSN: 1793-0421 (print), 1793-7310 (electronic) OR 17930421 (print), 17937310 (electronic)
ISSNL: 1793-0421 OR 17930421
MRclass: 11M32 (33C20 33F05)
MRnumber: 2652893
MRreviewer: Zhonghua Li
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: International Journal of Number Theory (IJNT)
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.worldscientific.com/worldscinet/ijnt
rawauthor: Jonathan M. Borwein and O-Yeat Chan
rawtitle: Duality in tails of multiple-zeta values
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/ijnt.bib

URL:
http://docserver.carma.newcastle.edu.au/1218/; https://www.worldscientific.com/doi/10.1142/S1793042110003058

abstract:
Duality relations are deduced for tails of multiple-zeta values using elementary methods. These formulas extend the classical duality formulas for multiple-zeta values.

rawabstract:
Duality relations are deduced for tails of multiple-zeta values using elementary methods. These formulas extend the classical duality formulas for multiple-zeta values.

entry:
@Article{Borwein:2010:DTM,
  author =       "Jonathan M. Borwein and O-Yeat Chan",
  title =        "Duality in tails of multiple-zeta values",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "6",
  number =       "3",
  pages =        "501--514",
  month =        may,
  year =         "2010",
  DOI =          "https://doi.org/10.1142/S1793042110003058",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  MRclass =      "11M32 (33C20 33F05)",
  MRnumber =     "2652893",
  MRreviewer =   "Zhonghua Li",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1218/;
                 https://www.worldscientific.com/doi/10.1142/S1793042110003058",
  abstract =     "Duality relations are deduced for tails of
                 multiple-zeta values using elementary methods. These
                 formulas extend the classical duality formulas for
                 multiple-zeta values.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2010:DTM",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borwein:2010:ECM
author: Jonathan Borwein and Peter B. Borwein
title: Experimental and computational mathematics: selected writings
publisher: Perfectly Scientific Press
address: Portland, OR, USA
pages: viii + 297
year: 2010
ISBN: 1-935638-05-X OR 193563805X
ISBN13: 978-1-935638-05-6 OR 9781935638056
MRclass: 11-06 (11-04 33-06)
MRnumber: 2841256
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 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein and Peter B. Borwein
rawtitle: Experimental and computational mathematics: selected writings
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Book{Borwein:2010:ECM,
  author =       "Jonathan Borwein and Peter B. Borwein",
  title =        "Experimental and computational mathematics: selected
                 writings",
  publisher =    "Perfectly Scientific Press",
  address =      "Portland, OR, USA",
  pages =        "viii + 297",
  year =         "2010",
  ISBN =         "1-935638-05-X",
  ISBN-13 =      "978-1-935638-05-6",
  MRclass =      "11-06 (11-04 33-06)",
  MRnumber =     "2841256",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "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:2010:ENE
author: Jonathan M. Borwein and Scott Sciffer
booktitle: Nonlinear analysis and optimization II. Optimization
title: An explicit non-expansive function whose subdifferential is the entire dual ball
volume: 514
publisher: pub-AMS
address: pub-AMS:adr
pages: 99--103
year: 2010
DOI: https://doi.org/10.1090/conm/514/10101
MRclass: 49J52
MRnumber: 2668255
MRreviewer: Shawn Xianfu Wang
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: Contemp. Math.
URL: http://docserver.carma.newcastle.edu.au/385/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Scott Sciffer
rawbooktitle: Nonlinear analysis and optimization {II}. {Optimization}
rawtitle: An explicit non-expansive function whose subdifferential is the entire dual ball
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2010:ENE,
  author =       "Jonathan M. Borwein and Scott Sciffer",
  booktitle =    "Nonlinear analysis and optimization {II}.
                 {Optimization}",
  title =        "An explicit non-expansive function whose
                 subdifferential is the entire dual ball",
  volume =       "514",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "99--103",
  year =         "2010",
  DOI =          "https://doi.org/10.1090/conm/514/10101",
  MRclass =      "49J52",
  MRnumber =     "2668255",
  MRreviewer =   "Shawn Xianfu Wang",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Contemp. Math.",
  URL =          "http://docserver.carma.newcastle.edu.au/385/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2010:FCV
author: Jonathan M. Borwein
booktitle: Variational analysis and generalized differentiation in optimization and control
title: Future challenges for variational analysis
volume: 47
publisher: pub-SV
address: pub-SV:adr
pages: 95--107
year: 2010
DOI: https://doi.org/10.1007/978-1-4419-0437-9_4
MRclass: 49J53
MRnumber: 2766756
MRreviewer: B. Mordukhovich
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: Springer Optim. Appl.
URL: http://docserver.carma.newcastle.edu.au/396/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawbooktitle: Variational analysis and generalized differentiation in optimization and control
rawtitle: Future challenges for variational analysis
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2010:FCV,
  author =       "Jonathan M. Borwein",
  booktitle =    "Variational analysis and generalized differentiation
                 in optimization and control",
  title =        "Future challenges for variational analysis",
  volume =       "47",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "95--107",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/978-1-4419-0437-9_4",
  MRclass =      "49J53",
  MRnumber =     "2766756",
  MRreviewer =   "B. Mordukhovich",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Springer Optim. Appl.",
  URL =          "http://docserver.carma.newcastle.edu.au/396/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2010:FLF
author: Jonathan M. Borwein and Jon Vanderwerff
title: Frechet--Legendre functions and reflexive Banach spaces
journal: j-J-CONVEX-ANAL
volume: 17
number: 3--4
pages: 915--924
year: 2010
ISSN: 0944-6532 (print), 2363-6394 (electronic) OR 09446532 (print), 23636394 (electronic)
MRclass: 52A41 (46G05 46N10 49J53 90C25)
MRnumber: 2731284
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 Hedi Attouch.
URL: http://www.heldermann.de/JCA/JCA17/JCA173/jca17057.htm
fjournal: Journal of Convex Analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.heldermann.de/JCA/jcacon.htm
rawauthor: Jonathan M. Borwein and Jon Vanderwerff
rawnote: Special volume in honour of Hedi Attouch.
rawtitle: {Fr{\'e}chet--Legendre} functions and reflexive {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
A 2001 article by Bauschke, Borwein and Combettes [2] showed how to extend naturally the classical definitions of essential smoothness and essential strict convexity from functions on R(n) in a compatible fashion to any Banach space. They were able, among other things, to show that substantial duality results hold for Legendre functions in reflexive spaces. That article focused on essential smoothness in the Gateaux sense. Our goal herein is to show that similar results hold for Frechet smoothness and to study related properties of such functions on reflexive Banach spaces.

rawabstract:
A 2001 article by Bauschke, Borwein and Combettes [2] showed how to extend naturally the classical definitions of essential smoothness and essential strict convexity from functions on R(n) in a compatible fashion to any Banach space. They were able, among other things, to show that substantial duality results hold for Legendre functions in reflexive spaces. That article focused on essential smoothness in the Gateaux sense. Our goal herein is to show that similar results hold for Frechet smoothness and to study related properties of such functions on reflexive Banach spaces.

entry:
@Article{Borwein:2010:FLF,
  author =       "Jonathan M. Borwein and Jon Vanderwerff",
  title =        "{Fr{\'e}chet--Legendre} functions and reflexive
                 {Banach} spaces",
  journal =      j-J-CONVEX-ANAL,
  volume =       "17",
  number =       "3--4",
  pages =        "915--924",
  year =         "2010",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "52A41 (46G05 46N10 49J53 90C25)",
  MRnumber =     "2731284",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Special volume in honour of Hedi Attouch.",
  URL =          "http://www.heldermann.de/JCA/JCA17/JCA173/jca17057.htm",
  abstract =     "A 2001 article by Bauschke, Borwein and Combettes [2]
                 showed how to extend naturally the classical
                 definitions of essential smoothness and essential
                 strict convexity from functions on R(n) in a compatible
                 fashion to any Banach space. They were able, among
                 other things, to show that substantial duality results
                 hold for Legendre functions in reflexive spaces. That
                 article focused on essential smoothness in the Gateaux
                 sense. Our goal herein is to show that similar results
                 hold for Frechet smoothness and to study related
                 properties of such functions on reflexive Banach
                 spaces.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Convex Analysis",
  journal-URL =  "http://www.heldermann.de/JCA/jcacon.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  unique-id =    "Borwein:2010:FLF",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2010:FYM
author: Jonathan M. Borwein
title: Fifty years of maximal monotonicity
journal: j-OPTIM-LETT
volume: 4
number: 4
pages: 473--490
year: 2010
DOI: https://doi.org/10.1007/s11590-010-0178-x
ISSN: 1862-4472 (print), 1862-4480 (electronic) OR 18624472 (print), 18624480 (electronic)
ISSNL: 1862-4472 OR 18624472
MRclass: 47H05 (47H09 49-02 49J53 90C25 90C33)
MRnumber: 2719898
MRreviewer: Simeon Reich
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1221/
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
rawtitle: Fifty years of maximal monotonicity
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Maximal monotone operator theory is about to turn (or just has turned) 50. I intend to briefly survey the history of the subject. I shall try to explain why maximal monotone operators are both interesting and important-culminating with a description of the remarkable progress made during the past decade.

rawabstract:
Maximal monotone operator theory is about to turn (or just has turned) 50. I intend to briefly survey the history of the subject. I shall try to explain why maximal monotone operators are both interesting and important-culminating with a description of the remarkable progress made during the past decade.

entry:
@Article{Borwein:2010:FYM,
  author =       "Jonathan M. Borwein",
  title =        "Fifty years of maximal monotonicity",
  journal =      j-OPTIM-LETT,
  volume =       "4",
  number =       "4",
  pages =        "473--490",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/s11590-010-0178-x",
  ISSN =         "1862-4472 (print), 1862-4480 (electronic)",
  ISSN-L =       "1862-4472",
  MRclass =      "47H05 (47H09 49-02 49J53 90C25 90C33)",
  MRnumber =     "2719898",
  MRreviewer =   "Simeon Reich",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1221/",
  abstract =     "Maximal monotone operator theory is about to turn (or
                 just has turned) 50. I intend to briefly survey the
                 history of the subject. I shall try to explain why
                 maximal monotone operators are both interesting and
                 important-culminating with a description of the
                 remarkable progress made during the past decade.",
  acknowledgement = ack-nhfb,
  ajournal =     "Optim. Lett.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Optimization Letters",
  journal-URL =  "http://link.springer.com/journal/11590",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  unique-id =    "Borwein:2010:FYM",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2010:HDB
author: Jonathan M. Borwein and O-Yeat Chan and R. E. Crandall
title: Higher-Dimensional Box Integrals
journal: j-EXP-MATH
volume: 19
number: 4
pages: 431--446
year: 2010
DOI: https://doi.org/10.1080/10586458.2010.10390634
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 33B30
MRnumber: 2778656
MRreviewer: Cristinel Mortici
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1223/; http://projecteuclid.org/euclid.em/1317758103
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 O-Yeat Chan and R. E. Crandall
rawtitle: Higher-Dimensional Box Integrals
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
http://projecteuclid.org/euclid.em; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/expmath.bib; http://www.tandfonline.com/toc/uexm20/19/4

abstract:
Herein, with the aid of substantial symbolic computation, we solve previously open problems in the theory of n-dimensional box integrals B(n)(s) := <vertical bar(r) over bar vertical bar(s)>, (r) over bar is an element of [0, 1](n). In particular, we resolve an elusive integral called kappa(5) that previously acted as a ``blockade'' against closed-form evaluation in n = 5 dimensions. In consequence, we now know that B(n) (integer) can be given a closed form for n = 1, 2, 3, 4, 5. We also find the general residue at the pole at s = n, this leading to new relations and definite integrals; for example, we are able to give the first nontrivial closed forms for six-dimensional box integrals and to show hyperclosure of B(6)(even). The Clausen function and its generalizations play a central role in these higher-dimensional evaluations. Our results provide stringent test scenarios for symbolic-algebra simplification methods.

rawabstract:
Herein, with the aid of substantial symbolic computation, we solve previously open problems in the theory of n-dimensional box integrals B(n)(s) := <vertical bar(r) over bar vertical bar(s)>, (r) over bar is an element of [0, 1](n). In particular, we resolve an elusive integral called kappa(5) that previously acted as a ``blockade'' against closed-form evaluation in n = 5 dimensions. In consequence, we now know that B(n) (integer) can be given a closed form for n = 1, 2, 3, 4, 5. We also find the general residue at the pole at s = n, this leading to new relations and definite integrals; for example, we are able to give the first nontrivial closed forms for six-dimensional box integrals and to show hyperclosure of B(6)(even). The Clausen function and its generalizations play a central role in these higher-dimensional evaluations. Our results provide stringent test scenarios for symbolic-algebra simplification methods.

entry:
@Article{Borwein:2010:HDB,
  author =       "Jonathan M. Borwein and O-Yeat Chan and R. E.
                 Crandall",
  title =        "Higher-Dimensional Box Integrals",
  journal =      j-EXP-MATH,
  volume =       "19",
  number =       "4",
  pages =        "431--446",
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2010.10390634",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "33B30",
  MRnumber =     "2778656",
  MRreviewer =   "Cristinel Mortici",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib;
                 http://www.tandfonline.com/toc/uexm20/19/4",
  URL =          "http://docserver.carma.newcastle.edu.au/1223/;
                 http://projecteuclid.org/euclid.em/1317758103",
  abstract =     "Herein, with the aid of substantial symbolic
                 computation, we solve previously open problems in the
                 theory of n-dimensional box integrals B(n)(s) :=
                 <vertical bar(r) over bar vertical bar(s)>, (r) over
                 bar is an element of [0, 1](n). In particular, we
                 resolve an elusive integral called kappa(5) that
                 previously acted as a ``blockade'' against closed-form
                 evaluation in n = 5 dimensions. In consequence, we now
                 know that B(n) (integer) can be given a closed form for
                 n = 1, 2, 3, 4, 5. We also find the general residue at
                 the pole at s = n, this leading to new relations and
                 definite integrals; for example, we are able to give
                 the first nontrivial closed forms for six-dimensional
                 box integrals and to show hyperclosure of B(6)(even).
                 The Clausen function and its generalizations play a
                 central role in these higher-dimensional evaluations.
                 Our results provide stringent test scenarios for
                 symbolic-algebra simplification methods.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  unique-id =    "Borwein:2010:HDB",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2010:MEPa
author: J. M. Borwein
booktitle: ICME10 Proceedings, July 2010
title: Mathematics by Experiment: Plausible Reasoning in the 21st Century
pages: ??--??
year: 2010
bibdate: Sat Aug 13 16:42:06 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 16:42:06 ???
URL: http://docserver.carma.newcastle.edu.au/272/
remark: CoLab Preprint 272.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein
rawbooktitle: ICME10 Proceedings, July 2010
rawtitle: Mathematics by Experiment: Plausible Reasoning in the 21st Century
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics.

rawabstract:
If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics.

entry:
@InProceedings{Borwein:2010:MEPa,
  author =       "J. M. Borwein",
  booktitle =    "ICME10 Proceedings, July 2010",
  title =        "Mathematics by Experiment: Plausible Reasoning in the
                 21st Century",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2010",
  bibdate =      "Sat Aug 13 16:42:06 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/272/",
  abstract =     "If mathematics describes an objective world just like
                 physics, there is no reason why inductive methods
                 should not be applied in mathematics just the same as
                 in physics.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CoLab Preprint 272.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2010:NSF
author: David Borwein and Jonathan M. Borwein and Isaac E. Leonard
title: $ L_p $ norms and the sinc function
journal: j-AMER-MATH-MONTHLY
volume: 117
number: 6
pages: 528--539
year: 2010
CODEN: AMMYAE
DOI: https://doi.org/10.4169/000298910X492817
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 26A09
MRnumber: 2662705
MRreviewer: Timo A. J. Tossavainen
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.jstor.org/journals/00029890.html
rawauthor: David Borwein and Jonathan M. Borwein and Isaac E. Leonard
rawtitle: {$ L_p $} norms and the sinc function
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
It's everywhere! It's everywhere! .... In this note we give elementary proofs of some of the striking asymptotic properties of the p-norm of the ubiquitous sinc function. Based on experimental evidence we conjecture some enticing further properties of the p-norm as a function of p. See, for example, http://www.carma.newcastle.edu.au/(similar to)jb616/oscillatory.pdf.

rawabstract:
It's everywhere! It's everywhere! .... In this note we give elementary proofs of some of the striking asymptotic properties of the p-norm of the ubiquitous sinc function. Based on experimental evidence we conjecture some enticing further properties of the p-norm as a function of p. See, for example, http://www.carma.newcastle.edu.au/(similar to)jb616/oscillatory.pdf.

entry:
@Article{Borwein:2010:NSF,
  author =       "David Borwein and Jonathan M. Borwein and Isaac E.
                 Leonard",
  title =        "{$ L_p $} norms and the sinc function",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "117",
  number =       "6",
  pages =        "528--539",
  year =         "2010",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/000298910X492817",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26A09",
  MRnumber =     "2662705",
  MRreviewer =   "Timo A. J. Tossavainen",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  abstract =     "It's everywhere! It's everywhere! .... In this note we
                 give elementary proofs of some of the striking
                 asymptotic properties of the p-norm of the ubiquitous
                 sinc function. Based on experimental evidence we
                 conjecture some enticing further properties of the
                 p-norm as a function of p. See, for example,
                 http://www.carma.newcastle.edu.au/(similar
                 to)jb616/oscillatory.pdf.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  unique-id =    "Borwein:2010:PNS",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2010:RWP
author: Jonathan M. Borwein and Dirk Nuyens and Armin Straub and James Wan
booktitle: 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
title: Random walks in the plane
publisher: Assoc. Discrete Math. Theor. Comput. Sci.
address: Nancy, France
pages: 191--202
year: 2010
MRclass: 05C81 (05A15)
MRnumber: 2673835
MRreviewer: Manuel Batista Branco
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: Discrete Math. Theor. Comput. Sci. Proc., AN
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
bookURL: http://math.sfsu.edu/fpsac/
rawauthor: Jonathan M. Borwein and Dirk Nuyens and Armin Straub and James Wan
rawbooktitle: {22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)}
rawtitle: Random walks in the plane
ORCID:
Borwein, Jonathan/0000-0002-1263-0646; Nuyens, Dirk/0000-0002-4555-2314; Straub, Armin/0000-0001-6802-6053

entry:
@InCollection{Borwein:2010:RWP,
  author =       "Jonathan M. Borwein and Dirk Nuyens and Armin Straub
                 and James Wan",
  booktitle =    "{22nd International Conference on Formal Power Series
                 and Algebraic Combinatorics (FPSAC 2010)}",
  title =        "Random walks in the plane",
  publisher =    "Assoc. Discrete Math. Theor. Comput. Sci.",
  address =      "Nancy, France",
  pages =        "191--202",
  year =         "2010",
  MRclass =      "05C81 (05A15)",
  MRnumber =     "2673835",
  MRreviewer =   "Manuel Batista Branco",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Discrete Math. Theor. Comput. Sci. Proc., AN",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  book-URL =     "http://math.sfsu.edu/fpsac/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Nuyens,
                 Dirk/0000-0002-4555-2314; Straub,
                 Armin/0000-0001-6802-6053",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2010:SCC
author: Jonathan M. Borwein and Warren B. Moors
title: Stability of closedness of convex cones under linear mappings II
journal: Journal of Nonlinear Analysis and Optimization: Theory & Applications
volume: 1
number: 1
pages: 1--7
year: 2010
ISSN: 1906-9685 OR 19069685
ISSNL: 1906-9685 OR 19069685
MRclass: 49J53 (47N10 90C05 90C31)
MRnumber: 2911681
MRreviewer: John R. Giles
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Journal of Nonlinear Analysis and Optimization. Theory and Applications
acknowledgement: ack-nhfb
ajournal: J. Nonlinear Anal. Optim.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sci.nu.ac.th/jnao
rawauthor: Jonathan M. Borwein and Warren B. Moors
rawtitle: Stability of closedness of convex cones under linear mappings {II}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1226/; http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/5

entry:
@Article{Borwein:2010:SCC,
  author =       "Jonathan M. Borwein and Warren B. Moors",
  title =        "Stability of closedness of convex cones under linear
                 mappings {II}",
  journal =      "Journal of Nonlinear Analysis and Optimization: Theory
                 \& Applications",
  volume =       "1",
  number =       "1",
  pages =        "1--7",
  year =         "2010",
  ISSN =         "1906-9685",
  ISSN-L =       "1906-9685",
  MRclass =      "49J53 (47N10 90C05 90C31)",
  MRnumber =     "2911681",
  MRreviewer =   "John R. Giles",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1226/;
                 http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/5",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Nonlinear Anal. Optim.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Nonlinear Analysis and Optimization. Theory
                 and Applications",
  journal-URL =  "http://www.sci.nu.ac.th/jnao",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:2010:TTT
author: Jonathan M. Borwein
title: Talking to Telstra: Two weeks spent with Australia's largest Telco
pages: 1--7
day: 27
month: sep
monthnumber: 9
year: 2010
bibdate: Tue Aug 16 10:00:52 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:00:52 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawtitle: Talking to {Telstra}: Two weeks spent with {Australia}'s largest {Telco}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
note:
Response to Australian Communications and Media Authority (ACMA) enquiry, Reconnecting the Customer, Sept 27, 2010.

