# bibtab

bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:1997:LFM
author: Heinz H. Bauschke and Jonathan M. Borwein
title: Legendre functions and the method of random Bregman projections
journal: j-J-CONVEX-ANAL
volume: 4
number: 1
pages: 27--67
year: 1997
ISSN: 0944-6532 (print), 2363-6394 (electronic) OR 09446532 (print), 23636394 (electronic)
MRclass: 49M45 (65K10 90C25)
MRnumber: 1459881
MRreviewer: Alfredo N. Iusem
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/96/; http://www.heldermann-verlag.de/jca/jca04/jca04002.pdf
fjournal: Journal of Convex Analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.heldermann.de/JCA/jcacon.htm
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein
rawtitle: {Legendre} functions and the method of random {Bregman} projections
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bauschke:1997:LFM,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein",
  title =        "{Legendre} functions and the method of random
                 {Bregman} projections",
  journal =      j-J-CONVEX-ANAL,
  volume =       "4",
  number =       "1",
  pages =        "27--67",
  year =         "1997",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "49M45 (65K10 90C25)",
  MRnumber =     "1459881",
  MRreviewer =   "Alfredo N. Iusem",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/96/;
                 http://www.heldermann-verlag.de/jca/jca04/jca04002.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Convex Analysis",
  journal-URL =  "http://www.heldermann.de/JCA/jcacon.htm",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Bauschke:1997:MCP
author: Heinz H. Bauschke and Jonathan M. Borwein and Adrian S. Lewis
booktitle: Recent developments in optimization theory and nonlinear analysis (Jerusalem, 1995)
title: The method of cyclic projections for closed convex sets in Hilbert space
volume: 204
publisher: pub-AMS
address: pub-AMS:adr
pages: 1--38
year: 1997
DOI: https://doi.org/10.1090/conm/204/02620
MRclass: 49M45 (47H99 47N10 65F10 90C25)
MRnumber: 1442992
MRreviewer: Alfredo N. Iusem
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: Contemp. Math.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein and Adrian S. Lewis
rawbooktitle: Recent developments in optimization theory and nonlinear analysis ({Jerusalem}, 1995)
rawtitle: The method of cyclic projections for closed convex sets in {Hilbert} space
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Bauschke:1997:MCP,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein and Adrian
                 S. Lewis",
  booktitle =    "Recent developments in optimization theory and
                 nonlinear analysis ({Jerusalem}, 1995)",
  title =        "The method of cyclic projections for closed convex
                 sets in {Hilbert} space",
  volume =       "204",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "1--38",
  year =         "1997",
  DOI =          "https://doi.org/10.1090/conm/204/02620",
  MRclass =      "49M45 (47H99 47N10 65F10 90C25)",
  MRnumber =     "1442992",
  MRreviewer =   "Alfredo N. Iusem",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Contemp. Math.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bauschke:1997:SCH
author: Heinz H. Bauschke and Jonathan M. Borwein and Wu Li
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 30
day: 26
month: sep
monthnumber: 9
year: 1997
bibdate: Thu Sep 01 07:28:55 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 07:28:55 ???
URL: http://docserver.carma.newcastle.edu.au/195
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein and Wu Li
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Strong conical hull intersection property, bounded linear regularity, Jameson's property ($G$), and error bounds in convex optimization

abstract:
The strong conical hull intersection property and bounded linear regularity are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. These fundamental notions occur in various branches of convex optimization (constrained approximation, convex feasibility problems, linear inequalities, for instance). It is shown that the standard constraint qualification from convex analysis implies bounded linear regularity, which in turn yields the strong conical hull intersection property. Jameson's duality for two cones, which relates bounded linear regularity to property (G), is re-derived and refined. For polyhedral cones, a statement dual to Hoffman's error bound result is obtained. A sharpening of a result on error bounds for convex inequalities by Auslender and Crouzeix is presented. Finally, for two subspaces, property (G) is quantified by the angle between the subspaces.

rawabstract:
The strong conical hull intersection property and bounded linear regularity are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. These fundamental notions occur in various branches of convex optimization (constrained approximation, convex feasibility problems, linear inequalities, for instance). It is shown that the standard constraint qualification from convex analysis implies bounded linear regularity, which in turn yields the strong conical hull intersection property. Jameson's duality for two cones, which relates bounded linear regularity to property (G), is re-derived and refined. For polyhedral cones, a statement dual to Hoffman's error bound result is obtained. A sharpening of a result on error bounds for convex inequalities by Auslender and Crouzeix is presented. Finally, for two subspaces, property (G) is quantified by the angle between the subspaces.

rawtitle:
Strong conical hull intersection property, bounded linear regularity, {Jameson}'s property ({$G$}), and error bounds in convex optimization

entry:
@TechReport{Bauschke:1997:SCH,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein and Wu Li",
  title =        "Strong conical hull intersection property, bounded
                 linear regularity, {Jameson}'s property ({$G$}), and
                 error bounds in convex optimization",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "30",
  day =          "26",
  month =        sep,
  year =         "1997",
  bibdate =      "Thu Sep 01 07:28:55 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/195",
  abstract =     "The strong conical hull intersection property and
                 bounded linear regularity are properties of a
                 collection of finitely many closed convex intersecting
                 sets in Euclidean space. These fundamental notions
                 occur in various branches of convex optimization
                 (constrained approximation, convex feasibility
                 problems, linear inequalities, for instance). It is
                 shown that the standard constraint qualification from
                 convex analysis implies bounded linear regularity,
                 which in turn yields the strong conical hull
                 intersection property. Jameson's duality for two cones,
                 which relates bounded linear regularity to property
                 (G), is re-derived and refined. For polyhedral cones, a
                 statement dual to Hoffman's error bound result is
                 obtained. A sharpening of a result on error bounds for
                 convex inequalities by Auslender and Crouzeix is
                 presented. Finally, for two subspaces, property (G) is
                 quantified by the angle between the subspaces.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:1997:ADE
author: J. M. Borwein and F. G. Garvan
title: Approximations to $ pi $ via the Dedekind eta function
crossref: Borwein:1997:OMP
pages: 89--115
year: 1997
MRclass: 11F20 (11Y60)
MRnumber: 1483915
MRreviewer: Bruce C. Berndt
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: CMS Conf. Proc.
URL: http://docserver.carma.newcastle.edu.au/158/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and F. G. Garvan
rawtitle: Approximations to $ \pi $ via the {Dedekind} eta function
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InProceedings{Borwein:1997:ADE,
  author =       "J. M. Borwein and F. G. Garvan",
  title =        "Approximations to $ \pi $ via the {Dedekind} eta
                 function",
  crossref =     "Borwein:1997:OMP",
  pages =        "89--115",
  year =         "1997",
  MRclass =      "11F20 (11Y60)",
  MRnumber =     "1483915",
  MRreviewer =   "Bruce C. Berndt",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "CMS Conf. Proc.",
  URL =          "http://docserver.carma.newcastle.edu.au/158/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:1997:AGMa
author: J. M. Borwein and P. B. Borwein
title: The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions
crossref: Berggren:1997:PSB
pages: 537--552
year: 1997
DOI: https://doi.org/10.1007/978-1-4757-2736-4_56
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibtimestamp: 2016.08.11 09:36:22 MDT
note: Reprint of cite Borwein:1984:AGM.
URL: http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_56
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein
rawnote: Reprint of \cite{Borwein:1984:AGM}.
rawtitle: The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InCollection{Borwein:1997:AGMa,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:1997:PSB",
  pages =        "537--552",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4757-2736-4_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Borwein:1984:AGM}.",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_56",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1997:AGMb
author: Jonathan A. Borwein and Petr Lisonek and John A. Macdonald
title: Arithmetic--Geometric Means Revisited
journal: j-MAPLE-TECH-NEWS
volume: 4
number: 1
pages: 20--27
month: Winter
year: 1997
ISSN: 1061-5733 OR 10615733
ISSNL: 1061-5733 OR 10615733
bibdate: Wed Jul 23 09:11:50 1997
bibtimestamp: 1997.07.23 09:11:50 ???
note: Special issue on Maple in the mathematical sciences.
URL: http://docserver.carma.newcastle.edu.au/4/
fjournal: Maple technical newsletter
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://web.mit.edu/maple/www/plibrary/mtn.html
rawauthor: Jonathan A. Borwein and Petr Lison{\v{e}}k and John A. Macdonald
rawnote: Special issue on Maple in the mathematical sciences.
rawtitle: Arithmetic--Geometric Means Revisited
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/maple-tech.bib

entry:
@Article{Borwein:1997:AGMb,
  author =       "Jonathan A. Borwein and Petr Lison{\v{e}}k and John A.
                 Macdonald",
  title =        "Arithmetic--Geometric Means Revisited",
  journal =      j-MAPLE-TECH-NEWS,
  volume =       "4",
  number =       "1",
  pages =        "20--27",
  month =        "Winter",
  year =         "1997",
  ISSN =         "1061-5733",
  ISSN-L =       "1061-5733",
  bibdate =      "Wed Jul 23 09:11:50 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-tech.bib",
  note =         "Special issue on Maple in the mathematical sciences.",
  URL =          "http://docserver.carma.newcastle.edu.au/4/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Maple technical newsletter",
  journal-URL =  "http://web.mit.edu/maple/www/plibrary/mtn.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1997:AIR
author: Jonathan M. Borwein and Petr Lisonek
title: Applications of integer relation algorithms
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 20--27
day: 18
month: nov
monthnumber: 11
year: 1997
bibdate: Thu Sep 01 07:39:40 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 07:39:40 ???
note: Published in cite Borwein:2000:AIR.
URL: http://docserver.carma.newcastle.edu.au/198
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Petr Lison{\v{e}}k
rawnote: Published in \cite{Borwein:2000:AIR}.
rawtitle: Applications of integer relation algorithms
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Let $a$ be a vector of real numbers. By an integer relation for $a$ we mean a non-zero integer vector $c$ such that $ c a^T = 0$. We discuss the algorithms for finding such integer relations from the user's point of view, by presenting examples of their applications and by reviewing the available software implementations.

remark:
Submitted to the Proceedings of the 9th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'97), July 1997, Vienna, Austria, to appear as a special issue of Discrete Mathematics.

rawabstract:
Let $a$ be a vector of real numbers. By an integer relation for $a$ we mean a non-zero integer vector $c$ such that $ c a^T = 0$. We discuss the algorithms for finding such integer relations from the user's point of view, by presenting examples of their applications and by reviewing the available software implementations.

entry:
@TechReport{Borwein:1997:AIR,
  author =       "Jonathan M. Borwein and Petr Lison{\v{e}}k",
  title =        "Applications of integer relation algorithms",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  day =          "18",
  month =        nov,
  year =         "1997",
  bibdate =      "Thu Sep 01 07:39:40 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2000:AIR}.",
  URL =          "http://docserver.carma.newcastle.edu.au/198",
  abstract =     "Let $a$ be a vector of real numbers. By an integer
                 relation for $a$ we mean a non-zero integer vector $c$
                 such that $ c a^T = 0$. We discuss the algorithms for
                 finding such integer relations from the user's point of
                 view, by presenting examples of their applications and
                 by reviewing the available software implementations.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Submitted to the Proceedings of the 9th International
                 Conference on Formal Power Series and Algebraic
                 Combinatorics (FPSAC'97), July 1997, Vienna, Austria,
                 to appear as a special issue of Discrete Mathematics.",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:1997:APD
author: J. M. Borwein and F. Garvan
booktitle: Organic Mathematics Proceedings, 12 April 1996
title: Approximating Pi with the Dedekind eta function
pages: ??--??
year: 1997
ISSN: 0731-1036 OR 07311036
bibdate: Mon Aug 15 14:37:48 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.15 14:37:48 ???
URL: http://www.cecm.sfu.ca/organics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and F. Garvan
rawbooktitle: Organic Mathematics Proceedings, {12 April 1996}
rawtitle: Approximating Pi with the {Dedekind} eta function
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InProceedings{Borwein:1997:APD,
  author =       "J. M. Borwein and F. Garvan",
  editor =       "????",
  booktitle =    "Organic Mathematics Proceedings, {12 April 1996}",
  title =        "Approximating Pi with the {Dedekind} eta function",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "1997",
  ISSN =         "0731-1036",
  bibdate =      "Mon Aug 15 14:37:48 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.cecm.sfu.ca/organics",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1997:CAM
author: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lisonek
title: Combinatorial aspects of multiple zeta values
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 12
day: 31
month: jul
monthnumber: 7
year: 1997
bibdate: Thu Sep 01 07:55:12 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 07:55:12 ???
URL: http://docserver.carma.newcastle.edu.au/201/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lison{\v{e}}k
rawtitle: Combinatorial aspects of multiple zeta values
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The fact that an integral representation of MZVs obeys a shuffle product rule allows the possibility of a combinatorial approach to them. Using this approach we prove a longstanding conjecture of Don Zagier about MZVs with certain repeated arguments. We also prove a similar cyclic sum identity. Finally, we present extensive computational evidence supporting an infinite family of conjectured MZV identities that simultaneously generalize the Zagier identity.

rawabstract:
Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The fact that an integral representation of MZVs obeys a shuffle product rule allows the possibility of a combinatorial approach to them. Using this approach we prove a longstanding conjecture of Don Zagier about MZVs with certain repeated arguments. We also prove a similar cyclic sum identity. Finally, we present extensive computational evidence supporting an infinite family of conjectured MZV identities that simultaneously generalize the Zagier identity.

entry:
@TechReport{Borwein:1997:CAM,
  author =       "Jonathan M. Borwein and David M. Bradley and David J.
                 Broadhurst and Petr Lison{\v{e}}k",
  title =        "Combinatorial aspects of multiple zeta values",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "12",
  day =          "31",
  month =        jul,
  year =         "1997",
  bibdate =      "Thu Sep 01 07:55:12 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/201/",
  abstract =     "Multiple zeta values (MZVs, also called Euler sums or
                 multiple harmonic series) are nested generalizations of
                 the classical Riemann zeta function evaluated at
                 integer values. The fact that an integral
                 representation of MZVs obeys a shuffle product rule
                 allows the possibility of a combinatorial approach to
                 them. Using this approach we prove a longstanding
                 conjecture of Don Zagier about MZVs with certain
                 repeated arguments. We also prove a similar cyclic sum
                 identity. Finally, we present extensive computational
                 evidence supporting an infinite family of conjectured
                 MZV identities that simultaneously generalize the
                 Zagier identity.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1997:CBS
author: Jon Borwein and Marian Fabian and Jon Vanderwerff
title: Characterizations of Banach spaces via convex and other locally Lipschitz functions
journal: Acta Mathematica Vietnamica
volume: 22
number: 1
pages: 53--69
year: 1997
ISSN: 0251-4184 (print), 2315-4144 (electronic) OR 02514184 (print), 23154144 (electronic)
ISSNL: 0251-4184 OR 02514184
MRclass: 46B20 (46G99 52A41)
MRnumber: 1479738
MRreviewer: Warren B. Moors
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: Special edition in honour of Huang Tuy's seventieth birthday.
URL: http://docserver.carma.newcastle.edu.au/179/
fjournal: Acta Mathematica Vietnamica
acknowledgement: ack-nhfb
ajournal: Acta Math. Vietnam.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jon Borwein and Marian Fabian and Jon Vanderwerff
rawnote: Special edition in honour of Huang Tuy's seventieth birthday.
rawtitle: Characterizations of {Banach} spaces via convex and other locally {Lipschitz} functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Various properties of Banach spaces, including the reflexivity and the Schur property of a space, are characterized in terms of properties of corresponding classes of locally Lipschitz functions on those spaces.

rawabstract:
Various properties of Banach spaces, including the reflexivity and the Schur property of a space, are characterized in terms of properties of corresponding classes of locally Lipschitz functions on those spaces.

entry:
@Article{Borwein:1997:CBS,
  author =       "Jon Borwein and Marian Fabian and Jon Vanderwerff",
  title =        "Characterizations of {Banach} spaces via convex and
                 other locally {Lipschitz} functions",
  journal =      "Acta Mathematica Vietnamica",
  volume =       "22",
  number =       "1",
  pages =        "53--69",
  year =         "1997",
  ISSN =         "0251-4184 (print), 2315-4144 (electronic)",
  ISSN-L =       "0251-4184",
  MRclass =      "46B20 (46G99 52A41)",
  MRnumber =     "1479738",
  MRreviewer =   "Warren B. Moors",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Special edition in honour of Huang Tuy's seventieth
                 birthday.",
  URL =          "http://docserver.carma.newcastle.edu.au/179/",
  abstract =     "Various properties of Banach spaces, including the
                 reflexivity and the Schur property of a space, are
                 characterized in terms of properties of corresponding
                 classes of locally Lipschitz functions on those
                 spaces.",
  acknowledgement = ack-nhfb,
  ajournal =     "Acta Math. Vietnam.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Acta Mathematica Vietnamica",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1997:CFB
author: Jon Borwein and Jon Vanderwerff
title: Convex functions on Banach spaces not containing $ l_1 $
journal: j-CAN-MATH-BULL
volume: 40
number: 1
pages: 10--18
year: 1997
CODEN: CMBUA3
DOI: https://doi.org/10.4153/CMB-1997-002-1
ISSN: 0008-4395 (print), 1496-4287 (electronic) OR 00084395 (print), 14964287 (electronic)
ISSNL: 0008-4395 OR 00084395
MRclass: 46B20 (46A55 46G05 46N10 52A41)
MRnumber: 1443721
MRreviewer: Li Xin Cheng
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1532/
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: Jon Borwein and Jon Vanderwerff
rawtitle: Convex functions on {Banach} spaces not containing $ l_1 $
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1997:CFB,
  author =       "Jon Borwein and Jon Vanderwerff",
  title =        "Convex functions on {Banach} spaces not containing $
                 l_1 $",
  journal =      j-CAN-MATH-BULL,
  volume =       "40",
  number =       "1",
  pages =        "10--18",
  year =         "1997",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-1997-002-1",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  MRclass =      "46B20 (46A55 46G05 46N10 52A41)",
  MRnumber =     "1443721",
  MRreviewer =   "Li Xin Cheng",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1532/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Canadian Mathematical Bulletin. Bulletin Canadien de
                 Math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cmb/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1997:CHP
author: J. M. Borwein and R. Girgensohn and Xianfu Wang
title: On the construction of Holder and proximal subderivatives
type: Report
institution: Department of Mathematics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 13
day: 14
month: mar
monthnumber: 3
year: 1997
bibdate: Thu Sep 01 06:39:15 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 06:39:15 ???
note: Published in cite Borwein:1998:CHP.
URL: http://docserver.carma.newcastle.edu.au/186/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and R. Girgensohn and Xianfu Wang
rawnote: Published in \cite{Borwein:1998:CHP}.
rawtitle: On the construction of {H{\"o}lder} and proximal subderivatives
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We construct Lipschitz functions such that for all $ s > 0 $ they are s-Holder, and so proximally, subdifferentiable only on dyadic rationals and nowhere else. As applications we construct Lipschitz functions with prescribed Holder and approximate subderivatives.

rawabstract:
We construct Lipschitz functions such that for all $ s > 0 $ they are s-H{\o}lder, and so proximally, subdifferentiable only on dyadic rationals and nowhere else. As applications we construct Lipschitz functions with prescribed Holder and approximate subderivatives.

entry:
@TechReport{Borwein:1997:CHP,
  author =       "J. M. Borwein and R. Girgensohn and Xianfu Wang",
  title =        "On the construction of {H{\"o}lder} and proximal
                 subderivatives",
  type =         "Report",
  institution =  "Department of Mathematics, Simon Fraser University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "13",
  day =          "14",
  month =        mar,
  year =         "1997",
  bibdate =      "Thu Sep 01 06:39:15 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:1998:CHP}.",
  URL =          "http://docserver.carma.newcastle.edu.au/186/",
  abstract =     "We construct Lipschitz functions such that for all $ s
                 > 0 $ they are s-H{\o}lder, and so proximally,
                 subdifferentiable only on dyadic rationals and nowhere
                 else. As applications we construct Lipschitz functions
                 with prescribed Holder and approximate
                 subderivatives.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1997:DDF
author: J. M. Borwein and Xianfu Wang
title: Distinct differentiable functions may share the same Clarke subdifferential at all points
journal: j-PROC-AM-MATH-SOC
volume: 125
number: 3
pages: 807--813
year: 1997
CODEN: PAMYAR
DOI: https://doi.org/10.1090/S0002-9939-97-03654-X
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 49J52 (26A16 26A24 58C20)
MRnumber: 1363449
MRreviewer: Doug Ward
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/112/
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. M. Borwein and Xianfu Wang
rawtitle: Distinct differentiable functions may share the same {Clarke} subdifferential at all points
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1997:DDF,
  author =       "J. M. Borwein and Xianfu Wang",
  title =        "Distinct differentiable functions may share the same
                 {Clarke} subdifferential at all points",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "125",
  number =       "3",
  pages =        "807--813",
  year =         "1997",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/S0002-9939-97-03654-X",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "49J52 (26A16 26A24 58C20)",
  MRnumber =     "1363449",
  MRreviewer =   "Doug Ward",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/112/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1997:DEM
author: Jonathan Borwein and Michael Monagan
title: Differential Equations in Maple: a Short Tutorial
journal: j-MAPLE-TECH-NEWS
volume: 4
number: 1
pages: 55--58
month: Winter
year: 1997
ISSN: 1061-5733 OR 10615733
ISSNL: 1061-5733 OR 10615733
bibdate: Wed Jul 23 09:11:50 1997
bibtimestamp: 1997.07.23 09:11:50 ???
fjournal: Maple technical newsletter
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://web.mit.edu/maple/www/plibrary/mtn.html
rawauthor: Jonathan Borwein and Michael Monagan
rawtitle: Differential Equations in {Maple}: a Short Tutorial
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-tech.bib

entry:
@Article{Borwein:1997:DEM,
  author =       "Jonathan Borwein and Michael Monagan",
  title =        "Differential Equations in {Maple}: a Short Tutorial",
  journal =      j-MAPLE-TECH-NEWS,
  volume =       "4",
  number =       "1",
  pages =        "55--58",
  month =        "Winter",
  year =         "1997",
  ISSN =         "1061-5733",
  ISSN-L =       "1061-5733",
  bibdate =      "Wed Jul 23 09:11:50 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-tech.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Maple technical newsletter",
  journal-URL =  "http://web.mit.edu/maple/www/plibrary/mtn.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1997:EDA
author: Jonathan Borwein and David Bradley
title: Empirically determined Apery-like formulae for $ zeta (4 n + 3) $
journal: j-EXP-MATH
volume: 6
number: 3
pages: 181--194
year: 1997
DOI: https://doi.org/10.1080/10586458.1997.10504608
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 11Y60 (11M06)
MRnumber: 1481588
MRreviewer: F. Beukers
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/163/; http://projecteuclid.org/euclid.em/1047920419
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 Borwein and David Bradley
rawtitle: Empirically determined {Ap{\'e}ry}-like formulae for $ \zeta (4 n + 3) $
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

entry:
@Article{Borwein:1997:EDA,
  author =       "Jonathan Borwein and David Bradley",
  title =        "Empirically determined {Ap{\'e}ry}-like formulae for
                 $ \zeta (4 n + 3) $",
  journal =      j-EXP-MATH,
  volume =       "6",
  number =       "3",
  pages =        "181--194",
  year =         "1997",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.1997.10504608",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11Y60 (11M06)",
  MRnumber =     "1481588",
  MRreviewer =   "F. Beukers",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/163/;
                 http://projecteuclid.org/euclid.em/1047920419",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1997:EFE
author: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst
title: Evaluations of $k$-fold Euler / Zagier sums: a compendium of results for arbitrary $k$
journal: j-ELECT-J-COMB
volume: 4
number: 2
pages: Research Paper 5
year: 1997
ISSN: 1077-8926 (print), 1097-1440 (electronic) OR 10778926 (print), 10971440 (electronic)
ISSNL: 1077-8926 OR 10778926
MRclass: 11M41 (11Y60)
MRnumber: 1444152
MRreviewer: Pavel Guerzhoy
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: The Wilf Festschrift (Philadelphia, PA, 1996).
URL: http://www.combinatorics.org/Volume_4/Abstracts/v4i2r5.html
fjournal: Electronic Journal of Combinatorics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst
rawnote: The Wilf Festschrift (Philadelphia, PA, 1996).
rawtitle: Evaluations of $k$-fold {Euler\slash Zagier} sums: a compendium of results for arbitrary $k$
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1997:EFE,
  author =       "Jonathan M. Borwein and David M. Bradley and David J.
                 Broadhurst",
  title =        "Evaluations of $k$-fold {Euler\slash Zagier} sums: a
                 compendium of results for arbitrary $k$",
  journal =      j-ELECT-J-COMB,
  volume =       "4",
  number =       "2",
  pages =        "Research Paper 5",
  year =         "1997",
  ISSN =         "1077-8926 (print), 1097-1440 (electronic)",
  ISSN-L =       "1077-8926",
  MRclass =      "11M41 (11Y60)",
  MRnumber =     "1444152",
  MRreviewer =   "Pavel Guerzhoy",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "The Wilf Festschrift (Philadelphia, PA, 1996).",
  URL =          "http://www.combinatorics.org/Volume_4/Abstracts/v4i2r5.html",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Electronic Journal of Combinatorics",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  pagecount =    "21",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1997:ESLa
author: Jonathan M. Borwein and Warren B. Moors
title: Essentially smooth Lipschitz functions
journal: j-J-FUNCT-ANAL
volume: 149
number: 2
pages: 305--351
year: 1997
CODEN: JFUAAW
DOI: https://doi.org/10.1006/jfan.1997.3101
ISSN: 0022-1236 (print), 1096-0783 (electronic) OR 00221236 (print), 10960783 (electronic)
ISSNL: 0022-1236 OR 00221236
MRclass: 58C20 (46G05 46N10 49J52)
MRnumber: 1472362
MRreviewer: Mari{\'a}n Fabian
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
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: Jonathan M. Borwein and Warren B. Moors
rawtitle: Essentially smooth {Lipschitz} functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/95/; http://www.sciencedirect.com/science/article/pii/S0022123697931013

abstract:
In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on separable Banach spaces. For example, we examine the relationship between integrability,D-representability, and strict differentiability. In addition to this, we show that on any separable Banach space there is a significant family of locally Lipschitz functions that are integrable,D-representable and possess desirable differentiability properties. We also present some striking applications of our results to distance functions.