remark:
The background for this document is provided by Jon's daughter, Naomi, in a talk at his funeral, and recorded at url http://jonborwein.org/2016/08/my-father-by-naomi-borwein/: ``In 2010 Jon changed his Internet and telephone provider to Telstra, the leading national telecommunications provider in Australia. Telstra started by providing service to J Brow-ein, and things went down hill from there. So Jon chronicled his month-long quest to fix his Internet and telephone connection in a highly amusing, but frustratingly bureaucratic, sixty page document. It ended up being obligatory reading for all the vice presidents at Telstra, and was sent as part of a package to the Australian Government's royal commission on the dysfunction of Big Telcos in the country. This was under the umbrella of the Australian Communications and Media Authority, which is an Australian Government statutory authority. Jon was personally thanked in the final report that was lodged in parliament.''

rawnote:
Response to Australian Communications and Media Authority (ACMA) enquiry, Reconnecting the Customer, Sept 27, 2010.

entry:
@Unpublished{Borwein:2010:TTT,
  author =       "Jonathan M. Borwein",
  title =        "Talking to {Telstra}: Two weeks spent with
                 {Australia}'s largest {Telco}",
  day =          "27",
  month =        sep,
  year =         "2010",
  bibdate =      "Tue Aug 16 10:00:52 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Response to Australian Communications and Media
                 Authority (ACMA) enquiry, Reconnecting the Customer,
                 Sept 27, 2010.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "The background for this document is provided by Jon's
                 daughter, Naomi, in a talk at his funeral, and recorded
                 at
                 \url{http://jonborwein.org/2016/08/my-father-by-naomi-borwein/}:
                 ``In 2010 Jon changed his Internet and telephone
                 provider to Telstra, the leading national
                 telecommunications provider in Australia. Telstra
                 started by providing service to J Brow-ein, and things
                 went down hill from there. So Jon chronicled his
                 month-long quest to fix his Internet and telephone
                 connection in a highly amusing, but frustratingly
                 bureaucratic, sixty page document. It ended up being
                 obligatory reading for all the vice presidents at
                 Telstra, and was sent as part of a package to the
                 Australian Government's royal commission on the
                 dysfunction of Big Telcos in the country. This was
                 under the umbrella of the Australian Communications and
                 Media Authority, which is an Australian Government
                 statutory authority. Jon was personally thanked in the
                 final report that was lodged in parliament.''",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bacak:2011:DCL
author: Miroslav Bacak and Jonathan M. Borwein
title: On difference convexity of locally Lipschitz functions
journal: j-OPTIMIZATION
volume: 60
number: 8--9
pages: 961--978
year: 2011
CODEN: OPTZDQ
DOI: https://doi.org/10.1080/02331931003770411
ISSN: 0233-1934, 0323-3898 OR 02331934, 03233898
ISSNL: 0233-1934 OR 02331934
MRclass: 49J53 (49-02)
MRnumber: 2860286
MRreviewer: Shawn Xianfu Wang
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/1446/
fjournal: Optimization
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.tandfonline.com/loi/gopt20
rawauthor: Miroslav Ba{\v{c}}{\'a}k and Jonathan M. Borwein
rawtitle: On difference convexity of locally {Lipschitz} functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We survey and enhance salient parts of the literature about difference convex (DC) functions with specific regard to current knowledge and applications of DC functions.

rawabstract:
We survey and enhance salient parts of the literature about difference convex (DC) functions with specific regard to current knowledge and applications of DC functions.

entry:
@Article{Bacak:2011:DCL,
  author =       "Miroslav Ba{\v{c}}{\'a}k and Jonathan M. Borwein",
  title =        "On difference convexity of locally {Lipschitz}
                 functions",
  journal =      j-OPTIMIZATION,
  volume =       "60",
  number =       "8--9",
  pages =        "961--978",
  year =         "2011",
  CODEN =        "OPTZDQ",
  DOI =          "https://doi.org/10.1080/02331931003770411",
  ISSN =         "0233-1934, 0323-3898",
  ISSN-L =       "0233-1934",
  MRclass =      "49J53 (49-02)",
  MRnumber =     "2860286",
  MRreviewer =   "Shawn Xianfu Wang",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1446/",
  abstract =     "We survey and enhance salient parts of the literature
                 about difference convex (DC) functions with specific
                 regard to current knowledge and applications of DC
                 functions.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Optimization",
  journal-URL =  "http://www.tandfonline.com/loi/gopt20",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  unique-id =    "Bacak:2011:DCL",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:2011:CPI
author: David H. Bailey and Jonathan M. Borwein and Andrew Mattingly and Glenn Wightwick
title: The Computation of Previously Inaccessible Digits of $ pi ^2 $ and Catalan's Constant
type: Report
pages: 18
day: 11
month: apr
monthnumber: 4
year: 2011
bibdate: Sat Apr 23 08:58:45 2011
bibtimestamp: 2011.04.23 08:58:45 ???
URL: http://crd.lbl.gov/~dhbailey/dhbpapers/bbp-bluegene.pdf
remark: Submitted to Notices of the AMS.
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^2 $ and {Catalan}'s Constant
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
institution:
Lawrence Berkeley National Laboratory; Centre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle; IBM Australia

address:
Berkeley, CA, USA; Callaghan, NSW 2308, Australia; St. Leonards, NSW 2065, Australia; Pyrmont, NSW 2009, Australia

entry:
@TechReport{Bailey:2011:CPI,
  author =       "David H. Bailey and Jonathan M. Borwein and Andrew
                 Mattingly and Glenn Wightwick",
  title =        "The Computation of Previously Inaccessible Digits of $
                 \pi^2 $ and {Catalan}'s Constant",
  type =         "Report",
  institution =  "Lawrence Berkeley National Laboratory; Centre for
                 Computer Assisted Research Mathematics and its
                 Applications (CARMA), University of Newcastle; IBM
                 Australia",
  address =      "Berkeley, CA, USA; Callaghan, NSW 2308, Australia; St.
                 Leonards, NSW 2065, Australia; Pyrmont, NSW 2009,
                 Australia",
  pages =        "18",
  day =          "11",
  month =        apr,
  year =         "2011",
  bibdate =      "Sat Apr 23 08:58:45 2011",
  bibsource =    "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://crd.lbl.gov/~dhbailey/dhbpapers/bbp-bluegene.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "Submitted to Notices of the AMS.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:2011:EAN
title: An Empirical Approach to the Normality of $ pi $
type: Report
number: CDMTCS-413
institution: Centre for Discrete Mathematics and Theoretical Computer Science, University of Auckland
address: Auckland, New Zealand
pages: i + 31
month: nov
monthnumber: 11
year: 2011
bibdate: Tue Aug 23 06:50:08 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.23 06:50:08 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawtitle: An Empirical Approach to the Normality of $ \pi $
author:
David H. Bailey and Jonathan M. Borwein and Cristian S. Calude and Michael J. Dinneen and Monica Dumitrescu and Alex Yee

URL:
http://docserver.carma.newcastle.edu.au/1382/; http://www.cs.auckland.ac.nz/research/groups/CDMTCS/researchreports/?download&paper_file=413

rawauthor:
David H. Bailey and Jonathan M. Borwein and Cristian S. Calude and Michael J. Dinneen and Monica Dumitrescu and Alex Yee

ORCID:
Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646; Calude, Cristian Sorin/0000-0002-8711-6799

entry:
@TechReport{Bailey:2011:EAN,
  author =       "David H. Bailey and Jonathan M. Borwein and Cristian
                 S. Calude and Michael J. Dinneen and Monica Dumitrescu
                 and Alex Yee",
  title =        "An Empirical Approach to the Normality of $ \pi $",
  type =         "Report",
  number =       "CDMTCS-413",
  institution =  "Centre for Discrete Mathematics and Theoretical
                 Computer Science, University of Auckland",
  address =      "Auckland, New Zealand",
  pages =        "i + 31",
  month =        nov,
  year =         "2011",
  bibdate =      "Tue Aug 23 06:50:08 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1382/;
                 http://www.cs.auckland.ac.nz/research/groups/CDMTCS/researchreports/?download&paper_file=413",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646; Calude, Cristian
                 Sorin/0000-0002-8711-6799",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2011:EEC
author: David H. Bailey and Jonathan M. Borwein
title: Exploratory experimentation and computation
journal: j-NAMS
volume: 58
number: 10
pages: 1410--1419
month: nov
monthnumber: 11
year: 2011
CODEN: AMNOAN
ISSN: 0002-9920 (print), 1088-9477 (electronic) OR 00029920 (print), 10889477 (electronic)
ISSNL: 0002-9920 OR 00029920
MRclass: 00A35
MRnumber: 2884022
MRreviewer: Eduard Glas
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/1396/; https://www.ams.org/notices/201110/rtx111001410p.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
rawtitle: Exploratory experimentation and computation
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
note:
Chinese translation in Mathematical Advances in Translation (Chinese Academy of Science), June 2012.

rawnote:
Chinese translation in Mathematical Advances in Translation (Chinese Academy of Science), June 2012.

entry:
@Article{Bailey:2011:EEC,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Exploratory experimentation and computation",
  journal =      j-NAMS,
  volume =       "58",
  number =       "10",
  pages =        "1410--1419",
  month =        nov,
  year =         "2011",
  CODEN =        "AMNOAN",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  MRclass =      "00A35",
  MRnumber =     "2884022",
  MRreviewer =   "Eduard Glas",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Chinese translation in Mathematical Advances in
                 Translation (Chinese Academy of Science), June 2012.",
  URL =          "http://docserver.carma.newcastle.edu.au/1396/;
                 https://www.ams.org/notices/201110/rtx111001410p.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:2011:GMDa
author: David H. Bailey and Jonathan M. Borwein
title: The Greatest Mathematical Discovery?
type: Report
institution: Lawrence Berkeley National Laboratory and Centre for Computer Assisted RMA, University of Newcastle
address: Berkeley, CA 94720, USA and Callaghan, NSW 2308, Australia
pages: 10
day: 8
month: may
monthnumber: 5
year: 2011
bibdate: Fri Aug 12 18:29:28 2016
bibtimestamp: 2016.08.12 18:29:28 ???
URL: http://www.davidhbailey.com/dhbpapers/decimal.pdf
keywords: decimal arithmetic history
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: The Greatest Mathematical Discovery?
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@TechReport{Bailey:2011:GMDa,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "The Greatest Mathematical Discovery?",
  type =         "Report",
  institution =  "Lawrence Berkeley National Laboratory and Centre for
                 Computer Assisted RMA, University of Newcastle",
  address =      "Berkeley, CA 94720, USA and Callaghan, NSW 2308,
                 Australia",
  pages =        "10",
  day =          "8",
  month =        may,
  year =         "2011",
  bibdate =      "Fri Aug 12 18:29:28 2016",
  bibsource =    "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.davidhbailey.com/dhbpapers/decimal.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "decimal arithmetic history",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2011:HPN
author: D. H. Bailey and J. M. Borwein
title: High-precision numerical integration: Progress and challenges
journal: j-J-SYMBOLIC-COMP
volume: 46
number: 7
pages: 741--754
month: jul
monthnumber: 7
year: 2011
CODEN: JSYCEH
DOI: https://doi.org/10.1016/j.jsc.2010.08.010
ISSN: 0747-7171 (print), 1095-855x (electronic) OR 07477171 (print), 1095855x (electronic)
ISSNL: 0747-7171 OR 07477171
MRclass: 65D30 (65Y05 68W30)
MRnumber: 2795208
MRreviewer: G. A. Evans
bibdate: Thu Aug 11 10:27:38 2016
bibtimestamp: 2016.08.11 10:27:38 ???
note: Special Issue in Honour of Keith Geddes on his 60th Birthday.
fjournal: Journal of Symbolic Computation
keywords: High-precision arithmetic; Ising theory; Numerical integration; Quadrature; Quantum field theory
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/07477171/
rawauthor: D. H. Bailey and J. M. Borwein
rawnote: Special Issue in Honour of Keith Geddes on his 60th Birthday.
rawtitle: High-precision numerical integration: Progress and challenges
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/jsymcomp.bib

URL:
http://docserver.carma.newcastle.edu.au/1444/; http://www.sciencedirect.com/science/article/pii/S0747717110001409

abstract:
One of the most fruitful advances in the field of experimental mathematics has been the development of practical methods for very high-precision numerical integration, a quest initiated by Keith Geddes and other researchers in the 1980s and 1990s. These techniques, when coupled with equally powerful integer relation detection methods, have resulted in the analytic evaluation of many integrals that previously were beyond the realm of symbolic techniques. This paper presents a survey of the current state-of-the-art in this area (including results by the present authors and others), mentions some new results, and then sketches what challenges lie ahead.

entry:
@Article{Bailey:2011:HPN,
  author =       "D. H. Bailey and J. M. Borwein",
  title =        "High-precision numerical integration: Progress and
                 challenges",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "46",
  number =       "7",
  pages =        "741--754",
  month =        jul,
  year =         "2011",
  CODEN =        "JSYCEH",
  DOI =          "https://doi.org/10.1016/j.jsc.2010.08.010",
  ISSN =         "0747-7171 (print), 1095-855x (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "65D30 (65Y05 68W30)",
  MRnumber =     "2795208",
  MRreviewer =   "G. A. Evans",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
  note =         "Special Issue in Honour of Keith Geddes on his 60th
                 Birthday.",
  URL =          "http://docserver.carma.newcastle.edu.au/1444/;
                 http://www.sciencedirect.com/science/article/pii/S0747717110001409",
  abstract =     "One of the most fruitful advances in the field of
                 experimental mathematics has been the development of
                 practical methods for very high-precision numerical
                 integration, a quest initiated by Keith Geddes and
                 other researchers in the 1980s and 1990s. These
                 techniques, when coupled with equally powerful integer
                 relation detection methods, have resulted in the
                 analytic evaluation of many integrals that previously
                 were beyond the realm of symbolic techniques. This
                 paper presents a survey of the current state-of-the-art
                 in this area (including results by the present authors
                 and others), mentions some new results, and then
                 sketches what challenges lie ahead.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171/",
  keywords =     "High-precision arithmetic; Ising theory; Numerical
                 integration; Quadrature; Quantum field theory",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:2011:BBT
author: H. H. Bauschke and J. M. Borwein and X. Wang and L. Yao
title: The Brezis--Browder Theorem in a general Banach space
journal: ArXiv e-prints
pages: 741--754
month: oct
monthnumber: 10
year: 2011
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/2011arXiv1110.5706B
keywords: Mathematics - Functional Analysis, 47A06 (Primary), 47H05, 47B65 (Secondary), 47N10, 90C25
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: H. H. Bauschke and J. M. Borwein and X. Wang and L. Yao
rawtitle: The {Br{\'e}zis--Browder} Theorem in a general {Banach} space
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
abstract:
During the 1970s Brezis and Browder presented a now classical characterization of maximal monotonicity of monotone linear relations in reflexive spaces. In this paper, we extend and refine their result to a general Banach space.

rawabstract:
During the 1970s Br{\'e}zis and Browder presented a now classical characterization of maximal monotonicity of monotone linear relations in reflexive spaces. In this paper, we extend and refine their result to a general Banach space.

entry:
@Article{Bauschke:2011:BBT,
  author =       "H. H. Bauschke and J. M. Borwein and X. Wang and L.
                 Yao",
  title =        "The {Br{\'e}zis--Browder} Theorem in a general
                 {Banach} space",
  journal =      "ArXiv e-prints",
  month =        oct,
  year =         "2011",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011arXiv1110.5706B",
  abstract =     "During the 1970s Br{\'e}zis and Browder presented a
                 now classical characterization of maximal monotonicity
                 of monotone linear relations in reflexive spaces. In
                 this paper, we extend and refine their result to a
                 general Banach space.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1110.5706",
  keywords =     "Mathematics - Functional Analysis, 47A06 (Primary),
                 47H05, 47B65 (Secondary), 47N10, 90C25",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:2011:CPM
author: H. H. Bauschke and J. M. Borwein and X. Wang and L. Yao
title: Construction of pathological maximally monotone operators on non-reflexive Banach spaces
journal: ArXiv e-prints
pages: 741--754
month: aug
monthnumber: 8
year: 2011
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/2011arXiv1108.1463B; http://docserver.carma.newcastle.edu.au/1090/
keywords: Mathematics - Functional Analysis, Primary 47A06, 47H05, Secondary 47B65, 47N1, 90C25
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: H. H. Bauschke and J. M. Borwein and X. Wang and L. Yao
rawtitle: Construction of pathological maximally monotone operators on non-reflexive {Banach} spaces
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper, we construct maximally monotone operators that are not of Gossez's dense-type (D) in many nonreflexive spaces. Many of these operators also fail to possess the Bronsted--Rockafellar (BR) property. Using these operators, we show that the partial inf-convolution of two BC--functions will not always be a BC--function. This provides a negative answer to a challenging question posed by Stephen Simons. Among other consequences, we deduce that every Banach space which contains an isomorphic copy of the James space $ mathbf J $ or its dual $ mathbf J^* $, or $ c_0 $ or its dual $ ell ^1 $, admits a non type (D) operator.

rawabstract:
In this paper, we construct maximally monotone operators that are not of Gossez's dense-type (D) in many nonreflexive spaces. Many of these operators also fail to possess the Br{\o}nsted--Rockafellar (BR) property. Using these operators, we show that the partial inf-convolution of two BC--functions will not always be a BC--function. This provides a negative answer to a challenging question posed by Stephen Simons. Among other consequences, we deduce that every Banach space which contains an isomorphic copy of the James space $ \mathbf {J} $ or its dual $ \mathbf {J}^* $, or $ c_0 $ or its dual $ \ell^1 $, admits a non type (D) operator.