rawabstract:
In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on separable Banach spaces. For example, we examine the relationship between integrability,D-representability, and strict differentiability. In addition to this, we show that on any separable Banach space there is a significant family of locally Lipschitz functions that are integrable,D-representable and possess desirable differentiability properties. We also present some striking applications of our results to distance functions.

entry:
@Article{Borwein:1997:ESLa,
  author =       "Jonathan M. Borwein and Warren B. Moors",
  title =        "Essentially smooth {Lipschitz} functions",
  journal =      j-J-FUNCT-ANAL,
  volume =       "149",
  number =       "2",
  pages =        "305--351",
  year =         "1997",
  CODEN =        "JFUAAW",
  DOI =          "https://doi.org/10.1006/jfan.1997.3101",
  ISSN =         "0022-1236 (print), 1096-0783 (electronic)",
  ISSN-L =       "0022-1236",
  MRclass =      "58C20 (46G05 46N10 49J52)",
  MRnumber =     "1472362",
  MRreviewer =   "Mari{\'a}n Fabian",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/95/;
                 http://www.sciencedirect.com/science/article/pii/S0022123697931013",
  abstract =     "In this paper we address some of the most fundamental
                 questions regarding the differentiability structure of
                 locally Lipschitz functions defined on separable Banach
                 spaces. For example, we examine the relationship
                 between integrability,D-representability, and strict
                 differentiability. In addition to this, we show that on
                 any separable Banach space there is a significant
                 family of locally Lipschitz functions that are
                 integrable,D-representable and possess desirable
                 differentiability properties. We also present some
                 striking applications of our results to distance
                 functions.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Functional Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00221236",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:1997:ESLb
author: Jonathan M. Borwein and Warren B. Moors
editor: F. Cucker and M. Shub
booktitle: Foundations of computational mathematics (Rio de Janeiro, 1997)
title: Essentially smooth Lipschitz functions: compositions and chain rules
publisher: pub-SV
address: pub-SV:adr
pages: 16--22
year: 1997
MRclass: 49J52 (46N10 58C20)
MRnumber: 1661969
MRreviewer: Mari{\'a}n Fabian
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Warren B. Moors
rawbooktitle: Foundations of computational mathematics ({Rio de Janeiro, 1997})
raweditor: F. Cucker and M. Shub
rawtitle: Essentially smooth {Lipschitz} functions: compositions and chain rules
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:1997:ESLb,
  author =       "Jonathan M. Borwein and Warren B. Moors",
  editor =       "F. Cucker and M. Shub",
  booktitle =    "Foundations of computational mathematics ({Rio de
                 Janeiro, 1997})",
  title =        "Essentially smooth {Lipschitz} functions: compositions
                 and chain rules",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "16--22",
  year =         "1997",
  MRclass =      "49J52 (46N10 58C20)",
  MRnumber =     "1661969",
  MRreviewer =   "Mari{\'a}n Fabian",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1997:GYI
author: Jonathan M. Borwein
title: A generalization of Young's $ l^p $ inequality
type: Report
institution: Department of Mathematics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 6
day: 24
month: jun
monthnumber: 6
year: 1997
bibdate: Thu Sep 01 06:48:28 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 06:48:28 ???
URL: http://docserver.carma.newcastle.edu.au/189/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawtitle: A generalization of {Young}'s $ l^p $ inequality
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We show that, for positive real numbers with $ a geq 1 + sum _i^N alpha _i $, the functionpar $$ frac r^a / a| Prod _i = 1^N x_i^alpha _i $$ par has a convex conjugate of the same form and so, in particular, obtain a clean proof that $f$ is convex.

rawabstract:
We show that, for positive real numbers with $ a \geq 1 + \sum_i^N \alpha_i $, the function\par $$ \frac {r^a / a}{| \Prod_{i = 1}^N x_i^{\alpha_i}} $$ \par has a convex conjugate of the same form and so, in particular, obtain a clean proof that $f$ is convex.

entry:
@TechReport{Borwein:1997:GYI,
  author =       "Jonathan M. Borwein",
  title =        "A generalization of {Young}'s $ l^p $ inequality",
  type =         "Report",
  institution =  "Department of Mathematics, Simon Fraser University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "6",
  day =          "24",
  month =        jun,
  year =         "1997",
  bibdate =      "Thu Sep 01 06:48:28 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/189/",
  abstract =     "We show that, for positive real numbers with $ a \geq
                 1 + \sum_i^N \alpha_i $, the function\par

                  $$ \frac {r^a / a}{| \Prod_{i = 1}^N x_i^{\alpha_i}}
                 $$ \par

                 has a convex conjugate of the same form and so, in
                 particular, obtain a clean proof that $f$ is convex.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:1997:LFM
author: Jonathan M. Borwein and Warren B. Moors
editor: B. M. Glover and D. Ralph
booktitle: Proceedings of the Optimization Miniconference III, University of Melbourne, July 1996
title: Lipschitz functions with minimal Clarke subdifferential mappings
publisher: University of Ballarat
address: Ballarat, VI, Australia
pages: 5--12
year: 1997
bibdate: Mon Aug 15 14:41:04 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.15 14:41:04 ???
URL: http://docserver.carma.newcastle.edu.au/178/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Warren B. Moors
rawbooktitle: {Proceedings of the Optimization Miniconference III, University of Melbourne, July 1996}
raweditor: B. M. Glover and D. Ralph
rawtitle: {Lipschitz} functions with minimal {Clarke} subdifferential mappings
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper we characterise, in terms of the upper Dini derivative, when the Clarke subdifferential mapping of a real-valued locally Lipschitz function is a minimal weak$^star $ cusco. We then use this characterisation to deduce some new results concerning Lipschitz functions with minimal subdifferential mappings.

rawabstract:
In this paper we characterise, in terms of the upper Dini derivative, when the Clarke subdifferential mapping of a real-valued locally Lipschitz function is a minimal weak$^\star $ cusco. We then use this characterisation to deduce some new results concerning Lipschitz functions with minimal subdifferential mappings.

entry:
@InProceedings{Borwein:1997:LFM,
  author =       "Jonathan M. Borwein and Warren B. Moors",
  editor =       "B. M. Glover and D. Ralph",
  booktitle =    "{Proceedings of the Optimization Miniconference III,
                 University of Melbourne, July 1996}",
  title =        "{Lipschitz} functions with minimal {Clarke}
                 subdifferential mappings",
  publisher =    "University of Ballarat",
  address =      "Ballarat, VI, Australia",
  pages =        "5--12",
  year =         "1997",
  bibdate =      "Mon Aug 15 14:41:04 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/178/",
  abstract =     "In this paper we characterise, in terms of the upper
                 Dini derivative, when the Clarke subdifferential
                 mapping of a real-valued locally Lipschitz function is
                 a minimal weak$^\star $ cusco. We then use this
                 characterisation to deduce some new results concerning
                 Lipschitz functions with minimal subdifferential
                 mappings.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1997:LFP
author: Jonathan M. Borwein and Warren B. Moors and Xianfu Wang
title: Lipschitz functions with prescribed derivatives and subderivatives
journal: j-NONLINEAR-ANAL
volume: 29
number: 1
pages: 53--63
year: 1997
CODEN: NOANDD
DOI: https://doi.org/10.1016/S0362-546X(96)00050-8
ISSN: 0362-546x (print), 1873-5215 (electronic) OR 0362546x (print), 18735215 (electronic)
ISSNL: 0362-546X OR 0362546X
MRclass: 49J52 (46G05 47N10 58C05)
MRnumber: 1447569
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.sciencedirect.com/journal/nonlinear-analysis
rawauthor: Jonathan M. Borwein and Warren B. Moors and Xianfu Wang
rawtitle: {Lipschitz} functions with prescribed derivatives and subderivatives
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/92/; http://www.sciencedirect.com/science/article/pii/S0362546X96000508

keywords:
Clarke subgradient; differentiability; Haar-null set; Lipschitz functions; maximal cyclically monotone operator; minimal cusco

entry:
@Article{Borwein:1997:LFP,
  author =       "Jonathan M. Borwein and Warren B. Moors and Xianfu
                 Wang",
  title =        "{Lipschitz} functions with prescribed derivatives and
                 subderivatives",
  journal =      j-NONLINEAR-ANAL,
  volume =       "29",
  number =       "1",
  pages =        "53--63",
  year =         "1997",
  CODEN =        "NOANDD",
  DOI =          "https://doi.org/10.1016/S0362-546X(96)00050-8",
  ISSN =         "0362-546x (print), 1873-5215 (electronic)",
  ISSN-L =       "0362-546X",
  MRclass =      "49J52 (46G05 47N10 58C05)",
  MRnumber =     "1447569",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/92/;
                 http://www.sciencedirect.com/science/article/pii/S0362546X96000508",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Nonlinear Analysis. Theory, Methods \& Applications.
                 An International Multidisciplinary Journal. Series A:
                 Theory and Methods",
  journal-URL =  "https://www.sciencedirect.com/journal/nonlinear-analysis",
  keywords =     "Clarke subgradient; differentiability; Haar-null set;
                 Lipschitz functions; maximal cyclically monotone
                 operator; minimal cusco",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borwein:1997:MIM
editor: Jonathan M. Borwein and Carolyn Watters and Ephraim J. Borowski
publisher: MathResources, Inc.
address: Halifax, NS, Canada
year: 1997
ISBN: 3-540-14650-4 OR 3540146504
ISBN13: 978-3-540-14650-6 OR 9783540146506
bibdate: Tue Aug 16 09:10:33 MDT 2016
bibtimestamp: 2016.08.16 09:10:33 MDT
URL: http://www.mathresources.com
ZMnumber: 0884.00004
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
raweditor: Jonathan M. Borwein and Carolyn Watters and Ephraim J. Borowski
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
The MathResource interactive math dictionary: version 1.0. The math visualizing program Newton and Leibniz didn't have. [An essential tool for high school, college and university students, teachers, scientists, engineers, researchers and anyone else who uses or studies mathematics]

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

remark:
1997 Eddie Award for best post-secondary reference software, by Education Software Review. MathProbe Media & Methods 1998 Awards Portfolio winner. LetsDoMath, 2000 Technology & Learning Award Winner. Integrated with MapleSoft help files in Maple 9.5.

rawtitle:
{The MathResource interactive math dictionary: version 1.0. The math visualizing program Newton and Leibniz didn't have. [An essential tool for high school, college and university students, teachers, scientists, engineers, researchers and anyone else who uses or studies mathematics]}

entry:
@Book{Borwein:1997:MIM,
  editor =       "Jonathan M. Borwein and Carolyn Watters and Ephraim J.
                 Borowski",
  title =        "{The MathResource interactive math dictionary: version
                 1.0. The math visualizing program Newton and Leibniz
                 didn't have. [An essential tool for high school,
                 college and university students, teachers, scientists,
                 engineers, researchers and anyone else who uses or
                 studies mathematics]}",
  publisher =    "MathResources, Inc.",
  address =      "Halifax, NS, Canada",
  pages =        "????",
  year =         "1997",
  ISBN =         "3-540-14650-4",
  ISBN-13 =      "978-3-540-14650-6",
  LCCN =         "????",
  bibdate =      "Tue Aug 16 09:10:33 MDT 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  URL =          "http://www.mathresources.com",
  ZMnumber =     "0884.00004",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "1997 Eddie Award for best post-secondary reference
                 software, by Education Software Review. MathProbe Media
                 \& Methods 1998 Awards Portfolio winner. LetsDoMath,
                 2000 Technology \& Learning Award Winner. Integrated
                 with MapleSoft help files in Maple 9.5.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1997:NEW
author: Jon Borwein and Michael Monagan
title: A Note from the Editors: Winter 1997, Vol. 4, No. 1
journal: j-MAPLE-TECH-NEWS
volume: 4
number: 1
pages: 1--1
month: Winter
year: 1997
ISSN: 1061-5733 OR 10615733
ISSNL: 1061-5733 OR 10615733
bibdate: Wed Jul 23 09:11:50 1997
bibtimestamp: 1997.07.23 09:11:50 ???
fjournal: Maple technical newsletter
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://web.mit.edu/maple/www/plibrary/mtn.html
rawauthor: Jon Borwein and Michael Monagan
rawtitle: A Note from the {Editors}: Winter 1997, Vol. 4, No. 1
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-tech.bib

entry:
@Article{Borwein:1997:NEW,
  author =       "Jon Borwein and Michael Monagan",
  title =        "A Note from the {Editors}: Winter 1997, Vol. 4, No.
                 1",
  journal =      j-MAPLE-TECH-NEWS,
  volume =       "4",
  number =       "1",
  pages =        "1--1",
  month =        "Winter",
  year =         "1997",
  ISSN =         "1061-5733",
  ISSN-L =       "1061-5733",
  bibdate =      "Wed Jul 23 09:11:50 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-tech.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Maple technical newsletter",
  journal-URL =  "http://web.mit.edu/maple/www/plibrary/mtn.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1997:NSP
author: Jonathan M. Borwein and Alejandro Jofre
title: A nonconvex separation property in Banach spaces
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 11
day: 13
month: nov
monthnumber: 11
year: 1997
bibdate: Thu Sep 01 07:36:57 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 07:36:57 ???
note: Published in cite Borwein:1998:NSP.
URL: http://docserver.carma.newcastle.edu.au/197
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Alejandro Jofr{\'e}
rawnote: Published in \cite{Borwein:1998:NSP}.
rawtitle: A nonconvex separation property in {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We establish, in infinite dimensional Banach space, a nonconvex separation property for general closed sets that is an extension of Hahn-Banach separation theorem. We provide some consequences in optimization, in particular the existence of singular multipliers and show the relation of our principle with the extremal principle of Mordukhovich.

rawabstract:
We establish, in infinite dimensional Banach space, a nonconvex separation property for general closed sets that is an extension of Hahn-Banach separation theorem. We provide some consequences in optimization, in particular the existence of singular multipliers and show the relation of our principle with the extremal principle of Mordukhovich.

entry:
@TechReport{Borwein:1997:NSP,
  author =       "Jonathan M. Borwein and Alejandro Jofr{\'e}",
  title =        "A nonconvex separation property in {Banach} spaces",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "11",
  day =          "13",
  month =        nov,
  year =         "1997",
  bibdate =      "Thu Sep 01 07:36:57 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:1998:NSP}.",
  URL =          "http://docserver.carma.newcastle.edu.au/197",
  abstract =     "We establish, in infinite dimensional Banach space, a
                 nonconvex separation property for general closed sets
                 that is an extension of Hahn-Banach separation theorem.
                 We provide some consequences in optimization, in
                 particular the existence of singular multipliers and
                 show the relation of our principle with the extremal
                 principle of Mordukhovich.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1997:OJP
author: Jonathan Borwein and Richard Smith
title: Online journal publication: two views from the electronic trenches
journal: Canadian Journal of Communication
volume: 22
pages: 135--152
year: 1997
bibdate: Mon Aug 15 14:35:28 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.15 14:35:28 ???
URL: http://edie.cprost.sfu.ca/~scom
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein and Richard Smith
rawtitle: Online journal publication: two views from the electronic trenches
ORCID: Borwein, Jonathan/0000-0002-1263-0646
remark:
Scholarly Communication in the Next Millennium, March 1997. Excerpted in extenso in Active Voice, the national bi-monthly newsletter of the Editors' Association of Canada.

entry:
@Article{Borwein:1997:OJP,
  author =       "Jonathan Borwein and Richard Smith",
  title =        "Online journal publication: two views from the
                 electronic trenches",
  journal =      "Canadian Journal of Communication",
  volume =       "22",
  number =       "??",
  pages =        "135--152",
  month =        "????",
  year =         "1997",
  DOI =          "",
  bibdate =      "Mon Aug 15 14:35:28 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://edie.cprost.sfu.ca/~scom",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Scholarly Communication in the Next Millennium, March
                 1997. Excerpted in extenso in Active Voice, the
                 national bi-monthly newsletter of the Editors'
                 Association of Canada.",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:1997:PEN
author: J. M. Borwein and P. B. Borwein and K. Dilcher
title: Pi, Euler Numbers, and Asymptotic Expansions
crossref: Berggren:1997:PSB
pages: 642--648
year: 1997
DOI: https://doi.org/10.1007/978-1-4757-2736-4_65
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:36:22 MDT
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein and K. Dilcher
rawtitle: Pi, {Euler} Numbers, and Asymptotic Expansions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1583/; http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_65

entry:
@InCollection{Borwein:1997:PEN,
  author =       "J. M. Borwein and P. B. Borwein and K. Dilcher",
  title =        "Pi, {Euler} Numbers, and Asymptotic Expansions",
  crossref =     "Berggren:1997:PSB",
  pages =        "642--648",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4757-2736-4_65",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1583/;
                 http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_65",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1997:PSS
title: Problems and Solutions: Solutions: 10335
journal: j-AMER-MATH-MONTHLY
volume: 104
number: 1
pages: 72--74
year: 1997
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2974831
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRnumber: 1542940
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.jstor.org/journals/00029890.html
rawtitle: Problems and Solutions: Solutions: 10335
ORCID: Borwein, Jonathan/0000-0002-1263-0646
author:
David Borwein and Jonathan Borwein and Heinz-Jurgen Seiffert and Robert D. Brown and Pawel Szeptycki

rawauthor:
David Borwein and Jonathan Borwein and Heinz-J{\"u}rgen Seiffert and Robert D. Brown and Pawel Szeptycki

entry:
@Article{Borwein:1997:PSS,
  author =       "David Borwein and Jonathan Borwein and
                 Heinz-J{\"u}rgen Seiffert and Robert D. Brown and Pawel
                 Szeptycki",
  title =        "Problems and Solutions: Solutions: 10335",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "104",
  number =       "1",
  pages =        "72--74",
  year =         "1997",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2974831",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRnumber =     "1542940",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:1997:RME
author: J. M. Borwein and P. B. Borwein and D. H. Bailey
title: Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
crossref: Berggren:1997:PSB
pages: ??--??
year: 1997
DOI: https://doi.org/10.1007/978-1-4757-2736-4_64
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:36:22 MDT
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein and D. H. Bailey
rawtitle: {Ramanujan}, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1587/; http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_64; http://www.cecm.sfu.ca/organics/papers/borwein/index.html

entry:
@InCollection{Borwein:1997:RME,
  author =       "J. M. Borwein and P. B. Borwein and D. H. Bailey",
  title =        "{Ramanujan}, Modular Equations, and Approximations to
                 Pi or How to Compute One Billion Digits of Pi",
  crossref =     "Berggren:1997:PSB",
  pages =        "??--??",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4757-2736-4_64",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1587/;
                 http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_64;
                 http://www.cecm.sfu.ca/organics/papers/borwein/index.html",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1997:SAD
author: J. M. Borwein and W. Sun
title: The stability analysis of dynamic SPECT systems
journal: j-NUM-MATH
volume: 77
number: 3
pages: 283--298
year: 1997
CODEN: NUMMA7
DOI: https://doi.org/10.1007/s002110050287
ISSN: 0029-599x (print), 0945-3245 (electronic) OR 0029599x (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65R30 (44A12 65R20 92C55)
MRnumber: 1469673
MRreviewer: Dominikus Noll
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:36:22 MDT
URL: http://docserver.carma.newcastle.edu.au/99/; http://link.springer.com/article/10.1007/s002110050287
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/211
rawauthor: J. M. Borwein and W. Sun
rawtitle: The stability analysis of dynamic {SPECT} systems
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1997:SAD,
  author =       "J. M. Borwein and W. Sun",
  title =        "The stability analysis of dynamic {SPECT} systems",
  journal =      j-NUM-MATH,
  volume =       "77",
  number =       "3",
  pages =        "283--298",
  year =         "1997",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s002110050287",
  ISSN =         "0029-599x (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65R30 (44A12 65R20 92C55)",
  MRnumber =     "1469673",
  MRreviewer =   "Dominikus Noll",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/99/;
                 http://link.springer.com/article/10.1007/s002110050287",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:1997:SAR
author: Jonathan M. Borwein and Jay Treiman and Qiji Zhu
title: Sensitivity analysis in reflexive Banach spaces
pages: 283--298
month: aug
monthnumber: 8
year: 1997
bibdate: Tue Aug 16 10:14:16 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:14:16 ???
note: Preprint.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Jay Treiman and Qiji Zhu
rawnote: Preprint.
rawtitle: Sensitivity analysis in reflexive {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Unpublished{Borwein:1997:SAR,
  author =       "Jonathan M. Borwein and Jay Treiman and Qiji Zhu",
  title =        "Sensitivity analysis in reflexive {Banach} spaces",
  month =        aug,
  year =         "1997",
  bibdate =      "Tue Aug 16 10:14:16 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Preprint.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:1997:SDIa
author: Jonathan M. Borwein
title: Symbolically discovered identities for ZETA(4N+3) and multidimensional polylogarithms
pages: 283--298
day: 31
month: jul
monthnumber: 7
year: 1997
bibdate: Tue Aug 16 10:19:46 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:19:46 ???
note: Penn State Number Theory Conference, July 31--Aug 3.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawnote: Penn State Number Theory Conference, July 31--Aug 3.
rawtitle: Symbolically discovered identities for ZETA(4N+3) and multidimensional polylogarithms
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Unpublished{Borwein:1997:SDIa,
  author =       "Jonathan M. Borwein",
  title =        "Symbolically discovered identities for ZETA(4N+3) and
                 multidimensional polylogarithms",
  day =          "31",
  month =        jul,
  year =         "1997",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Penn State Number Theory Conference, July 31--Aug 3.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1997:SDIb
author: Jonathan M. Borwein and Warren B. Moors
title: Separable determination of integrability and minimality of the Clarke subdifferential mapping
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 10
day: 30
month: sep
monthnumber: 9
year: 1997
bibdate: Thu Sep 01 07:33:19 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 07:33:19 ???
note: Published in cite Borwein:2000:SDI.
URL: http://docserver.carma.newcastle.edu.au/196
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Warren B. Moors
rawnote: Published in \cite{Borwein:2000:SDI}.
rawtitle: Separable determination of integrability and minimality of the {Clarke} subdifferential mapping
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper we show that the study of integrability and D-representability of Lipschitz functions defined on arbitrary Banach spaces reduces to the study of these properties on separable Banach spaces

rawabstract:
In this paper we show that the study of integrability and D-representability of Lipschitz functions defined on arbitrary Banach spaces reduces to the study of these properties on separable Banach spaces

entry:
@TechReport{Borwein:1997:SDIb,
  author =       "Jonathan M. Borwein and Warren B. Moors",
  title =        "Separable determination of integrability and
                 minimality of the {Clarke} subdifferential mapping",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "10",
  day =          "30",
  month =        sep,
  year =         "1997",
  bibdate =      "Thu Sep 01 07:33:19 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2000:SDI}.",
  URL =          "http://docserver.carma.newcastle.edu.au/196",
  abstract =     "In this paper we show that the study of integrability
                 and D-representability of Lipschitz functions defined
                 on arbitrary Banach spaces reduces to the study of
                 these properties on separable Banach spaces",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1997:SRM
author: Jonathan M. Borwein and Warren B. Moors and Yongheng Shao
title: Subgradient representation of multifunctions
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 14
day: 21
month: feb
monthnumber: 2
year: 1997
bibdate: Wed Aug 31 15:45:10 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 15:45:10 ???
note: Published in cite Borwein:1999:SRM.
URL: http://docserver.carma.newcastle.edu.au/184/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Warren B. Moors and Yongheng Shao
rawnote: Published in \cite{Borwein:1999:SRM}.
rawtitle: Subgradient representation of multifunctions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We provide necessary and sufficient conditions for a minimal upper semicontinuous multifunction defined on a separable Banach space to be the subdifferential mapping of a Lipschitz function.

rawabstract:
We provide necessary and sufficient conditions for a minimal upper semicontinuous multifunction defined on a separable Banach space to be the subdifferential mapping of a Lipschitz function.

entry:
@TechReport{Borwein:1997:SRM,
  author =       "Jonathan M. Borwein and Warren B. Moors and Yongheng
                 Shao",
  title =        "Subgradient representation of multifunctions",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "14",
  day =          "21",
  month =        feb,
  year =         "1997",
  bibdate =      "Wed Aug 31 15:45:10 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:1999:SRM}.",
  URL =          "http://docserver.carma.newcastle.edu.au/184/",
  abstract =     "We provide necessary and sufficient conditions for a
                 minimal upper semicontinuous multifunction defined on a
                 separable Banach space to be the subdifferential
                 mapping of a Lipschitz function.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:1997:SRR
author: J. M. Borwein and E. Wong
editor: L. Vinet
booktitle: Advances in mathematical sciences: CRM's 25 years (Montreal, PQ, 1994)
title: A survey of results relating to Giuga's conjecture on primality
volume: 11
publisher: pub-AMS
address: pub-AMS:adr
pages: 13--27
year: 1997
MRclass: 11A51 (11Y11)
MRnumber: 1479668
MRreviewer: Andrew Granville
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: CRM Proc. Lecture Notes
URL: http://docserver.carma.newcastle.edu.au/101/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and E. Wong
rawbooktitle: Advances in mathematical sciences: {CRM}'s 25 years ({Montreal}, {PQ}, 1994)
raweditor: L. Vinet
rawtitle: A survey of results relating to {Giuga}'s conjecture on primality
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:1997:SRR,
  author =       "J. M. Borwein and E. Wong",
  editor =       "L. Vinet",
  booktitle =    "Advances in mathematical sciences: {CRM}'s 25 years
                 ({Montreal}, {PQ}, 1994)",
  title =        "A survey of results relating to {Giuga}'s conjecture
                 on primality",
  volume =       "11",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "13--27",
  year =         "1997",
  MRclass =      "11A51 (11Y11)",
  MRnumber =     "1479668",
  MRreviewer =   "Andrew Granville",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "CRM Proc. Lecture Notes",
  URL =          "http://docserver.carma.newcastle.edu.au/101/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1997:VAN
author: Jonathan M. Borwein and Qiji J. Zhu
journal: j-NONLINEAR-ANAL
volume: 28
number: 5
pages: 889--915
year: 1997
CODEN: NOANDD
DOI: https://doi.org/10.1016/0362-546X(95)00186-Y
ISSN: 0362-546x (print), 1873-5215 (electronic) OR 0362546x (print), 18735215 (electronic)
ISSNL: 0362-546X OR 0362546X
MRclass: 49K40
MRnumber: 1422192
MRreviewer: Vera Zeidan
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.sciencedirect.com/journal/nonlinear-analysis
rawauthor: Jonathan M. Borwein and Qiji J. Zhu
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Variational analysis in nonreflexive spaces and applications to control problems with $ L^1 $ perturbations

URL:
http://docserver.carma.newcastle.edu.au/78/; http://www.sciencedirect.com/science/article/pii/0362546X9500186Y

keywords:
Weak-Hadamard sub-derivatives; Clarke-subdifferentials; control system; $G$-subdifferentials; Holder sub-derivatives; infinite horizon problems; sensitivity analysis; smooth renorms; variational principles

rawtitle:
Variational analysis in nonreflexive spaces and applications to control problems with {$ L^1 $} perturbations

entry:
@Article{Borwein:1997:VAN,
  author =       "Jonathan M. Borwein and Qiji J. Zhu",
  title =        "Variational analysis in nonreflexive spaces and
                 applications to control problems with {$ L^1 $}
                 perturbations",
  journal =      j-NONLINEAR-ANAL,
  volume =       "28",
  number =       "5",
  pages =        "889--915",
  year =         "1997",
  CODEN =        "NOANDD",
  DOI =          "https://doi.org/10.1016/0362-546X(95)00186-Y",
  ISSN =         "0362-546x (print), 1873-5215 (electronic)",
  ISSN-L =       "0362-546X",
  MRclass =      "49K40",
  MRnumber =     "1422192",
  MRreviewer =   "Vera Zeidan",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/78/;
                 http://www.sciencedirect.com/science/article/pii/0362546X9500186Y",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Nonlinear Analysis. Theory, Methods \& Applications.
                 An International Multidisciplinary Journal. Series A:
                 Theory and Methods",
  journal-URL =  "https://www.sciencedirect.com/journal/nonlinear-analysis",
  keywords =     "Weak-Hadamard sub-derivatives;
                 Clarke-subdifferentials; control system;
                 $G$-subdifferentials; H{\"o}lder sub-derivatives;
                 infinite horizon problems; sensitivity analysis; smooth
                 renorms; variational principles",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:1997:WOM
title: What is organic mathematics?
crossref: Borwein:1997:OMP
pages: 1--18
year: 1997
ISSN: 0731-1036 OR 07311036
ISSNL: 0731-1036 OR 07311036
MRclass: 00A99 (00A30 01A99)
MRnumber: 1483911
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: CMS/AMS Conference Proceedings
URL: http://docserver.carma.newcastle.edu.au/157/; http://www.cecm.sfu.ca/organics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawtitle: What is organic mathematics?
ORCID: Borwein, Jonathan/0000-0002-1263-0646
author:
Jonathan M. Borwein and Peter B. Borwein and Robert M. Corless and Loki Jorgenson and Nathalie Sinclair

rawauthor:
Jonathan M. Borwein and Peter B. Borwein and Robert M. Corless and Loki J{\"o}rgenson and Nathalie Sinclair

entry:
@InProceedings{Borwein:1997:WOM,
  author =       "Jonathan M. Borwein and Peter B. Borwein and Robert M.
                 Corless and Loki J{\"o}rgenson and Nathalie Sinclair",
  title =        "What is organic mathematics?",
  crossref =     "Borwein:1997:OMP",
  pages =        "1--18",
  year =         "1997",
  ISSN =         "0731-1036",
  ISSN-L =       "0731-1036",
  MRclass =      "00A99 (00A30 01A99)",
  MRnumber =     "1483911",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "CMS/AMS Conference Proceedings",
  URL =          "http://docserver.carma.newcastle.edu.au/157/;
                 http://www.cecm.sfu.ca/organics",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Galvin:1997:PSP
title: Problems and Solutions: Problems: 10599--10605
journal: j-AMER-MATH-MONTHLY
volume: 104
number: 6
pages: 566--567
year: 1997
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2975086
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRnumber: 1543038
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.jstor.org/journals/00029890.html
rawtitle: Problems and Solutions: Problems: 10599--10605
ORCID: Borwein, Jonathan/0000-0002-1263-0646
author:
Fred Galvin and Franz Rothe and Wen-Xiu Ma and Dan Sachelarie and Vlad Sachelarie and Yury J. Ionin and Robin R. Lewis and Joseph Rosenblatt and Jonathan M. Borwein and C. G. Pinner

rawauthor:
Fred Galvin and Franz Rothe and Wen-Xiu Ma and Dan Sachelarie and Vlad Sachelarie and Yury J. Ionin and Robin R. Lewis and Joseph Rosenblatt and Jonathan M. Borwein and C. G. Pinner

entry:
@Article{Galvin:1997:PSP,
  author =       "Fred Galvin and Franz Rothe and Wen-Xiu Ma and Dan
                 Sachelarie and Vlad Sachelarie and Yury J. Ionin and
                 Robin R. Lewis and Joseph Rosenblatt and Jonathan M.
                 Borwein and C. G. Pinner",
  title =        "Problems and Solutions: Problems: 10599--10605",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "104",
  number =       "6",
  pages =        "566--567",
  year =         "1997",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2975086",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRnumber =     "1543038",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bauschke:1998:COM
author: Heinz H. Bauschke and Jonathan M. Borwein
title: Conical open mapping theorems and regularity
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 14
day: 10
month: nov
monthnumber: 11
year: 1998
bibdate: Thu Sep 01 08:35:40 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 08:35:40 ???
note: Published in cite Bauschke:1999:COM.
URL: http://docserver.carma.newcastle.edu.au/208/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein
rawnote: Published in \cite{Bauschke:1999:COM}.
rawtitle: Conical open mapping theorems and regularity
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Suppose $T$ is a continuous linear operator between two Hilbert spaces $X$ and $Y$ and let $K$ be a closed convex nonempty cone in $X$. We investigate the possible existence of $ delta > 0$ such that $ delta B_Y cap T(K) subseteq T(B_X cap K)$, where $ B_X$, $ B_Y$ denote the closed unit balls in $X$ and $Y$ respectively. This property, which we call openness relative to $K$, is a generalization of the classical openness of linear operators. We relate relative openness to Jameson's property (G), to the strong conical hull intersection property, to bounded linear regularity, and to metric regularity. Our results allow a simple construction of two closed convex cones that have the strong conical hull intersection property but fail to be boundedly linearly regular.

rawabstract:
Suppose $T$ is a continuous linear operator between two Hilbert spaces $X$ and $Y$ and let $K$ be a closed convex nonempty cone in $X$. We investigate the possible existence of $ \delta > 0$ such that $ \delta B_Y \cap T(K) \subseteq T(B_X \cap K)$, where $ B_X$, $ B_Y$ denote the closed unit balls in $X$ and $Y$ respectively. This property, which we call openness relative to $K$, is a generalization of the classical openness of linear operators. We relate relative openness to Jameson's property (G), to the strong conical hull intersection property, to bounded linear regularity, and to metric regularity. Our results allow a simple construction of two closed convex cones that have the strong conical hull intersection property but fail to be boundedly linearly regular.

entry:
@TechReport{Bauschke:1998:COM,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein",
  title =        "Conical open mapping theorems and regularity",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "14",
  day =          "10",
  month =        nov,
  year =         "1998",
  bibdate =      "Thu Sep 01 08:35:40 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Bauschke:1999:COM}.",
  URL =          "http://docserver.carma.newcastle.edu.au/208/",
  abstract =     "Suppose $T$ is a continuous linear operator between
                 two Hilbert spaces $X$ and $Y$ and let $K$ be a closed
                 convex nonempty cone in $X$. We investigate the
                 possible existence of $ \delta > 0$ such that $ \delta
                 B_Y \cap T(K) \subseteq T(B_X \cap K)$, where $ B_X$, $
                 B_Y$ denote the closed unit balls in $X$ and $Y$
                 respectively. This property, which we call openness
                 relative to $K$, is a generalization of the classical
                 openness of linear operators. We relate relative
                 openness to Jameson's property (G), to the strong
                 conical hull intersection property, to bounded linear
                 regularity, and to metric regularity. Our results allow
                 a simple construction of two closed convex cones that
                 have the strong conical hull intersection property but
                 fail to be boundedly linearly regular.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bauschke:1998:MRS
author: Heinz H. Bauschke and Jonathan M. Borwein and Paul Tseng
title: Metric regularity, strong CHIP, and CHIP are distinct properties
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 17
day: 20
month: jul
monthnumber: 7
year: 1998
MRclass: 90C25 (46C05, 52A15, 52A20)
bibdate: Thu Sep 01 08:17:03 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 08:17:03 ???
URL: http://docserver.carma.newcastle.edu.au/204
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein and Paul Tseng
rawtitle: Metric regularity, strong {CHIP}, and {CHIP} are distinct properties
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Metric regularity, the strong conical hull intersection property (strong CHIP), and the conical hull intersection property (CHIP) are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. It was shown recently that these properties are fundamental in several branches of convex optimization, including convex feasibility problems, error bounds, Fenchel duality, and constrained approximation. It was known that regularity implies strong CHIP, which in turn implies CHIP; moreover, the three properties always hold for subspaces. The question whether or not converse implications are true for general convex sets was open.par We show that --- even for convex cones --- the converse implications need not hold by constructing counter-examples in $ mathbb R^4 $.

rawabstract:
Metric regularity, the strong conical hull intersection property (strong CHIP), and the conical hull intersection property (CHIP) are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. It was shown recently that these properties are fundamental in several branches of convex optimization, including convex feasibility problems, error bounds, Fenchel duality, and constrained approximation. It was known that regularity implies strong CHIP, which in turn implies CHIP; moreover, the three properties always hold for subspaces. The question whether or not converse implications are true for general convex sets was open.\par We show that --- even for convex cones --- the converse implications need not hold by constructing counter-examples in $ \mathbb {R}^4 $.

entry:
@TechReport{Bauschke:1998:MRS,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein and Paul
                 Tseng",
  title =        "Metric regularity, strong {CHIP}, and {CHIP} are
                 distinct properties",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "17",
  day =          "20",
  month =        jul,
  year =         "1998",
  MRclass =      "90C25 (46C05, 52A15, 52A20)",
  bibdate =      "Thu Sep 01 08:17:03 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/204",
  abstract =     "Metric regularity, the strong conical hull
                 intersection property (strong CHIP), and the conical
                 hull intersection property (CHIP) are properties of a
                 collection of finitely many closed convex intersecting
                 sets in Euclidean space. It was shown recently that
                 these properties are fundamental in several branches of
                 convex optimization, including convex feasibility
                 problems, error bounds, Fenchel duality, and
                 constrained approximation. It was known that regularity
                 implies strong CHIP, which in turn implies CHIP;
                 moreover, the three properties always hold for
                 subspaces. The question whether or not converse
                 implications are true for general convex sets was
                 open.\par

                 We show that --- even for convex cones --- the converse
                 implications need not hold by constructing
                 counter-examples in $ \mathbb {R}^4 $.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1998:BHS
author: Jonathan M. Borwein
title: Brouwer--Heyting sequences converge
journal: j-MATH-INTEL
volume: 20
number: 1
pages: 14--15
year: 1998
CODEN: MAINDC
DOI: https://doi.org/10.1007/BF03024393
ISSN: 0343-6993 (print), 1866-7414 (electronic) OR 03436993 (print), 18667414 (electronic)
ISSNL: 0343-6993 OR 03436993
MRclass: 11A63
MRnumber: 1601815
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: The Mathematical Intelligencer
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/283
rawauthor: Jonathan M. Borwein
rawtitle: {Brouwer--Heyting} sequences converge
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1998:BHS,
  author =       "Jonathan M. Borwein",
  title =        "{Brouwer--Heyting} sequences converge",
  journal =      j-MATH-INTEL,
  volume =       "20",
  number =       "1",
  pages =        "14--15",
  year =         "1998",
  CODEN =        "MAINDC",
  DOI =          "https://doi.org/10.1007/BF03024393",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  MRclass =      "11A63",
  MRnumber =     "1601815",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The Mathematical Intelligencer",
  journal-URL =  "http://link.springer.com/journal/283",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1998:CAMa
author: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lisonek
title: Combinatorial aspects of multiple zeta values
journal: ArXiv Mathematics e-prints
pages: 14--15
month: dec
monthnumber: 12
year: 1998
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/1998math.....12020B; http://docserver.carma.newcastle.edu.au/201/
keywords: Number Theory, Combinatorics, Numerical Analysis, 05A19, 11M99, 68R15 (Primary) 11Y99 (Secondary)
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lison{\v{e}}k
rawtitle: Combinatorial aspects of multiple zeta values
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The fact that an integral representation of MZVs obeys a shuffle product rule allows the possibility of a combinatorial approach to them. Using this approach we prove a longstanding conjecture of Don Zagier about MZVs with certain repeated arguments. We also prove a similar cyclic sum identity. Finally, we present extensive computational evidence supporting an infinite family of conjectured MZV identities that simultaneously generalize the Zagier identity.

entry:
@Article{Borwein:1998:CAMa,
  author =       "Jonathan M. Borwein and David M. Bradley and David J.
                 Broadhurst and Petr Lison{\v{e}}k",
  title =        "Combinatorial aspects of multiple zeta values",
  journal =      "ArXiv Mathematics e-prints",
  month =        dec,
  year =         "1998",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/1998math.....12020B;
                 http://docserver.carma.newcastle.edu.au/201/",
  abstract =     "Multiple zeta values (MZVs, also called Euler sums or
                 multiple harmonic series) are nested generalizations of
                 the classical Riemann zeta function evaluated at
                 integer values. The fact that an integral
                 representation of MZVs obeys a shuffle product rule
                 allows the possibility of a combinatorial approach to
                 them. Using this approach we prove a longstanding
                 conjecture of Don Zagier about MZVs with certain
                 repeated arguments. We also prove a similar cyclic sum
                 identity. Finally, we present extensive computational
                 evidence supporting an infinite family of conjectured
                 MZV identities that simultaneously generalize the
                 Zagier identity.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "math/9812020",
  keywords =     "Number Theory, Combinatorics, Numerical Analysis,
                 05A19, 11M99, 68R15 (Primary) 11Y99 (Secondary)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1998:CAMb
author: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lisonek
title: Combinatorial aspects of multiple zeta values
journal: j-ELECT-J-COMB
volume: 5
pages: Research Paper 38
year: 1998
ISSN: 1077-8926 (print), 1097-1440 (electronic) OR 10778926 (print), 10971440 (electronic)
ISSNL: 1077-8926 OR 10778926
MRclass: 11M41 (05A19 11Y60)
MRnumber: 1637378
MRreviewer: Jerzy Browkin
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Electronic Journal of Combinatorics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lison{\v{e}}k
rawtitle: Combinatorial aspects of multiple zeta values
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/201/; http://www.combinatorics.org/Volume_5/Abstracts/v5i1r38.html

entry:
@Article{Borwein:1998:CAMb,
  author =       "Jonathan M. Borwein and David M. Bradley and David J.
                 Broadhurst and Petr Lison{\v{e}}k",
  title =        "Combinatorial aspects of multiple zeta values",
  journal =      j-ELECT-J-COMB,
  volume =       "5",
  pages =        "Research Paper 38",
  year =         "1998",
  ISSN =         "1077-8926 (print), 1097-1440 (electronic)",
  ISSN-L =       "1077-8926",
  MRclass =      "11M41 (05A19 11Y60)",
  MRnumber =     "1637378",
  MRreviewer =   "Jerzy Browkin",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/201/;
                 http://www.combinatorics.org/Volume_5/Abstracts/v5i1r38.html",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Electronic Journal of Combinatorics",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  pagecount =    "12",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1998:CDA
author: Jonathan M. Borwein and Pierre Marechal and David Naugler
title: A convex dual approach to the computation of NMR complex spectra
type: Report
institution: Department of Mathematics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 14
day: 10
month: nov
monthnumber: 11
year: 1998
bibdate: Thu Sep 01 08:31:11 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 08:31:11 ???
note: Published in cite Borwein:2000:CDA.
URL: http://docserver.carma.newcastle.edu.au/207/
keywords: convex duality; Entropy optimization; nuclear magnetic resonance; spectral analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Pierre Mar{\'e}chal and David Naugler
rawnote: Published in \cite{Borwein:2000:CDA}.
rawtitle: A convex dual approach to the computation of {NMR} complex spectra
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
The particular entropy method proposed by Hoch em et al. [7] for the computation of NMR complex spectra allows an elegant application of the concepts of duality theory. Correspondingly, duality theory casts new light on their choice of entropy. The purpose of this paper is to present the relevant theoretical developments together with some numerical illustrations.

rawabstract:
The particular entropy method proposed by Hoch {\em et al.} [7] for the computation of NMR complex spectra allows an elegant application of the concepts of duality theory. Correspondingly, duality theory casts new light on their choice of entropy. The purpose of this paper is to present the relevant theoretical developments together with some numerical illustrations.

entry:
@TechReport{Borwein:1998:CDA,
  author =       "Jonathan M. Borwein and Pierre Mar{\'e}chal and David
                 Naugler",
  title =        "A convex dual approach to the computation of {NMR}
                 complex spectra",
  type =         "Report",
  institution =  "Department of Mathematics, Simon Fraser University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "14",
  day =          "10",
  month =        nov,
  year =         "1998",
  bibdate =      "Thu Sep 01 08:31:11 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2000:CDA}.",
  URL =          "http://docserver.carma.newcastle.edu.au/207/",
  abstract =     "The particular entropy method proposed by Hoch {\em et
                 al.} [7] for the computation of NMR complex spectra
                 allows an elegant application of the concepts of
                 duality theory. Correspondingly, duality theory casts
                 new light on their choice of entropy. The purpose of
                 this paper is to present the relevant theoretical
                 developments together with some numerical
                 illustrations.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "convex duality; Entropy optimization; nuclear magnetic
                 resonance; spectral analysis",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1998:CHP
author: J. M. Borwein and R. Girgensohn and Xianfu Wang
title: On the construction of Holder and proximal subderivatives
journal: j-CAN-MATH-BULL
volume: 41
number: 4
pages: 497--507
year: 1998
CODEN: CMBUA3
DOI: https://doi.org/10.4153/CMB-1998-065-9
ISSN: 0008-4395 (print), 1496-4287 (electronic) OR 00084395 (print), 14964287 (electronic)
ISSNL: 0008-4395 OR 00084395
MRclass: 49J52 (26A16 26A24)
MRnumber: 1658271
MRreviewer: Lionel Thibault
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/186/
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: J. M. Borwein and R. Girgensohn and Xianfu Wang
rawtitle: On the construction of {H{\"o}lder} and proximal subderivatives
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1998:CHP,
  author =       "J. M. Borwein and R. Girgensohn and Xianfu Wang",
  title =        "On the construction of {H{\"o}lder} and proximal
                 subderivatives",
  journal =      j-CAN-MATH-BULL,
  volume =       "41",
  number =       "4",
  pages =        "497--507",
  year =         "1998",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-1998-065-9",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  MRclass =      "49J52 (26A16 26A24)",
  MRnumber =     "1658271",
  MRreviewer =   "Lionel Thibault",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/186/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Canadian Mathematical Bulletin. Bulletin Canadien de
                 Math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cmb/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1998:CML
author: David Borwein and Jonathan M. Borwein and Christopher Pinner
title: Convergence of Madelung-like lattice sums
journal: j-TRANS-AM-MATH-SOC
volume: 350
number: 8
pages: 3131--3167
month: aug
monthnumber: 8
year: 1998
CODEN: TAMTAM
DOI: https://doi.org/10.1090/S0002-9947-98-01983-7
ISSN: 0002-9947 (print), 1088-6850 (electronic) OR 00029947 (print), 10886850 (electronic)
ISSNL: 0002-9947 OR 00029947
MRclass: 11P21 (11M41 11Z05 30B50 40A05)
MRnumber: 1433111
MRreviewer: Hartmut Menzer
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/104/; https://www.jstor.org/stable/117772
fjournal: Transactions of the American Mathematical Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/journals/tran/
rawauthor: David Borwein and Jonathan M. Borwein and Christopher Pinner
rawtitle: Convergence of {Madelung}-like lattice sums
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1998:CML,
  author =       "David Borwein and Jonathan M. Borwein and Christopher
                 Pinner",
  title =        "Convergence of {Madelung}-like lattice sums",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "350",
  number =       "8",
  pages =        "3131--3167",
  month =        aug,
  year =         "1998",
  CODEN =        "TAMTAM",
  DOI =          "https://doi.org/10.1090/S0002-9947-98-01983-7",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "11P21 (11M41 11Z05 30B50 40A05)",
  MRnumber =     "1433111",
  MRreviewer =   "Hartmut Menzer",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/104/;
                 https://www.jstor.org/stable/117772",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Transactions of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/tran/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1998:CMV
author: J. M. Borwein and Xianfu Wang
title: The converse of the mean value theorem may fail generically
journal: j-AMER-MATH-MONTHLY
volume: 105
number: 9
pages: 847--848
month: nov
monthnumber: 11
year: 1998
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2589216
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 26A24
MRnumber: 1650850
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1530/; https://www.jstor.org/stable/2589216
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.jstor.org/journals/00029890.html
rawauthor: J. M. Borwein and Xianfu Wang
rawtitle: The converse of the mean value theorem may fail generically
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1998:CMV,
  author =       "J. M. Borwein and Xianfu Wang",
  title =        "The converse of the mean value theorem may fail
                 generically",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "105",
  number =       "9",
  pages =        "847--848",
  month =        nov,
  year =         "1998",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2589216",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26A24",
  MRnumber =     "1650850",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1530/;
                 https://www.jstor.org/stable/2589216",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1998:CRE
author: Jonathan M. Borwein and Warren B. Moors
title: A chain rule for essentially smooth Lipschitz functions
journal: j-SIAM-J-OPT
volume: 8
number: 2
pages: 300--308
year: 1998
CODEN: SJOPE8
DOI: https://doi.org/10.1137/S1052623496297838
ISSN: 1052-6234 (print), 1095-7189 (electronic) OR 10526234 (print), 10957189 (electronic)
ISSNL: 1052-6234 OR 10526234
MRclass: 49J52 (46N10 58C20)
MRnumber: 1618794
MRreviewer: John R. Giles
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/151/
fjournal: SIAM Journal on Optimization
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://epubs.siam.org/siopt
rawauthor: Jonathan M. Borwein and Warren B. Moors
rawtitle: A chain rule for essentially smooth {Lipschitz} functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1998:CRE,
  author =       "Jonathan M. Borwein and Warren B. Moors",
  title =        "A chain rule for essentially smooth {Lipschitz}
                 functions",
  journal =      j-SIAM-J-OPT,
  volume =       "8",
  number =       "2",
  pages =        "300--308",
  year =         "1998",
  CODEN =        "SJOPE8",
  DOI =          "https://doi.org/10.1137/S1052623496297838",
  ISSN =         "1052-6234 (print), 1095-7189 (electronic)",
  ISSN-L =       "1052-6234",
  MRclass =      "49J52 (46N10 58C20)",
  MRnumber =     "1618794",
  MRreviewer =   "John R. Giles",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/151/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIAM Journal on Optimization",
  journal-URL =  "http://epubs.siam.org/siopt",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1998:CSR
author: Jonathan M. Borwein and David M. Bradley and Richard E. Crandall
title: Computational Strategies for the Riemann Zeta Function
type: Report
number: CECM-98-118
institution: inst-CECM
address: inst-CECM:adr
pages: 68
day: 30
month: oct
monthnumber: 10
year: 1998
bibdate: Mon Oct 24 11:29:15 2011
bibtimestamp: 2011.10.24 11:29:15 ???
note: Published in cite Borwein:2000:CSR.
URL: http://docserver.carma.newcastle.edu.au/211; http://people.reed.edu/~crandall/papers/attach01.pdf
acknowledgement: ack-nhfb
rawauthor: Jonathan M. Borwein and David M. Bradley and Richard E. Crandall
rawnote: Published in \cite{Borwein:2000:CSR}.
rawtitle: Computational Strategies for the {Riemann} Zeta Function
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/bibnet/authors/c/crandall-richard-e.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the incidence of what we call ``value recycling.''

authordates:
Jonathan Michael Borwein (20 May 1951--2 August 2016); Richard Eugene Crandall (29 December 1947--20 December 2012)

rawabstract:
We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the incidence of what we call ``value recycling.''

entry:
@TechReport{Borwein:1998:CSR,
  author =       "Jonathan M. Borwein and David M. Bradley and Richard
                 E. Crandall",
  title =        "Computational Strategies for the {Riemann} Zeta
                 Function",
  type =         "Report",
  number =       "CECM-98-118",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "68",
  day =          "30",
  month =        oct,
  year =         "1998",
  bibdate =      "Mon Oct 24 11:29:15 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Borwein:2000:CSR}.",
  URL =          "http://docserver.carma.newcastle.edu.au/211;
                 http://people.reed.edu/~crandall/papers/attach01.pdf",
  abstract =     "We provide a compendium of evaluation methods for the
                 Riemann zeta function, presenting formulae ranging from
                 historical attempts to recently found convergent series
                 to curious oddities old and new. We concentrate
                 primarily on practical computational issues, such
                 issues depending on the domain of the argument, the
                 desired speed of computation, and the incidence of what
                 we call ``value recycling.''",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August 2016);
                 Richard Eugene Crandall (29 December 1947--20 December
                 2012)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1998:DIS
author: J. M. Borwein and S. P. Fitzpatrick
title: Duality inequalities and sandwiched functions
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 15
day: 8
month: jul
monthnumber: 7
year: 1998
MRclass: 49J52, 90C25 (26B25, 46N10, 47H10, 52A41)
bibdate: Thu Sep 01 08:12:48 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 08:12:48 ???
URL: http://docserver.carma.newcastle.edu.au/204
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and S. P. Fitzpatrick
rawtitle: Duality inequalities and sandwiched functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We establish a mixed convex-Lipschitz mean value inequality from which recent results of Clarke and Ledyaev and of Lewis and Ralph follow naturally. We also provide various refinements and extensions. Finally, we answer affirmatively several open questions on the existence of ``squeeze'' theorems for a finite number of Lipschitz functions.