entry:
@Article{Bauschke:2011:CPM,
  author =       "H. H. Bauschke and J. M. Borwein and X. Wang and L.
                 Yao",
  title =        "Construction of pathological maximally monotone
                 operators on non-reflexive {Banach} spaces",
  journal =      "ArXiv e-prints",
  month =        aug,
  year =         "2011",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011arXiv1108.1463B;
                 http://docserver.carma.newcastle.edu.au/1090/",
  abstract =     "In this paper, we construct maximally monotone
                 operators that are not of Gossez's dense-type (D) in
                 many nonreflexive spaces. Many of these operators also
                 fail to possess the Br{\o}nsted--Rockafellar (BR)
                 property. Using these operators, we show that the
                 partial inf-convolution of two BC--functions will not
                 always be a BC--function. This provides a negative
                 answer to a challenging question posed by Stephen
                 Simons. Among other consequences, we deduce that every
                 Banach space which contains an isomorphic copy of the
                 James space $ \mathbf {J} $ or its dual $ \mathbf {J}^*
                 $, or $ c_0 $ or its dual $ \ell^1 $, admits a non type
                 (D) operator.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1108.1463",
  keywords =     "Mathematics - Functional Analysis, Primary 47A06,
                 47H05, Secondary 47B65, 47N1, 90C25",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:2011:EMM
author: H. H. Bauschke and J. M. Borwein and X. Wang and L. Yao
title: Every maximally monotone operator of Fitzpatrick--Phelps type is actually of dense type
journal: ArXiv e-prints
pages: 741--754
month: apr
monthnumber: 4
year: 2011
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/2011arXiv1104.0750B; http://docserver.carma.newcastle.edu.au/1442/
keywords: Mathematics - Functional Analysis, Primary 47H05, Secondary 46B10, 47N10, 90C25
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: H. H. Bauschke and J. M. Borwein and X. Wang and L. Yao
rawtitle: Every maximally monotone operator of {Fitzpatrick--Phelps} type is actually of dense type
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
abstract:
We show that every maximally monotone operator of Fitzpatrick--Phelps type defined on a real Banach space must be of dense type. This provides an affirmative answer to a question posed by Stephen Simons in 2001 and implies that various important notions of monotonicity coincide.

rawabstract:
We show that every maximally monotone operator of Fitzpatrick--Phelps type defined on a real Banach space must be of dense type. This provides an affirmative answer to a question posed by Stephen Simons in 2001 and implies that various important notions of monotonicity coincide.

entry:
@Article{Bauschke:2011:EMM,
  author =       "H. H. Bauschke and J. M. Borwein and X. Wang and L.
                 Yao",
  title =        "Every maximally monotone operator of
                 {Fitzpatrick--Phelps} type is actually of dense type",
  journal =      "ArXiv e-prints",
  month =        apr,
  year =         "2011",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011arXiv1104.0750B;
                 http://docserver.carma.newcastle.edu.au/1442/",
  abstract =     "We show that every maximally monotone operator of
                 Fitzpatrick--Phelps type defined on a real Banach space
                 must be of dense type. This provides an affirmative
                 answer to a question posed by Stephen Simons in 2001
                 and implies that various important notions of
                 monotonicity coincide.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1104.0750",
  keywords =     "Mathematics - Functional Analysis, Primary 47H05,
                 Secondary 46B10, 47N10, 90C25",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:2011:MML
author: Heinz H. Bauschke and Jonathan M. Borwein and Xianfu Wang and Liangjin Yao
journal: ArXiv e-prints
pages: 15
day: 21
month: mar
monthnumber: 3
year: 2011
bibdate: Tue Aug 16 09:57:56 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:57:56 ???
URL: http://adsabs.harvard.edu/abs/2011arXiv1103.6239B; http://arxiv.org/abs/1103.6239
keywords: Mathematics - Functional Analysis, Primary 47A06, 47H05, Secondary 47B65, 47N10, 90C25
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein and Xianfu Wang and Liangjin Yao
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
title:
For maximally monotone linear relations, dense type, negative-infimum type, and Fitzpatrick--Phelps type all coincide with monotonicity of the adjoint

abstract:
It is shown that, for maximally monotone linear relations defined on a general Banach space, the monotonicities of dense type, of negative-infimum type, and of Fitzpatrick--Phelps type are the same and equivalent to monotonicity of the adjoint. This result also provides affirmative answers to two problems: one posed by Phelps and Simons, and the other by Simons.

rawabstract:
It is shown that, for maximally monotone linear relations defined on a general Banach space, the monotonicities of dense type, of negative-infimum type, and of Fitzpatrick--Phelps type are the same and equivalent to monotonicity of the adjoint. This result also provides affirmative answers to two problems: one posed by Phelps and Simons, and the other by Simons.

rawtitle:
For maximally monotone linear relations, dense type, negative-infimum type, and {Fitzpatrick--Phelps} type all coincide with monotonicity of the adjoint

entry:
@Article{Bauschke:2011:MML,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein and Xianfu
                 Wang and Liangjin Yao",
  title =        "For maximally monotone linear relations, dense type,
                 negative-infimum type, and {Fitzpatrick--Phelps} type
                 all coincide with monotonicity of the adjoint",
  journal =      "ArXiv e-prints",
  pages =        "15",
  day =          "21",
  month =        mar,
  year =         "2011",
  bibdate =      "Tue Aug 16 09:57:56 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011arXiv1103.6239B;
                 http://arxiv.org/abs/1103.6239",
  abstract =     "It is shown that, for maximally monotone linear
                 relations defined on a general Banach space, the
                 monotonicities of dense type, of negative-infimum type,
                 and of Fitzpatrick--Phelps type are the same and
                 equivalent to monotonicity of the adjoint. This result
                 also provides affirmative answers to two problems: one
                 posed by Phelps and Simons, and the other by Simons.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1103.6239",
  keywords =     "Mathematics - Functional Analysis, Primary 47A06,
                 47H05, Secondary 47B65, 47N10, 90C25",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:2011:MOB
author: H. H. Bauschke and J. M. Borwein and X. Wang and L. Yao
title: Monotone operators and ``bigger conjugate'' functions
journal: ArXiv e-prints
pages: 15
month: aug
monthnumber: 8
year: 2011
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/2011arXiv1108.2578B; http://docserver.carma.newcastle.edu.au/1477/
keywords: Mathematics - Functional Analysis, Primary 47A06, 47H05, Secondary 47B65, 47N10, 90C25
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: H. H. Bauschke and J. M. Borwein and X. Wang and L. Yao
rawtitle: Monotone operators and ``bigger conjugate'' functions
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
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 Br{\'e}zis, Crandall and Pazy. Our work also reinforces the importance of understanding unbounded skew linear relations to construct monotone operators with unexpected properties.

entry:
@Article{Bauschke:2011:MOB,
  author =       "H. H. Bauschke and J. M. Borwein and X. Wang and L.
                 Yao",
  title =        "Monotone operators and ``bigger conjugate''
                 functions",
  journal =      "ArXiv e-prints",
  month =        aug,
  year =         "2011",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011arXiv1108.2578B;
                 http://docserver.carma.newcastle.edu.au/1477/",
  abstract =     "We study a question posed by Stephen Simons in his
                 2008 monograph involving ``bigger conjugate'' (BC)
                 functions and the partial infimal convolution. As
                 Simons demonstrated in his monograph, these function
                 have been crucial to the understanding and advancement
                 of the state-of-the-art of harder problems in monotone
                 operator theory, especially the sum problem. In this
                 paper, we provide some tools for further analysis of
                 BC--functions which allow us to answer Simons' problem
                 in the negative. We are also able to refute a similar
                 but much harder conjecture which would have generalized
                 a classical result of Br{\'e}zis, Crandall and Pazy.
                 Our work also reinforces the importance of
                 understanding unbounded skew linear relations to
                 construct monotone operators with unexpected
                 properties.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1108.2578",
  keywords =     "Mathematics - Functional Analysis, Primary 47A06,
                 47H05, Secondary 47B65, 47N10, 90C25",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2011:BRI
author: Jonathan Michael Borwein
journal: j-IEEE-CONTROL-SYST-MAG
volume: 31
number: 1
pages: 74--77
year: 2011
CODEN: ISMAD7
DOI: https://doi.org/10.1109/MCS.2010.939261
ISSN: 1066-033X (print), 1941-000X (electronic) OR 1066033X (print), 1941000X (electronic)
ISSNL: 1066-033X OR 1066033X
MRclass: 00A17
MRnumber: 2789813
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: IEEE Control Systems Magazine
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Michael Borwein
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Book Review: booktitle Implicit functions and solution mappings, by Asen L. Dontchev and R. Tyrrell Rockafellar, Springer, 2009, ISBN 10: 0-387-87820-3, ISBN 13: 978-0-387-87820-1

rawtitle:
Book Review: {{\booktitle{Implicit functions and solution mappings}}, by Asen L. Dontchev and R. Tyrrell Rockafellar, Springer, 2009, ISBN 10: 0-387-87820-3, ISBN 13: 978-0-387-87820-1}

entry:
@Article{Borwein:2011:BRI,
  author =       "Jonathan Michael Borwein",
  title =        "Book Review: {{\booktitle{Implicit functions and
                 solution mappings}}, by Asen L. Dontchev and R. Tyrrell
                 Rockafellar, Springer, 2009, ISBN 10: 0-387-87820-3,
                 ISBN 13: 978-0-387-87820-1}",
  journal =      j-IEEE-CONTROL-SYST-MAG,
  volume =       "31",
  number =       "1",
  pages =        "74--77",
  year =         "2011",
  CODEN =        "ISMAD7",
  DOI =          "https://doi.org/10.1109/MCS.2010.939261",
  ISSN =         "1066-033X (print), 1941-000X (electronic)",
  ISSN-L =       "1066-033X",
  MRclass =      "00A17",
  MRnumber =     "2789813",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "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 =     "IEEE Control Systems Magazine",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2011:CBF
author: Jonathan M. Borwein and Simeon Reich and Shoham Sabach
title: A characterization of Bregman firmly nonexpansive operators using a new monotonicity concept
journal: j-J-NONLINEAR-CONVEX-ANAL
volume: 12
number: 1
pages: 161--184
year: 2011
ISSN: 1345-4773 (print), 1880-5221 (electronic) OR 13454773 (print), 18805221 (electronic)
ISSNL: 1345-4773 OR 13454773
MRclass: 47H05 (26B25 47H09 94A17)
MRnumber: 2816416
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/1445/
fjournal: Journal of Nonlinear and Convex Analysis
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 Simeon Reich and Shoham Sabach
rawtitle: A characterization of {Bregman} firmly nonexpansive operators using a new monotonicity concept
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
The property of nonexpansivity (1-Lipschitz) is very important in the analysis of many optimization problems. In this paper we study a more general notion of nonexpansivity - Bregman nonexpansivity. We present a characterization of Bregman firmly nonexpansive operators in general reflexive Banach spaces. This characterization allows us to construct Bregman firmly nonexpansive operators explicitly. We provide several examples of such operators with respect to the Boltzmann-Shannon entropy and the Fermi-Dirac entropy in Euclidean spaces. We also compute resolvents with respect to these functions.

rawabstract:
The property of nonexpansivity (1-Lipschitz) is very important in the analysis of many optimization problems. In this paper we study a more general notion of nonexpansivity - Bregman nonexpansivity. We present a characterization of Bregman firmly nonexpansive operators in general reflexive Banach spaces. This characterization allows us to construct Bregman firmly nonexpansive operators explicitly. We provide several examples of such operators with respect to the Boltzmann-Shannon entropy and the Fermi-Dirac entropy in Euclidean spaces. We also compute resolvents with respect to these functions.

entry:
@Article{Borwein:2011:CBF,
  author =       "Jonathan M. Borwein and Simeon Reich and Shoham
                 Sabach",
  title =        "A characterization of {Bregman} firmly nonexpansive
                 operators using a new monotonicity concept",
  journal =      j-J-NONLINEAR-CONVEX-ANAL,
  volume =       "12",
  number =       "1",
  pages =        "161--184",
  year =         "2011",
  ISSN =         "1345-4773 (print), 1880-5221 (electronic)",
  ISSN-L =       "1345-4773",
  MRclass =      "47H05 (26B25 47H09 94A17)",
  MRnumber =     "2816416",
  MRreviewer =   "Patrick L. Combettes",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1445/",
  abstract =     "The property of nonexpansivity (1-Lipschitz) is very
                 important in the analysis of many optimization
                 problems. In this paper we study a more general notion
                 of nonexpansivity - Bregman nonexpansivity. We present
                 a characterization of Bregman firmly nonexpansive
                 operators in general reflexive Banach spaces. This
                 characterization allows us to construct Bregman firmly
                 nonexpansive operators explicitly. We provide several
                 examples of such operators with respect to the
                 Boltzmann-Shannon entropy and the Fermi-Dirac entropy
                 in Euclidean spaces. We also compute resolvents with
                 respect to these functions.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Nonlinear and Convex Analysis",
  journal-URL =  "http://www.ybook.co.jp/jnca.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  unique-id =    "Borwein:2011:CBF",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2011:DRA
author: Jonathan M. Borwein and Brailey Sims
title: The Douglas--Rachford Algorithm in the Absence of Convexity
crossref: Bauschke:2011:FPA
pages: 93--109
year: 2011
DOI: https://doi.org/10.1007/978-1-4419-9569-8_6
MRclass: 47N10 (47H10 47J25 65J15 90C26)
MRnumber: 2858834
MRreviewer: A. G. Kartsatos
bibdate: Sat Aug 13 16:00:55 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 16:00:55 ???
series: Springer Optim. Appl.
URL: http://link.springer.com/chapter/10.1007/978-1-4419-9569-8_6
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Brailey Sims
rawtitle: The {Douglas--Rachford} Algorithm in the Absence of Convexity
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:2011:DRA,
  author =       "Jonathan M. Borwein and Brailey Sims",
  title =        "The {Douglas--Rachford} Algorithm in the Absence of
                 Convexity",
  crossref =     "Bauschke:2011:FPA",
  pages =        "93--109",
  year =         "2011",
  DOI =          "https://doi.org/10.1007/978-1-4419-9569-8_6",
  MRclass =      "47N10 (47H10 47J25 65J15 90C26)",
  MRnumber =     "2858834",
  MRreviewer =   "A. G. Kartsatos",
  bibdate =      "Sat Aug 13 16:00:55 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Springer Optim. Appl.",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4419-9569-8_6",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2011:DSU
author: Jonathan M. Borwein and A. Straub and J. Wan and Wadim Zudilin
title: Densities of short uniform random walks
journal: ArXiv e-prints
pages: 93--109
month: mar
monthnumber: 3
year: 2011
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/2011arXiv1103.2995B; http://docserver.carma.newcastle.edu.au/1388/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and A. Straub and J. Wan and Wadim Zudilin
rawtitle: Densities of short uniform random walks
abstract:
We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and less completely those with five steps. As one of the main results, we obtain a hypergeometric representation of the density for four steps, which complements the classical elliptic representation in the case of three steps. It appears unrealistic to expect similar results for more than five steps. New results are also presented concerning the moments of uniform random walks and, in particular, their derivatives. Relations with Mahler measures are discussed.

keywords:
Mathematics - Classical Analysis and ODEs, Mathematics - Number Theory, 60G50 (Primary) 33C20, 34M25, 44A10 (Secondary)

rawabstract:
We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and less completely those with five steps. As one of the main results, we obtain a hypergeometric representation of the density for four steps, which complements the classical elliptic representation in the case of three steps. It appears unrealistic to expect similar results for more than five steps. New results are also presented concerning the moments of uniform random walks and, in particular, their derivatives. Relations with Mahler measures are discussed.

ORCID:
Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053; Zudilin, Wadim/0000-0001-9551-2903

entry:
@Article{Borwein:2011:DSU,
  author =       "Jonathan M. Borwein and A. Straub and J. Wan and Wadim
                 Zudilin",
  title =        "Densities of short uniform random walks",
  journal =      "ArXiv e-prints",
  month =        mar,
  year =         "2011",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011arXiv1103.2995B;
                 http://docserver.carma.newcastle.edu.au/1388/",
  abstract =     "We study the densities of uniform random walks in the
                 plane. A special focus is on the case of short walks
                 with three or four steps and less completely those with
                 five steps. As one of the main results, we obtain a
                 hypergeometric representation of the density for four
                 steps, which complements the classical elliptic
                 representation in the case of three steps. It appears
                 unrealistic to expect similar results for more than
                 five steps. New results are also presented concerning
                 the moments of uniform random walks and, in particular,
                 their derivatives. Relations with Mahler measures are
                 discussed.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1103.2995",
  keywords =     "Mathematics - Classical Analysis and ODEs, Mathematics
                 - Number Theory, 60G50 (Primary) 33C20, 34M25, 44A10
                 (Secondary)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053; Zudilin,
                 Wadim/0000-0001-9551-2903",
  primaryclass = "math.CA",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borwein:2011:EMB
author: Jonathan Borwein and Keith Devlin
publisher: Spektrum Akademischer Verlag
address: Heidelberg, Germany
pages: xii + 158
year: 2011
DOI: https://doi.org/10.1007/978-3-8274-2662-8
ISBN: 3-8274-2661-8, 3-8274-2662-6 (e-book) OR 3827426618, 3827426626 (ebook)
ISBN13: 978-3-8274-2661-1, 978-3-8274-2662-8 (e-book) OR 9783827426611, 9783827426628 (ebook)
LCCN: QA8.7 .B67 2011
MRclass: 00A35 (01A75 11-04 11Y16 11Y60)
MRnumber: 3052999
bibdate: Thu Aug 11 17:05:04 MDT 2016
bibtimestamp: 2016.08.11 17:05:04 MDT
note: German translation by Roland Girgensohn of cite Borwein:2009:CCI, with updates.
URL: http://link.springer.com/book/10.1007/978-3-8274-2662-8
language: German
remark: Life Science and Basic Disciplines (German Language) (Springer-11777).
subject: Mathematics, general; Computermathematik
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein and Keith Devlin
rawnote: German translation by Roland Girgensohn of \cite{Borwein:2009:CCI}, with updates.
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Experimentelle Mathematik: Eine beispielorientierte Einfuhrung. (German) [Experimental mathematics: an example-oriented introduction]