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

rawabstract:
We establish a mixed convex-Lipschitz mean value inequality from which recent results of Clarke and Ledyaev and of Lewis and Ralph follow naturally. We also provide various refinements and extensions. Finally, we answer affirmatively several open questions on the existence of ``squeeze'' theorems for a finite number of Lipschitz functions.

entry:
@TechReport{Borwein:1998:DIS,
  author =       "J. M. Borwein and S. P. Fitzpatrick",
  title =        "Duality inequalities and sandwiched functions",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "15",
  day =          "8",
  month =        jul,
  year =         "1998",
  MRclass =      "49J52, 90C25 (26B25, 46N10, 47H10, 52A41)",
  bibdate =      "Thu Sep 01 08:12:48 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/204",
  abstract =     "We establish a mixed convex-Lipschitz mean value
                 inequality from which recent results of Clarke and
                 Ledyaev and of Lewis and Ralph follow naturally. We
                 also provide various refinements and extensions.
                 Finally, we answer affirmatively several open questions
                 on the existence of ``squeeze'' theorems for a finite
                 number of Lipschitz functions.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Ekeland variational principle; Fenchel duality;
                 mean-value inequalities; Nonconvex separation; sandwich
                 theorem; Schauder fixed point theorem",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1998:DRDa
author: Jonathan M. Borwein and David J. Broadhurst
journal: ArXiv High Energy Physics --- Theory e-prints
pages: 15
month: nov
monthnumber: 11
year: 1998
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: Jonathan M. Borwein and David J. Broadhurst
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links

URL:
http://adsabs.harvard.edu/abs/1998hep.th...11173B; http://arxiv.org/abs/hep-th/9811173; http://docserver.carma.newcastle.edu.au/213/

abstract:
We identify 998 closed hyperbolic 3-manifolds whose volumes are rationally related to Dedekind zeta values, with coprime integers $a$ and $b$ giving $ a / rm bvol(M) = ( - D)^3 / 2 / (2 pi )^2n - 4 (zeta _K(2)) / (2 zeta (2))$ for a manifold $M$ whose invariant trace field $K$ has a single complex place, discriminant $D$, degree $n$, and Dedekind zeta value $ zeta _K(2)$. The largest numerator of the 998 invariants of Hodgson--Weeks manifolds is, astoundingly, $ a = 2^4 times 23 times 37 times 691 = 9 408 656$; the largest denominator is merely $ b = 9$. We also study the rational invariant $ a / b$ for single-complex-place cusped manifolds, complementary to knots and links, both within and beyond the Hildebrand-Weeks census. Within the censi, we identify 152 distinct Dedekind zetas rationally related to volumes. Moreover, 91 census manifolds have volumes reducible to pairs of these zeta values. Motivated by studies of Feynman diagrams, we find a 10-component 24-crossing link in the case $ n = 2$ and $ D = - 20$. It is one of 5 alternating platonic links, the other 4 being quartic. For 8 of 10 quadratic fields distinguished by rational relations between Dedekind zeta values and volumes of Feynman orthoschemes, we find corresponding links. Feynman links with $ D = - 39$ and $ D = - 84$ are missing; we expect them to be as beautiful as the 8 drawn here. Dedekind-zeta invariants are obtained for knots from Feynman diagrams with up to 11 loops. We identify a sextic 18-crossing positive Feynman knot whose rational invariant, $ a / b = 26$, is 390 times that of the cubic 16-crossing non-alternating knot with maximal $ D_9$ symmetry. Our results are secure, numerically, yet appear very hard to prove by analysis.

keywords:
High Energy Physics - Theory, Mathematics - Classical Analysis and ODEs, Mathematics - Geometric Topology, Mathematics - Number Theory

rawabstract:
We identify 998 closed hyperbolic 3-manifolds whose volumes are rationally related to Dedekind zeta values, with coprime integers $a$ and $b$ giving $ a / {\rm bvol}(M) = ( - D)^{3 / 2} / (2 \pi)^{2n - 4} (\zeta_K(2)) / (2 \zeta (2))$ for a manifold $M$ whose invariant trace field $K$ has a single complex place, discriminant $D$, degree $n$, and Dedekind zeta value $ \zeta_K(2)$. The largest numerator of the 998 invariants of Hodgson--Weeks manifolds is, astoundingly, $ a = 2^4 \times 23 \times 37 \times 691 = 9 \, 408 \, 656$; the largest denominator is merely $ b = 9$. We also study the rational invariant $ a / b$ for single-complex-place cusped manifolds, complementary to knots and links, both within and beyond the Hildebrand-Weeks census. Within the censi, we identify 152 distinct Dedekind zetas rationally related to volumes. Moreover, 91 census manifolds have volumes reducible to pairs of these zeta values. Motivated by studies of Feynman diagrams, we find a 10-component 24-crossing link in the case $ n = 2$ and $ D = - 20$. It is one of 5 alternating platonic links, the other 4 being quartic. For 8 of 10 quadratic fields distinguished by rational relations between Dedekind zeta values and volumes of Feynman orthoschemes, we find corresponding links. Feynman links with $ D = - 39$ and $ D = - 84$ are missing; we expect them to be as beautiful as the 8 drawn here. Dedekind-zeta invariants are obtained for knots from Feynman diagrams with up to 11 loops. We identify a sextic 18-crossing positive Feynman knot whose rational invariant, $ a / b = 26$, is 390 times that of the cubic 16-crossing non-alternating knot with maximal $ D_9$ symmetry. Our results are secure, numerically, yet appear very hard to prove by analysis.

rawtitle:
Determinations of rational {Dedekind}-zeta invariants of hyperbolic manifolds and {Feynman} knots and links

entry:
@Article{Borwein:1998:DRDa,
  author =       "Jonathan M. Borwein and David J. Broadhurst",
  title =        "Determinations of rational {Dedekind}-zeta invariants
                 of hyperbolic manifolds and {Feynman} knots and links",
  journal =      "ArXiv High Energy Physics --- Theory e-prints",
  month =        nov,
  year =         "1998",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/1998hep.th...11173B;
                 http://arxiv.org/abs/hep-th/9811173;
                 http://docserver.carma.newcastle.edu.au/213/",
  abstract =     "We identify 998 closed hyperbolic 3-manifolds whose
                 volumes are rationally related to Dedekind zeta values,
                 with coprime integers $a$ and $b$ giving $ a / {\rm
                 bvol}(M) = ( - D)^{3 / 2} / (2 \pi)^{2n - 4}
                 (\zeta_K(2)) / (2 \zeta (2))$ for a manifold $M$ whose
                 invariant trace field $K$ has a single complex place,
                 discriminant $D$, degree $n$, and Dedekind zeta value $
                 \zeta_K(2)$. The largest numerator of the 998
                 invariants of Hodgson--Weeks manifolds is,
                 astoundingly, $ a = 2^4 \times 23 \times 37 \times 691
                 = 9 \, 408 \, 656$; the largest denominator is merely $
                 b = 9$. We also study the rational invariant $ a / b$
                 for single-complex-place cusped manifolds,
                 complementary to knots and links, both within and
                 beyond the Hildebrand-Weeks census. Within the censi,
                 we identify 152 distinct Dedekind zetas rationally
                 related to volumes. Moreover, 91 census manifolds have
                 volumes reducible to pairs of these zeta values.
                 Motivated by studies of Feynman diagrams, we find a
                 10-component 24-crossing link in the case $ n = 2$ and
                 $ D = - 20$. It is one of 5 alternating platonic links,
                 the other 4 being quartic. For 8 of 10 quadratic fields
                 distinguished by rational relations between Dedekind
                 zeta values and volumes of Feynman orthoschemes, we
                 find corresponding links. Feynman links with $ D = -
                 39$ and $ D = - 84$ are missing; we expect them to be
                 as beautiful as the 8 drawn here. Dedekind-zeta
                 invariants are obtained for knots from Feynman diagrams
                 with up to 11 loops. We identify a sextic 18-crossing
                 positive Feynman knot whose rational invariant, $ a / b
                 = 26$, is 390 times that of the cubic 16-crossing
                 non-alternating knot with maximal $ D_9$ symmetry. Our
                 results are secure, numerically, yet appear very hard
                 to prove by analysis.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "hep-th/9811173",
  keywords =     "High Energy Physics - Theory, Mathematics - Classical
                 Analysis and ODEs, Mathematics - Geometric Topology,
                 Mathematics - Number Theory",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1998:DRDb
author: Jonathan M. Borwein and David J. Broadhurst
type: CECM Preprint
number: CECM-98-120, OUT-4102-76, hep-th/9811173
institution: inst-CECM
address: inst-CECM:adr
pages: 53
month: nov
monthnumber: 11
year: 1998
bibdate: Tue Aug 16 10:14:52 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:14:52 ???
note: arXiv preprint hep-th/9811173.
URL: http://docserver.carma.newcastle.edu.au/213/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David J. Broadhurst
rawnote: arXiv preprint hep-th/9811173.
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links

abstract:
We identify 998 closed hyperbolic 3-manifolds whose volumes are rationally related to Dedekind zeta values, with coprime integers $a$ and $b$ givingpar $$ frac ab mathrm vol(mathcal M) = frac ( - D)^3 / 2(2 pi )^2 n - 4 frac zeta _K(2)2 zeta (2) $$ par for a manifold $M$ whose invariant trace field $K$ has a single complex place, discriminant $D$, degree $n$, and Dedekind zeta value $ zeta _K(2)$. The largest numerator of the 998 invariants of Hodgson-Weeks manifolds is, astoundingly, $ a = 2^4 times 23 times 37 times 691 = 9, 408, 656$; the largest denominator is merely $ b = 9$. We also study the rational invariant $ a / b$ for single-complex-place cusped manifolds, complementary to knots and links, both within and beyond the Hildebrand-Weeks census. Within the censi, we identify 152 distinct Dedekind zetas rationally related to volumes. Moreover, 91 census manifolds have volumes reducible to pairs of these zeta values. Motivated by studies of Feynman diagrams, we find a 10-component 24-crossing link in the case $ n = 2$ and $ D = - 20$. It is one of 5 alternating platonic links, the other 4 being quartic. For 8 of 10 quadratic fields distinguished by rational relations between Dedekind zeta values and volumes of Feynman orthoschemes, we find corresponding links. Feynman links with $ D = - 39$ and $ D = - 84$ are missing; we expect them to be as beautiful as the 8 drawn here. Dedekind-zeta invariants are obtained for knots from Feynman diagrams with up to 11 loops. We identify a sextic 18-crossing positive Feynman knot whose rational invariant, $ a / b = 26$, is 390 times that of the cubic 16-crossing non-alternating knot with maximal $ D_g$ symmetry. Our results are secure, numerically, yet appear very hard to prove by analysis.

rawabstract:
We identify 998 closed hyperbolic 3-manifolds whose volumes are rationally related to Dedekind zeta values, with coprime integers $a$ and $b$ giving\par $$ \frac {a}{b} \mathrm {vol}(\mathcal {M}) = \frac {( - D)^{3 / 2}}{(2 \pi)^{2 n - 4}} \frac {\zeta_K(2)}{2 \zeta (2)} $$ \par for a manifold $M$ whose invariant trace field $K$ has a single complex place, discriminant $D$, degree $n$, and Dedekind zeta value $ \zeta_K(2)$. The largest numerator of the 998 invariants of Hodgson-Weeks manifolds is, astoundingly, $ a = 2^4 \times 23 \times 37 \times 691 = 9, 408, 656$; the largest denominator is merely $ b = 9$. We also study the rational invariant $ a / b$ for single-complex-place cusped manifolds, complementary to knots and links, both within and beyond the Hildebrand-Weeks census. Within the censi, we identify 152 distinct Dedekind zetas rationally related to volumes. Moreover, 91 census manifolds have volumes reducible to pairs of these zeta values. Motivated by studies of Feynman diagrams, we find a 10-component 24-crossing link in the case $ n = 2$ and $ D = - 20$. It is one of 5 alternating platonic links, the other 4 being quartic. For 8 of 10 quadratic fields distinguished by rational relations between Dedekind zeta values and volumes of Feynman orthoschemes, we find corresponding links. Feynman links with $ D = - 39$ and $ D = - 84$ are missing; we expect them to be as beautiful as the 8 drawn here. Dedekind-zeta invariants are obtained for knots from Feynman diagrams with up to 11 loops. We identify a sextic 18-crossing positive Feynman knot whose rational invariant, $ a / b = 26$, is 390 times that of the cubic 16-crossing non-alternating knot with maximal $ D_g$ symmetry. Our results are secure, numerically, yet appear very hard to prove by analysis.

rawtitle:
Determinations of rational {Dedekind}-zeta invariants of hyperbolic manifolds and {Feynman} knots and links

entry:
@TechReport{Borwein:1998:DRDb,
  author =       "Jonathan M. Borwein and David J. Broadhurst",
  title =        "Determinations of rational {Dedekind}-zeta invariants
                 of hyperbolic manifolds and {Feynman} knots and links",
  type =         "CECM Preprint",
  number =       "CECM-98-120, OUT-4102-76, hep-th/9811173",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "53",
  month =        nov,
  year =         "1998",
  bibdate =      "Tue Aug 16 10:14:52 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "arXiv preprint hep-th/9811173.",
  URL =          "http://docserver.carma.newcastle.edu.au/213/",
  abstract =     "We identify 998 closed hyperbolic 3-manifolds whose
                 volumes are rationally related to Dedekind zeta values,
                 with coprime integers $a$ and $b$ giving\par

                  $$ \frac {a}{b} \mathrm {vol}(\mathcal {M}) = \frac {(
                 - D)^{3 / 2}}{(2 \pi)^{2 n - 4}} \frac {\zeta_K(2)}{2
                 \zeta (2)} $$ \par

                 for a manifold $M$ whose invariant trace field $K$ has
                 a single complex place, discriminant $D$, degree $n$,
                 and Dedekind zeta value $ \zeta_K(2)$. The largest
                 numerator of the 998 invariants of Hodgson-Weeks
                 manifolds is, astoundingly, $ a = 2^4 \times 23 \times
                 37 \times 691 = 9, 408, 656$; the largest denominator
                 is merely $ b = 9$. We also study the rational
                 invariant $ a / b$ for single-complex-place cusped
                 manifolds, complementary to knots and links, both
                 within and beyond the Hildebrand-Weeks census. Within
                 the censi, we identify 152 distinct Dedekind zetas
                 rationally related to volumes. Moreover, 91 census
                 manifolds have volumes reducible to pairs of these zeta
                 values. Motivated by studies of Feynman diagrams, we
                 find a 10-component 24-crossing link in the case $ n =
                 2$ and $ D = - 20$. It is one of 5 alternating platonic
                 links, the other 4 being quartic. For 8 of 10 quadratic
                 fields distinguished by rational relations between
                 Dedekind zeta values and volumes of Feynman
                 orthoschemes, we find corresponding links. Feynman
                 links with $ D = - 39$ and $ D = - 84$ are missing; we
                 expect them to be as beautiful as the 8 drawn here.
                 Dedekind-zeta invariants are obtained for knots from
                 Feynman diagrams with up to 11 loops. We identify a
                 sextic 18-crossing positive Feynman knot whose rational
                 invariant, $ a / b = 26$, is 390 times that of the
                 cubic 16-crossing non-alternating knot with maximal $
                 D_g$ symmetry. Our results are secure, numerically, yet
                 appear very hard to prove by analysis.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1998:ETE
author: Jonathan M. Borwein and Robert M. Corless
title: Emerging tools for experimental mathematics
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 28
day: 27
month: nov
monthnumber: 11
year: 1998
bibdate: Thu Sep 01 08:05:55 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 08:05:55 ???
note: Published in cite Borwein:1999:ETE.
URL: http://docserver.carma.newcastle.edu.au/203
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Robert M. Corless
rawnote: Published in \cite{Borwein:1999:ETE}.
rawtitle: Emerging tools for experimental mathematics
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Using mostly elementary examples, we discuss the use of some recent and emerging tools for experimental mathematics. The tools discussed include so-called ``inverse symbolic computation'', lattice reduction algorithms such as ``LLL'', and ``PSLQ'', and Sloane and Plouffe's integer sequence lookup program.

rawabstract:
Using mostly elementary examples, we discuss the use of some recent and emerging tools for experimental mathematics. The tools discussed include so-called ``inverse symbolic computation'', lattice reduction algorithms such as ``LLL'', and ``PSLQ'', and Sloane and Plouffe's integer sequence lookup program.

entry:
@TechReport{Borwein:1998:ETE,
  author =       "Jonathan M. Borwein and Robert M. Corless",
  title =        "Emerging tools for experimental mathematics",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "28",
  day =          "27",
  month =        nov,
  year =         "1998",
  bibdate =      "Thu Sep 01 08:05:55 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:1999:ETE}.",
  URL =          "http://docserver.carma.newcastle.edu.au/203",
  abstract =     "Using mostly elementary examples, we discuss the use
                 of some recent and emerging tools for experimental
                 mathematics. The tools discussed include so-called
                 ``inverse symbolic computation'', lattice reduction
                 algorithms such as ``LLL'', and ``PSLQ'', and Sloane
                 and Plouffe's integer sequence lookup program.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1998:GYI
author: Jonathan M. Borwein
title: A generalization of Young's $ l^p $ inequality
journal: j-MATH-INEQUAL-APPL
volume: 1
number: 1
pages: 131--136
year: 1998
DOI: https://doi.org/10.7153/mia-01-11
ISSN: 1331-4343 (print), 1848-9966 (electronic) OR 13314343 (print), 18489966 (electronic)
ISSNL: 1331-4343 OR 13314343
MRclass: 90C25 (26B25 52A41)
MRnumber: 1492917
MRreviewer: G{\'e}rard Lebourg
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/189/
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
rawtitle: A generalization of {Young}'s $ l^p $ inequality
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1998:GYI,
  author =       "Jonathan M. Borwein",
  title =        "A generalization of {Young}'s $ l^p $ inequality",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "1",
  number =       "1",
  pages =        "131--136",
  year =         "1998",
  DOI =          "https://doi.org/10.7153/mia-01-11",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  ISSN-L =       "1331-4343",
  MRclass =      "90C25 (26B25 52A41)",
  MRnumber =     "1492917",
  MRreviewer =   "G{\'e}rard Lebourg",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/189/",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Inequal. Appl.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1998:LCE
author: Jonathan M. Borwein and Qiji J. Zhu
title: Limiting convex examples for nonconvex subdifferential calculus
journal: j-J-CONVEX-ANAL
volume: 5
number: 2
pages: 221--235
year: 1998
ISSN: 0944-6532 (print), 2363-6394 (electronic) OR 09446532 (print), 23636394 (electronic)
MRclass: 49J52 (26B05)
MRnumber: 1670340
MRreviewer: Lionel Thibault
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/191/; http://www.heldermann-verlag.de/jca/jca05/j163.pdf
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 Qiji J. Zhu
rawtitle: Limiting convex examples for nonconvex subdifferential calculus
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1998:LCE,
  author =       "Jonathan M. Borwein and Qiji J. Zhu",
  title =        "Limiting convex examples for nonconvex subdifferential
                 calculus",
  journal =      j-J-CONVEX-ANAL,
  volume =       "5",
  number =       "2",
  pages =        "221--235",
  year =         "1998",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "49J52 (26B05)",
  MRnumber =     "1670340",
  MRreviewer =   "Lionel Thibault",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/191/;
                 http://www.heldermann-verlag.de/jca/jca05/j163.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Convex Analysis",
  journal-URL =  "http://www.heldermann.de/JCA/jcacon.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1998:LFM
author: Jonathan M. Borwein and Xianfu Wang
title: Lipschitz functions with maximal Clarke subdifferentials are generic
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 221--235
day: 11
month: sep
monthnumber: 9
year: 1998
bibdate: Thu Sep 01 08:26:34 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 08:26:34 ???
note: Published in cite Borwein:2000:LFM.
URL: http://docserver.carma.newcastle.edu.au/206/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Xianfu Wang
rawnote: Published in \cite{Borwein:2000:LFM}.
rawtitle: {Lipschitz} functions with maximal {Clarke} subdifferentials are generic
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We show that on a separable Banach space most Lipschitz functions have maximal Clarke subdifferential mappings. In particular, the generic nonexpansive function has the dual unit ball as its Clarke subdifferential at every point. Diverse corollaries are given.

rawabstract:
We show that on a separable Banach space most Lipschitz functions have maximal Clarke subdifferential mappings. In particular, the generic nonexpansive function has the dual unit ball as its Clarke subdifferential at every point. Diverse corollaries are given.

entry:
@TechReport{Borwein:1998:LFM,
  author =       "Jonathan M. Borwein and Xianfu Wang",
  title =        "{Lipschitz} functions with maximal {Clarke}
                 subdifferentials are generic",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  day =          "11",
  month =        sep,
  year =         "1998",
  bibdate =      "Thu Sep 01 08:26:34 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2000:LFM}.",
  URL =          "http://docserver.carma.newcastle.edu.au/206/",
  abstract =     "We show that on a separable Banach space most
                 Lipschitz functions have maximal Clarke subdifferential
                 mappings. In particular, the generic nonexpansive
                 function has the dual unit ball as its Clarke
                 subdifferential at every point. Diverse corollaries are
                 given.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1998:MPW
author: Jonathan Borwein
title: Mathematical Publication on the Web
journal: j-SIGSAM
volume: 32
number: 1
pages: 4--7
month: mar
monthnumber: 3
year: 1998
CODEN: SIGSBZ
DOI: https://doi.org/10.1145/294833.294836
ISSN: 0163-5824 (print), 1557-9492 (electronic) OR 01635824 (print), 15579492 (electronic)
ISSNL: 0163-5824 OR 01635824
bibdate: Wed Aug 10 12:08:56 2016
bibtimestamp: 2016.08.10 12:08:56 ???
URL: http://docserver.carma.newcastle.edu.au/190/; http://doi.acm.org/10.1145/294833.294836
fjournal: SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
issue: 123
rawauthor: Jonathan Borwein
rawtitle: Mathematical Publication on the {Web}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/sigsam.bib

entry:
@Article{Borwein:1998:MPW,
  author =       "Jonathan Borwein",
  title =        "Mathematical Publication on the {Web}",
  journal =      j-SIGSAM,
  volume =       "32",
  number =       "1",
  pages =        "4--7",
  month =        mar,
  year =         "1998",
  CODEN =        "SIGSBZ",
  DOI =          "https://doi.org/10.1145/294833.294836",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Wed Aug 10 12:08:56 2016",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/190/;
                 http://doi.acm.org/10.1145/294833.294836",
  acknowledgement = ack-nhfb,
  acmid =        "294836",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIGSAM Bulletin (ACM Special Interest Group on
                 Symbolic and Algebraic Manipulation)",
  issue =        "123",
  issue-date =   "March 1998",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
  numpages =     "4",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1998:NCC
author: Jonathan M. Borwein and Jay S. Treiman and Qiji J. Zhu
title: Necessary conditions for constrained optimization problems with semicontinuous and continuous data
journal: j-TRANS-AM-MATH-SOC
volume: 350
number: 6
pages: 2409--2429
year: 1998
CODEN: TAMTAM
DOI: https://doi.org/10.1090/S0002-9947-98-01984-9
ISSN: 0002-9947 (print), 1088-6850 (electronic) OR 00029947 (print), 10886850 (electronic)
ISSNL: 0002-9947 OR 00029947
MRclass: 90C48 (49J52)
MRnumber: 1433112
MRreviewer: B. Mordukhovich
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/116/
fjournal: Transactions of the American Mathematical Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/journals/tran/
rawauthor: Jonathan M. Borwein and Jay S. Treiman and Qiji J. Zhu
rawtitle: Necessary conditions for constrained optimization problems with semicontinuous and continuous data
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1998:NCC,
  author =       "Jonathan M. Borwein and Jay S. Treiman and Qiji J.
                 Zhu",
  title =        "Necessary conditions for constrained optimization
                 problems with semicontinuous and continuous data",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "350",
  number =       "6",
  pages =        "2409--2429",
  year =         "1998",
  CODEN =        "TAMTAM",
  DOI =          "https://doi.org/10.1090/S0002-9947-98-01984-9",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "90C48 (49J52)",
  MRnumber =     "1433112",
  MRreviewer =   "B. Mordukhovich",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/116/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Transactions of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/tran/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1998:NSE
author: Jonathan M. Borwein and Warren B. Moors
title: Null sets and essentially smooth Lipschitz functions
journal: j-SIAM-J-OPT
volume: 8
number: 2
pages: 309--323
year: 1998
CODEN: SJOPE8
DOI: https://doi.org/10.1137/S1052623496305213
ISSN: 1052-6234 (print), 1095-7189 (electronic) OR 10526234 (print), 10957189 (electronic)
ISSNL: 1052-6234 OR 10526234
MRclass: 49J52 (46N10 58C20)
MRnumber: 1618798
MRreviewer: John R. Giles
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/162/
fjournal: SIAM Journal on Optimization
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://epubs.siam.org/siopt
rawauthor: Jonathan M. Borwein and Warren B. Moors
rawtitle: Null sets and essentially smooth {Lipschitz} functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1998:NSE,
  author =       "Jonathan M. Borwein and Warren B. Moors",
  title =        "Null sets and essentially smooth {Lipschitz}
                 functions",
  journal =      j-SIAM-J-OPT,
  volume =       "8",
  number =       "2",
  pages =        "309--323",
  year =         "1998",
  CODEN =        "SJOPE8",
  DOI =          "https://doi.org/10.1137/S1052623496305213",
  ISSN =         "1052-6234 (print), 1095-7189 (electronic)",
  ISSN-L =       "1052-6234",
  MRclass =      "49J52 (46N10 58C20)",
  MRnumber =     "1618798",
  MRreviewer =   "John R. Giles",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/162/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIAM Journal on Optimization",
  journal-URL =  "http://epubs.siam.org/siopt",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1998:NSP
author: Jonathan M. Borwein and Alejandro Jofre
title: A nonconvex separation property in Banach spaces
journal: j-Z-OPER-RES
volume: 48
number: 2
pages: 169--179
year: 1998
CODEN: ZMMRFZ
DOI: https://doi.org/10.1007/s001860050019
ISSN: 1432-2994 (print), 1432-5217 (electronic) OR 14322994 (print), 14325217 (electronic)
ISSNL: 1432-2994 OR 14322994
MRclass: 46B20 (46A22 46N10 49J53 90C48)
MRnumber: 1662819
MRreviewer: S. Simons
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: Set-valued optimization.
URL: http://docserver.carma.newcastle.edu.au/197/
fjournal: Zeitschrift fur Operations Research. Mathematical Methods of Operations Research
acknowledgement: ack-nhfb
ajournal: ZOR---Math. Methods Oper. Res.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/186
rawauthor: Jonathan M. Borwein and Alejandro Jofr{\'e}
rawnote: Set-valued optimization.
rawtitle: A nonconvex separation property in {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1998:NSP,
  author =       "Jonathan M. Borwein and Alejandro Jofr{\'e}",
  title =        "A nonconvex separation property in {Banach} spaces",
  journal =      j-Z-OPER-RES,
  volume =       "48",
  number =       "2",
  pages =        "169--179",
  year =         "1998",
  CODEN =        "ZMMRFZ",
  DOI =          "https://doi.org/10.1007/s001860050019",
  ISSN =         "1432-2994 (print), 1432-5217 (electronic)",
  ISSN-L =       "1432-2994",
  MRclass =      "46B20 (46A22 46N10 49J53 90C48)",
  MRnumber =     "1662819",
  MRreviewer =   "S. Simons",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Set-valued optimization.",
  URL =          "http://docserver.carma.newcastle.edu.au/197/",
  acknowledgement = ack-nhfb,
  ajournal =     "ZOR---Math. Methods Oper. Res.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Zeitschrift f{\"u}r Operations Research. Mathematical
                 Methods of Operations Research",
  journal-URL =  "http://link.springer.com/journal/186",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  xxjournal =    "Math. Methods Oper. Res.",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borwein:1998:PAS
author: Jonathan M. Borwein and Peter B. Borwein
title: Pi and the AGM: A study in analytic number theory and computational complexity
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xvi + 414
year: 1998
ISBN: 0-471-83138-7, 0-471-31515-X (paperback) OR 0471831387, 047131515X (paperback)
ISBN13: 978-0-471-83138-9, 978-0-471-31515-5 (paperback) OR 9780471831389, 9780471315155 (paperback)
MRclass: 11Y60 (11B65 68Q25)
MRnumber: 1641658
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: Reprint of the 1987 original.
series: Canadian Mathematical Society Series of Monographs and Advanced Texts, 4
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Peter B. Borwein
rawnote: Reprint of the 1987 original.
rawtitle: Pi and the {AGM}: A study in analytic number theory and computational complexity
ORCID: Borwein, Jonathan/0000-0002-1263-0646
subject:
Number theory; Computational complexity; Elliptic functions; Pi; Nombres, Theorie des; Complexite de calcul (Informatique); Fonctions elliptiques; Computational complexity; Elliptic functions; Number theory; Pi; Algebraische Funktion; Arithmetisch-geometrisches Mittel; Berechnung; Geschichte; Pi (Zahl); Nombres, Theorie des; Complexite de calcul (informatique); Fonctions elliptiques; Pi (le nombre); Arithmetisch-geometrisches Mittel; Algebraische Funktion; Pi (Zahl); Berechnung; Geschichte; moyenne arithmetique; moyenne geometrique; iteration; fonction elliptique; complexite calcul; theorie nombre

TOC:
1 Complete Elliptic Integrals and the Arithmetic-Geometric Mean Iteration / 1 1.1 The Arithmetic--Geometric Mean Iteration / 1 1.2 Gauss's Derivation of the Fundamental Limit Formula / 5 1.3 Basic Properties of Complete Elliptic Integrals / 7 1.4 Quadratic Transformations and Iterations and a Third Proof of the Fundamental Limit Formula / 11 1.5 Jacobi's Differential Equation and a Fourth Proof of the Fundamental Limit Theorem / 18 1.6 Legendre's Relation / 23 1.7 Elliptic Functions / 28 2 Theta Functions and the Arithmetic--Geometric Mean Iteration / 33 2.1 A Theta Series Solution to the AGM / 33 2.2 Poisson Summation / 36 2.3 Poisson Summation and the AGM / 40 2.4 The Derived Iteration and Some Convergence Results / 44 2.5 Two Algorithms for 7T / 46 2.6 General Theta Functions / 52 2.7 The Landen Transformation / 57 3 Jacobi's Triple-Product and Some Number Theoretic Applications / 62 3.1 Jacobi's Triple-Product Identity / 62 3.2 Some Further Theta Function Identities / 67 3.3 A Combinatorial Approach to the Triple-Product Identity / 76 3.4 Bressoud's ``Easy Proof'' of the Rogers--Ramanujan Identities / 78 3.5 Some Number Theoretic Applications / 81 3.6 The Mellin Transform and the Zeta Function / 87 3.7 Evaluation of Sums of Reciprocals of Fibonacci Sequences / 91 4 Higher Order Transformations / 102 4.1 A First Approach to Higher Order Transformations / 102 4.2 An Elementary Transcendental Approach to Higher Order Transformations / 109 4.3 Elliptic Modular Functions / 112 4.4 The Modular Equations for $lambda $ and $j$ / 119 4.5 The Modular Equation in $u$--$v$ Form / 126 4.6 The Multiplier / 136 4.7 Cubic Modular Identities / 142 5 Modular Equations and Algebraic Approximations to $ pi $ / 152 5.1 Singular Values of the Second Kind / 152 5.2 Calculation of $alpha $ / 155 5.3 Further Formulae for $alpha $ / 164 5.4 Recursive Approximation to $ pi $ / 169 5.5 Generalized Elliptic Integrals and Rational and Algebraic Series for $ 1 / pi $ and $ 1 / K $ / 177 5.6 Other Approximations / 191 6 The Complexity of Algebraic Functions / 200 6.1 Complexity Concerns / 200 6.2 The Fast Fourier Transform (FFT) / 204 6.3 Fast Multiplication / 209 6.4 Newton's Method and the Complexity of Algebraic Functions / 212 7 Algorithms for the Elementary Functions / 219 7.1 $ pi $ and Log / 219 7.2 Theta Function Algorithms for Log / 224 7.3 The Complexity of Elementary and Elliptic Functions / 226 8 General Means and Iterations / 230 8.1 Abstract Means / 230 8.2 Equivalence of Means / 239 8.3 Compound Means / 243 8.4 Convergence Rates and Some Examples / 249 8.5 Carlson's Integrals and More Examples 256 / 281 8.6 Series Expansions of Certain Means / 263 8.7 Multidimensional Means and Iterations / 266 8.8 Algebraic Iterations and Functional Relations / 273 9 Some Additional Applications / 281 9.1 Sums of Two Squares / 281 9.2 (Chemical) Lattice Sums / 288 9.3 Odd-Dimensional Sums and Benson's Formula / 301 9.4 The Quintuple-Product Identity / 306 9.5 Quintic and Septic Multipliers and Iterations / 309 10 Other Approaches to the Elementary Functions / 316 10.1 Classical Approximations / 316 10.2 Reduced Complexity Methods / 326 11 Pi / 337 11.1 On the History of the Calculation of $ pi $ / 337 11.2 On the Transcendence of $ pi $ / 347 11.3 Irrationality Measures / 362 Bibliography / 387 Symbol List / 396 Index / 405

shortTOC:
1. Complete Elliptic Integrals and the Arithmetic--Geometric Mean Iteration 2. Theta Functions and the Arithmetic--Geometric Mean Iteration 3. Jacobi's Triple-Product and Some Number Theoretic Applications 4. Higher Order Transformations 5. Modular Equations and Algebraic Approximations to $ pi $ 6. The Complexity of Algebraic Functions 7. Algorithms for the Elementary Functions 8. General Means and Iterations 9. Some Additional Applications 10. Other Approaches to the Elementary Functions 11. Pi

rawshortTOC:
1. Complete Elliptic Integrals and the Arithmetic--Geometric Mean Iteration \\ 2. Theta Functions and the Arithmetic--Geometric Mean Iteration \\ 3. Jacobi's Triple-Product and Some Number Theoretic Applications \\ 4. Higher Order Transformations \\ 5. Modular Equations and Algebraic Approximations to $ \pi $ \\ 6. The Complexity of Algebraic Functions \\ 7. Algorithms for the Elementary Functions \\ 8. General Means and Iterations \\ 9. Some Additional Applications \\ 10. Other Approaches to the Elementary Functions \\ 11. Pi

rawTOC:
1 Complete Elliptic Integrals and the Arithmetic-Geometric Mean Iteration / 1 \\ 1.1 The Arithmetic--Geometric Mean Iteration / 1 \\ 1.2 Gauss's Derivation of the Fundamental Limit Formula / 5 \\ 1.3 Basic Properties of Complete Elliptic Integrals / 7 \\ 1.4 Quadratic Transformations and Iterations and a Third Proof of the Fundamental Limit Formula / 11 \\ 1.5 Jacobi's Differential Equation and a Fourth Proof of the Fundamental Limit Theorem / 18 \\ 1.6 Legendre's Relation / 23 \\ 1.7 Elliptic Functions / 28 \\ 2 Theta Functions and the Arithmetic--Geometric Mean Iteration / 33 \\ 2.1 A Theta Series Solution to the AGM / 33 \\ 2.2 Poisson Summation / 36 \\ 2.3 Poisson Summation and the AGM / 40 \\ 2.4 The Derived Iteration and Some Convergence Results / 44 \\ 2.5 Two Algorithms for 7T / 46 \\ 2.6 General Theta Functions / 52 \\ 2.7 The Landen Transformation / 57 \\ 3 Jacobi's Triple-Product and Some Number Theoretic Applications / 62 \\ 3.1 Jacobi's Triple-Product Identity / 62 \\ 3.2 Some Further Theta Function Identities / 67 \\ 3.3 A Combinatorial Approach to the Triple-Product Identity / 76 \\ 3.4 Bressoud's ``Easy Proof'' of the Rogers--Ramanujan Identities / 78 \\ 3.5 Some Number Theoretic Applications / 81 \\ 3.6 The Mellin Transform and the Zeta Function / 87 \\ 3.7 Evaluation of Sums of Reciprocals of Fibonacci Sequences / 91 \\ 4 Higher Order Transformations / 102 \\ 4.1 A First Approach to Higher Order Transformations / 102 \\ 4.2 An Elementary Transcendental Approach to Higher Order Transformations / 109 \\ 4.3 Elliptic Modular Functions / 112 \\ 4.4 The Modular Equations for $\lambda$ and $j$ / 119 \\ 4.5 The Modular Equation in $u$--$v$ Form / 126 \\ 4.6 The Multiplier / 136 \\ 4.7 Cubic Modular Identities / 142 \\ 5 Modular Equations and Algebraic Approximations to $ \pi $ / 152 \\ 5.1 Singular Values of the Second Kind / 152 \\ 5.2 Calculation of $\alpha$ / 155 \\ 5.3 Further Formulae for $\alpha$ / 164 \\ 5.4 Recursive Approximation to $ \pi $ / 169 \\ 5.5 Generalized Elliptic Integrals and Rational and Algebraic Series for $ 1 / \pi $ and $ 1 / K $ / 177 \\ 5.6 Other Approximations / 191 \\ 6 The Complexity of Algebraic Functions / 200 \\ 6.1 Complexity Concerns / 200 \\ 6.2 The Fast Fourier Transform (FFT) / 204 \\ 6.3 Fast Multiplication / 209 \\ 6.4 Newton's Method and the Complexity of Algebraic Functions / 212 \\ 7 Algorithms for the Elementary Functions / 219 \\ 7.1 $ \pi $ and Log / 219 \\ 7.2 Theta Function Algorithms for Log / 224 \\ 7.3 The Complexity of Elementary and Elliptic Functions / 226 \\ 8 General Means and Iterations / 230 \\ 8.1 Abstract Means / 230 \\ 8.2 Equivalence of Means / 239 \\ 8.3 Compound Means / 243 \\ 8.4 Convergence Rates and Some Examples / 249 \\ 8.5 Carlson's Integrals and More Examples 256 / 281 \\ 8.6 Series Expansions of Certain Means / 263 \\ 8.7 Multidimensional Means and Iterations / 266 \\ 8.8 Algebraic Iterations and Functional Relations / 273 \\ 9 Some Additional Applications / 281 \\ 9.1 Sums of Two Squares / 281 \\ 9.2 (Chemical) Lattice Sums / 288 \\ 9.3 Odd-Dimensional Sums and Benson's Formula / 301 \\ 9.4 The Quintuple-Product Identity / 306 \\ 9.5 Quintic and Septic Multipliers and Iterations / 309 \\ 10 Other Approaches to the Elementary Functions / 316 \\ 10.1 Classical Approximations / 316 \\ 10.2 Reduced Complexity Methods / 326 \\ 11 Pi / 337 \\ 11.1 On the History of the Calculation of $ \pi $ / 337 \\ 11.2 On the Transcendence of $ \pi $ / 347 \\ 11.3 Irrationality Measures / 362 \\ Bibliography / 387 \\ Symbol List / 396 \\ Index / 405

entry:
@Book{Borwein:1998:PAS,
  author =       "Jonathan M. Borwein and Peter B. Borwein",
  title =        "Pi and the {AGM}: A study in analytic number theory
                 and computational complexity",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xvi + 414",
  year =         "1998",
  ISBN =         "0-471-83138-7, 0-471-31515-X (paperback)",
  ISBN-13 =      "978-0-471-83138-9, 978-0-471-31515-5 (paperback)",
  MRclass =      "11Y60 (11B65 68Q25)",
  MRnumber =     "1641658",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Reprint of the 1987 original.",
  series =       "Canadian Mathematical Society Series of Monographs and
                 Advanced Texts, 4",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  shorttableofcontents = "1. Complete Elliptic Integrals and the
                 Arithmetic--Geometric Mean Iteration \\
                 2. Theta Functions and the Arithmetic--Geometric Mean
                 Iteration \\
                 3. Jacobi's Triple-Product and Some Number Theoretic
                 Applications \\
                 4. Higher Order Transformations \\
                 5. Modular Equations and Algebraic Approximations to $
                 \pi $ \\
                 6. The Complexity of Algebraic Functions \\
                 7. Algorithms for the Elementary Functions \\
                 8. General Means and Iterations \\
                 9. Some Additional Applications \\
                 10. Other Approaches to the Elementary Functions \\
                 11. Pi",
  subject =      "Number theory; Computational complexity; Elliptic
                 functions; Pi; Nombres, Th{\'e}orie des; Complexit{\'e}
                 de calcul (Informatique); Fonctions elliptiques;
                 Computational complexity; Elliptic functions; Number
                 theory; Pi; Algebraische Funktion;
                 Arithmetisch-geometrisches Mittel; Berechnung;
                 Geschichte; Pi (Zahl); Nombres, Th{\'e}orie des;
                 Complexit{\'e} de calcul (informatique); Fonctions
                 elliptiques; Pi (le nombre); Arithmetisch-geometrisches
                 Mittel; Algebraische Funktion; Pi (Zahl); Berechnung;
                 Geschichte; moyenne arithm{\'e}tique; moyenne
                 g{\'e}om{\'e}trique; it{\'e}ration; fonction
                 elliptique; complexit{\'e} calcul; th{\'e}orie nombre",
  tableofcontents = "1 Complete Elliptic Integrals and the
                 Arithmetic-Geometric Mean Iteration / 1 \\
                 1.1 The Arithmetic--Geometric Mean Iteration / 1 \\
                 1.2 Gauss's Derivation of the Fundamental Limit Formula
                 / 5 \\
                 1.3 Basic Properties of Complete Elliptic Integrals / 7
                 \\
                 1.4 Quadratic Transformations and Iterations and a
                 Third Proof of the Fundamental Limit Formula / 11 \\
                 1.5 Jacobi's Differential Equation and a Fourth Proof
                 of the Fundamental Limit Theorem / 18 \\
                 1.6 Legendre's Relation / 23 \\
                 1.7 Elliptic Functions / 28 \\
                 2 Theta Functions and the Arithmetic--Geometric Mean
                 Iteration / 33 \\
                 2.1 A Theta Series Solution to the AGM / 33 \\
                 2.2 Poisson Summation / 36 \\
                 2.3 Poisson Summation and the AGM / 40 \\
                 2.4 The Derived Iteration and Some Convergence Results
                 / 44 \\
                 2.5 Two Algorithms for 7T / 46 \\
                 2.6 General Theta Functions / 52 \\
                 2.7 The Landen Transformation / 57 \\
                 3 Jacobi's Triple-Product and Some Number Theoretic
                 Applications / 62 \\
                 3.1 Jacobi's Triple-Product Identity / 62 \\
                 3.2 Some Further Theta Function Identities / 67 \\
                 3.3 A Combinatorial Approach to the Triple-Product
                 Identity / 76 \\
                 3.4 Bressoud's ``Easy Proof'' of the Rogers--Ramanujan
                 Identities / 78 \\
                 3.5 Some Number Theoretic Applications / 81 \\
                 3.6 The Mellin Transform and the Zeta Function / 87 \\
                 3.7 Evaluation of Sums of Reciprocals of Fibonacci
                 Sequences / 91 \\
                 4 Higher Order Transformations / 102 \\
                 4.1 A First Approach to Higher Order Transformations /
                 102 \\
                 4.2 An Elementary Transcendental Approach to Higher
                 Order Transformations / 109 \\
                 4.3 Elliptic Modular Functions / 112 \\
                 4.4 The Modular Equations for $\lambda$ and $j$ / 119
                 \\
                 4.5 The Modular Equation in $u$--$v$ Form / 126 \\
                 4.6 The Multiplier / 136 \\
                 4.7 Cubic Modular Identities / 142 \\
                 5 Modular Equations and Algebraic Approximations to $
                 \pi $ / 152 \\
                 5.1 Singular Values of the Second Kind / 152 \\
                 5.2 Calculation of $\alpha$ / 155 \\
                 5.3 Further Formulae for $\alpha$ / 164 \\
                 5.4 Recursive Approximation to $ \pi $ / 169 \\
                 5.5 Generalized Elliptic Integrals and Rational and
                 Algebraic Series for $ 1 / \pi $ and $ 1 / K $ / 177
                 \\
                 5.6 Other Approximations / 191 \\
                 6 The Complexity of Algebraic Functions / 200 \\
                 6.1 Complexity Concerns / 200 \\
                 6.2 The Fast Fourier Transform (FFT) / 204 \\
                 6.3 Fast Multiplication / 209 \\
                 6.4 Newton's Method and the Complexity of Algebraic
                 Functions / 212 \\
                 7 Algorithms for the Elementary Functions / 219 \\
                 7.1 $ \pi $ and Log / 219 \\
                 7.2 Theta Function Algorithms for Log / 224 \\
                 7.3 The Complexity of Elementary and Elliptic Functions
                 / 226 \\
                 8 General Means and Iterations / 230 \\
                 8.1 Abstract Means / 230 \\
                 8.2 Equivalence of Means / 239 \\
                 8.3 Compound Means / 243 \\
                 8.4 Convergence Rates and Some Examples / 249 \\
                 8.5 Carlson's Integrals and More Examples 256 / 281 \\
                 8.6 Series Expansions of Certain Means / 263 \\
                 8.7 Multidimensional Means and Iterations / 266 \\
                 8.8 Algebraic Iterations and Functional Relations / 273
                 \\
                 9 Some Additional Applications / 281 \\
                 9.1 Sums of Two Squares / 281 \\
                 9.2 (Chemical) Lattice Sums / 288 \\
                 9.3 Odd-Dimensional Sums and Benson's Formula / 301 \\
                 9.4 The Quintuple-Product Identity / 306 \\
                 9.5 Quintic and Septic Multipliers and Iterations / 309
                 \\
                 10 Other Approaches to the Elementary Functions / 316
                 \\
                 10.1 Classical Approximations / 316 \\
                 10.2 Reduced Complexity Methods / 326 \\
                 11 Pi / 337 \\
                 11.1 On the History of the Calculation of $ \pi $ / 337
                 \\
                 11.2 On the Transcendence of $ \pi $ / 347 \\
                 11.3 Irrationality Measures / 362 \\
                 Bibliography / 387 \\
                 Symbol List / 396 \\
                 Index / 405",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1998:R
author: Jonathan Borwein and Kwok-Kwong Stephen Choi
title: On the representations of $ x y + y z + z x $
type: Report
institution: Department of Mathematics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 8
year: 1998
bibdate: Thu Sep 01 08:48:35 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 08:48:35 ???
URL: http://docserver.carma.newcastle.edu.au/212
remark: Undated, but PDF file metadata has 98:119-Borwein-Choi.dvi. No abstract
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein and Kwok-Kwong Stephen Choi
rawtitle: On the representations of $ x y + y z + z x $
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@TechReport{Borwein:1998:R,
  author =       "Jonathan Borwein and Kwok-Kwong Stephen Choi",
  title =        "On the representations of $ x y + y z + z x $",
  type =         "Report",
  institution =  "Department of Mathematics, Simon Fraser University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "8",
  year =         "1998",
  bibdate =      "Thu Sep 01 08:48:35 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/212",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Undated, but PDF file metadata has
                 98:119-Borwein-Choi.dvi. No abstract",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1998:SVM
author: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lisonek
title: Special Values of Multiple Polylogarithms
type: CECM Research Report
number: 98-106
institution: inst-CECM
address: inst-CECM:adr
pages: 45
day: 14
month: may
monthnumber: 5
year: 1998
bibdate: Thu Sep 01 07:48:47 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 07:48:47 ???
URL: http://docserver.carma.newcastle.edu.au/200
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lison{\v{e}}k
rawtitle: Special Values of Multiple Polylogarithms
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, we have been forced to consider multidimensional extensions encompassing the classical polylogarithm, Euler sums, and the Riemann zeta function. Here, we provide a general framework within which previously isolated results can now be properly understood. Applying the theory developed herein, we prove several previously conjectured evaluations, including a longstanding conjecture of Don Zagier.