TOC:
Front Matter / i--xii Was ist Experimentelle Mathematik? / 1-16 Was ist die billiardste Dezimalstelle von $pi $? / 17---28 Was ist diese Zahl? / 29--38 Die wichtigste Funktion in der Mathematik / 39--48 Werten Sie das folgende Integral aus! / 49--60 Gluckstreffer / 61--69 Berechnungen von $pi $ / 71--79 Der Computer kennt mehr Mathematik als Sie / 81--91 Treib es bis zum Limit! / 93--104 Vorsicht! Gefahr beim Gebrauch des Computers! / 105--113 Was wir Ihnen bisher nicht verraten haben / 115--130 Back Matter / 131--158

rawtitle:
{Experimentelle Mathematik: Eine beispielorientierte Einf{\"u}hrung}. ({German}) [{Experimental} mathematics: an example-oriented introduction]

rawTOC:
Front Matter / i--xii \\ Was ist Experimentelle Mathematik? / 1-16 \\ Was ist die billiardste Dezimalstelle von $\pi$? / 17---28 \\ Was ist diese Zahl? / 29--38 \\ Die wichtigste Funktion in der Mathematik / 39--48 \\ Werten Sie das folgende Integral aus! / 49--60 \\ Gl{\"u}ckstreffer / 61--69 \\ Berechnungen von $\pi$ / 71--79 \\ Der Computer kennt mehr Mathematik als Sie / 81--91 \\ Treib es bis zum Limit! / 93--104 \\ Vorsicht! Gefahr beim Gebrauch des Computers! / 105--113 \\ Was wir Ihnen bisher nicht verraten haben / 115--130 \\ Back Matter / 131--158

entry:
@Book{Borwein:2011:EMB,
  author =       "Jonathan Borwein and Keith Devlin",
  title =        "{Experimentelle Mathematik: Eine beispielorientierte
                 Einf{\"u}hrung}. ({German}) [{Experimental}
                 mathematics: an example-oriented introduction]",
  publisher =    "Spektrum Akademischer Verlag",
  address =      "Heidelberg, Germany",
  pages =        "xii + 158",
  year =         "2011",
  DOI =          "https://doi.org/10.1007/978-3-8274-2662-8",
  ISBN =         "3-8274-2661-8, 3-8274-2662-6 (e-book)",
  ISBN-13 =      "978-3-8274-2661-1, 978-3-8274-2662-8 (e-book)",
  LCCN =         "QA8.7 .B67 2011",
  MRclass =      "00A35 (01A75 11-04 11Y16 11Y60)",
  MRnumber =     "3052999",
  bibdate =      "Thu Aug 11 17:05:04 MDT 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "German translation by Roland Girgensohn of
                 \cite{Borwein:2009:CCI}, with updates.",
  URL =          "http://link.springer.com/book/10.1007/978-3-8274-2662-8",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  language =     "German",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Life Science and Basic Disciplines (German Language)
                 (Springer-11777).",
  subject =      "Mathematics, general; Computermathematik",
  tableofcontents = "Front Matter / i--xii \\
                 Was ist Experimentelle Mathematik? / 1-16 \\
                 Was ist die billiardste Dezimalstelle von $\pi$? /
                 17---28 \\
                 Was ist diese Zahl? / 29--38 \\
                 Die wichtigste Funktion in der Mathematik / 39--48 \\
                 Werten Sie das folgende Integral aus! / 49--60 \\
                 Gl{\"u}ckstreffer / 61--69 \\
                 Berechnungen von $\pi$ / 71--79 \\
                 Der Computer kennt mehr Mathematik als Sie / 81--91 \\
                 Treib es bis zum Limit! / 93--104 \\
                 Vorsicht! Gefahr beim Gebrauch des Computers! /
                 105--113 \\
                 Was wir Ihnen bisher nicht verraten haben / 115--130
                 \\
                 Back Matter / 131--158",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2011:ERF
author: Jonathan M. Borwein and D. Russell Luke
title: Entropic Regularization of the $ ell _0 $ Function
crossref: Bauschke:2011:FPA
pages: 65--92
year: 2011
DOI: https://doi.org/10.1007/978-1-4419-9569-8_5
MRclass: 49M20 (49N15 65K10 90C30)
MRnumber: 2858833
MRreviewer: Aris Daniilidis
bibdate: Sat Aug 13 16:00:55 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 16:00:55 ???
series: Springer Optim. Appl.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and D. Russell Luke
rawtitle: Entropic Regularization of the $ \ell_0 $ Function
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1451/; http://link.springer.com/chapter/10.1007/978-1-4419-9569-8_5

entry:
@InCollection{Borwein:2011:ERF,
  author =       "Jonathan M. Borwein and D. Russell Luke",
  title =        "Entropic Regularization of the $ \ell_0 $ Function",
  crossref =     "Bauschke:2011:FPA",
  pages =        "65--92",
  year =         "2011",
  DOI =          "https://doi.org/10.1007/978-1-4419-9569-8_5",
  MRclass =      "49M20 (49N15 65K10 90C30)",
  MRnumber =     "2858833",
  MRreviewer =   "Aris Daniilidis",
  bibdate =      "Sat Aug 13 16:00:55 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Springer Optim. Appl.",
  URL =          "http://docserver.carma.newcastle.edu.au/1451/;
                 http://link.springer.com/chapter/10.1007/978-1-4419-9569-8_5",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borwein:2011:IMM
author: Jonathan M. Borwein and Matthew P. Skerritt
title: An introduction to modern mathematical computing: with Maple
publisher: pub-SV
address: pub-SV:adr
pages: xvi + 216
year: 2011
DOI: https://doi.org/10.1007/978-1-4614-0122-3
ISBN: 1-4614-0121-6 OR 1461401216
ISBN13: 978-1-4614-0121-6 OR 9781461401216
LCCN: QA76.6 .B665 2011
MRclass: 65-01 (15-01 26-01 68-01)
MRnumber: 2808248
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
series: Springer Undergraduate Texts in Mathematics and Technology
URL: http://docserver.carma.newcastle.edu.au/1727/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Matthew P. Skerritt
rawtitle: An introduction to modern mathematical computing: with {Maple}
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/maple-extract.bib

TOC:
Front Matter / i--xvi Number Theory / 1--65 Calculus / 67--128 Linear Algebra / 129--185 Visualization and Geometry: A Postscript / 187--201 Back Matter / 211--216

rawTOC:
Front Matter / i--xvi \\ Number Theory / 1--65 \\ Calculus / 67--128 \\ Linear Algebra / 129--185 \\ Visualization and Geometry: A Postscript / 187--201 \\ Back Matter / 211--216

entry:
@Book{Borwein:2011:IMM,
  author =       "Jonathan M. Borwein and Matthew P. Skerritt",
  title =        "An introduction to modern mathematical computing: with
                 {Maple}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 216",
  year =         "2011",
  DOI =          "https://doi.org/10.1007/978-1-4614-0122-3",
  ISBN =         "1-4614-0121-6",
  ISBN-13 =      "978-1-4614-0121-6",
  LCCN =         "QA76.6 .B665 2011",
  MRclass =      "65-01 (15-01 26-01 68-01)",
  MRnumber =     "2808248",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  series =       "Springer Undergraduate Texts in Mathematics and
                 Technology",
  URL =          "http://docserver.carma.newcastle.edu.au/1727/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  tableofcontents = "Front Matter / i--xvi \\
                 Number Theory / 1--65 \\
                 Calculus / 67--128 \\
                 Linear Algebra / 129--185 \\
                 Visualization and Geometry: A Postscript / 187--201 \\
                 Back Matter / 211--216",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2011:LEW
author: J. M. Borwein
title: Letter to the Editor: Why are mathematics papers so dull?
journal: j-SIAM-NEWS
volume: 44
number: 6
pages: 7--7
month: jul
monthnumber: 7
year: 2011
ISSN: 0036-1437 OR 00361437
ISSNL: 0036-1437 OR 00361437
bibdate: Sat Aug 13 15:55:33 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 15:55:33 ???
URL: http://www.siam.org/news/news.php?id=1903
fjournal: SIAM News
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.siam.org/news/
rawauthor: J. M. Borwein
rawtitle: Letter to the {Editor}: Why are mathematics papers so dull?
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2011:LEW,
  author =       "J. M. Borwein",
  title =        "Letter to the {Editor}: Why are mathematics papers so
                 dull?",
  journal =      j-SIAM-NEWS,
  volume =       "44",
  number =       "6",
  pages =        "7--7",
  month =        jul # "\slash " # aug,
  year =         "2011",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Sat Aug 13 15:55:33 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.siam.org/news/news.php?id=1903",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2011:LHM
author: Jonathan M. Borwein and Judy-Anne Osborn
journal: j-MATH-INTEL
volume: 33
number: 4
pages: 63--69
month: dec
monthnumber: 12
year: 2011
CODEN: MAINDC
DOI: https://doi.org/10.1007/s00283-011-9260-1
ISSN: 0343-6993 (print), 1866-7414 (electronic) OR 03436993 (print), 18667414 (electronic)
ISSNL: 0343-6993 OR 03436993
MRclass: 00A17
MRnumber: 2906477
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://link.springer.com/article/10.1007/s00283-011-9260-1
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: Jonathan M. Borwein and Judy-Anne Osborn
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
booktitle Loving and hating mathematics, by Reuben Hersh and Vera John-Steiner. Princeton and Oxford: Princeton University Press, 2010, 428 pp., US$29.95. ISBN-10: 0-691-14247-5, ISBN-13: 978-0-691-14247-0 [book review of refcno 2731560]

rawtitle:
{{\booktitle{Loving and hating mathematics}}, by Reuben Hersh and Vera John-Steiner. Princeton and Oxford: Princeton University Press, 2010, 428 pp., US\$29.95. ISBN-10: 0-691-14247-5, ISBN-13: 978-0-691-14247-0 [book review of \refcno 2731560]}

entry:
@Article{Borwein:2011:LHM,
  author =       "Jonathan M. Borwein and Judy-Anne Osborn",
  title =        "{{\booktitle{Loving and hating mathematics}}, by
                 Reuben Hersh and Vera John-Steiner. Princeton and
                 Oxford: Princeton University Press, 2010, 428 pp.,
                 US\$29.95. ISBN-10: 0-691-14247-5, ISBN-13:
                 978-0-691-14247-0 [book review of \refcno 2731560]}",
  journal =      j-MATH-INTEL,
  volume =       "33",
  number =       "4",
  pages =        "63--69",
  month =        dec,
  year =         "2011",
  CODEN =        "MAINDC",
  DOI =          "https://doi.org/10.1007/s00283-011-9260-1",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  MRclass =      "00A17",
  MRnumber =     "2906477",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://link.springer.com/article/10.1007/s00283-011-9260-1",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The Mathematical Intelligencer",
  journal-URL =  "http://link.springer.com/journal/283",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2011:LSEa
author: J. M. Borwein and A. Straub
title: Log-sine evaluations of Mahler measures
journal: ArXiv e-prints
pages: 63--69
month: mar
monthnumber: 3
year: 2011
bibdate: Thu Aug 11 07:19:54 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 07:19:54 ???
keywords: Mathematics - Classical Analysis and ODEs, Mathematical Physics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and A. Straub
rawtitle: Log-sine evaluations of {Mahler} measures
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053
URL:
http://adsabs.harvard.edu/abs/2011arXiv1103.3893B https://arxiv.org/abs/1103.3893; https://arxiv.org/pdf/1103.3893.pdf

abstract:
We provide evaluations of several recently studied higher and multiple Mahler measures using log-sine integrals. This is complemented with an analysis of generating functions and identities for log-sine integrals which allows the evaluations to be expressed in terms of zeta values or more general polylogarithmic terms. The machinery developed is then applied to evaluation of further families of multiple Mahler measures.

rawabstract:
We provide evaluations of several recently studied higher and multiple Mahler measures using log-sine integrals. This is complemented with an analysis of generating functions and identities for log-sine integrals which allows the evaluations to be expressed in terms of zeta values or more general polylogarithmic terms. The machinery developed is then applied to evaluation of further families of multiple Mahler measures.

entry:
@Article{Borwein:2011:LSEa,
  author =       "J. M. Borwein and A. Straub",
  title =        "Log-sine evaluations of {Mahler} measures",
  journal =      "ArXiv e-prints",
  month =        mar,
  year =         "2011",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011arXiv1103.3893B
                 https://arxiv.org/abs/1103.3893;
                 https://arxiv.org/pdf/1103.3893.pdf",
  abstract =     "We provide evaluations of several recently studied
                 higher and multiple Mahler measures using log-sine
                 integrals. This is complemented with an analysis of
                 generating functions and identities for log-sine
                 integrals which allows the evaluations to be expressed
                 in terms of zeta values or more general polylogarithmic
                 terms. The machinery developed is then applied to
                 evaluation of further families of multiple Mahler
                 measures.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1103.3893",
  keywords =     "Mathematics - Classical Analysis and ODEs,
                 Mathematical Physics",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053",
  primaryclass = "math.CA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2011:LSEb
author: David Borwein and Jonathan M. Borwein and Armin Straub and James Wan
title: Log-sine evaluations of Mahler measures, II
journal: ArXiv e-prints
pages: 63--69
month: mar
monthnumber: 3
year: 2011
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/2011arXiv1103.3035B; http://docserver.carma.newcastle.edu.au/1435/
keywords: Mathematics - Classical Analysis and ODEs, Mathematical Physics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David Borwein and Jonathan M. Borwein and Armin Straub and James Wan
rawtitle: Log-sine evaluations of {Mahler} measures, {II}
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053
abstract:
We continue the analysis of higher and multiple Mahler measures using log-sine integrals as started in ``Log-sine evaluations of Mahler measures'' and ``Special values of generalized log-sine integrals'' by two of the authors. This motivates a detailed study of various multiple polylogarithms and worked examples are given. Our techniques enable the reduction of several multiple Mahler measures, and supply an easy proof of two conjectures by Boyd.

rawabstract:
We continue the analysis of higher and multiple Mahler measures using log-sine integrals as started in ``Log-sine evaluations of Mahler measures'' and ``Special values of generalized log-sine integrals'' by two of the authors. This motivates a detailed study of various multiple polylogarithms and worked examples are given. Our techniques enable the reduction of several multiple Mahler measures, and supply an easy proof of two conjectures by Boyd.

entry:
@Article{Borwein:2011:LSEb,
  author =       "David Borwein and Jonathan M. Borwein and Armin Straub
                 and James Wan",
  title =        "Log-sine evaluations of {Mahler} measures, {II}",
  journal =      "ArXiv e-prints",
  month =        mar,
  year =         "2011",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011arXiv1103.3035B;
                 http://docserver.carma.newcastle.edu.au/1435/",
  abstract =     "We continue the analysis of higher and multiple Mahler
                 measures using log-sine integrals as started in
                 ``Log-sine evaluations of Mahler measures'' and
                 ``Special values of generalized log-sine integrals'' by
                 two of the authors. This motivates a detailed study of
                 various multiple polylogarithms and worked examples are
                 given. Our techniques enable the reduction of several
                 multiple Mahler measures, and supply an easy proof of
                 two conjectures by Boyd.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1103.3035",
  keywords =     "Mathematics - Classical Analysis and ODEs,
                 Mathematical Physics",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053",
  primaryclass = "math.CA",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2011:MHM
author: Jonathan M. Borwein and Wadim Zudilin
title: Math Honours: Multiple Zeta Values
type: Classroom notes
institution: Centre for Computer Assisted RMA, University of Newcastle
address: Callaghan, NSW 2308, Australia
pages: 65
day: 19
month: oct
monthnumber: 10
year: 2011
bibdate: Fri Nov 04 16:04:34 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.11.04 16:04:34 ???
URL: http://carma.newcastle.edu.au/MZVs/mzv.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Wadim Zudilin
rawtitle: Math Honours: Multiple Zeta Values
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Zudilin, Wadim/0000-0001-9551-2903
TOC:
1. Introduction to multiple zeta values (MZVs) 2. Method of partial fractions 3. Algebra of MZVs 4. Generalized polylogarithms and generating functions of MZVs 5. Duality theorem. Sum theorem and Ohno's relations 6. Quasi-shuffle products. Derivations 7. $q$-Analogues of MZVs 8. Other extensions and open questions

rawTOC:
1. Introduction to multiple zeta values (MZVs) \\ 2. Method of partial fractions \\ 3. Algebra of MZVs \\ 4. Generalized polylogarithms and generating functions of MZVs \\ 5. Duality theorem. Sum theorem and Ohno's relations \\ 6. Quasi-shuffle products. Derivations \\ 7. $q$-Analogues of MZVs \\ 8. Other extensions and open questions

entry:
@TechReport{Borwein:2011:MHM,
  author =       "Jonathan M. Borwein and Wadim Zudilin",
  title =        "Math Honours: Multiple Zeta Values",
  type =         "Classroom notes",
  institution =  "Centre for Computer Assisted RMA, University of
                 Newcastle",
  address =      "Callaghan, NSW 2308, Australia",
  pages =        "65",
  day =          "19",
  month =        oct,
  year =         "2011",
  bibdate =      "Fri Nov 04 16:04:34 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://carma.newcastle.edu.au/MZVs/mzv.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Zudilin,
                 Wadim/0000-0001-9551-2903",
  tableofcontents = "1. Introduction to multiple zeta values (MZVs) \\
                 2. Method of partial fractions \\
                 3. Algebra of MZVs \\
                 4. Generalized polylogarithms and generating functions
                 of MZVs \\
                 5. Duality theorem. Sum theorem and Ohno's relations
                 \\
                 6. Quasi-shuffle products. Derivations \\
                 7. $q$-Analogues of MZVs \\
                 8. Other extensions and open questions",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2011:MMS
author: Jonathan Borwein
booktitle: Proceedings of the 2011 International Workshop on Symbolic--Numeric Computation
title: Mahler Measures, Short Walks and Log-sine Integrals: A Case Study in Hybrid Computation
publisher: pub-ACM
address: pub-ACM:adr
pages: 1--1
year: 2011
DOI: https://doi.org/10.1145/2331684.2331685
ISBN: 1-4503-0515-6 OR 1450305156
ISBN13: 978-1-4503-0515-0 OR 9781450305150
bibdate: Wed Aug 10 12:08:56 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 12:08:56 ???
series: SNC '11
URL: http://doi.acm.org/10.1145/2331684.2331685
keywords: Mahler measures, log-sine integral, short walks
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein
rawbooktitle: Proceedings of the 2011 International Workshop on Symbolic--Numeric Computation
rawtitle: {Mahler} Measures, Short Walks and Log-sine Integrals: A Case Study in Hybrid Computation
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InProceedings{Borwein:2011:MMS,
  author =       "Jonathan Borwein",
  booktitle =    "Proceedings of the 2011 International Workshop on
                 Symbolic--Numeric Computation",
  title =        "{Mahler} Measures, Short Walks and Log-sine Integrals:
                 A Case Study in Hybrid Computation",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "1--1",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/2331684.2331685",
  ISBN =         "1-4503-0515-6",
  ISBN-13 =      "978-1-4503-0515-0",
  bibdate =      "Wed Aug 10 12:08:56 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "SNC '11",
  URL =          "http://doi.acm.org/10.1145/2331684.2331685",
  acknowledgement = ack-nhfb,
  acmid =        "2331685",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Mahler measures, log-sine integral, short walks",
  location =     "San Jose, California",
  numpages =     "1",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2011:MOE
author: J. M. Borwein and R. Burachik and L. Yao
title: Monotone Operators without Enlargements
journal: ArXiv e-prints
pages: 1--1
day: 11
month: oct
monthnumber: 10
year: 2011
bibdate: Thu Aug 11 07:19:54 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 07:19:54 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and R. Burachik and L. Yao
rawtitle: Monotone Operators without Enlargements
ORCID: Burachik, Regina/0000-0003-1332-6213; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://adsabs.harvard.edu/abs/2011arXiv1110.3102B; http://arxiv.org/abs/1110.3102; http://docserver.carma.newcastle.edu.au/1447/

abstract:
Enlargements have proven to be useful tools for studying maximally monotone mappings. It is therefore natural to ask in which cases the enlargement does not change the original mapping. Svaiter has recently characterized non-enlargeable operators in reflexive Banach spaces and has also given some partial results in the nonreflexive case. In the present paper, we provide another characterization of non-enlargeable operators in nonreflexive Banach spaces under a closedness assumption on the graph. Furthermore, and still for general Banach spaces, we present a new proof of the maximality of the sum of two maximally monotone linear relations. We also present a new proof of the maximality of the sum of a maximally monotone linear relation and a normal cone operator when the domain of the linear relation intersects the interior of the domain of the normal cone.