rawabstract:
Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, we have been forced to consider multidimensional extensions encompassing the classical polylogarithm, Euler sums, and the Riemann zeta function. Here, we provide a general framework within which previously isolated results can now be properly understood. Applying the theory developed herein, we prove several previously conjectured evaluations, including a longstanding conjecture of Don Zagier.

entry:
@TechReport{Borwein:1998:SVM,
  author =       "Jonathan M. Borwein and David M. Bradley and David J.
                 Broadhurst and Petr Lison{\v{e}}k",
  title =        "Special Values of Multiple Polylogarithms",
  type =         "CECM Research Report",
  number =       "98-106",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "45",
  day =          "14",
  month =        may,
  year =         "1998",
  bibdate =      "Thu Sep 01 07:48:47 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/200",
  abstract =     "Historically, the polylogarithm has attracted
                 specialists and non-specialists alike with its lovely
                 evaluations. Much the same can be said for Euler sums
                 (or multiple harmonic sums), which, within the past
                 decade, have arisen in combinatorics, knot theory and
                 high-energy physics. More recently, we have been forced
                 to consider multidimensional extensions encompassing
                 the classical polylogarithm, Euler sums, and the
                 Riemann zeta function. Here, we provide a general
                 framework within which previously isolated results can
                 now be properly understood. Applying the theory
                 developed herein, we prove several previously
                 conjectured evaluations, including a longstanding
                 conjecture of Don Zagier.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:1998:TAP
author: Jonathan Borwein
title: Talking about Pi
pages: 45
day: 20
month: jan
monthnumber: 1
year: 1998
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
note: The original URL is no longer found, but the archive URL worked on 26-Apr-2011.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein
rawnote: The original URL is no longer found, but the archive URL worked on 26-Apr-2011.
rawtitle: Talking about Pi
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/pi.bib

entry:
@Unpublished{Borwein:1998:TAP,
  author =       "Jonathan Borwein",
  title =        "Talking about Pi",
  day =          "20",
  month =        jan,
  year =         "1998",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  note =         "The original URL is no longer found, but the archive
                 URL worked on 26-Apr-2011.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Marechal:1998:APR
author: P. Marechal and D. Togane and A. Celler and J. M. Borwein
booktitle: 1998 IEEE Nuclear Science Symposium. Conference Record. Toronto, ON, Canada, November 8--14, 1998
title: Assessment of the performance of reconstruction processes for computed tomography
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1353--1357
year: 1998
DOI: https://doi.org/10.1109/NSSMIC.1998.774404
ISSN: 1082-3654 OR 10823654
ISSNL: 1082-3654 OR 10823654
bibdate: Fri Aug 12 11:41:45 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 11:41:45 ???
URL: http://docserver.carma.newcastle.edu.au/1529/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: P. Marechal and D. Togane and A. Celler and J. M. Borwein
rawbooktitle: {1998 IEEE Nuclear Science Symposium. Conference Record. Toronto, ON, Canada, November 8--14, 1998}
rawtitle: Assessment of the performance of reconstruction processes for computed tomography
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
This paper deals with the assessment of the performance of reconstruction methods for computed tomography, including filtered backprojection and `entropy-like' methods. For each of these methods, the influence of errors in the measured data on the reconstructed image is analyzed. A small perturbation of the data vector induces a perturbation of the reconstructed object which can be computed by means of the sensitivity matrix. Using appropriate matrix computation techniques, an upper bound on the size of the reconstruction error is determined, as well as the pattern of noise in the sinogram that will result in the largest reconstruction error. Simulations will illustrate our analysis and demonstrate its utility in the interpretation of computed images and in the selection of reconstruction parameters

keywords:
Attenuation; computed tomography; Computed tomography; computerised tomography; Convolution; data vector; entropy-like methods; filtered backprojection; Image analysis; image reconstruction; Image reconstruction; image reconstruction processes; Integral equations; interpolation; inverse problems; Inverse problems; iterative methods; Mathematics; matrix computation techniques; maximum entropy methods; medical image processing; pattern of noise; performance assessment; positron emission tomography; Radon transforms; Radon-type inverse problem; reconstruction error size; reconstruction parameters selection; regularization scheme; sensitivity analysis; sensitivity matrix; singular value decomposition; sinogram; small perturbation; Transforms; upper bound; X-ray scattering

rawabstract:
This paper deals with the assessment of the performance of reconstruction methods for computed tomography, including filtered backprojection and `entropy-like' methods. For each of these methods, the influence of errors in the measured data on the reconstructed image is analyzed. A small perturbation of the data vector induces a perturbation of the reconstructed object which can be computed by means of the sensitivity matrix. Using appropriate matrix computation techniques, an upper bound on the size of the reconstruction error is determined, as well as the pattern of noise in the sinogram that will result in the largest reconstruction error. Simulations will illustrate our analysis and demonstrate its utility in the interpretation of computed images and in the selection of reconstruction parameters

entry:
@InProceedings{Marechal:1998:APR,
  author =       "P. Marechal and D. Togane and A. Celler and J. M.
                 Borwein",
  booktitle =    "{1998 IEEE Nuclear Science Symposium. Conference
                 Record. Toronto, ON, Canada, November 8--14, 1998}",
  title =        "Assessment of the performance of reconstruction
                 processes for computed tomography",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1353--1357",
  year =         "1998",
  DOI =          "https://doi.org/10.1109/NSSMIC.1998.774404",
  ISSN =         "1082-3654",
  ISSN-L =       "1082-3654",
  bibdate =      "Fri Aug 12 11:41:45 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1529/",
  abstract =     "This paper deals with the assessment of the
                 performance of reconstruction methods for computed
                 tomography, including filtered backprojection and
                 `entropy-like' methods. For each of these methods, the
                 influence of errors in the measured data on the
                 reconstructed image is analyzed. A small perturbation
                 of the data vector induces a perturbation of the
                 reconstructed object which can be computed by means of
                 the sensitivity matrix. Using appropriate matrix
                 computation techniques, an upper bound on the size of
                 the reconstruction error is determined, as well as the
                 pattern of noise in the sinogram that will result in
                 the largest reconstruction error. Simulations will
                 illustrate our analysis and demonstrate its utility in
                 the interpretation of computed images and in the
                 selection of reconstruction parameters",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Attenuation; computed tomography; Computed tomography;
                 computerised tomography; Convolution; data vector;
                 entropy-like methods; filtered backprojection; Image
                 analysis; image reconstruction; Image reconstruction;
                 image reconstruction processes; Integral equations;
                 interpolation; inverse problems; Inverse problems;
                 iterative methods; Mathematics; matrix computation
                 techniques; maximum entropy methods; medical image
                 processing; pattern of noise; performance assessment;
                 positron emission tomography; Radon transforms;
                 Radon-type inverse problem; reconstruction error size;
                 reconstruction parameters selection; regularization
                 scheme; sensitivity analysis; sensitivity matrix;
                 singular value decomposition; sinogram; small
                 perturbation; Transforms; upper bound; X-ray
                 scattering",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Bauschke:1999:COM
author: Heinz H. Bauschke and Jonathan M. Borwein
editor: J. Giles and B. Ninness
title: Conical open mapping theorems and regularity
volume: 36
pages: 1--10
year: 1999
bibdate: Mon Aug 15 14:33:16 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.15 14:33:16 ???
URL: http://docserver.carma.newcastle.edu.au/208/
remark: Preprint PDF file of 14 pages is dated 10-Nov-1998.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein
raweditor: J. Giles and B. Ninness
rawtitle: Conical open mapping theorems and regularity
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
booktitle:
Proceedings of the Centre for Mathematics and its Applications (Australian National University) National Symposium on Functional Analysis, Optimization and Applications, March 1998

abstract:
Suppose $T$ is a continuous linear operator between two Hilbert spaces $X$ and $Y$ and let $K$ be a closed convex nonempty cone in $X$. We investigate the possible existence of $ delta > 0$ such that $ delta B_Y cap T(K) subseteq T(B_X cap K)$, where $ B_X$, $ B_Y$ denote the closed unit balls in $X$ and $Y$ respectively. This property, which we call openness relative to $K$, is a generalization of the classical openness of linear operators. We relate relative openness to Jameson's property (G), to the strong conical hull intersection property, to bounded linear regularity, and to metric regularity. Our results allow a simple construction of two closed convex cones that have the strong conical hull intersection property but fail to be boundedly linearly regular.

rawabstract:
Suppose $T$ is a continuous linear operator between two Hilbert spaces $X$ and $Y$ and let $K$ be a closed convex nonempty cone in $X$. We investigate the possible existence of $ \delta > 0$ such that $ \delta B_Y \cap T(K) \subseteq T(B_X \cap K)$, where $ B_X$, $ B_Y$ denote the closed unit balls in $X$ and $Y$ respectively. This property, which we call openness relative to $K$, is a generalization of the classical openness of linear operators. We relate relative openness to Jameson's property (G), to the strong conical hull intersection property, to bounded linear regularity, and to metric regularity. Our results allow a simple construction of two closed convex cones that have the strong conical hull intersection property but fail to be boundedly linearly regular.

rawbooktitle:
{Proceedings of the Centre for Mathematics and its Applications (Australian National University) National Symposium on Functional Analysis, Optimization and Applications, March 1998}

entry:
@InProceedings{Bauschke:1999:COM,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein",
  editor =       "J. Giles and B. Ninness",
  booktitle =    "{Proceedings of the Centre for Mathematics and its
                 Applications (Australian National University) National
                 Symposium on Functional Analysis, Optimization and
                 Applications, March 1998}",
  title =        "Conical open mapping theorems and regularity",
  volume =       "36",
  publisher =    "????",
  address =      "????",
  pages =        "1--10",
  year =         "1999",
  bibdate =      "Mon Aug 15 14:33:16 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/208/",
  abstract =     "Suppose $T$ is a continuous linear operator between
                 two Hilbert spaces $X$ and $Y$ and let $K$ be a closed
                 convex nonempty cone in $X$. We investigate the
                 possible existence of $ \delta > 0$ such that $ \delta
                 B_Y \cap T(K) \subseteq T(B_X \cap K)$, where $ B_X$, $
                 B_Y$ denote the closed unit balls in $X$ and $Y$
                 respectively. This property, which we call openness
                 relative to $K$, is a generalization of the classical
                 openness of linear operators. We relate relative
                 openness to Jameson's property (G), to the strong
                 conical hull intersection property, to bounded linear
                 regularity, and to metric regularity. Our results allow
                 a simple construction of two closed convex cones that
                 have the strong conical hull intersection property but
                 fail to be boundedly linearly regular.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "Preprint PDF file of 14 pages is dated 10-Nov-1998.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:1999:EAD
author: Heinz H. Bauschke and Dominikus Noll and Anna Celler and Jonathan M. Borwein
title: An EM algorithm for dynamic SPECT
journal: j-IEEE-TRANS-MED-IMAG
volume: 18
number: 3
pages: 252--261
month: mar
monthnumber: 3
year: 1999
CODEN: ITMID4
DOI: https://doi.org/10.1109/42.764899
ISSN: 0278-0062 (print), 1558-254x (electronic) OR 02780062 (print), 1558254x (electronic)
ISSNL: 0278-0062 OR 02780062
bibdate: Wed Aug 10 12:08:56 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 12:08:56 ???
URL: http://docserver.carma.newcastle.edu.au/187; http://www.ncbi.nlm.nih.gov/pubmed/10363703
fjournal: IEEE Transactions on Medical Imaging
remark: Preprint is 19 pages, and titled booktitle An EM algorithm for dynamic SPECT tomography.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=42
rawauthor: Heinz H. Bauschke and Dominikus Noll and Anna Celler and Jonathan M. Borwein
rawtitle: An {EM} algorithm for dynamic {SPECT}
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
keywords:
Algorithms; arbitrary decaying activities; Cameras; compartmental modeling; Computed tomography; dynamic SPECT; EM algorithm; exponentials sum; Face detection; Head; Heuristic algorithms; Humans; Instruments; M step; medical diagnostic imaging; Models, Statistical; Nuclear medicine; nuclear medicine; numerical tests; Pharmaceuticals; physiological models; Positron emission tomography; Reproducibility of Results; single photon emission computed tomography; Single photon emission computed tomography; Tomography, Emission-Computed, Single-Photon; underlying probabilistic models

entry:
@Article{Bauschke:1999:EAD,
  author =       "Heinz H. Bauschke and Dominikus Noll and Anna Celler
                 and Jonathan M. Borwein",
  title =        "An {EM} algorithm for dynamic {SPECT}",
  journal =      j-IEEE-TRANS-MED-IMAG,
  volume =       "18",
  number =       "3",
  pages =        "252--261",
  month =        mar,
  year =         "1999",
  CODEN =        "ITMID4",
  DOI =          "https://doi.org/10.1109/42.764899",
  ISSN =         "0278-0062 (print), 1558-254x (electronic)",
  ISSN-L =       "0278-0062",
  bibdate =      "Wed Aug 10 12:08:56 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/187;
                 http://www.ncbi.nlm.nih.gov/pubmed/10363703",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "IEEE Transactions on Medical Imaging",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=42",
  keywords =     "Algorithms; arbitrary decaying activities; Cameras;
                 compartmental modeling; Computed tomography; dynamic
                 SPECT; EM algorithm; exponentials sum; Face detection;
                 Head; Heuristic algorithms; Humans; Instruments; M
                 step; medical diagnostic imaging; Models, Statistical;
                 Nuclear medicine; nuclear medicine; numerical tests;
                 Pharmaceuticals; physiological models; Positron
                 emission tomography; Reproducibility of Results; single
                 photon emission computed tomography; Single photon
                 emission computed tomography; Tomography,
                 Emission-Computed, Single-Photon; underlying
                 probabilistic models",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "Preprint is 19 pages, and titled \booktitle{An EM
                 algorithm for dynamic SPECT tomography}.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:1999:MMD
author: Heinz H. Bauschke and Jonathan M. Borwein
journal: j-PAC-J-MATH
volume: 189
number: 1
pages: 1--20
year: 1999
CODEN: PJMAAI
DOI: https://doi.org/10.2140/pjm.1999.189.1
ISSN: 0030-8730 (print), 1945-5844 (electronic) OR 00308730 (print), 19455844 (electronic)
ISSNL: 0030-8730 OR 00308730
MRclass: 47H05 (47B99 49J52)
MRnumber: 1687802
MRreviewer: Pando Georgiev
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/180/
fjournal: Pacific Journal of Mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://msp.org/pjm
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
title:
Maximal monotonicity of dense type, local maximal monotonicity, and monotonicity of the conjugate are all the same for continuous linear operators

entry:
@Article{Bauschke:1999:MMD,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein",
  title =        "Maximal monotonicity of dense type, local maximal
                 monotonicity, and monotonicity of the conjugate are all
                 the same for continuous linear operators",
  journal =      j-PAC-J-MATH,
  volume =       "189",
  number =       "1",
  pages =        "1--20",
  year =         "1999",
  CODEN =        "PJMAAI",
  DOI =          "https://doi.org/10.2140/pjm.1999.189.1",
  ISSN =         "0030-8730 (print), 1945-5844 (electronic)",
  ISSN-L =       "0030-8730",
  MRclass =      "47H05 (47B99 49J52)",
  MRnumber =     "1687802",
  MRreviewer =   "Pando Georgiev",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/180/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Pacific Journal of Mathematics",
  journal-URL =  "http://msp.org/pjm",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:1999:SCH
author: Heinz H. Bauschke and Jonathan M. Borwein and Wu Li
journal: j-MATH-PROG
volume: 86
number: 1, Ser. A
pages: 135--160
year: 1999
CODEN: MHPGA4
DOI: https://doi.org/10.1007/s101070050083
ISSN: 0025-5610 (print), 1436-4646 (electronic) OR 00255610 (print), 14364646 (electronic)
ISSNL: 0025-5610 OR 00255610
MRclass: 90C46 (41A29 90C31)
MRnumber: 1712477
MRreviewer: Charles K. Chui
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/195/
fjournal: Mathematical Programming. A Publication of the Mathematical Programming Society
remark: CECM Research Report 98:107.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/10107
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein and Wu Li
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
title:
Strong conical hull intersection property, bounded linear regularity, Jameson's property $ (G) $, and error bounds in convex optimization

rawtitle:
Strong conical hull intersection property, bounded linear regularity, {Jameson}'s property {$ (G) $}, and error bounds in convex optimization

entry:
@Article{Bauschke:1999:SCH,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein and Wu Li",
  title =        "Strong conical hull intersection property, bounded
                 linear regularity, {Jameson}'s property {$ (G) $}, and
                 error bounds in convex optimization",
  journal =      j-MATH-PROG,
  volume =       "86",
  number =       "1, Ser. A",
  pages =        "135--160",
  year =         "1999",
  CODEN =        "MHPGA4",
  DOI =          "https://doi.org/10.1007/s101070050083",
  ISSN =         "0025-5610 (print), 1436-4646 (electronic)",
  ISSN-L =       "0025-5610",
  MRclass =      "90C46 (41A29 90C31)",
  MRnumber =     "1712477",
  MRreviewer =   "Charles K. Chui",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/195/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematical Programming. A Publication of the
                 Mathematical Programming Society",
  journal-URL =  "http://link.springer.com/journal/10107",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "CECM Research Report 98:107.",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borowski:1999:DMa
author: E. J. (Ephraim J.) Borowski and Jonathan M. Borwein
title: Dictionary of mathematics
publisher: Unwin Hyman
address: London, UK
pages: 660
year: 1999
ISBN: 0-261-67198-7 OR 0261671987
ISBN13: 978-0-261-67198-0 OR 9780261671980
bibdate: Tue Aug 16 09:03:32 MDT 2016
bibtimestamp: 2016.08.16 09:03:32 MDT
subject: Mathematics; Dictionaries
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: E. J. (Ephraim J.) Borowski and Jonathan M. Borwein
rawtitle: Dictionary of mathematics
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Book{Borowski:1999:DMa,
  author =       "E. J. (Ephraim J.) Borowski and Jonathan M. Borwein",
  title =        "Dictionary of mathematics",
  publisher =    "Unwin Hyman",
  address =      "London, UK",
  pages =        "660",
  year =         "1999",
  ISBN =         "0-261-67198-7",
  ISBN-13 =      "978-0-261-67198-0",
  LCCN =         "????",
  bibdate =      "Tue Aug 16 09:03:32 MDT 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject =      "Mathematics; Dictionaries",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borowski:1999:DMb
author: E. J. (Ephraim J.) Borowski and Jonathan M. Borwein
title: Dictionary of mathematics
publisher: pub-HARPERCOLLINS
address: pub-HARPERCOLLINS:adr
pages: 672
year: 1999
ISBN: 0-00-434347-6 (paperback) OR 0004343476 (paperback)
ISBN13: 978-0-00-434347-1 (paperback) OR 9780004343471 (paperback)
bibdate: Mon Oct 23 07:36:34 MDT 2017
bibtimestamp: 2017.10.23 07:36:34 MDT
remark: Originally published in cite Borowski:1988:DM.
subject: Mathematics; Dictionaries; Mathematics.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: E. J. (Ephraim J.) Borowski and Jonathan M. Borwein
rawtitle: Dictionary of mathematics
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
This dictionary of mathematics contains over 9,000 definitions and 400 diagrams and covers subjects such as abstract analysis; number theory; topology; vectors; differential equations and more.

rawabstract:
This dictionary of mathematics contains over 9,000 definitions and 400 diagrams and covers subjects such as abstract analysis; number theory; topology; vectors; differential equations and more.

entry:
@Book{Borowski:1999:DMb,
  author =       "E. J. (Ephraim J.) Borowski and Jonathan M. Borwein",
  title =        "Dictionary of mathematics",
  publisher =    pub-HARPERCOLLINS,
  address =      pub-HARPERCOLLINS:adr,
  pages =        "672",
  year =         "1999",
  ISBN =         "0-00-434347-6 (paperback)",
  ISBN-13 =      "978-0-00-434347-1 (paperback)",
  LCCN =         "????",
  bibdate =      "Mon Oct 23 07:36:34 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  abstract =     "This dictionary of mathematics contains over 9,000
                 definitions and 400 diagrams and covers subjects such
                 as abstract analysis; number theory; topology; vectors;
                 differential equations and more.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Originally published in \cite{Borowski:1988:DM}.",
  subject =      "Mathematics; Dictionaries; Mathematics.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1999:CEL
author: Jonathan Borwein and Yves Lucet and Boris Mordukhovich
title: Compactly epi-Lipschitzian convex sets and functions in normed spaces
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 20
day: 9
month: jun
monthnumber: 6
year: 1999
bibdate: Thu Sep 01 08:42:56 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 08:42:56 ???
note: Published in cite Borwein:2000:CEL.
URL: http://docserver.carma.newcastle.edu.au/210/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein and Yves Lucet and Boris Mordukhovich
rawnote: Published in \cite{Borwein:2000:CEL}.
rawtitle: Compactly epi-{Lipschitzian} convex sets and functions in normed spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We provide several characterizations of compact epi-Lipschitzness for closed convex sets in normed vector spaces. In particular, we show that a closed convex set is compactly epi-Lipschitzian if and only if it has nonempty relative interior, finite codimension, and spans a closed subspace.par Next, we establish that all boundary points of compactly epi-Lipschitzian sets are proper support points. We provide the corresponding results for functions hy using inf-convolutions and the Legendre Fenchel transform. We also give an application to constrained optimization with compactly epi-Lipschitzian data via a generalized Slater condition involving relative interiors.

rawabstract:
We provide several characterizations of compact epi-Lipschitzness for closed convex sets in normed vector spaces. In particular, we show that a closed convex set is compactly epi-Lipschitzian if and only if it has nonempty relative interior, finite codimension, and spans a closed subspace.\par Next, we establish that all boundary points of compactly epi-Lipschitzian sets are proper support points. We provide the corresponding results for functions hy using inf-convolutions and the Legendre Fenchel transform. We also give an application to constrained optimization with compactly epi-Lipschitzian data via a generalized Slater condition involving relative interiors.

entry:
@TechReport{Borwein:1999:CEL,
  author =       "Jonathan Borwein and Yves Lucet and Boris
                 Mordukhovich",
  title =        "Compactly epi-{Lipschitzian} convex sets and functions
                 in normed spaces",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "20",
  day =          "9",
  month =        jun,
  year =         "1999",
  bibdate =      "Thu Sep 01 08:42:56 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2000:CEL}.",
  URL =          "http://docserver.carma.newcastle.edu.au/210/",
  abstract =     "We provide several characterizations of compact
                 epi-Lipschitzness for closed convex sets in normed
                 vector spaces. In particular, we show that a closed
                 convex set is compactly epi-Lipschitzian if and only if
                 it has nonempty relative interior, finite codimension,
                 and spans a closed subspace.\par

                 Next, we establish that all boundary points of
                 compactly epi-Lipschitzian sets are proper support
                 points. We provide the corresponding results for
                 functions hy using inf-convolutions and the Legendre
                 Fenchel transform. We also give an application to
                 constrained optimization with compactly
                 epi-Lipschitzian data via a generalized Slater
                 condition involving relative interiors.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1999:CSFa
author: Jonathan M. Borwein and John Read and Adrian S. Lewis and Qiji Zhu
title: Convex spectral functions of compact operators
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 27
day: 10
month: mar
monthnumber: 3
year: 1999
bibdate: Thu Sep 01 10:08:54 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 10:08:54 ???
note: Published in cite Borwein:2000:CSF.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and John Read and Adrian S. Lewis and Qiji Zhu
rawnote: Published in \cite{Borwein:2000:CSF}.
rawtitle: Convex spectral functions of compact operators
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We consider functions on the space of compact self-adjoint Hilbert space operators. Specifically, we study those extended-real functions which depend only on the operators' spectral sequences. Examples include the norms of the Schatten $p$-spaces, the Calderen norms, the $k$'th largest eigenvalue, and some infinite-dimensional self-concordant barriers. We show how various convex and nonsmooth-analytic properties of such functions follow from the corresponding properties of the restrictions to the space of diagonal operators, and we derive subdifferential and conjugacy formulas.

rawabstract:
We consider functions on the space of compact self-adjoint Hilbert space operators. Specifically, we study those extended-real functions which depend only on the operators' spectral sequences. Examples include the norms of the Schatten $p$-spaces, the Calder{\'e}n norms, the $k$'th largest eigenvalue, and some infinite-dimensional self-concordant barriers. We show how various convex and nonsmooth-analytic properties of such functions follow from the corresponding properties of the restrictions to the space of diagonal operators, and we derive subdifferential and conjugacy formulas.

entry:
@TechReport{Borwein:1999:CSFa,
  author =       "Jonathan M. Borwein and John Read and Adrian S. Lewis
                 and Qiji Zhu",
  title =        "Convex spectral functions of compact operators",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "27",
  day =          "10",
  month =        mar,
  year =         "1999",
  bibdate =      "Thu Sep 01 10:08:54 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2000:CSF}.",
  abstract =     "We consider functions on the space of compact
                 self-adjoint Hilbert space operators. Specifically, we
                 study those extended-real functions which depend only
                 on the operators' spectral sequences. Examples include
                 the norms of the Schatten $p$-spaces, the Calder{\'e}n
                 norms, the $k$'th largest eigenvalue, and some
                 infinite-dimensional self-concordant barriers. We show
                 how various convex and nonsmooth-analytic properties of
                 such functions follow from the corresponding properties
                 of the restrictions to the space of diagonal operators,
                 and we derive subdifferential and conjugacy formulas.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1999:CSFb
author: Jonathan M. Borwein and Adrian S. Lewis and Qiji J. Zhu
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 18
year: 1999
MRclass: 49J52, 47B10
bibdate: Thu Sep 01 10:33:31 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 10:33:31 ???
URL: http://docserver.carma.newcastle.edu.au/251/
keywords: Convex spectral functions; differentiability; rearrangement invariant functions
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Adrian S. Lewis and Qiji J. Zhu
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Convex spectral functions of compact operators, Part II: Lower semicontinuity and rearrangement invariance

abstract:
It was shown in Part I of this work that the Gateaux differentiability of a convex unitarily invariant function is characterized by that of a similar induced rearrangement invariant function on the corresponding spectral space. A natural question is then whether this is also the case for Frechet differentibility. In this paper we show the answer is positive. Although the result appears very natural, the proof turns out to be quite technically involved.

rawabstract:
It was shown in Part I of this work that the Gateaux differentiability of a convex unitarily invariant function is characterized by that of a similar induced rearrangement invariant function on the corresponding spectral space. A natural question is then whether this is also the case for Fr{\'e}chet differentibility. In this paper we show the answer is positive. Although the result appears very natural, the proof turns out to be quite technically involved.

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

entry:
@TechReport{Borwein:1999:CSFb,
  author =       "Jonathan M. Borwein and Adrian S. Lewis and Qiji J.
                 Zhu",
  title =        "Convex spectral functions of compact operators, {Part
                 II}: {Lower} semicontinuity and rearrangement
                 invariance",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "18",
  year =         "1999",
  MRclass =      "49J52, 47B10",
  bibdate =      "Thu Sep 01 10:33:31 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/251/",
  abstract =     "It was shown in Part I of this work that the Gateaux
                 differentiability of a convex unitarily invariant
                 function is characterized by that of a similar induced
                 rearrangement invariant function on the corresponding
                 spectral space. A natural question is then whether this
                 is also the case for Fr{\'e}chet differentibility. In
                 this paper we show the answer is positive. Although the
                 result appears very natural, the proof turns out to be
                 quite technically involved.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Convex spectral functions; differentiability;
                 rearrangement invariant functions",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1999:ESB
author: Jonathan M. Borwein and Boris S. Mordukhovich and Yongheng Shao
title: On the Equivalence of Some Basic Principles in Variational Analysis
journal: j-J-MATH-ANAL-APPL
volume: 229
number: 1
pages: 228--257
year: 1999
CODEN: JMANAK
DOI: https://doi.org/10.1006/jmaa.1998.6157
ISSN: 0022-247X (print), 1096-0813 (electronic) OR 0022247X (print), 10960813 (electronic)
ISSNL: 0022-247X OR 0022247X
MRclass: 49J52 (46N10)
MRnumber: 1664320
MRreviewer: Abderrahim Jourani
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
fjournal: Journal of Mathematical Analysis and Applications
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/0022247X
rawauthor: Jonathan M. Borwein and Boris S. Mordukhovich and Yongheng Shao
rawtitle: On the Equivalence of Some Basic Principles in Variational Analysis
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/192/; http://www.sciencedirect.com/science/article/pii/S0022247X98961571

abstract:
The primary goal of this paper is to study relationships between certain basic principles of variational analysis and its applications to nonsmooth calculus and optimization. Considering a broad class of Banach spaces admitting smooth renorms with respect to some bornology, we establish an equivalence between useful versions of a smooth variational principle for lower semicontinuous functions, an extremal principle for nonconvex sets, and an enhanced fuzzy sum rule formulated in terms of viscosity normals and subgradients with controlled ranks. Further refinements of the equivalence result are obtained in the case of a Frechet differentiable norm. Based on the new enhanced sum rule, we provide a simplified proof for the refined sequential description of approximate normals and subgradients in smooth spaces.

keywords:
fuzzy calculus; generalized differentiation; Nonsmooth analysis; smooth Banach spaces; variational and extremal principles; viscosity normals and subdifferentials

rawabstract:
The primary goal of this paper is to study relationships between certain basic principles of variational analysis and its applications to nonsmooth calculus and optimization. Considering a broad class of Banach spaces admitting smooth renorms with respect to some bornology, we establish an equivalence between useful versions of a smooth variational principle for lower semicontinuous functions, an extremal principle for nonconvex sets, and an enhanced fuzzy sum rule formulated in terms of viscosity normals and subgradients with controlled ranks. Further refinements of the equivalence result are obtained in the case of a Fr{\'e}chet differentiable norm. Based on the new enhanced sum rule, we provide a simplified proof for the refined sequential description of approximate normals and subgradients in smooth spaces.

entry:
@Article{Borwein:1999:ESB,
  author =       "Jonathan M. Borwein and Boris S. Mordukhovich and
                 Yongheng Shao",
  title =        "On the Equivalence of Some Basic Principles in
                 Variational Analysis",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "229",
  number =       "1",
  pages =        "228--257",
  year =         "1999",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1006/jmaa.1998.6157",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "49J52 (46N10)",
  MRnumber =     "1664320",
  MRreviewer =   "Abderrahim Jourani",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/192/;
                 http://www.sciencedirect.com/science/article/pii/S0022247X98961571",
  abstract =     "The primary goal of this paper is to study
                 relationships between certain basic principles of
                 variational analysis and its applications to nonsmooth
                 calculus and optimization. Considering a broad class of
                 Banach spaces admitting smooth renorms with respect to
                 some bornology, we establish an equivalence between
                 useful versions of a smooth variational principle for
                 lower semicontinuous functions, an extremal principle
                 for nonconvex sets, and an enhanced fuzzy sum rule
                 formulated in terms of viscosity normals and
                 subgradients with controlled ranks. Further refinements
                 of the equivalence result are obtained in the case of a
                 Fr{\'e}chet differentiable norm. Based on the new
                 enhanced sum rule, we provide a simplified proof for
                 the refined sequential description of approximate
                 normals and subgradients in smooth spaces.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "fuzzy calculus; generalized differentiation; Nonsmooth
                 analysis; smooth Banach spaces; variational and
                 extremal principles; viscosity normals and
                 subdifferentials",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1999:ETE
author: Jonathan M. Borwein and Robert M. Corless
title: Emerging tools for experimental mathematics
journal: j-AMER-MATH-MONTHLY
volume: 106
number: 10
pages: 889--909
year: 1999
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2589743
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 68W30 (00A05 11Yxx)
MRnumber: 1732501
MRreviewer: Michael M. Dediu
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/203/; https://www.jstor.org/stable/2589743
fjournal: American Mathematical Monthly
remark: CECM Research Report 98:110.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.jstor.org/journals/00029890.html
rawauthor: Jonathan M. Borwein and Robert M. Corless
rawtitle: Emerging tools for experimental mathematics
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1999:ETE,
  author =       "Jonathan M. Borwein and Robert M. Corless",
  title =        "Emerging tools for experimental mathematics",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "106",
  number =       "10",
  pages =        "889--909",
  year =         "1999",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2589743",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "68W30 (00A05 11Yxx)",
  MRnumber =     "1732501",
  MRreviewer =   "Michael M. Dediu",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/203/;
                 https://www.jstor.org/stable/2589743",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Research Report 98:110.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1999:GSBa
author: Jonathan M. Borwein and Warren B. Moors and Xianfu Wang
title: Generalized subdifferentials: a Baire categorical approach
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 19
day: 8
month: mar
monthnumber: 3
year: 1999
bibdate: Thu Sep 01 10:00:12 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 10:00:12 ???
note: Published in cite Borwein:2001:GSB.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Warren B. Moors and Xianfu Wang
rawnote: Published in \cite{Borwein:2001:GSB}.
rawtitle: Generalized subdifferentials: a {Baire} categorical approach
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We use Baire categorical arguments to construct pathological locally Lipschitz functions. The origins of this approach can be traced back to Banach and Mazurkiewicz (1931) who independently used similar categorical arguments to show that ``almost every continuous real-valued function defined on [0,1] is nowhere differentiable''. As with the results of Banach and Mazurkiewicz, it appears that it is easier to show that almost every function possesses a certain property than to construct a single concrete example. Among the most striking results contained in this paper are: Almost every 1-Lipschitz function defined on a Banach space has a Clarke subdifferential mapping that is identically equal to the dual ball; if T-1; T-2,ldots ,T-n is a family of maximal cyclically monotone operators defined on a Banach space X then there exists a real-valued locally Lipschitz function g such that partial derivative (0g)(x) =co T-1(x); T-2(x),ldots ,T-n(x) for each x is an element of X; in a separable Banach space each non-empty weak* compact convex subset in the dual space is identically equal to the approximate subdifferential mapping of some Lipschitz function and for locally Lipschitz functions defined on separable spaces the notions of strong and weak integrability coincide.

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

entry:
@TechReport{Borwein:1999:GSBa,
  author =       "Jonathan M. Borwein and Warren B. Moors and Xianfu
                 Wang",
  title =        "Generalized subdifferentials: a {Baire} categorical
                 approach",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "19",
  day =          "8",
  month =        mar,
  year =         "1999",
  bibdate =      "Thu Sep 01 10:00:12 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2001:GSB}.",
  abstract =     "We use Baire categorical arguments to construct
                 pathological locally Lipschitz functions. The origins
                 of this approach can be traced back to Banach and
                 Mazurkiewicz (1931) who independently used similar
                 categorical arguments to show that ``almost every
                 continuous real-valued function defined on [0,1] is
                 nowhere differentiable''. As with the results of Banach
                 and Mazurkiewicz, it appears that it is easier to show
                 that almost every function possesses a certain property
                 than to construct a single concrete example. Among the
                 most striking results contained in this paper are:
                 Almost every 1-Lipschitz function defined on a Banach
                 space has a Clarke subdifferential mapping that is
                 identically equal to the dual ball; if \{T-1;
                 T-2,\ldots{},T-n\} is a family of maximal cyclically
                 monotone operators defined on a Banach space X then
                 there exists a real-valued locally Lipschitz function g
                 such that partial derivative (0g)(x) =co \{T-1(x);
                 T-2(x),\ldots{},T-n(x)\} for each x is an element of X;
                 in a separable Banach space each non-empty weak*
                 compact convex subset in the dual space is identically
                 equal to the approximate subdifferential mapping of
                 some Lipschitz function and for locally Lipschitz
                 functions defined on separable spaces the notions of
                 strong and weak integrability coincide.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1999:GSBb
author: Jonathan M. Borwein and Warren B. Moors and Xianfu Wang
title: Generalized subdifferentials: a Baire categorical approach
institution: inst-CECM
address: inst-CECM:adr
pages: 6
day: 15
month: apr
monthnumber: 4
year: 1999
MRclass: 49J52, 26A27
bibdate: Thu Sep 01 10:03:41 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 10:03:41 ???
note: Published in cite Borwein:1999:GSBc.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Warren B. Moors and Xianfu Wang
rawnote: Published in \cite{Borwein:1999:GSBc}.
rawtitle: Generalized subdifferentials: a {Baire} categorical approach
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Dans ce compte rendu, nous decrivons comment utiliser des arguments de type categorie de Baire pour construire certaines fonctions localement Lipschitz pathologiques. Les origines de cette approche remontent a Banach et Mazurkiewicz (1931) qui, de maniere independante, utiliserent une approche semblable pour mon- trer que ``presque toutes les fonctions relles continues definies sur [0,1] sont nulle part differentiables''. Comme dans les resultats de Banach et Mazurkiewicz, il s avere qu il est plus facile de montrer que presque toutes les fonctions possedent une certaine pro- priete que de construire un seul exemple concret. Apres une description du cadre de base de la construction, l'article continue en donnant de nombreuses applications. Parmis les resultats les plus surprenants, citons le suivant : ``Presque toutes les fonctions 1-Lipschitz definies sur un espace de Banach admettent une application sous-difterentielle de Clarke qui est identiquement egale a la boule unite dans l'espace dual.''

keywords:
Baire category; Banach spaces; differentiability; subdifferentials; upper semi continuous set valued map.

rawabstract:
Dans ce compte rendu, nous decrivons comment utiliser des arguments de type cat{\'e}gorie de Baire pour construire certaines fonctions localement Lipschitz pathologiques. Les origines de cette approche remontent a Banach et Mazurkiewicz (1931) qui, de mani{\'e}re ind{\'e}pendante, utilis{\'e}rent une approche semblable pour mon- trer que ``presque toutes les fonctions r{\'e}lles continues d{\'e}finies sur [0,1] sont nulle part diff{\'e}rentiables''. Comme dans les r{\'e}sultats de Banach et Mazurkiewicz, il s avere qu il est plus facile de montrer que presque toutes les fonctions possedent une certaine pro- pri{\'e}t{\'e} que de construire un seul exemple concret. Apres une description du cadre de base de la construction, l'article continue en donnant de nombreuses applications. Parmis les r{\'e}sultats les plus surprenants, citons le suivant : ``Presque toutes les fonctions 1-Lipschitz d{\'e}finies sur un espace de Banach admettent une application sous-dift{\'e}rentielle de Clarke qui est identiquement {\'e}gale a la boule unit{\'e} dans l'espace dual.''

entry:
@TechReport{Borwein:1999:GSBb,
  author =       "Jonathan M. Borwein and Warren B. Moors and Xianfu
                 Wang",
  title =        "Generalized subdifferentials: a {Baire} categorical
                 approach",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "6",
  day =          "15",
  month =        apr,
  year =         "1999",
  MRclass =      "49J52, 26A27",
  bibdate =      "Thu Sep 01 10:03:41 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:1999:GSBc}.",
  abstract =     "Dans ce compte rendu, nous decrivons comment utiliser
                 des arguments de type cat{\'e}gorie de Baire pour
                 construire certaines fonctions localement Lipschitz
                 pathologiques. Les origines de cette approche remontent
                 a Banach et Mazurkiewicz (1931) qui, de mani{\'e}re
                 ind{\'e}pendante, utilis{\'e}rent une approche
                 semblable pour mon- trer que ``presque toutes les
                 fonctions r{\'e}lles continues d{\'e}finies sur [0,1]
                 sont nulle part diff{\'e}rentiables''. Comme dans les
                 r{\'e}sultats de Banach et Mazurkiewicz, il s avere qu
                 il est plus facile de montrer que presque toutes les
                 fonctions possedent une certaine pro- pri{\'e}t{\'e}
                 que de construire un seul exemple concret. Apres une
                 description du cadre de base de la construction,
                 l'article continue en donnant de nombreuses
                 applications. Parmis les r{\'e}sultats les plus
                 surprenants, citons le suivant : ``Presque toutes les
                 fonctions 1-Lipschitz d{\'e}finies sur un espace de
                 Banach admettent une application
                 sous-dift{\'e}rentielle de Clarke qui est identiquement
                 {\'e}gale a la boule unit{\'e} dans l'espace dual.''",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Baire category; Banach spaces; differentiability;
                 subdifferentials; upper semi continuous set valued
                 map.",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1999:GSBc
author: Jonathan M. Borwein and Warren B. Moors and Xianfu Wang
title: Generalized subdifferentials: a Baire categorical approach
journal: C. R. Math. Acad. Sci. Soc. R. Can.
volume: 21
number: 4
pages: 132--138
year: 1999
ISSN: 0706-1994 OR 07061994
MRclass: 49J52 (46G05 58C20)
MRnumber: 1728265
MRreviewer: Mari{\'a}n Fabian
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/234/
remark: CECM Preprint 99:128. The journal web site has no online archives before volume 27 (2005).
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://mr.math.ca/article/
rawauthor: Jonathan M. Borwein and Warren B. Moors and Xianfu Wang
rawtitle: Generalized subdifferentials: a {Baire} categorical approach
ORCID: Borwein, Jonathan/0000-0002-1263-0646
fjournal:
Comptes Rendus Mathematiques de l'Academie des Sciences. La Societe Royale du Canada. Mathematical Reports of the Academy of Science. The Royal Society of Canada

entry:
@Article{Borwein:1999:GSBc,
  author =       "Jonathan M. Borwein and Warren B. Moors and Xianfu
                 Wang",
  title =        "Generalized subdifferentials: a {Baire} categorical
                 approach",
  journal =      "C. R. Math. Acad. Sci. Soc. R. Can.",
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  number =       "4",
  pages =        "132--138",
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  MRnumber =     "1728265",
  MRreviewer =   "Mari{\'a}n Fabian",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/234/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Comptes Rendus Math{\'e}matiques de l'Acad{\'e}mie des
                 Sciences. La Soci{\'e}t{\'e} Royale du Canada.
                 Mathematical Reports of the Academy of Science. The
                 Royal Society of Canada",
  journal-URL =  "https://mr.math.ca/article/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 99:128. The journal web site has no
                 online archives before volume 27 (2005).",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:1999:ITDb
author: J. M. Borwein and T. Stanway
editor: John Grant McGloughlin
booktitle: Canadian Mathematics Education Study Group (CMESG) Proceedings 1999 Annual Meeting
title: The impact of technology on the doing of mathematics
publisher: Memorial University Press
address: St. Johns, NL, Canada
pages: 3--6
year: 1999
bibdate: Mon Aug 15 14:30:19 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.15 14:30:19 ???
URL: http://docserver.carma.newcastle.edu.au/248/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and T. Stanway
rawbooktitle: {Canadian Mathematics Education Study Group (CMESG) Proceedings 1999 Annual Meeting}
raweditor: John Grant McGloughlin
rawtitle: The impact of technology on the doing of mathematics
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InProceedings{Borwein:1999:ITDb,
  author =       "J. M. Borwein and T. Stanway",
  editor =       "John Grant McGloughlin",
  booktitle =    "{Canadian Mathematics Education Study Group (CMESG)
                 Proceedings 1999 Annual Meeting}",
  title =        "The impact of technology on the doing of mathematics",
  publisher =    "Memorial University Press",
  address =      "St. Johns, NL, Canada",
  pages =        "3--6",
  year =         "1999",
  bibdate =      "Mon Aug 15 14:30:19 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/248/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1999:MFAa
author: Jonathan M. Borwein and Qiji J. Zhu*
title: Multifunctional and functional analytic techniques in nonsmooth analysis
type: Report
institution: Department of Mathematics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 97
day: 2
month: nov
monthnumber: 11
year: 1999
bibdate: Thu Sep 01 10:44:29 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 10:44:29 ???
URL: http://docserver.carma.newcastle.edu.au/49
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Qiji J. Zhu*
rawtitle: Multifunctional and functional analytic techniques in nonsmooth analysis
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
These lectures center on the structure of real-valued Lipschitz functions, and their generalized derivatives on Banach spaces. We pay some attention to the role of measure and category and will try to illustrate a number of different techniques. These published notes are much more detailed and comprehensive than the lectures as given. Much of this development is based on recent joint work with Warren Moors (Wellington) and others.par The exposition will be organized around the following interwoven themes.par $ bullet $ Set-valued analysis. Minimal upper semi-continuous multifunctions (`uscos and cuscos') and related topological tools. Selections and single-valuedness. Relations to differentiability.par $ bullet $ Measure and category as competing notions of smallness: Haar null sets and generic sets in Banach spaces. Other concepts of prevalence.par $ bullet $ `Utility grade' renorming theory and its application to the study of viscosity subderivatives and (partially) smooth variational principles. ``Fuzzy'' calculus and some equivalent reformulations.par $ bullet $ The structure of Lipschitz functions. Especially the calculus of essentially smooth Lipschitz functions and the vector-lattice algebra they generate. Chain rules, and questions of integrability and representability.par $ bullet $ Applications to and examples of distance functions. Minimality of distance functions and proximal normal formulae revisited. More general perturbation functions.par $ bullet $ Convex functions and related sequences in Banach space. How properties of given Banach spaces are reflected in the convex functions they support. Conjugates and subdifferentials of eigenvalue functions.

rawabstract:
These lectures center on the structure of real-valued Lipschitz functions, and their generalized derivatives on Banach spaces. We pay some attention to the role of measure and category and will try to illustrate a number of different techniques. These published notes are much more detailed and comprehensive than the lectures as given. Much of this development is based on recent joint work with Warren Moors (Wellington) and others.\par The exposition will be organized around the following interwoven themes.\par $ \bullet $ Set-valued analysis. Minimal upper semi-continuous multifunctions (`uscos and cuscos') and related topological tools. Selections and single-valuedness. Relations to differentiability.\par $ \bullet $ Measure and category as competing notions of smallness: Haar null sets and generic sets in Banach spaces. Other concepts of prevalence.\par $ \bullet $ `Utility grade' renorming theory and its application to the study of viscosity subderivatives and (partially) smooth variational principles. ``Fuzzy'' calculus and some equivalent reformulations.\par $ \bullet $ The structure of Lipschitz functions. Especially the calculus of essentially smooth Lipschitz functions and the vector-lattice algebra they generate. Chain rules, and questions of integrability and representability.\par $ \bullet $ Applications to and examples of distance functions. Minimality of distance functions and proximal normal formulae revisited. More general perturbation functions.\par $ \bullet $ Convex functions and related sequences in Banach space. How properties of given Banach spaces are reflected in the convex functions they support. Conjugates and subdifferentials of eigenvalue functions.

entry:
@TechReport{Borwein:1999:MFAa,
  author =       "Jonathan M. Borwein and Qiji J. Zhu*",
  title =        "Multifunctional and functional analytic techniques in
                 nonsmooth analysis",
  type =         "Report",
  institution =  "Department of Mathematics, Simon Fraser University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "97",
  day =          "2",
  month =        nov,
  year =         "1999",
  bibdate =      "Thu Sep 01 10:44:29 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/49",
  abstract =     "These lectures center on the structure of real-valued
                 Lipschitz functions, and their generalized derivatives
                 on Banach spaces. We pay some attention to the role of
                 measure and category and will try to illustrate a
                 number of different techniques. These published notes
                 are much more detailed and comprehensive than the
                 lectures as given. Much of this development is based on
                 recent joint work with Warren Moors (Wellington) and
                 others.\par

                 The exposition will be organized around the following
                 interwoven themes.\par

                 $ \bullet $ Set-valued analysis. Minimal upper
                 semi-continuous multifunctions (`uscos and cuscos') and
                 related topological tools. Selections and
                 single-valuedness. Relations to
                 differentiability.\par

                 $ \bullet $ Measure and category as competing notions
                 of smallness: Haar null sets and generic sets in Banach
                 spaces. Other concepts of prevalence.\par

                 $ \bullet $ `Utility grade' renorming theory and its
                 application to the study of viscosity subderivatives
                 and (partially) smooth variational principles.
                 ``Fuzzy'' calculus and some equivalent
                 reformulations.\par

                 $ \bullet $ The structure of Lipschitz functions.
                 Especially the calculus of essentially smooth Lipschitz
                 functions and the vector-lattice algebra they generate.
                 Chain rules, and questions of integrability and
                 representability.\par

                 $ \bullet $ Applications to and examples of distance
                 functions. Minimality of distance functions and
                 proximal normal formulae revisited. More general
                 perturbation functions.\par

                 $ \bullet $ Convex functions and related sequences in
                 Banach space. How properties of given Banach spaces are
                 reflected in the convex functions they support.
                 Conjugates and subdifferentials of eigenvalue
                 functions.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:1999:MFAb
author: Jonathan M. Borwein and Qiji J. Zhu
editor: F. H. Clarke and R. J. Stern
booktitle: Nonlinear analysis, differential equations and control (Montreal, QC, 1998)
title: Multifunctional and functional analytic techniques in nonsmooth analysis
volume: 528
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: 61--157
year: 1999
MRclass: 49J52 (26A16 26E25 46N10)
MRnumber: 1695006
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
series: NATO Sci. Ser. C Math. Phys. Sci.
URL: http://docserver.carma.newcastle.edu.au/49/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Qiji J. Zhu
rawbooktitle: Nonlinear analysis, differential equations and control ({Montreal, QC, 1998})
raweditor: F. H. Clarke and R. J. Stern
rawtitle: Multifunctional and functional analytic techniques in nonsmooth analysis
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:1999:MFAb,
  author =       "Jonathan M. Borwein and Qiji J. Zhu",
  editor =       "F. H. Clarke and R. J. Stern",
  booktitle =    "Nonlinear analysis, differential equations and control
                 ({Montreal, QC, 1998})",
  title =        "Multifunctional and functional analytic techniques in
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  volume =       "528",
  publisher =    pub-KLUWER,
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  series =       "NATO Sci. Ser. C Math. Phys. Sci.",
  URL =          "http://docserver.carma.newcastle.edu.au/49/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1999:NCMb
author: J. M. Borwein and T. Stanway
title: Numerical and computational mathematics (at the undergraduate level)
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 22
day: 31
month: aug
monthnumber: 8
year: 1999
bibdate: Thu Sep 01 10:18:27 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 10:18:27 ???
note: Published in cite Borwein:2000:NCMa.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and T. Stanway
rawnote: Published in \cite{Borwein:2000:NCMa}.
rawtitle: Numerical and computational mathematics (at the undergraduate level)
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We present an argument for including numerical and computational methods in the undergraduate mathematics curriculum. The argument is supported by presenting a number of specific examples; some fairly elementary and some less elementary. We conclude by inviting the reader to reflect on the impact that experimental mathematics might have on the undergraduate curriculum and we offer a final example which serendipitously presented itself during the late stages of preparing this paper.