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

rawabstract:
Enlargements have proven to be useful tools for studying maximally monotone mappings. It is therefore natural to ask in which cases the enlargement does not change the original mapping. Svaiter has recently characterized non-enlargeable operators in reflexive Banach spaces and has also given some partial results in the nonreflexive case. In the present paper, we provide another characterization of non-enlargeable operators in nonreflexive Banach spaces under a closedness assumption on the graph. Furthermore, and still for general Banach spaces, we present a new proof of the maximality of the sum of two maximally monotone linear relations. We also present a new proof of the maximality of the sum of a maximally monotone linear relation and a normal cone operator when the domain of the linear relation intersects the interior of the domain of the normal cone.

entry:
@Article{Borwein:2011:MOE,
  author =       "J. M. Borwein and R. Burachik and L. Yao",
  title =        "Monotone Operators without Enlargements",
  journal =      "ArXiv e-prints",
  day =          "11",
  month =        oct,
  year =         "2011",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011arXiv1110.3102B;
                 http://arxiv.org/abs/1110.3102;
                 http://docserver.carma.newcastle.edu.au/1447/",
  abstract =     "Enlargements have proven to be useful tools for
                 studying maximally monotone mappings. It is therefore
                 natural to ask in which cases the enlargement does not
                 change the original mapping. Svaiter has recently
                 characterized non-enlargeable operators in reflexive
                 Banach spaces and has also given some partial results
                 in the nonreflexive case. In the present paper, we
                 provide another characterization of non-enlargeable
                 operators in nonreflexive Banach spaces under a
                 closedness assumption on the graph. Furthermore, and
                 still for general Banach spaces, we present a new proof
                 of the maximality of the sum of two maximally monotone
                 linear relations. We also present a new proof of the
                 maximality of the sum of a maximally monotone linear
                 relation and a normal cone operator when the domain of
                 the linear relation intersects the interior of the
                 domain of the normal cone.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1110.3102",
  keywords =     "Mathematics - Functional Analysis, Mathematics -
                 Optimization and Control, Primary 47A06, 47H05,
                 Secondary 47B65, 47N10, 90C25",
  ORCID-numbers = "Burachik, Regina/0000-0003-1332-6213; Borwein,
                 Jonathan/0000-0002-1263-0646",
  pagecount =    "26",
  primaryclass = "math.FA",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:2011:MOT
author: Jonathan M. Borwein and Andrew Eberhard and Liangjin Yao
title: Monotone operators of type FPV
pages: 1--1
month: aug
monthnumber: 8
year: 2011
bibdate: Tue Aug 16 09:59:46 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:59:46 ???
note: Preprint.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Andrew Eberhard and Liangjin Yao
rawnote: Preprint.
rawtitle: Monotone operators of type {FPV}
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Eberhard, Andrew/0000-0003-2977-3456
entry:
@Unpublished{Borwein:2011:MOT,
  author =       "Jonathan M. Borwein and Andrew Eberhard and Liangjin
                 Yao",
  title =        "Monotone operators of type {FPV}",
  month =        aug,
  year =         "2011",
  bibdate =      "Tue Aug 16 09:59:46 2016",
  bibsource =    "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; Eberhard,
                 Andrew/0000-0003-2977-3456",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2011:MRGa
author: David Borwein and Jonathan M. Borwein and M. Larry Glasser and James G. Wan
title: Moments of Ramanujan's generalized elliptic integrals and extensions of Catalan's constant
journal: j-J-MATH-ANAL-APPL
volume: 384
number: 2
pages: 478--496
year: 2011
CODEN: JMANAK
DOI: https://doi.org/10.1016/j.jmaa.2011.06.001
ISSN: 0022-247X (print), 1096-0813 (electronic) OR 0022247X (print), 10960813 (electronic)
ISSNL: 0022-247X OR 0022247X
MRclass: 33E05 (33C05)
MRnumber: 2825201
MRreviewer: Diego E. Dominici
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: Catalan's constant; Elliptic integrals; Hypergeometric functions; Moments
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 M. Larry Glasser and James G. Wan
rawtitle: Moments of {Ramanujan}'s generalized elliptic integrals and extensions of {Catalan}'s constant
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1443/; http://www.sciencedirect.com/science/article/pii/S0022247X1100549X

abstract:
We undertake a thorough investigation of the moments of Ramanujan's alternative elliptic integrals and of related hypergeometric functions. Along the way we are able to give some surprising closed forms for Catalan-related constants and various new hypergeometric identities.

rawabstract:
We undertake a thorough investigation of the moments of Ramanujan's alternative elliptic integrals and of related hypergeometric functions. Along the way we are able to give some surprising closed forms for Catalan-related constants and various new hypergeometric identities.

entry:
@Article{Borwein:2011:MRGa,
  author =       "David Borwein and Jonathan M. Borwein and M. Larry
                 Glasser and James G. Wan",
  title =        "Moments of {Ramanujan}'s generalized elliptic
                 integrals and extensions of {Catalan}'s constant",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "384",
  number =       "2",
  pages =        "478--496",
  year =         "2011",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/j.jmaa.2011.06.001",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "33E05 (33C05)",
  MRnumber =     "2825201",
  MRreviewer =   "Diego E. Dominici",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1443/;
                 http://www.sciencedirect.com/science/article/pii/S0022247X1100549X",
  abstract =     "We undertake a thorough investigation of the moments
                 of Ramanujan's alternative elliptic integrals and of
                 related hypergeometric functions. Along the way we are
                 able to give some surprising closed forms for
                 Catalan-related constants and various new
                 hypergeometric identities.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "Catalan's constant; Elliptic integrals; Hypergeometric
                 functions; Moments",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2011:PSE
author: D. Borwein and Jonathan M. Borwein
title: Proof of some experimentally conjectured formulas for $ pi $
type: Preprint
address: London, ON, Canada and Callaghan, NSW 2308, Australia
pages: 478--496
day: 4
month: dec
monthnumber: 12
year: 2011
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. Borwein and Jonathan M. Borwein
rawtitle: Proof of some experimentally conjectured formulas for $ \pi $
ORCID: Borwein, Jonathan/0000-0002-1263-0646
institution:
Department of Mathematics, University of Western Ontario and Centre for Computer-assisted Research Mathematics and its Applications (CARMA), School of Mathematical and Physical Sciences, University of Newcastle

abstract:
A recent paper by M. Jauregui and C. Tsallis cite Jauregui:2010:NRD, which explores applications of the $q$-exponential function and formal representations of the Dirac function, contains a set of experimentally discovered formulae for $ pi $ as finite series of gamma function ratios. Herein, we prove rigorously these identities as special cases of Pfaff--Saalschutz evaluation for $_3 F_2 (a, b, c atop d, e | 1)$ functions. We likewise prove and extend a corresponding integral identity given in cite Jauregui:2010:NRD.

rawabstract:
A recent paper by M. Jauregui and C. Tsallis \cite{Jauregui:2010:NRD}, which explores applications of the $q$-exponential function and formal representations of the Dirac function, contains a set of experimentally discovered formulae for $ \pi $ as finite series of gamma function ratios. Herein, we prove rigorously these identities as special cases of Pfaff--Saalsch{\"u}tz evaluation for $_3 F_2 ({a, b, c} \atop {d, e} | 1)$ functions. We likewise prove and extend a corresponding integral identity given in \cite{Jauregui:2010:NRD}.

entry:
@TechReport{Borwein:2011:PSE,
  author =       "D. Borwein and Jonathan M. Borwein",
  title =        "Proof of some experimentally conjectured formulas for
                 $ \pi $",
  type =         "Preprint",
  institution =  "Department of Mathematics, University of Western
                 Ontario and Centre for Computer-assisted Research
                 Mathematics and its Applications (CARMA), School of
                 Mathematical and Physical Sciences, University of
                 Newcastle",
  address =      "London, ON, Canada and Callaghan, NSW 2308,
                 Australia",
  day =          "4",
  month =        dec,
  year =         "2011",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  abstract =     "A recent paper by M. Jauregui and C. Tsallis
                 \cite{Jauregui:2010:NRD}, which explores applications
                 of the $q$-exponential function and formal
                 representations of the Dirac function, contains a set
                 of experimentally discovered formulae for $ \pi $ as
                 finite series of gamma function ratios. Herein, we
                 prove rigorously these identities as special cases of
                 Pfaff--Saalsch{\"u}tz evaluation for $_3 F_2 ({a, b, c}
                 \atop {d, e} | 1)$ functions. We likewise prove and
                 extend a corresponding integral identity given in
                 \cite{Jauregui:2010:NRD}.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2011:SAP
author: Jonathan M. Borwein and Dirk Nuyens and Armin Straub and James Wan
title: Some arithmetic properties of short random walk integrals
journal: j-RAMANUJAN-J
volume: 26
number: 1
pages: 109--132
year: 2011
CODEN: RAJOF9
DOI: https://doi.org/10.1007/s11139-011-9325-y
ISSN: 1382-4090 (print), 1572-9303 (electronic) OR 13824090 (print), 15729303 (electronic)
ISSNL: 1382-4090 OR 13824090
MRclass: 60G50 (33C20)
MRnumber: 2837721
MRreviewer: Florian Sobieczky
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/1440/
fjournal: The Ramanujan Journal
ZMnumber: 1233.60024
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11139
rawauthor: Jonathan M. Borwein and Dirk Nuyens and Armin Straub and James Wan
rawtitle: Some arithmetic properties of short random walk integrals
abstract:
We study the moments of the distance traveled by a walk in the plane with unit steps in random directions. While this historically interesting random walk is well understood from a modern probabilistic point of view, our own interest is in determining explicit closed forms for the moment functions and their arithmetic values at integers when only a small number of steps is taken. As a consequence of a more general evaluation, a closed form is obtained for the average distance traveled in three steps. This evaluation, as well as its proof, rely on explicit combinatorial properties, such as recurrence equations of the even moments (which are lifted to functional equations). The corresponding general combinatorial and analytic features are collected and made explicit in the case of 3 and 4 steps. Explicit hypergeometric expressions are given for the moments of a 3-step and 4-step walk and a general conjecture for even length walks is made.

rawabstract:
We study the moments of the distance traveled by a walk in the plane with unit steps in random directions. While this historically interesting random walk is well understood from a modern probabilistic point of view, our own interest is in determining explicit closed forms for the moment functions and their arithmetic values at integers when only a small number of steps is taken. As a consequence of a more general evaluation, a closed form is obtained for the average distance traveled in three steps. This evaluation, as well as its proof, rely on explicit combinatorial properties, such as recurrence equations of the even moments (which are lifted to functional equations). The corresponding general combinatorial and analytic features are collected and made explicit in the case of 3 and 4 steps. Explicit hypergeometric expressions are given for the moments of a 3-step and 4-step walk and a general conjecture for even length walks is made.

ORCID:
Borwein, Jonathan/0000-0002-1263-0646; Nuyens, Dirk/0000-0002-4555-2314; Straub, Armin/0000-0001-6802-6053

entry:
@Article{Borwein:2011:SAP,
  author =       "Jonathan M. Borwein and Dirk Nuyens and Armin Straub
                 and James Wan",
  title =        "Some arithmetic properties of short random walk
                 integrals",
  journal =      j-RAMANUJAN-J,
  volume =       "26",
  number =       "1",
  pages =        "109--132",
  year =         "2011",
  CODEN =        "RAJOF9",
  DOI =          "https://doi.org/10.1007/s11139-011-9325-y",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  MRclass =      "60G50 (33C20)",
  MRnumber =     "2837721",
  MRreviewer =   "Florian Sobieczky",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1440/",
  ZMnumber =     "1233.60024",
  abstract =     "We study the moments of the distance traveled by a
                 walk in the plane with unit steps in random directions.
                 While this historically interesting random walk is well
                 understood from a modern probabilistic point of view,
                 our own interest is in determining explicit closed
                 forms for the moment functions and their arithmetic
                 values at integers when only a small number of steps is
                 taken. As a consequence of a more general evaluation, a
                 closed form is obtained for the average distance
                 traveled in three steps. This evaluation, as well as
                 its proof, rely on explicit combinatorial properties,
                 such as recurrence equations of the even moments (which
                 are lifted to functional equations). The corresponding
                 general combinatorial and analytic features are
                 collected and made explicit in the case of 3 and 4
                 steps. Explicit hypergeometric expressions are given
                 for the moments of a 3-step and 4-step walk and a
                 general conjecture for even length walks is made.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The {Ramanujan} Journal",
  journal-URL =  "http://link.springer.com/journal/11139",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Nuyens,
                 Dirk/0000-0002-4555-2314; Straub,
                 Armin/0000-0001-6802-6053",
  researcherid-numbers = "Nuyens, Dirk/A-7426-2016",
  unique-id =    "Borwein:2011:SAP",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2011:SVGa
author: Jonathan M. Borwein and Armin Straub
title: Special Values of Generalized Log-sine Integrals
journal: ArXiv e-prints
pages: 109--132
month: mar
monthnumber: 3
year: 2011
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/2011arXiv1103.4298B; http://docserver.carma.newcastle.edu.au/1398/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Armin Straub
rawtitle: Special Values of Generalized Log-sine Integrals
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053
abstract:
We study generalized log-sine integrals at special values. At $ pi $ and multiples thereof explicit evaluations are obtained in terms of Nielsen polylogarithms at $ pm 1 $. For general arguments we present algorithmic evaluations involving Nielsen polylogarithms at related arguments. In particular, we consider log-sine integrals at $ pi / 3 $ which evaluate in terms of polylogarithms at the sixth root of unity. An implementation of our results for the computer algebra systems Mathematica and SAGE is provided.

keywords:
Mathematics - Classical Analysis and ODEs, Computer Science - Symbolic Computation, Mathematical Physics

rawabstract:
We study generalized log-sine integrals at special values. At $ \pi $ and multiples thereof explicit evaluations are obtained in terms of Nielsen polylogarithms at $ \pm 1 $. For general arguments we present algorithmic evaluations involving Nielsen polylogarithms at related arguments. In particular, we consider log-sine integrals at $ \pi / 3 $ which evaluate in terms of polylogarithms at the sixth root of unity. An implementation of our results for the computer algebra systems Mathematica and SAGE is provided.

entry:
@Article{Borwein:2011:SVGa,
  author =       "Jonathan M. Borwein and Armin Straub",
  title =        "Special Values of Generalized Log-sine Integrals",
  journal =      "ArXiv e-prints",
  month =        mar,
  year =         "2011",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011arXiv1103.4298B;
                 http://docserver.carma.newcastle.edu.au/1398/",
  abstract =     "We study generalized log-sine integrals at special
                 values. At $ \pi $ and multiples thereof explicit
                 evaluations are obtained in terms of Nielsen
                 polylogarithms at $ \pm 1 $. For general arguments we
                 present algorithmic evaluations involving Nielsen
                 polylogarithms at related arguments. In particular, we
                 consider log-sine integrals at $ \pi / 3 $ which
                 evaluate in terms of polylogarithms at the sixth root
                 of unity. An implementation of our results for the
                 computer algebra systems Mathematica and SAGE is
                 provided.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1103.4298",
  keywords =     "Mathematics - Classical Analysis and ODEs, Computer
                 Science - Symbolic Computation, Mathematical Physics",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053",
  primaryclass = "math.CA",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2011:SVGb
author: Jonathan M. Borwein and Armin Straub
booktitle: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation
title: Special Values of Generalized Log-sine Integrals
publisher: pub-ACM
address: pub-ACM:adr
pages: 43--50
year: 2011
DOI: https://doi.org/10.1145/1993886.1993899
ISBN: 1-4503-0675-6 OR 1450306756
ISBN13: 978-1-4503-0675-1 OR 9781450306751
MRclass: 11R06 (33B99 68W30)
MRnumber: 2895193
bibdate: Wed Aug 10 12:08:56 2016
bibtimestamp: 2016.08.10 12:08:56 ???
note: Awarded ISSAC 2011 Best SIGSAM-ACM Student Paper Prize.
series: ISSAC '11
URL: http://docserver.carma.newcastle.edu.au/1398/; http://doi.acm.org/10.1145/1993886.1993899
keywords: Clausen functions, log-sine integrals, multiple polylogarithms, multiple zeta values
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Armin Straub
rawbooktitle: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation
rawnote: Awarded ISSAC 2011 Best SIGSAM-ACM Student Paper Prize.
rawtitle: Special Values of Generalized Log-sine 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/mathematica.bib

entry:
@InProceedings{Borwein:2011:SVGb,
  author =       "Jonathan M. Borwein and Armin Straub",
  booktitle =    "Proceedings of the 36th International Symposium on
                 Symbolic and Algebraic Computation",
  title =        "Special Values of Generalized Log-sine Integrals",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "43--50",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993899",
  ISBN =         "1-4503-0675-6",
  ISBN-13 =      "978-1-4503-0675-1",
  MRclass =      "11R06 (33B99 68W30)",
  MRnumber =     "2895193",
  bibdate =      "Wed Aug 10 12:08:56 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  note =         "Awarded ISSAC 2011 Best SIGSAM-ACM Student Paper
                 Prize.",
  series =       "ISSAC '11",
  URL =          "http://docserver.carma.newcastle.edu.au/1398/;
                 http://doi.acm.org/10.1145/1993886.1993899",
  acknowledgement = ack-nhfb,
  acmid =        "1993899",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Clausen functions, log-sine integrals, multiple
                 polylogarithms, multiple zeta values",
  location =     "San Jose, California, USA",
  numpages =     "8",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Alladi:2012:PRA
author: Krishnaswami Alladi and George E. Andrews and Jonathan M. Borwein
title: Preface to Ramanujan's 125th anniversary special issue
journal: j-RAMANUJAN-J
volume: 29
number: 1--3
pages: 1--2
month: dec
monthnumber: 12
year: 2012
CODEN: RAJOF9
DOI: https://doi.org/10.1007/s11139-012-9448-9
ISSN: 1382-4090 (print), 1572-9303 (electronic) OR 13824090 (print), 15729303 (electronic)
ISSNL: 1382-4090 OR 13824090
MRclass: 11-06 (01A70)
MRnumber: 2994085
bibdate: Fri Aug 12 08:52:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 08:52:38 ???
URL: http://link.springer.com/article/10.1007/s11139-012-9448-9
fjournal: The Ramanujan Journal
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11139
rawauthor: Krishnaswami Alladi and George E. Andrews and Jonathan M. Borwein
rawtitle: Preface to {Ramanujan}'s 125th anniversary special issue
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Alladi:2012:PRA,
  author =       "Krishnaswami Alladi and George E. Andrews and Jonathan
                 M. Borwein",
  title =        "Preface to {Ramanujan}'s 125th anniversary special
                 issue",
  journal =      j-RAMANUJAN-J,
  volume =       "29",
  number =       "1--3",
  pages =        "1--2",
  month =        dec,
  year =         "2012",
  CODEN =        "RAJOF9",
  DOI =          "https://doi.org/10.1007/s11139-012-9448-9",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  MRclass =      "11-06 (01A70)",
  MRnumber =     "2994085",
  bibdate =      "Fri Aug 12 08:52:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://link.springer.com/article/10.1007/s11139-012-9448-9",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The {Ramanujan} Journal",
  journal-URL =  "http://link.springer.com/journal/11139",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Amdeberhan:2012:FEC
author: Tewodros Amdeberhan and David Borwein and Jonathan M. Borwein and Armin Straub
title: On formulas for $ pi $ experimentally conjectured by Jauregui--Tsallis
journal: j-J-MATH-PHYS
volume: 53
number: 7
pages: 073708
month: jul
monthnumber: 7
year: 2012
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.4735283
ISSN: 0022-2488 OR 00222488
ISSNL: 0022-2488 OR 00222488
MRclass: 33C20 (11Y60 30D15 33C45)
MRnumber: 2985267
MRreviewer: Tatiana Hessami Pilehrood
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/2012JMP....53g3708A; http://docserver.carma.newcastle.edu.au/1378/
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://jmp.aip.org/
onlinedate: Sep 2012
rawauthor: Tewodros Amdeberhan and David Borwein and Jonathan M. Borwein and Armin Straub
rawtitle: On formulas for $ \pi $ experimentally conjectured by {Jauregui--Tsallis}
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053
abstract:
In a recent study of representing Dirac's delta distribution using q-exponentials, Jauregui and Tsallis experimentally discovered formulae for $ pi $ as hypergeometric series as well as certain integrals. Herein, we offer rigorous proofs of these identities using various methods and our primary intent is to lay down an illustration of the many technical underpinnings of such evaluations. This includes an explicit discussion of creative telescoping and Carlson's Theorem. We also generalize the Jauregui--Tsallis identities to integrals involving Chebyshev polynomials. In our pursuit, we provide an interesting tour through various topics from classical analysis to the theory of special functions.

remark:
From the Acknowledgments: ``Thanks are due to Nelson Beebe for directing the authors to the open conjectures which led to this paper.''

rawabstract:
In a recent study of representing Dirac's delta distribution using q-exponentials, Jauregui and Tsallis experimentally discovered formulae for $ \pi $ as hypergeometric series as well as certain integrals. Herein, we offer rigorous proofs of these identities using various methods and our primary intent is to lay down an illustration of the many technical underpinnings of such evaluations. This includes an explicit discussion of creative telescoping and Carlson's Theorem. We also generalize the Jauregui--Tsallis identities to integrals involving Chebyshev polynomials. In our pursuit, we provide an interesting tour through various topics from classical analysis to the theory of special functions.

entry:
@Article{Amdeberhan:2012:FEC,
  author =       "Tewodros Amdeberhan and David Borwein and Jonathan M.
                 Borwein and Armin Straub",
  title =        "On formulas for $ \pi $ experimentally conjectured by
                 {Jauregui--Tsallis}",
  journal =      j-J-MATH-PHYS,
  volume =       "53",
  number =       "7",
  pages =        "073708",
  month =        jul,
  year =         "2012",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.4735283",
  ISSN =         "0022-2488",
  ISSN-L =       "0022-2488",
  MRclass =      "33C20 (11Y60 30D15 33C45)",
  MRnumber =     "2985267",
  MRreviewer =   "Tatiana Hessami Pilehrood",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2012JMP....53g3708A;
                 http://docserver.carma.newcastle.edu.au/1378/",
  abstract =     "In a recent study of representing Dirac's delta
                 distribution using q-exponentials, Jauregui and Tsallis
                 experimentally discovered formulae for $ \pi $ as
                 hypergeometric series as well as certain integrals.
                 Herein, we offer rigorous proofs of these identities
                 using various methods and our primary intent is to lay
                 down an illustration of the many technical
                 underpinnings of such evaluations. This includes an
                 explicit discussion of creative telescoping and
                 Carlson's Theorem. We also generalize the
                 Jauregui--Tsallis identities to integrals involving
                 Chebyshev polynomials. In our pursuit, we provide an
                 interesting tour through various topics from classical
                 analysis to the theory of special functions.",
  acknowledgement = ack-nhfb,
  article-number = "073708",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eid =          "073708",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  onlinedate =   "Sep 2012",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053",
  pagecount =    "15",
  remark =       "From the Acknowledgments: ``Thanks are due to Nelson
                 Beebe for directing the authors to the open conjectures
                 which led to this paper.''",
  unique-id =    "Amdeberhan:2012:FPE",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: AragonArtacho:2012:GCN
author: F. J. Aragon Artacho and J. M. Borwein
title: Global convergence of a non-convex Douglas--Rachford iteration
journal: ArXiv e-prints
pages: 073708
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/2012arXiv1203.2392A; http://docserver.carma.newcastle.edu.au/1061/
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
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
abstract:
We establish a region of convergence for the proto-typical non-convex Douglas--Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex iteration [2] was only able to establish local convergence, and was ineffective in that no explicit region of convergence could be given.

rawabstract:
We establish a region of convergence for the proto-typical non-convex Douglas--Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex iteration [2] was only able to establish local convergence, and was ineffective in that no explicit region of convergence could be given.

entry:
@Article{AragonArtacho:2012:GCN,
  author =       "F. J. {Arag{\'o}n Artacho} and J. M. Borwein",
  title =        "Global convergence of a non-convex {Douglas--Rachford}
                 iteration",
  journal =      "ArXiv e-prints",
  month =        mar,
  year =         "2012",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2012arXiv1203.2392A;
                 http://docserver.carma.newcastle.edu.au/1061/",
  abstract =     "We establish a region of convergence for the
                 proto-typical non-convex Douglas--Rachford iteration
                 which finds a point on the intersection of a line and a
                 circle. Previous work on the non-convex iteration [2]
                 was only able to establish local convergence, and was
                 ineffective in that no explicit region of convergence
                 could be given.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1203.2392",
  keywords =     "Mathematics - Optimization and Control",
  ORCID-numbers = "Aragon Artacho, Francisco Javier/0000-0002-2445-8011;
                 Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.OC",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2012:AIS
author: David H. Bailey and Jonathan M. Borwein
title: Ancient Indian Square Roots: An Exercise in Forensic Paleo-Mathematics
journal: j-AMER-MATH-MONTHLY
volume: 119
number: 8
pages: 646--657
month: oct
monthnumber: 10
year: 2012
CODEN: AMMYAE
DOI: https://doi.org/10.4169/amer.math.monthly.119.08.646
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 01A32
MRnumber: 2988227
MRreviewer: S. G. Dani
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1385/; http://www.jstor.org/stable/10.4169
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.jstor.org/journals/00029890.html
rawauthor: David H. Bailey and Jonathan M. Borwein
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
bibsource:
http://www.jstor.org/journals/00029890.html; http://www.jstor.org/stable/10.4169/amermathmont.119.issue-8; 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/elefunt.bib

abstract:
This article examines the computation of square roots in ancient India in the context of the discovery of positional decimal arithmetic.

rawabstract:
This article examines the computation of square roots in ancient India in the context of the discovery of positional decimal arithmetic.

entry:
@Article{Bailey:2012:AIS,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Ancient {Indian} Square Roots: An Exercise in Forensic
                 Paleo-Mathematics",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "119",
  number =       "8",
  pages =        "646--657",
  month =        oct,
  year =         "2012",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.119.08.646",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "01A32",
  MRnumber =     "2988227",
  MRreviewer =   "S. G. Dani",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/10.4169/amermathmont.119.issue-8;
                 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/elefunt.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1385/;
                 http://www.jstor.org/stable/10.4169",
  abstract =     "This article examines the computation of square roots
                 in ancient India in the context of the discovery of
                 positional decimal arithmetic.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  unique-id =    "Bailey:2012:AIS",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2012:EAN
title: An Empirical Approach to the Normality of $ pi $
journal: j-EXP-MATH
volume: 21
number: 4
pages: 375--384
year: 2012
DOI: https://doi.org/10.1080/10586458.2012.665333
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 11K16 (03D32 11A63)
MRnumber: 3004253
MRreviewer: John H. Loxton
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1382/
fjournal: Experimental Mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.tandfonline.com/loi/uexm20
rawtitle: An Empirical Approach to the Normality of $ \pi $
author:
David H. Bailey and Jonathan M. Borwein and Cristian S. Calude and Michael J. Dinneen and Monica Dumitrescu and Alex Yee

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

abstract:
Using the results of several extremely large recent computations [Yee and Kondo 11], we tested positively the normality of a prefix of roughly four trillion hexadecimal digits of p. This result was used by a Poisson process model of normality of p: in this model, it is extraordinarily unlikely that p is not asymptotically normal base 16, given the normality of its initial segment.

rawabstract:
Using the results of several extremely large recent computations [Yee and Kondo 11], we tested positively the normality of a prefix of roughly four trillion hexadecimal digits of p. This result was used by a Poisson process model of normality of p: in this model, it is extraordinarily unlikely that p is not asymptotically normal base 16, given the normality of its initial segment.

ORCID:
Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646; Calude, Cristian Sorin/0000-0002-8711-6799

entry:
@Article{Bailey:2012:EAN,
  author =       "David H. Bailey and Jonathan M. Borwein and Cristian
                 S. Calude and Michael J. Dinneen and Monica Dumitrescu
                 and Alex Yee",
  title =        "An Empirical Approach to the Normality of $ \pi $",
  journal =      j-EXP-MATH,
  volume =       "21",
  number =       "4",
  pages =        "375--384",
  year =         "2012",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2012.665333",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11K16 (03D32 11A63)",
  MRnumber =     "3004253",
  MRreviewer =   "John H. Loxton",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1382/",
  abstract =     "Using the results of several extremely large recent
                 computations [Yee and Kondo 11], we tested positively
                 the normality of a prefix of roughly four trillion
                 hexadecimal digits of p. This result was used by a
                 Poisson process model of normality of p: in this model,
                 it is extraordinarily unlikely that p is not
                 asymptotically normal base 16, given the normality of
                 its initial segment.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646; Calude, Cristian
                 Sorin/0000-0002-8711-6799",
  unique-id =    "Bailey:2012:EAN",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2012:EEC
author: David H. Bailey and Jonathan M. Borwein
title: Exploration, Experimentation and Computation
journal: International Advances in Mathematics
volume: 31
number: 1
pages: 1--14
month: jan
monthnumber: 1
year: 2012
ISSN: 1003-3092 OR 10033092
ISSNL: 1003-3092 OR 10033092
bibdate: Fri Sep 30 08:44:21 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 08:44:21 ???
note: Chinese translation of cite Bailey:2011:EEC.
URL: http://www.davidhbailey.com/dhbpapers/expexp-chinese.pdf
language: Chinese
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:2011:EEC}.
rawtitle: Exploration, Experimentation and Computation
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bailey:2012:EEC,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Exploration, Experimentation and Computation",
  journal =      "International Advances in Mathematics",
  volume =       "31",
  number =       "1",
  pages =        "1--14",
  month =        jan,
  year =         "2012",
  ISSN =         "1003-3092",
  ISSN-L =       "1003-3092",
  bibdate =      "Fri Sep 30 08:44:21 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Chinese translation of \cite{Bailey:2011:EEC}.",
  URL =          "http://www.davidhbailey.com/dhbpapers/expexp-chinese.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  language =     "Chinese",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Bailey:2012:EEM
author: David H. Bailey and Jonathan M. Borwein
title: Exploratory experimentation in mathematics: selected works
publisher: Perfectly Scientific Press
address: Portland, OR, USA
pages: 364
year: 2012
ISBN: 1-935638-24-6 OR 1935638246
ISBN13: 978-1-935638-24-7 OR 9781935638247
LCCN: QA76.95 .B34 2012
bibdate: Tue Aug 16 08:41:02 MDT 2016
bibtimestamp: 2016.08.16 08:41:02 MDT
subject: Mathematics; Experiments; Experiments.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Exploratory experimentation in mathematics: selected works
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Book{Bailey:2012:EEM,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Exploratory experimentation in mathematics: selected
                 works",
  publisher =    "Perfectly Scientific Press",
  address =      "Portland, OR, USA",
  pages =        "364",
  year =         "2012",
  ISBN =         "1-935638-24-6",
  ISBN-13 =      "978-1-935638-24-7",
  LCCN =         "QA76.95 .B34 2012",
  bibdate =      "Tue Aug 16 08:41:02 MDT 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 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",
  subject =      "Mathematics; Experiments; Experiments.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2012:HHC
author: David H. Bailey and Jonathan M. Borwein
title: Hand-to-hand combat with thousand-digit integrals
journal: j-J-COMPUT-SCI
volume: 3
number: 3
pages: 77--86
year: 2012
DOI: https://doi.org/10.1016/j.jocs.2010.12.004
ISSN: 1877-7503 (print), 1877-7511 (electronic) OR 18777503 (print), 18777511 (electronic)
ISSNL: 1877-7503 OR 18777503
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: Scientific Computation Methods and Applications.
fjournal: Journal of Computational Science
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.sciencedirect.com/journal/journal-of-computational-science
rawauthor: David H. Bailey and Jonathan M. Borwein
rawnote: Scientific Computation Methods and Applications.
rawtitle: Hand-to-hand combat with thousand-digit integrals
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1393/; http://www.sciencedirect.com/science/article/pii/S1877750310000773

abstract:
In this paper we describe numerical investigations of definite integrals that arise by considering the moments of multi-step uniform random walks in the plane, together with a closely related class of integrals involving the elliptic functions K, K', E and E'. We find that in many cases such integrals can be ``experimentally'' evaluated in closed form or that intriguing linear relations exist within a class of similar integrals. Discovering these identities and relations often requires the evaluation of integrals to extreme precision, combined with large-scale runs of the ``PSLQ'' integer relation algorithm. This paper presents details of the techniques used in these calculations and mentions some of the many difficulties that can arise.

keywords:
Elliptic integrals; Experimental mathematics; High-precision computing; Numerical integration; Random walks

rawabstract:
In this paper we describe numerical investigations of definite integrals that arise by considering the moments of multi-step uniform random walks in the plane, together with a closely related class of integrals involving the elliptic functions K, K', E and E'. We find that in many cases such integrals can be ``experimentally'' evaluated in closed form or that intriguing linear relations exist within a class of similar integrals. Discovering these identities and relations often requires the evaluation of integrals to extreme precision, combined with large-scale runs of the ``PSLQ'' integer relation algorithm. This paper presents details of the techniques used in these calculations and mentions some of the many difficulties that can arise.

entry:
@Article{Bailey:2012:HHC,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Hand-to-hand combat with thousand-digit integrals",
  journal =      j-J-COMPUT-SCI,
  volume =       "3",
  number =       "3",
  pages =        "77--86",
  year =         "2012",
  DOI =          "https://doi.org/10.1016/j.jocs.2010.12.004",
  ISSN =         "1877-7503 (print), 1877-7511 (electronic)",
  ISSN-L =       "1877-7503",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Scientific Computation Methods and Applications.",
  URL =          "http://docserver.carma.newcastle.edu.au/1393/;
                 http://www.sciencedirect.com/science/article/pii/S1877750310000773",
  abstract =     "In this paper we describe numerical investigations of
                 definite integrals that arise by considering the
                 moments of multi-step uniform random walks in the
                 plane, together with a closely related class of
                 integrals involving the elliptic functions K, K', E and
                 E'. We find that in many cases such integrals can be
                 ``experimentally'' evaluated in closed form or that
                 intriguing linear relations exist within a class of
                 similar integrals. Discovering these identities and
                 relations often requires the evaluation of integrals to
                 extreme precision, combined with large-scale runs of
                 the ``PSLQ'' integer relation algorithm. This paper
                 presents details of the techniques used in these
                 calculations and mentions some of the many difficulties
                 that can arise.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Computational Science",
  journal-URL =  "https://www.sciencedirect.com/journal/journal-of-computational-science",
  keywords =     "Elliptic integrals; Experimental mathematics;
                 High-precision computing; Numerical integration; Random
                 walks",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2012:HPC
author: David H. Bailey and Roberto Barrio and Jonathan M. Borwein
title: High-precision computation: Mathematical physics and dynamics
journal: j-APPL-MATH-COMP
volume: 218
number: 20
pages: 10106--10121
day: 15
month: jun
monthnumber: 6
year: 2012
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/j.amc.2012.03.087
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
MRclass: 65Y04 (68M07)
MRnumber: 2921767
bibdate: Thu Aug 11 10:27:38 2016
bibtimestamp: 2016.08.11 10:27:38 ???
fjournal: Applied Mathematics and Computation
keywords: Dynamical systems; Experimental mathematics; High-precision computation; Mathematical physics
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 Roberto Barrio and Jonathan M. Borwein
rawtitle: High-precision computation: Mathematical physics and dynamics
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/applmathcomput2010.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://docserver.carma.newcastle.edu.au/775/; http://www.sciencedirect.com/science/article/pii/S0096300312003505

abstract:
At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion effort. This paper presents an overview of recent applications of these techniques and provides some analysis of their numerical requirements. We conclude that high-precision arithmetic facilities are now an indispensable component of a modern large-scale scientific computing environment.

rawabstract:
At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion effort. This paper presents an overview of recent applications of these techniques and provides some analysis of their numerical requirements. We conclude that high-precision arithmetic facilities are now an indispensable component of a modern large-scale scientific computing environment.

entry:
@Article{Bailey:2012:HPC,
  author =       "David H. Bailey and Roberto Barrio and Jonathan M.
                 Borwein",
  title =        "High-precision computation: Mathematical physics and
                 dynamics",
  journal =      j-APPL-MATH-COMP,
  volume =       "218",
  number =       "20",
  pages =        "10106--10121",
  day =          "15",
  month =        jun,
  year =         "2012",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2012.03.087",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "65Y04 (68M07)",
  MRnumber =     "2921767",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/775/;
                 http://www.sciencedirect.com/science/article/pii/S0096300312003505",
  abstract =     "At the present time, IEEE 64-bit floating-point
                 arithmetic is sufficiently accurate for most scientific
                 applications. However, for a rapidly growing body of
                 important scientific computing applications, a higher
                 level of numeric precision is required. Such
                 calculations are facilitated by high-precision software
                 packages that include high-level language translation
                 modules to minimize the conversion effort. This paper
                 presents an overview of recent applications of these
                 techniques and provides some analysis of their
                 numerical requirements. We conclude that high-precision
                 arithmetic facilities are now an indispensable
                 component of a modern large-scale scientific computing
                 environment.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
  keywords =     "Dynamical systems; Experimental mathematics;
                 High-precision computation; Mathematical physics",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Barrio, Roberto/L-4983-2014",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Bailey:2012:ND
editor: David H. Bailey and Jonathan M. Borwein
booktitle: Exploratory Experimentation in Mathematics: Selected Works
title: Normality and the Digits of $ pi $
publisher: Perfectly Scientific Press
address: Portland, OR, USA
pages: 10106--10121
day: 3
month: feb
monthnumber: 2
year: 2012
bibdate: Fri Sep 30 08:47:20 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 08:47:20 ???
URL: http://www.davidhbailey.com/dhbpapers/normality-digits-pi.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawbooktitle: Exploratory Experimentation in Mathematics: Selected Works
raweditor: David H. Bailey and Jonathan M. Borwein
rawtitle: Normality and the Digits of $ \pi $
abstract:
The question of whether (and why) the digits of well-known constants of mathematics are statistically random in some sense has long fascinated mathematicians. Indeed, one prime motivation in computing and analyzing digits of $ pi $ is to explore the age-old question of whether and why these digits appear ``random.'' The first computation on ENIAC in 1949 of $ pi $ to 2037 decimal places was proposed by John von Neumann to shed some light on the distribution of $ pi $ (and of $e$) [8, pp. 277--281].

rawabstract:
The question of whether (and why) the digits of well-known constants of mathematics are statistically random in some sense has long fascinated mathematicians. Indeed, one prime motivation in computing and analyzing digits of $ \pi $ is to explore the age-old question of whether and why these digits appear ``random.'' The first computation on ENIAC in 1949 of $ \pi $ to 2037 decimal places was proposed by John von Neumann to shed some light on the distribution of $ \pi $ (and of $e$) [8, pp. 277--281].

ORCID:
Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646; Calude, Cristian Sorin/0000-0002-8711-6799

entry:
@InCollection{Bailey:2012:ND,
  author =       "David H. Bailey and Jonathan M. Borwein and Cristian
                 S. Calude and Michael J. Dinneen and Monica Dumitrescu
                 and Alex Yee",
  editor =       "David H. Bailey and Jonathan M. Borwein",
  booktitle =    "Exploratory Experimentation in Mathematics: Selected
                 Works",
  title =        "Normality and the Digits of $ \pi $",
  publisher =    "Perfectly Scientific Press",
  address =      "Portland, OR, USA",
  day =          "3",
  month =        feb,
  year =         "2012",
  bibdate =      "Fri Sep 30 08:47:20 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/normality-digits-pi.pdf",
  abstract =     "The question of whether (and why) the digits of
                 well-known constants of mathematics are statistically
                 random in some sense has long fascinated
                 mathematicians. Indeed, one prime motivation in
                 computing and analyzing digits of $ \pi $ is to explore
                 the age-old question of whether and why these digits
                 appear ``random.'' The first computation on ENIAC in
                 1949 of $ \pi $ to 2037 decimal places was proposed by
                 John von Neumann to shed some light on the distribution
                 of $ \pi $ (and of $e$) [8, pp. 277--281].",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646; Calude, Cristian
                 Sorin/0000-0002-8711-6799",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Bailey:2012:NP
author: D. H. Bailey and J. M. Borwein and C. S. Calude and M. J. Dinneen and M. Dumitrescu and A. Yee
title: Normality and pi
pages: 10106--10121
month: feb
monthnumber: 2
year: 2012
bibdate: Tue Aug 16 09:57:02 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 09:57:02 ???
note: Preprint.
URL: http://www.carma.newcastle.edu.au/jon/normality-long.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. H. Bailey and J. M. Borwein and C. S. Calude and M. J. Dinneen and M. Dumitrescu and A. Yee
rawnote: Preprint.
rawtitle: Normality and pi
entry:
@Unpublished{Bailey:2012:NP,
  author =       "D. H. Bailey and J. M. Borwein and C. S. Calude and M.
                 J. Dinneen and M. Dumitrescu and A. Yee",
  title =        "Normality and pi",
  month =        feb,
  year =         "2012",
  bibdate =      "Tue Aug 16 09:57:02 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Preprint.",
  URL =          "http://www.carma.newcastle.edu.au/jon/normality-long.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646; Calude, Cristian
                 Sorin/0000-0002-8711-6799",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:2012:NSC
author: David H. Bailey and Jonathan M. Borwein
title: Nonnormality of Stoneham constants
journal: j-RAMANUJAN-J
volume: 29
number: 1--3
pages: 409--422
year: 2012
CODEN: RAJOF9
DOI: https://doi.org/10.1007/s11139-012-9417-3
ISSN: 1382-4090 (print), 1572-9303 (electronic) OR 13824090 (print), 15729303 (electronic)
ISSNL: 1382-4090 OR 13824090
MRclass: 11K16 (11K31)
MRnumber: 2994109
MRreviewer: Robert F. Tichy
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/1386/
fjournal: The Ramanujan Journal
ZMnumber: 1336.11055
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 Jonathan M. Borwein
rawtitle: Nonnormality of {Stoneham} constants
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
abstract:
This paper examines ``Stoneham constants,'' namely real numbers of the form , for coprime integers ba parts per thousand yen2 and ca parts per thousand yen2. These are of interest because, according to previous studies, alpha (b,c) is known to be b-normal, meaning that every m-long string of base-b digits appears in the base-b expansion of the constant with precisely the limiting frequency b (-m) . So, for example, the constant is 2-normal. More recently it was established that alpha (b,c) is not bc-normal, so, for example, alpha (2,3) is provably not 6-normal. In this paper, we extend these findings by showing that alpha (b,c) is not B-normal, where B=b (p) c (q) r, for integers b and c as above, p,q,ra parts per thousand yen1, neither b nor c divide r, and the condition D=c (q/p) r (1/p) /b (c-1)< 1 is satisfied. It is not known whether or not this is a complete catalog of bases to which alpha (b,c) is nonnormal. We also show that the sum of two B-nonnormal Stoneham constants as defined above, subject to some restrictions, is B-nonnormal.

rawabstract:
This paper examines ``Stoneham constants,'' namely real numbers of the form , for coprime integers ba parts per thousand yen2 and ca parts per thousand yen2. These are of interest because, according to previous studies, alpha (b,c) is known to be b-normal, meaning that every m-long string of base-b digits appears in the base-b expansion of the constant with precisely the limiting frequency b (-m) . So, for example, the constant is 2-normal. More recently it was established that alpha (b,c) is not bc-normal, so, for example, alpha (2,3) is provably not 6-normal. In this paper, we extend these findings by showing that alpha (b,c) is not B-normal, where B=b (p) c (q) r, for integers b and c as above, p,q,ra parts per thousand yen1, neither b nor c divide r, and the condition D=c (q/p) r (1/p) /b (c-1)< 1 is satisfied. It is not known whether or not this is a complete catalog of bases to which alpha (b,c) is nonnormal. We also show that the sum of two B-nonnormal Stoneham constants as defined above, subject to some restrictions, is B-nonnormal.

entry:
@Article{Bailey:2012:NSC,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Nonnormality of {Stoneham} constants",
  journal =      j-RAMANUJAN-J,
  volume =       "29",
  number =       "1--3",
  pages =        "409--422",
  year =         "2012",
  CODEN =        "RAJOF9",
  DOI =          "https://doi.org/10.1007/s11139-012-9417-3",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  MRclass =      "11K16 (11K31)",
  MRnumber =     "2994109",
  MRreviewer =   "Robert F. Tichy",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1386/",
  ZMnumber =     "1336.11055",
  abstract =     "This paper examines ``Stoneham constants,'' namely
                 real numbers of the form , for coprime integers ba
                 parts per thousand yen2 and ca parts per thousand yen2.
                 These are of interest because, according to previous
                 studies, alpha (b,c) is known to be b-normal, meaning
                 that every m-long string of base-b digits appears in
                 the base-b expansion of the constant with precisely the
                 limiting frequency b (-m) . So, for example, the
                 constant is 2-normal. More recently it was established
                 that alpha (b,c) is not bc-normal, so, for example,
                 alpha (2,3) is provably not 6-normal. In this paper, we
                 extend these findings by showing that alpha (b,c) is
                 not B-normal, where B=b (p) c (q) r, for integers b and
                 c as above, p,q,ra parts per thousand yen1, neither b
                 nor c divide r, and the condition D=c (q/p) r (1/p) /b
                 (c-1)< 1 is satisfied. It is not known whether or not
                 this is a complete catalog of bases to which alpha
                 (b,c) is nonnormal. We also show that the sum of two
                 B-nonnormal Stoneham constants as defined above,
                 subject to some restrictions, is B-nonnormal.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The {Ramanujan} Journal",
  journal-URL =  "http://link.springer.com/journal/11139",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  unique-id =    "Bailey:2012:NSC",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:2012:SMP
author: David H. Bailey and Jonathan M. Borwein
title: Solution to Monthly Problem 11650
type: Report
address: Berkeley, CA 94720, USA and Callaghan, NSW 2308, Australia and Jeddah 80200, Saudi Arabia.
pages: 2
day: 14
month: jun
monthnumber: 6
year: 2012
bibdate: Fri Sep 30 08:56:31 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.30 08:56:31 ???
URL: http://www.davidhbailey.com/dhbpapers/amm-11650.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Solution to Monthly Problem 11650
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 and King Abdulaziz University

entry:
@TechReport{Bailey:2012:SMP,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Solution to Monthly Problem 11650",
  type =         "Report",
  institution =  "Lawrence Berkeley National Laboratory and Centre for
                 Computer Assisted Research Mathematics and its
                 Applications (CARMA), University of Newcastle and King
                 Abdulaziz University",
  address =      "Berkeley, CA 94720, USA and Callaghan, NSW 2308,
                 Australia and Jeddah 80200, Saudi Arabia.",
  pages =        "2",
  day =          "14",
  month =        jun,
  year =         "2012",
  bibdate =      "Fri Sep 30 08:56:31 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/amm-11650.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:2012:BBT
author: Heinz H. Bauschke and Jonathan M. Borwein and Xianfu Wang and Liangjin Yao
title: The Brezis--Browder theorem in a general Banach space
journal: j-J-FUNCT-ANAL
volume: 262
number: 12
pages: 4948--4971
year: 2012
CODEN: JFUAAW
DOI: https://doi.org/10.1016/j.jfa.2012.03.023
ISSN: 0022-1236 (print), 1096-0783 (electronic) OR 00221236 (print), 10960783 (electronic)
ISSNL: 0022-1236 OR 00221236
MRclass: 47H05 (47H04 49N15)
MRnumber: 2916057
MRreviewer: Simeon Reich
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
URL: http://www.sciencedirect.com/science/article/pii/S0022123612001462
fjournal: Journal of Functional Analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/00221236
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein and Xianfu Wang and Liangjin Yao
rawtitle: The {Br{\'e}zis--Browder} theorem in a general {Banach} space
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
abstract:
During the 1970s Brezis and Browder presented a now classical characterization of maximal monotonicity of monotone linear relations in reflexive spaces. In this paper, we extend (and refine) their result to a general Banach space. We also provide an affirmative answer to a problem posed by Phelps and Simons.

keywords:
Adjoint; Brezis--Browder Theorem; Linear relation; Monotone operator; Operator of type (D); Operator of type (FP); Operator of type (NI); Set-valued operator; Skew operator; Symmetric operator

rawabstract:
During the 1970s Br{\'e}zis and Browder presented a now classical characterization of maximal monotonicity of monotone linear relations in reflexive spaces. In this paper, we extend (and refine) their result to a general Banach space. We also provide an affirmative answer to a problem posed by Phelps and Simons.

entry:
@Article{Bauschke:2012:BBT,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein and Xianfu
                 Wang and Liangjin Yao",
  title =        "The {Br{\'e}zis--Browder} theorem in a general
                 {Banach} space",
  journal =      j-J-FUNCT-ANAL,
  volume =       "262",
  number =       "12",
  pages =        "4948--4971",
  year =         "2012",
  CODEN =        "JFUAAW",
  DOI =          "https://doi.org/10.1016/j.jfa.2012.03.023",
  ISSN =         "0022-1236 (print), 1096-0783 (electronic)",
  ISSN-L =       "0022-1236",
  MRclass =      "47H05 (47H04 49N15)",
  MRnumber =     "2916057",
  MRreviewer =   "Simeon Reich",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022123612001462",
  abstract =     "During the 1970s Br{\'e}zis and Browder presented a
                 now classical characterization of maximal monotonicity
                 of monotone linear relations in reflexive spaces. In
                 this paper, we extend (and refine) their result to a
                 general Banach space. We also provide an affirmative
                 answer to a problem posed by Phelps and Simons.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Functional Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00221236",
  keywords =     "Adjoint; Br{\'e}zis--Browder Theorem; Linear relation;
                 Monotone operator; Operator of type (D); Operator of
                 type (FP); Operator of type (NI); Set-valued operator;
                 Skew operator; Symmetric operator",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:2012:CPM
author: Heinz H. Bauschke and Jonathan M. Borwein and Xianfu Wang and Liangjin Yao
title: Construction of pathological maximally monotone operators on non-reflexive Banach spaces
journal: j-SET-VALUED-VAR-ANAL
volume: 20
number: 3
pages: 387--415
year: 2012
DOI: https://doi.org/10.1007/s11228-012-0209-0
ISSN: 1877-0533 (print), 1877-0541 (electronic) OR 18770533 (print), 18770541 (electronic)
ISSNL: 1877-0533 OR 18770533
MRclass: 47H05 (47A06 47B65)
MRnumber: 2949634
MRreviewer: Simeon Reich
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://arxiv.org/abs/1108.1463; http://docserver.carma.newcastle.edu.au/1090/
fjournal: Set-Valued and Variational Analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11228
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein and Xianfu Wang and Liangjin Yao
rawtitle: Construction of pathological maximally monotone operators on non-reflexive {Banach} spaces
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646;
abstract:
In this paper, we construct maximally monotone operators that are not of Gossez's dense-type (D) in many nonreflexive spaces. Many of these operators also fail to possess the Bronsted-Rockafellar (BR) property. Using these operators, we show that the partial inf-convolution of two BC-functions will not always be a BC-function. This provides a negative answer to a challenging question posed by Stephen Simons. Among other consequences, we deduce-in a uniform fashion-that every Banach space which contains an isomorphic copy of the James space or its dual , or c (0) or its dual a''''(1), admits a non type (D) operator. The existence of non type (D) operators in spaces containing a''''(1) or c (0) has been proved recently by Bueno and Svaiter.

rawabstract:
In this paper, we construct maximally monotone operators that are not of Gossez's dense-type (D) in many nonreflexive spaces. Many of these operators also fail to possess the Bronsted-Rockafellar (BR) property. Using these operators, we show that the partial inf-convolution of two BC-functions will not always be a BC-function. This provides a negative answer to a challenging question posed by Stephen Simons. Among other consequences, we deduce-in a uniform fashion-that every Banach space which contains an isomorphic copy of the James space or its dual , or c (0) or its dual a''''(1), admits a non type (D) operator. The existence of non type (D) operators in spaces containing a''''(1) or c (0) has been proved recently by Bueno and Svaiter.

entry:
@Article{Bauschke:2012:CPM,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein and Xianfu
                 Wang and Liangjin Yao",
  title =        "Construction of pathological maximally monotone
                 operators on non-reflexive {Banach} spaces",
  journal =      j-SET-VALUED-VAR-ANAL,
  volume =       "20",
  number =       "3",
  pages =        "387--415",
  year =         "2012",
  DOI =          "https://doi.org/10.1007/s11228-012-0209-0",
  ISSN =         "1877-0533 (print), 1877-0541 (electronic)",
  ISSN-L =       "1877-0533",
  MRclass =      "47H05 (47A06 47B65)",
  MRnumber =     "2949634",
  MRreviewer =   "Simeon Reich",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/1108.1463;
                 http://docserver.carma.newcastle.edu.au/1090/",
  abstract =     "In this paper, we construct maximally monotone
                 operators that are not of Gossez's dense-type (D) in
                 many nonreflexive spaces. Many of these operators also
                 fail to possess the Bronsted-Rockafellar (BR) property.
                 Using these operators, we show that the partial
                 inf-convolution of two BC-functions will not always be
                 a BC-function. This provides a negative answer to a
                 challenging question posed by Stephen Simons. Among
                 other consequences, we deduce-in a uniform fashion-that
                 every Banach space which contains an isomorphic copy of
                 the James space or its dual , or c (0) or its dual
                 a''''(1), admits a non type (D) operator. The existence
                 of non type (D) operators in spaces containing a''''(1)
                 or c (0) has been proved recently by Bueno and
                 Svaiter.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Set-Valued and Variational Analysis",
  journal-URL =  "http://link.springer.com/journal/11228",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646;",
  unique-id =    "Bauschke:2012:CPM",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:2012:EMM
author: Heinz H. Bauschke and Jonathan M. Borwein and Xianfu Wang and Liangjin Yao
title: Every maximally monotone operator of Fitzpatrick--Phelps type is actually of dense type
journal: j-OPTIM-LETT
volume: 6
number: 8
pages: 1875--1881
year: 2012
DOI: https://doi.org/10.1007/s11590-011-0383-2
ISSN: 1862-4472 (print), 1862-4480 (electronic) OR 18624472 (print), 18624480 (electronic)
ISSNL: 1862-4472 OR 18624472
MRclass: 47H05 (47H04 49J53)
MRnumber: 2996490
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/1104.0750; http://docserver.carma.newcastle.edu.au/1442/
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: Heinz H. Bauschke and Jonathan M. Borwein and Xianfu Wang and Liangjin Yao
rawtitle: Every maximally monotone operator of {Fitzpatrick--Phelps} type is actually of dense type
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646;
abstract:
We show that every maximally monotone operator of Fitzpatrick-Phelps type defined on a real Banach space must be of dense type. This provides an affirmative answer to a question posed by Stephen Simons in 2001 and implies that various important notions of monotonicity coincide.

rawabstract:
We show that every maximally monotone operator of Fitzpatrick-Phelps type defined on a real Banach space must be of dense type. This provides an affirmative answer to a question posed by Stephen Simons in 2001 and implies that various important notions of monotonicity coincide.

entry:
@Article{Bauschke:2012:EMM,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein and Xianfu
                 Wang and Liangjin Yao",
  title =        "Every maximally monotone operator of
                 {Fitzpatrick--Phelps} type is actually of dense type",
  journal =      j-OPTIM-LETT,
  volume =       "6",
  number =       "8",
  pages =        "1875--1881",
  year =         "2012",
  DOI =          "https://doi.org/10.1007/s11590-011-0383-2",
  ISSN =         "1862-4472 (print), 1862-4480 (electronic)",
  ISSN-L =       "1862-4472",
  MRclass =      "47H05 (47H04 49J53)",
  MRnumber =     "2996490",
  MRreviewer =   "Patrick L. Combettes",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/1104.0750;
                 http://docserver.carma.newcastle.edu.au/1442/",
  abstract =     "We show that every maximally monotone operator of
                 Fitzpatrick-Phelps type defined on a real Banach space
                 must be of dense type. This provides an affirmative
                 answer to a question posed by Stephen Simons in 2001
                 and implies that various important notions of
                 monotonicity coincide.",
  acknowledgement = ack-nhfb,
  ajournal =     "Optim. Lett.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Optimization Letters",
  journal-URL =  "http://link.springer.com/journal/11590",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646;",
  unique-id =    "Bauschke:2012:EMM",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2012:CUC
author: Jonathan M. Borwein and Jon Vanderwerff
title: Constructions of Uniformly Convex Functions
journal: j-CAN-MATH-BULL
volume: 55
number: 4
pages: 697--707
month: dec
monthnumber: 12
year: 2012
CODEN: CMBUA3
DOI: https://doi.org/10.4153/CMB-2011-049-2
ISSN: 0008-4395 (print), 1496-4287 (electronic) OR 00084395 (print), 14964287 (electronic)
ISSNL: 0008-4395 OR 00084395
MRclass: 49J53 (46G05 52A41 90C25)
MRnumber: 2994675
MRreviewer: Constantin Z{\u{a}}linescu
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/778/
fjournal: Canadian Mathematical Bulletin. Bulletin Canadien de Mathematiques
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://cms.math.ca/cmb/
rawauthor: Jonathan M. Borwein and Jon Vanderwerff
rawtitle: Constructions of Uniformly Convex Functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
http://cms.math.ca/cmb/v55/; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib

abstract:
We give precise conditions under which the composition of a norm with a convex function yields a uniformly convex function on a Banach space. Various applications are given to functions of power type. The results are dualized to study uniform smoothness and several examples are provided.

rawabstract:
We give precise conditions under which the composition of a norm with a convex function yields a uniformly convex function on a Banach space. Various applications are given to functions of power type. The results are dualized to study uniform smoothness and several examples are provided.

entry:
@Article{Borwein:2012:CUC,
  author =       "Jonathan M. Borwein and Jon Vanderwerff",
  title =        "Constructions of Uniformly Convex Functions",
  journal =      j-CAN-MATH-BULL,
  volume =       "55",
  number =       "4",
  pages =        "697--707",
  month =        dec,
  year =         "2012",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-2011-049-2",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  MRclass =      "49J53 (46G05 52A41 90C25)",
  MRnumber =     "2994675",
  MRreviewer =   "Constantin Z{\u{a}}linescu",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://cms.math.ca/cmb/v55/;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/canmathbull.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/778/",
  abstract =     "We give precise conditions under which the composition
                 of a norm with a convex function yields a uniformly
                 convex function on a Banach space. Various applications
                 are given to functions of power type. The results are
                 dualized to study uniform smoothness and several
                 examples are provided.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Canadian Mathematical Bulletin. Bulletin Canadien de
                 Math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cmb/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2012:CZD
author: Jonathan M. Borwein and Regina S. Burachik and Liangjin Yao
title: Conditions for zero duality gap in convex programming
journal: ArXiv e-prints
pages: 10
month: nov
monthnumber: 11
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/2012arXiv1211.4953B; http://docserver.carma.newcastle.edu.au/1465/
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: Conditions for zero duality gap in convex programming
ORCID: Burachik, Regina/0000-0003-1332-6213; Borwein, Jonathan/0000-0002-1263-0646
abstract:
We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is weaker than all existing constraint qualifications, including the closed epigraph condition. Our dual condition was inspired by, and is weaker than, the so-called Bertsekas' condition for monotropic programming problems. We give several corollaries of our result and special cases as applications. We pay special attention to the polyhedral and sublinear cases, and their implications in convex optimization.

keywords:
Mathematics - Functional Analysis, Mathematics - Optimization and Control, 49J52, 48N15 (Primary) 90C25, 90C30, 90C46 (Secondary)

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

entry:
@Article{Borwein:2012:CZD,
  author =       "Jonathan M. Borwein and Regina S. Burachik and
                 Liangjin Yao",
  title =        "Conditions for zero duality gap in convex
                 programming",
  journal =      "ArXiv e-prints",
  pages =        "10",
  month =        nov,
  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/2012arXiv1211.4953B;
                 http://docserver.carma.newcastle.edu.au/1465/",
  abstract =     "We introduce and study a new dual condition which
                 characterizes zero duality gap in nonsmooth convex
                 optimization. We prove that our condition is weaker
                 than all existing constraint qualifications, including
                 the closed epigraph condition. Our dual condition was
                 inspired by, and is weaker than, the so-called
                 Bertsekas' condition for monotropic programming
                 problems. We give several corollaries of our result and
                 special cases as applications. We pay special attention
                 to the polyhedral and sublinear cases, and their
                 implications in convex optimization.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1211.4953",
  keywords =     "Mathematics - Functional Analysis, Mathematics -
                 Optimization and Control, 49J52, 48N15 (Primary) 90C25,
                 90C30, 90C46 (Secondary)",
  ORCID-numbers = "Burachik, Regina/0000-0003-1332-6213; Borwein,
                 Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2012:DSU
author: Jonathan M. Borwein and Armin Straub and James Wan and Wadim Zudilin
title: Densities of short uniform random walks
journal: j-CAN-J-MATH
volume: 64
number: 5
pages: 961--990
year: 2012
CODEN: CJMAAB
DOI: https://doi.org/10.4153/CJM-2011-079-2
ISSN: 0008-414X (print), 1496-4279 (electronic) OR 0008414X (print), 14964279 (electronic)
ISSNL: 0008-414X OR 0008414X
MRclass: 60G50 (11R06 33C20 82B41)
MRnumber: 2979573
MRreviewer: Aklilu Zeleke
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 an appendix by Don Zagier.
URL: http://arxiv.org/abs/1103.2995; http://docserver.carma.newcastle.edu.au/1388/
fjournal: Canadian Journal of Mathematics. Journal Canadien de Mathematiques
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://cms.math.ca/cjm/
rawauthor: Jonathan M. Borwein and Armin Straub and James Wan and Wadim Zudilin
rawnote: With an appendix by Don Zagier.
rawtitle: Densities of short uniform random walks
abstract:
We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and, less completely, those with five steps. As one of the main results, we obtain a hypergeometric representation of the density for four steps, which complements the classical elliptic representation in the case of three steps. It appears unrealistic to expect similar results for more than five steps. New results are also presented concerning the moments of uniform random walks and, in particular, their derivatives. Relations with Mahler measures are discussed.

rawabstract:
We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and, less completely, those with five steps. As one of the main results, we obtain a hypergeometric representation of the density for four steps, which complements the classical elliptic representation in the case of three steps. It appears unrealistic to expect similar results for more than five steps. New results are also presented concerning the moments of uniform random walks and, in particular, their derivatives. Relations with Mahler measures are discussed.

ORCID:
Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053; Zudilin, Wadim/0000-0001-9551-2903

entry:
@Article{Borwein:2012:DSU,
  author =       "Jonathan M. Borwein and Armin Straub and James Wan and
                 Wadim Zudilin",
  title =        "Densities of short uniform random walks",
  journal =      j-CAN-J-MATH,
  volume =       "64",
  number =       "5",
  pages =        "961--990",
  year =         "2012",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-2011-079-2",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  MRclass =      "60G50 (11R06 33C20 82B41)",
  MRnumber =     "2979573",
  MRreviewer =   "Aklilu Zeleke",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "With an appendix by Don Zagier.",
  URL =          "http://arxiv.org/abs/1103.2995;
                 http://docserver.carma.newcastle.edu.au/1388/",
  abstract =     "We study the densities of uniform random walks in the
                 plane. A special focus is on the case of short walks
                 with three or four steps and, less completely, those
                 with five steps. As one of the main results, we obtain
                 a hypergeometric representation of the density for four
                 steps, which complements the classical elliptic
                 representation in the case of three steps. It appears
                 unrealistic to expect similar results for more than
                 five steps. New results are also presented concerning
                 the moments of uniform random walks and, in particular,
                 their derivatives. Relations with Mahler measures are
                 discussed.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Canadian Journal of Mathematics. Journal Canadien de
                 Math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053; Zudilin,
                 Wadim/0000-0001-9551-2903",
  unique-id =    "Borwein:2012:DSU",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2012:EED
author: Jonathan Michael Borwein
title: Exploratory Experimentation: Digitally-assisted Discovery and Proof
crossref: Hanna:2012:PPM
pages: 69--96
year: 2012
DOI: https://doi.org/10.1007/978-94-007-2129-6_4
bibdate: Sat Aug 13 15:47:54 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.13 15:47:54 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Michael Borwein
rawtitle: Exploratory Experimentation: Digitally-assisted Discovery and Proof
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/393/; http://link.springer.com/chapter/10.1007/978-94-007-2129-6_4

entry:
@InCollection{Borwein:2012:EED,
  author =       "Jonathan Michael Borwein",
  title =        "Exploratory Experimentation: Digitally-assisted
                 Discovery and Proof",
  crossref =     "Hanna:2012:PPM",
  pages =        "69--96",
  year =         "2012",
  DOI =          "https://doi.org/10.1007/978-94-007-2129-6_4",
  bibdate =      "Sat Aug 13 15:47:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/393/;
                 http://link.springer.com/chapter/10.1007/978-94-007-2129-6_4",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borwein:2012:IMM
author: Jonathan M. Borwein and Matthew P. Skerritt
title: An introduction to modern mathematical computing: with Mathematicareg
publisher: pub-SV
address: pub-SV:adr
pages: 69--96
year: 2012
DOI: https://doi.org/10.1007/978-1-4614-4253-0
ISBN: 1-4614-4252-4 (print), 1-4614-4253-2 (e-book) OR 1461442524 (print), 1461442532 (ebook)
ISSN: 1867-5506 (print), 1867-5514 (electronic) OR 18675506 (print), 18675514 (electronic)
ISSNL: 1867-5506 OR 18675506
LCCN: QA76.95 .B67 2012
bibdate: Tue Aug 16 08:35:55 MDT 2016
bibtimestamp: 2016.08.16 08:35:55 MDT
series: Springer undergraduate texts in mathematics and technology
URL: http://public.eblib.com/choice/publicfullrecord.aspx?p=1030664
subject: Mathematics; Data processing; Computer science; Mathematics.; Data processing.
TOC: Number theory Calculus Linear algebra Visualization and geometry: a postscript
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Matthew P. Skerritt
rawtitle: An introduction to modern mathematical computing: with {Mathematica}\reg{}
rawTOC: Number theory \\ Calculus \\ Linear algebra \\ Visualization and geometry: a postscript
ORCID: Borwein, Jonathan/0000-0002-1263-0646
ISBN13:
978-1-4614-4252-3 (print), 978-1-4614-4253-0 (e-book) OR 9781461442523 (print), 9781461442530 (ebook)

bibsource:
fsz3950.oclc.org:210/WorldCato; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/mathematica.bib

abstract:
Thirty years ago, mathematical computation was difficult to perform and thus used sparingly. However, mathematical computation has become far more accessible due to the emergence of the personal computer, the discovery of fiber-optics and the consequent development of the modern internet, and the creation of Maple, Mathematica, and Matlab. An Introduction to Modern Mathematical Computing: With Mathematica looks beyond teaching the syntax and semantics of Mathematica and similar programs, and focuses on why they are necessary tools for anyone who engages in mathematics. It is an essential read for mathematicians, mathematics educators, computer scientists, engineers, scientists, and anyone who wishes to expand their knowledge of mathematics. This volume will also explain how to become an ``experimental mathematician,'' and will supply useful information about how to create better proofs. The text covers material in elementary number theory, calculus, multivariable calculus, introductory linear algebra, and visualization and interactive geometric computation. It is intended for upper-undergraduate students, and as a reference guide for anyone who wishes to learn to use the Mathematica program. Also by J. M. Borwein and M. B. Skerritt: An Introduction to Modern Mathematical Computing: With Maple c2011, ISBN: 978-1-4614-0121-6, 216 p. and 81 color illustrations.

rawabstract:
Thirty years ago, mathematical computation was difficult to perform and thus used sparingly. However, mathematical computation has become far more accessible due to the emergence of the personal computer, the discovery of fiber-optics and the consequent development of the modern internet, and the creation of Maple, Mathematica, and Matlab. An Introduction to Modern Mathematical Computing: With Mathematica looks beyond teaching the syntax and semantics of Mathematica and similar programs, and focuses on why they are necessary tools for anyone who engages in mathematics. It is an essential read for mathematicians, mathematics educators, computer scientists, engineers, scientists, and anyone who wishes to expand their knowledge of mathematics. This volume will also explain how to become an ``experimental mathematician,'' and will supply useful information about how to create better proofs. The text covers material in elementary number theory, calculus, multivariable calculus, introductory linear algebra, and visualization and interactive geometric computation. It is intended for upper-undergraduate students, and as a reference guide for anyone who wishes to learn to use the Mathematica program. Also by J. M. Borwein and M. B. Skerritt: An Introduction to Modern Mathematical Computing: With Maple c2011, ISBN: 978-1-4614-0121-6, 216 p. and 81 color illustrations.

entry:
@Book{Borwein:2012:IMM,
  author =       "Jonathan M. Borwein and Matthew P. Skerritt",
  title =        "An introduction to modern mathematical computing: with
                 {Mathematica}\reg{}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  year =         "2012",
  DOI =          "https://doi.org/10.1007/978-1-4614-4253-0",
  ISBN =         "1-4614-4252-4 (print), 1-4614-4253-2 (e-book)",
  ISBN-13 =      "978-1-4614-4252-3 (print), 978-1-4614-4253-0
                 (e-book)",
  ISSN =         "1867-5506 (print), 1867-5514 (electronic)",
  ISSN-L =       "1867-5506",
  LCCN =         "QA76.95 .B67 2012",
  bibdate =      "Tue Aug 16 08:35:55 MDT 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCato;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  series =       "Springer undergraduate texts in mathematics and
                 technology",
  URL =          "http://public.eblib.com/choice/publicfullrecord.aspx?p=1030664",
  abstract =     "Thirty years ago, mathematical computation was
                 difficult to perform and thus used sparingly. However,
                 mathematical computation has become far more accessible
                 due to the emergence of the personal computer, the
                 discovery of fiber-optics and the consequent
                 development of the modern internet, and the creation of
                 Maple, Mathematica, and Matlab. An Introduction to
                 Modern Mathematical Computing: With Mathematica looks
                 beyond teaching the syntax and semantics of Mathematica
                 and similar programs, and focuses on why they are
                 necessary tools for anyone who engages in mathematics.
                 It is an essential read for mathematicians, mathematics
                 educators, computer scientists, engineers, scientists,
                 and anyone who wishes to expand their knowledge of
                 mathematics. This volume will also explain how to
                 become an ``experimental mathematician,'' and will
                 supply useful information about how to create better
                 proofs. The text covers material in elementary number
                 theory, calculus, multivariable calculus, introductory
                 linear algebra, and visualization and interactive
                 geometric computation. It is intended for
                 upper-undergraduate students, and as a reference guide
                 for anyone who wishes to learn to use the Mathematica
                 program. Also by J. M. Borwein and M. B. Skerritt: An
                 Introduction to Modern Mathematical Computing: With
                 Maple c2011, ISBN: 978-1-4614-0121-6, 216 p. and 81
                 color illustrations.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject =      "Mathematics; Data processing; Computer science;
                 Mathematics.; Data processing.",
  tableofcontents = "Number theory \\
                 Calculus \\
                 Linear algebra \\
                 Visualization and geometry: a postscript",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2012:LPA
author: Jonathan M. Borwein
title: The Life of Pi: From Archimedes to ENIAC and Beyond
type: Report
address: Callaghan, NSW 2308, Australia
pages: 30
day: 19
month: jun
monthnumber: 6
year: 2012
bibdate: Sat Sep 03 16:38:50 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.03 16:38:50 ???
note: Prepared for Berggren Festschrift. Updated and revised version of cite Borwein:2008:VPG.
URL: http://carma.newcastle.edu.au/jon/pi-2012.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawnote: Prepared for Berggren Festschrift. Updated and revised version of \cite{Borwein:2008:VPG}.
rawtitle: The Life of Pi: From {Archimedes} to {ENIAC} and Beyond
ORCID: Borwein, Jonathan/0000-0002-1263-0646
institution:
Centre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle

entry:
@TechReport{Borwein:2012:LPA,
  author =       "Jonathan M. Borwein",
  title =        "The Life of Pi: From {Archimedes} to {ENIAC} and
                 Beyond",
  type =         "Report",
  institution =  "Centre for Computer Assisted Research Mathematics and
                 its Applications (CARMA), University of Newcastle",
  address =      "Callaghan, NSW 2308, Australia",
  pages =        "30",
  day =          "19",
  month =        jun,
  year =         "2012",
  bibdate =      "Sat Sep 03 16:38:50 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Prepared for Berggren Festschrift. Updated and revised
                 version of \cite{Borwein:2008:VPG}.",
  URL =          "http://carma.newcastle.edu.au/jon/pi-2012.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2012:LSEa
author: Jonathan M. Borwein and Armin Straub
title: Log-sine evaluations of Mahler measures
journal: j-J-AUSTRAL-MATH-SOC
volume: 92
number: 1
pages: 15--36
year: 2012
CODEN: JAUMAX
DOI: https://doi.org/10.1017/S1446788712000067
ISSN: 1446-7887 (print), 1446-8107 (electronic) OR 14467887 (print), 14468107 (electronic)
ISSNL: 1446-7887 OR 14467887
MRclass: 33E20 (11R06 33F10)
MRnumber: 2945674
MRreviewer: Qiang Wu
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 Armin Straub
rawtitle: Log-sine evaluations of {Mahler} measures
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053
URL:
http://docserver.carma.newcastle.edu.au/1384/; http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8610681

abstract:
We provide evaluations of several recently studied higher and multiple Mahler measures using log-sine integrals. This is complemented with an analysis of generating functions and identities for log-sine integrals which allows the evaluations to be expressed in terms of zeta values or more general polylogarithmic terms. The machinery developed is then applied to evaluation of further families of multiple Mahler measures.

entry:
@Article{Borwein:2012:LSEa,
  author =       "Jonathan M. Borwein and Armin Straub",
  title =        "Log-sine evaluations of {Mahler} measures",
  journal =      j-J-AUSTRAL-MATH-SOC,
  volume =       "92",
  number =       "1",
  pages =        "15--36",
  year =         "2012",
  CODEN =        "JAUMAX",
  DOI =          "https://doi.org/10.1017/S1446788712000067",
  ISSN =         "1446-7887 (print), 1446-8107 (electronic)",
  ISSN-L =       "1446-7887",
  MRclass =      "33E20 (11R06 33F10)",
  MRnumber =     "2945674",
  MRreviewer =   "Qiang Wu",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1384/;
                 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8610681",
  abstract =     "We provide evaluations of several recently studied
                 higher and multiple Mahler measures using log-sine
                 integrals. This is complemented with an analysis of
                 generating functions and identities for log-sine
                 integrals which allows the evaluations to be expressed
                 in terms of zeta values or more general polylogarithmic
                 terms. The machinery developed is then applied to
                 evaluation of further families of multiple Mahler
                 measures.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of the Australian Mathematical Society",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053",
  unique-id =    "Borwein:2012:LSE",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2012:LSEb
author: David Borwein and Jonathan M. Borwein and Armin Straub and James Wan
title: Log-sine evaluations of Mahler measures, II
journal: j-INTEGERS
volume: 12
number: 6
pages: 1179--1212
year: 2012
CODEN: INTEHN
DOI: https://doi.org/10.1515/integers-2012-0035
ISSN: 1867-0652 (print), 1867-0660 (electronic) OR 18670652 (print), 18670660 (electronic)
MRclass: 11R06
MRnumber: 3011556
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/1103.3035; http://docserver.carma.newcastle.edu.au/1435/
fjournal: Integers
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.degruyter.com/view/j/integ
rawauthor: David Borwein and Jonathan M. Borwein and Armin Straub and James Wan
rawtitle: Log-sine evaluations of {Mahler} measures, {II}
ORCID: Borwein, Jonathan/0000-0002-1263-0646; Straub, Armin/0000-0001-6802-6053
entry:
@Article{Borwein:2012:LSEb,
  author =       "David Borwein and Jonathan M. Borwein and Armin Straub
                 and James Wan",
  title =        "Log-sine evaluations of {Mahler} measures, {II}",
  journal =      j-INTEGERS,
  volume =       "12",
  number =       "6",
  pages =        "1179--1212",
  year =         "2012",
  CODEN =        "INTEHN",
  DOI =          "https://doi.org/10.1515/integers-2012-0035",
  ISSN =         "1867-0652 (print), 1867-0660 (electronic)",
  MRclass =      "11R06",
  MRnumber =     "3011556",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://arxiv.org/abs/1103.3035;
                 http://docserver.carma.newcastle.edu.au/1435/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Integers",
  journal-URL =  "http://www.degruyter.com/view/j/integ",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646; Straub,
                 Armin/0000-0001-6802-6053",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2012:LTI
author: J. M. Borwein and L. Yao
title: Legendre-type integrands and convex integral functions
journal: ArXiv e-prints
pages: 1179--1212
month: aug
monthnumber: 8
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/2012arXiv1208.5217B; http://docserver.carma.newcastle.edu.au/1455/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and L. Yao
rawtitle: {Legendre}-type integrands and convex integral functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper, we study the properties of integral functionals induced on $ L^1_E(S, mu ) $ by closed convex functions on a Euclidean space $E$. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann--Shannon entropy and the Fermi--Dirac entropy are strongly rotund. We also study convergence in measure and give various limiting counterexample.

keywords:
Mathematics - Functional Analysis, Mathematics - Optimization and Control, Primary 46B20, 34H05, Secondary 47H05, 47N10, 90C25

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

entry:
@Article{Borwein:2012:LTI,
  author =       "J. M. Borwein and L. Yao",
  title =        "{Legendre}-type integrands and convex integral
                 functions",
  journal =      "ArXiv e-prints",
  month =        aug,
  year =         "2012",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2012arXiv1208.5217B;
                 http://docserver.carma.newcastle.edu.au/1455/",
  abstract =     "In this paper, we study the properties of integral
                 functionals induced on $ L^1_{E(S, \mu)} $ by closed
                 convex functions on a Euclidean space $E$. We give
                 sufficient conditions for such integral functions to be
                 strongly rotund (well-posed). We show that in this
                 generality functions such as the Boltzmann--Shannon
                 entropy and the Fermi--Dirac entropy are strongly
                 rotund. We also study convergence in measure and give
                 various limiting counterexample.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "1208.5217",
  keywords =     "Mathematics - Functional Analysis, Mathematics -
                 Optimization and Control, Primary 46B20, 34H05,
                 Secondary 47H05, 47N10, 90C25",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  primaryclass = "math.FA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2012:MEF
author: Jonathan M. Borwein
title: Maximum entropy and feasibility methods for convex and nonconvex inverse problems
journal: j-OPTIMIZATION
volume: 61
number: 1
pages: 1--33
year: 2012
CODEN: OPTZDQ
DOI: https://doi.org/10.1080/02331934.2011.632502
ISSN: 0233-1934, 0323-3898 OR 02331934, 03233898
ISSNL: 0233-1934 OR 02331934
MRclass: 49-02 (45Q05 49J53 90C25 94A17)
MRnumber: 2875572
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/1439/
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
rawtitle: Maximum entropy and feasibility methods for convex and nonconvex inverse problems
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We discuss informally two approaches to solving convex and nonconvex feasibility problems - via entropy optimization and via algebraic iterative methods. We shall highlight the advantages and disadvantages of each and give various related applications and limiting examples. While some of the results are very classical, they are not as well-known to practitioners as they should be. A key role is played by the Fenchel conjugate.

rawabstract:
We discuss informally two approaches to solving convex and nonconvex feasibility problems - via entropy optimization and via algebraic iterative methods. We shall highlight the advantages and disadvantages of each and give various related applications and limiting examples. While some of the results are very classical, they are not as well-known to practitioners as they should be. A key role is played by the Fenchel conjugate.

entry:
@Article{Borwein:2012:MEF,
  author =       "Jonathan M. Borwein",
  title =        "Maximum entropy and feasibility methods for convex and
                 nonconvex inverse problems",
  journal =      j-OPTIMIZATION,
  volume =       "61",
  number =       "1",
  pages =        "1--33",
  year =         "2012",
  CODEN =        "OPTZDQ",
  DOI =          "https://doi.org/10.1080/02331934.2011.632502",
  ISSN =         "0233-1934, 0323-3898",
  ISSN-L =       "0233-1934",
  MRclass =      "49-02 (45Q05 49J53 90C25 94A17)",
  MRnumber =     "2875572",
  MRreviewer =   "Patrick L. Combettes",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1439/",
  abstract =     "We discuss informally two approaches to solving convex
                 and nonconvex feasibility problems - via entropy
                 optimization and via algebraic iterative methods. We
                 shall highlight the advantages and disadvantages of
                 each and give various related applications and limiting
                 examples. While some of the results are very classical,
                 they are not as well-known to practitioners as they
                 should be. A key role is played by the Fenchel
                 conjugate.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Optimization",
  journal-URL =  "http://www.tandfonline.com/loi/gopt20",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  unique-id =    "Borwein:2012:MEF",
}