rawabstract:
We present an argument for including numerical and computational methods in the undergraduate mathematics curriculum. The argument is supported by presenting a number of specific examples; some fairly elementary and some less elementary. We conclude by inviting the reader to reflect on the impact that experimental mathematics might have on the undergraduate curriculum and we offer a final example which serendipitously presented itself during the late stages of preparing this paper.

entry:
@TechReport{Borwein:1999:NCMb,
  author =       "J. M. Borwein and T. Stanway",
  title =        "Numerical and computational mathematics (at the
                 undergraduate level)",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "22",
  day =          "31",
  month =        aug,
  year =         "1999",
  bibdate =      "Thu Sep 01 10:18:27 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2000:NCMa}.",
  abstract =     "We present an argument for including numerical and
                 computational methods in the undergraduate mathematics
                 curriculum. The argument is supported by presenting a
                 number of specific examples; some fairly elementary and
                 some less elementary. We conclude by inviting the
                 reader to reflect on the impact that experimental
                 mathematics might have on the undergraduate curriculum
                 and we offer a final example which serendipitously
                 presented itself during the late stages of preparing
                 this paper.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1999:PSS
author: Jonathan M. Borwein and C. G. Pinner and David Bradley
title: Problems and Solutions: Solutions: An Infinite Product: 10605
journal: j-AMER-MATH-MONTHLY
volume: 106
number: 2
pages: 173--174
year: 1999
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2589069
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRnumber: 1543419
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.jstor.org/journals/00029890.html
rawauthor: Jonathan M. Borwein and C. G. Pinner and David Bradley
rawtitle: Problems and Solutions: Solutions: An Infinite Product: 10605
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1999:PSS,
  author =       "Jonathan M. Borwein and C. G. Pinner and David
                 Bradley",
  title =        "Problems and Solutions: Solutions: An Infinite
                 Product: 10605",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "106",
  number =       "2",
  pages =        "173--174",
  year =         "1999",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2589069",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRnumber =     "1543419",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1999:PSVa
author: Jonathan M. Borwein and Jay S. Treiman and Qiji J. Zhu
title: Partially smooth variational principles and applications
journal: j-NONLINEAR-ANAL
volume: 35
number: 8
pages: 1031--1059
year: 1999
CODEN: NOANDD
DOI: https://doi.org/10.1016/S0362-546X(98)00113-8
ISSN: 0362-546x (print), 1873-5215 (electronic) OR 0362546x (print), 18735215 (electronic)
ISSNL: 0362-546X OR 0362546X
MRclass: 49J53 (46T20 47H99)
MRnumber: 1707806
MRreviewer: B. Mordukhovich
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
keywords: Fuzzy sum rules; Mean value inequalities and partially smooth spaces; Smooth variational principle
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.sciencedirect.com/journal/nonlinear-analysis
rawauthor: Jonathan M. Borwein and Jay S. Treiman and Qiji J. Zhu
rawtitle: Partially smooth variational principles and applications
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/182/; http://www.sciencedirect.com/science/article/pii/S0362546X98001138

abstract:
We discuss a smooth variational principle for partially smooth viscosity subdifferentials and explore its applications in nonsmooth analysis.

rawabstract:
We discuss a smooth variational principle for partially smooth viscosity subdifferentials and explore its applications in nonsmooth analysis.

entry:
@Article{Borwein:1999:PSVa,
  author =       "Jonathan M. Borwein and Jay S. Treiman and Qiji J.
                 Zhu",
  title =        "Partially smooth variational principles and
                 applications",
  journal =      j-NONLINEAR-ANAL,
  volume =       "35",
  number =       "8",
  pages =        "1031--1059",
  year =         "1999",
  CODEN =        "NOANDD",
  DOI =          "https://doi.org/10.1016/S0362-546X(98)00113-8",
  ISSN =         "0362-546x (print), 1873-5215 (electronic)",
  ISSN-L =       "0362-546X",
  MRclass =      "49J53 (46T20 47H99)",
  MRnumber =     "1707806",
  MRreviewer =   "B. Mordukhovich",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/182/;
                 http://www.sciencedirect.com/science/article/pii/S0362546X98001138",
  abstract =     "We discuss a smooth variational principle for
                 partially smooth viscosity subdifferentials and explore
                 its applications in nonsmooth analysis.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Nonlinear Analysis. Theory, Methods \& Applications.
                 An International Multidisciplinary Journal. Series A:
                 Theory and Methods",
  journal-URL =  "https://www.sciencedirect.com/journal/nonlinear-analysis",
  keywords =     "Fuzzy sum rules; Mean value inequalities and partially
                 smooth spaces; Smooth variational principle",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1999:SM
author: D. Borwein and J. M. Borwein and P. Marechal
title: Surprise maximization
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 16
day: 25
month: jul
monthnumber: 7
year: 1999
bibdate: Thu Sep 01 08:38:24 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 08:38:24 ???
note: Published in cite Borwein:2000:SM.
URL: http://docserver.carma.newcastle.edu.au/209/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. Borwein and J. M. Borwein and P. Mar{\'e}chal
rawnote: Published in \cite{Borwein:2000:SM}.
rawtitle: Surprise maximization
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
The Surprise Examination or Unexpected Hanging Paradox has long fascinated mathematicians and philosophers, as the number of publications devoted to it attests. For an exhaustive bibliography on the subject, see [1]. We examine and solve the optimization problems arising from an information theoretic avoidance of the Paradox. These problems provide a very satisfactory application of both the Kuhn-Tucker theory and of various classical inequalities and estimation techniques. We assume some elementary knowledge of optimization but recall the necessary convex analytic concepts in the course of the paper. Readers unfamiliar with this background may simply skip a couple of proofs and a few technical details.

rawabstract:
The Surprise Examination or Unexpected Hanging Paradox has long fascinated mathematicians and philosophers, as the number of publications devoted to it attests. For an exhaustive bibliography on the subject, see [1]. We examine and solve the optimization problems arising from an information theoretic avoidance of the Paradox. These problems provide a very satisfactory application of both the Kuhn-Tucker theory and of various classical inequalities and estimation techniques. We assume some elementary knowledge of optimization but recall the necessary convex analytic concepts in the course of the paper. Readers unfamiliar with this background may simply skip a couple of proofs and a few technical details.

entry:
@TechReport{Borwein:1999:SM,
  author =       "D. Borwein and J. M. Borwein and P. Mar{\'e}chal",
  title =        "Surprise maximization",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "16",
  day =          "25",
  month =        jul,
  year =         "1999",
  bibdate =      "Thu Sep 01 08:38:24 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2000:SM}.",
  URL =          "http://docserver.carma.newcastle.edu.au/209/",
  abstract =     "The Surprise Examination or Unexpected Hanging Paradox
                 has long fascinated mathematicians and philosophers, as
                 the number of publications devoted to it attests. For
                 an exhaustive bibliography on the subject, see [1]. We
                 examine and solve the optimization problems arising
                 from an information theoretic avoidance of the Paradox.
                 These problems provide a very satisfactory application
                 of both the Kuhn-Tucker theory and of various classical
                 inequalities and estimation techniques. We assume some
                 elementary knowledge of optimization but recall the
                 necessary convex analytic concepts in the course of the
                 paper. Readers unfamiliar with this background may
                 simply skip a couple of proofs and a few technical
                 details.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1999:SRM
author: Jonathan M. Borwein and Warren B. Moors and Yongheng Shao
title: Subgradient representation of multifunctions
journal: j-J-AUSTRAL-MATH-SOC-SER-B
volume: 40
number: 3
pages: 301--313
month: jan
monthnumber: 1
year: 1999
CODEN: JAMMDU
DOI: https://doi.org/10.1017/S0334270000010924
ISSN: 0334-2700 OR 03342700
ISSNL: 0334-2700 OR 03342700
MRclass: 49J52 (47H04)
MRnumber: 1674589
MRreviewer: Constantin Z{\u{a}}linescu
bibdate: Fri Sep 30 10:53:26 2016
bibtimestamp: 2016.09.30 10:53:26 ???
note: Volume in honour of B. Craven and B. Mond.
fjournal: Journal of the Australian Mathematical Society. Series B, Applied Mathematics
acknowledgement: ack-nhfb
ajournal: J. Austral Math. Soc. Ser. B
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://journals.cambridge.org/action/displayJournal?jid=ANZ
onlinedate: 17 February 2009
rawauthor: Jonathan M. Borwein and Warren B. Moors and Yongheng Shao
rawnote: Volume in honour of B. Craven and B. Mond.
rawtitle: Subgradient representation of multifunctions
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/anziamj.bib

URL:
http://docserver.carma.newcastle.edu.au/184/; http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=3964380; https://www.cambridge.org/core/journals/anziam-journal/article/subgradient-representation-of-multifunctions/A035439B7CEE8FBA04EAD6EB6888CDDB

entry:
@Article{Borwein:1999:SRM,
  author =       "Jonathan M. Borwein and Warren B. Moors and Yongheng
                 Shao",
  title =        "Subgradient representation of multifunctions",
  journal =      j-J-AUSTRAL-MATH-SOC-SER-B,
  volume =       "40",
  number =       "3",
  pages =        "301--313",
  month =        jan,
  year =         "1999",
  CODEN =        "JAMMDU",
  DOI =          "https://doi.org/10.1017/S0334270000010924",
  ISSN =         "0334-2700",
  ISSN-L =       "0334-2700",
  MRclass =      "49J52 (47H04)",
  MRnumber =     "1674589",
  MRreviewer =   "Constantin Z{\u{a}}linescu",
  bibdate =      "Fri Sep 30 10:53:26 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/anziamj.bib",
  note =         "Volume in honour of B. Craven and B. Mond.",
  URL =          "http://docserver.carma.newcastle.edu.au/184/;
                 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=3964380;
                 https://www.cambridge.org/core/journals/anziam-journal/article/subgradient-representation-of-multifunctions/A035439B7CEE8FBA04EAD6EB6888CDDB",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Austral Math. Soc. Ser. B",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of the Australian Mathematical Society. Series
                 B, Applied Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
  onlinedate =   "17 February 2009",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1999:SSC
author: Jonathan M. Borwein and Qiji J. Zhu
title: A survey of subdifferential calculus with applications
journal: j-NONLINEAR-ANAL
volume: 38
number: 6
pages: 687--773
year: 1999
CODEN: NOANDD
DOI: https://doi.org/10.1016/S0362-546X(98)00142-4
ISSN: 0362-546x (print), 1873-5215 (electronic) OR 0362546x (print), 18735215 (electronic)
ISSNL: 0362-546X OR 0362546X
MRclass: 49J52 (46G05 46N10 49-02 49J53 58C05)
MRnumber: 1710152
MRreviewer: Philip D. Loewen
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
remark: CECM Research Report 98:105.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.sciencedirect.com/journal/nonlinear-analysis
rawauthor: Jonathan M. Borwein and Qiji J. Zhu
rawtitle: A survey of subdifferential calculus with applications
ORCID: Borwein, Jonathan/0000-0002-1263-0646
note:
Dedicated to Francis Clarke on the occasion of his fiftieth birthday and the twenty-fifth birthday of the Clarke generalized gradient. See addendum cite Borwein:2002:ASS.

URL:
http://docserver.carma.newcastle.edu.au/199/; http://www.sciencedirect.com/science/article/pii/S0362546X98001424

abstract:
This survey is an account of the current status of subdifferential research. It is intended to serve as an entry point for researchers and graduate students in a wide variety of pure and applied analysis areas who might profitably use subdifferentials as tools.

keywords:
Coderivative calculus; Constrained optimization problems; Generalized gradients; Geometric subdifferential; Hamilton--Jacobi equations; Implicit function theorems; Limiting coderivatives; Limiting subdifferentials; Mean value inequalities; Mean value theorems; Metric regularity; Open mapping; Proximal subdifferential; Sensitivity; Smooth spaces; Subdifferential calculus; Viscosity solutions; Viscosity subdifferential

rawabstract:
This survey is an account of the current status of subdifferential research. It is intended to serve as an entry point for researchers and graduate students in a wide variety of pure and applied analysis areas who might profitably use subdifferentials as tools.

rawnote:
Dedicated to Francis Clarke on the occasion of his fiftieth birthday and the twenty-fifth birthday of the Clarke generalized gradient. See addendum \cite{Borwein:2002:ASS}.

entry:
@Article{Borwein:1999:SSC,
  author =       "Jonathan M. Borwein and Qiji J. Zhu",
  title =        "A survey of subdifferential calculus with
                 applications",
  journal =      j-NONLINEAR-ANAL,
  volume =       "38",
  number =       "6",
  pages =        "687--773",
  year =         "1999",
  CODEN =        "NOANDD",
  DOI =          "https://doi.org/10.1016/S0362-546X(98)00142-4",
  ISSN =         "0362-546x (print), 1873-5215 (electronic)",
  ISSN-L =       "0362-546X",
  MRclass =      "49J52 (46G05 46N10 49-02 49J53 58C05)",
  MRnumber =     "1710152",
  MRreviewer =   "Philip D. Loewen",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Dedicated to Francis Clarke on the occasion of his
                 fiftieth birthday and the twenty-fifth birthday of the
                 Clarke generalized gradient. See addendum
                 \cite{Borwein:2002:ASS}.",
  URL =          "http://docserver.carma.newcastle.edu.au/199/;
                 http://www.sciencedirect.com/science/article/pii/S0362546X98001424",
  abstract =     "This survey is an account of the current status of
                 subdifferential research. It is intended to serve as an
                 entry point for researchers and graduate students in a
                 wide variety of pure and applied analysis areas who
                 might profitably use subdifferentials as tools.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Nonlinear Analysis. Theory, Methods \& Applications.
                 An International Multidisciplinary Journal. Series A:
                 Theory and Methods",
  journal-URL =  "https://www.sciencedirect.com/journal/nonlinear-analysis",
  keywords =     "Coderivative calculus; Constrained optimization
                 problems; Generalized gradients; Geometric
                 subdifferential; Hamilton--Jacobi equations; Implicit
                 function theorems; Limiting coderivatives; Limiting
                 subdifferentials; Mean value inequalities; Mean value
                 theorems; Metric regularity; Open mapping; Proximal
                 subdifferential; Sensitivity; Smooth spaces;
                 Subdifferential calculus; Viscosity solutions;
                 Viscosity subdifferential",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Research Report 98:105.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1999:STC
author: J. M. Borwein and X. Wang
title: Subdifferentiability of typical continuous functions
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 10
day: 13
month: aug
monthnumber: 8
year: 1999
bibdate: Thu Sep 01 10:11:30 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 10:11:30 ???
note: Published in cite Borwein:2001:STC.
URL: http://docserver.carma.newcastle.edu.au/241/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and X. Wang
rawnote: Published in \cite{Borwein:2001:STC}.
rawtitle: Subdifferentiability of typical continuous functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We prove a ``typical'' subdifferentiability principle and apply it to a variety of complete metric spaces of continuous functions on separable Banach spaces; so as to obtain existence of functions with maximal subdifferentials when ordered by inclusion. The relationship between continuous functions with maximal subdifferentials and nowhere monotone functions is discussed.

rawabstract:
We prove a ``typical'' subdifferentiability principle and apply it to a variety of complete metric spaces of continuous functions on separable Banach spaces; so as to obtain existence of functions with maximal subdifferentials when ordered by inclusion. The relationship between continuous functions with maximal subdifferentials and nowhere monotone functions is discussed.

entry:
@TechReport{Borwein:1999:STC,
  author =       "J. M. Borwein and X. Wang",
  title =        "Subdifferentiability of typical continuous functions",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "10",
  day =          "13",
  month =        aug,
  year =         "1999",
  bibdate =      "Thu Sep 01 10:11:30 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2001:STC}.",
  URL =          "http://docserver.carma.newcastle.edu.au/241/",
  abstract =     "We prove a ``typical'' subdifferentiability principle
                 and apply it to a variety of complete metric spaces of
                 continuous functions on separable Banach spaces; so as
                 to obtain existence of functions with maximal
                 subdifferentials when ordered by inclusion. The
                 relationship between continuous functions with maximal
                 subdifferentials and nowhere monotone functions is
                 discussed.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1999:SVM
author: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lisonek
title: Special Values of Multiple Polylogarithms
journal: ArXiv Mathematics e-prints
pages: 10
month: oct
monthnumber: 10
year: 1999
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/1999math.....10045B; http://docserver.carma.newcastle.edu.au/200/
keywords: Mathematics - Classical Analysis and ODEs, Mathematics - Combinatorics, 40B05, 33E20
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lison{\v{e}}k
rawtitle: Special Values of Multiple Polylogarithms
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, we have been forced to consider multidimensional extensions encompassing the classical polylogarithm, Euler sums, and the Riemann zeta function. Here, we provide a general framework within which previously isolated results can now be properly understood. Applying the theory developed herein, we prove several previously conjectured evaluations, including an intriguing conjecture of Don Zagier.

rawabstract:
Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, we have been forced to consider multidimensional extensions encompassing the classical polylogarithm, Euler sums, and the Riemann zeta function. Here, we provide a general framework within which previously isolated results can now be properly understood. Applying the theory developed herein, we prove several previously conjectured evaluations, including an intriguing conjecture of Don Zagier.

entry:
@Article{Borwein:1999:SVM,
  author =       "Jonathan M. Borwein and David M. Bradley and David J.
                 Broadhurst and Petr Lison{\v{e}}k",
  title =        "Special Values of Multiple Polylogarithms",
  journal =      "ArXiv Mathematics e-prints",
  month =        oct,
  year =         "1999",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/1999math.....10045B;
                 http://docserver.carma.newcastle.edu.au/200/",
  abstract =     "Historically, the polylogarithm has attracted
                 specialists and non-specialists alike with its lovely
                 evaluations. Much the same can be said for Euler sums
                 (or multiple harmonic sums), which, within the past
                 decade, have arisen in combinatorics, knot theory and
                 high-energy physics. More recently, we have been forced
                 to consider multidimensional extensions encompassing
                 the classical polylogarithm, Euler sums, and the
                 Riemann zeta function. Here, we provide a general
                 framework within which previously isolated results can
                 now be properly understood. Applying the theory
                 developed herein, we prove several previously
                 conjectured evaluations, including an intriguing
                 conjecture of Don Zagier.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "math/9910045",
  keywords =     "Mathematics - Classical Analysis and ODEs, Mathematics
                 - Combinatorics, 40B05, 33E20",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Marechal:1999:CSA
author: P. Marechal and D. Togane and A. Celler and J. M. Borwein
title: Computation and stability analysis for regularized tomographic reconstructions
journal: j-IEEE-TRANS-NUCL-SCI
volume: 46
pages: 2177--2184
month: dec
monthnumber: 12
year: 1999
CODEN: IRNSAM
DOI: https://doi.org/10.1109/23.819301
ISSN: 0018-9499 (print), 1558-1578 (electronic) OR 00189499 (print), 15581578 (electronic)
ISSNL: 0018-9499 OR 00189499
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/1999ITNS...46.2177M
fjournal: IEEE Transactions on Nuclear Science
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23
rawauthor: P. Marechal and D. Togane and A. Celler and J. M. Borwein
rawtitle: Computation and stability analysis for regularized tomographic reconstructions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Marechal:1999:CSA,
  author =       "P. Marechal and D. Togane and A. Celler and J. M.
                 Borwein",
  title =        "Computation and stability analysis for regularized
                 tomographic reconstructions",
  journal =      j-IEEE-TRANS-NUCL-SCI,
  volume =       "46",
  pages =        "2177--2184",
  month =        dec,
  year =         "1999",
  CODEN =        "IRNSAM",
  DOI =          "https://doi.org/10.1109/23.819301",
  ISSN =         "0018-9499 (print), 1558-1578 (electronic)",
  ISSN-L =       "0018-9499",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/1999ITNS...46.2177M",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "IEEE Transactions on Nuclear Science",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:199x:KC
author: David H. Bailey and Jonathan M. Borwein and Richard E. Crandall
title: On the Khintchine constant
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 19
year: 199x
bibdate: Wed Aug 31 08:55:14 2022
bibtimestamp: 2022.08.31 08:55:14 ???
note: Published in cite Bailey:1997:KC
remark: Undated.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein and Richard E. Crandall
rawnote: Published in \cite{Bailey:1997:KC}
rawtitle: On the {Khintchine} constant
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/bibnet/authors/c/crandall-richard-e.bib

entry:
@TechReport{Bailey:199x:KC,
  author =       "David H. Bailey and Jonathan M. Borwein and Richard E.
                 Crandall",
  title =        "On the {Khintchine} constant",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "19",
  year =         "199x",
  bibdate =      "Wed Aug 31 08:55:14 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
  note =         "Published in \cite{Bailey:1997:KC}",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Undated.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:199x:SCF
author: Jonathan M. Borwein and Jon D. Vanderwerff
title: A Survey of Convex Functions and Sequential Convergence
institution: Faculty of Computer Science, Dalhousie University
address: Halifax, NS, B3H2W5 Canada
pages: 1--10
year: 199x
bibdate: Mon Aug 29 17:09:33 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.29 17:09:33 ???
URL: https://carma.newcastle.edu.au/jon/Preprints/Books/CUP/CUPold/convsurvey.pdf
abstract: Study various properties of convex functions related to sequential convergence.
remark: Undated: same URL as cite Borwein:1990:SDPa, but PDF file matches the title in this entry.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawabstract: Study various properties of convex functions related to sequential convergence.
rawauthor: Jonathan M. Borwein and Jon D. Vanderwerff
rawtitle: A Survey of Convex Functions and Sequential Convergence
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@TechReport{Borwein:199x:SCF,
  author =       "Jonathan M. Borwein and Jon D. Vanderwerff",
  title =        "A Survey of Convex Functions and Sequential
                 Convergence",
  institution =  "Faculty of Computer Science, Dalhousie University",
  address =      "Halifax, NS, B3H2W5 Canada",
  pages =        "1--10",
  year =         "199x",
  bibdate =      "Mon Aug 29 17:09:33 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "https://carma.newcastle.edu.au/jon/Preprints/Books/CUP/CUPold/convsurvey.pdf",
  abstract =     "Study various properties of convex functions related
                 to sequential convergence.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  pagecount =    "10",
  remark =       "Undated: same URL as \cite{Borwein:1990:SDPa}, but PDF
                 file matches the title in this entry.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:19xx:ASW
author: Jonathan Borwein and Lou Shitou
title: Asymptotics of a Sequence of Witt Vectors
type: Report
institution: Department of Mathematics, Statistics and Computing Science, Dalhousie University
address: Halifax, NS B3H 3J5, Canada
pages: 13
year: 19xx
bibdate: Fri Nov 11 07:09:34 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.11.11 07:09:34 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein and Lou Shitou
rawtitle: Asymptotics of a Sequence of {Witt} Vectors
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We provide asymptotic and order information about the Witt vectors and integers $ d_n $ appearing in $ Prod _n geq 1 (1 / (1 + d_n t^n / n!)) = (1 - t) e^t $.

remark:
Undated report. The second author also appears in journal databases with family name Lou, and personal name Shi-Tuo.

rawabstract:
We provide asymptotic and order information about the Witt vectors and integers $ d_n $ appearing in $ \Prod_{n \geq 1} (1 / (1 + d_n t^n / n!)) = (1 - t) e^t $.

entry:
@TechReport{Borwein:19xx:ASW,
  author =       "Jonathan Borwein and Lou Shitou",
  title =        "Asymptotics of a Sequence of {Witt} Vectors",
  type =         "Report",
  institution =  "Department of Mathematics, Statistics and Computing
                 Science, Dalhousie University",
  address =      "Halifax, NS B3H 3J5, Canada",
  pages =        "13",
  year =         "19xx",
  bibdate =      "Fri Nov 11 07:09:34 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  abstract =     "We provide asymptotic and order information about the
                 Witt vectors and integers $ d_n $ appearing in $
                 \Prod_{n \geq 1} (1 / (1 + d_n t^n / n!)) = (1 - t) e^t
                 $.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Undated report. The second author also appears in
                 journal databases with family name Lou, and personal
                 name Shi-Tuo.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:19xx:CFF
author: J. M. Borwein and P. B. Borwein
title: On the Complexity of Familiar Functions and Numbers
type: Report
institution: Department of Mathematics, Statistics and Computing Science, Dalhousie University
address: Halifax, NS B3H 3J5, Canada
pages: 30
year: 19xx
MRclass: 6BC25, 41A30, 1OA30
bibdate: Fri Nov 11 07:08:04 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.11.11 07:08:04 ???
remark: Undated report
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein
rawtitle: On the Complexity of Familiar Functions and Numbers
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
This paper examines low-complexity approximations to familiar functions and numbers. The intent is to suggest that a taxonomy of such functions and numbers based on their computational complexity is possible. A central theme is that traditional methods of approximation are often very far from optimal, while good or optimal methods are often very far from obvious For most functions provably optimal methods are not known, however the gap between what is known and what is possible is often small. A considerable number of open problems are posed and a number of related examples are presented.

keywords:
$pi $; algebraic approximation; computation of digits; Elementary functions; low complexity approximation; open problems; rational approximation; reduced complexity approximation

rawabstract:
This paper examines low-complexity approximations to familiar functions and numbers. The intent is to suggest that a taxonomy of such functions and numbers based on their computational complexity is possible. A central theme is that traditional methods of approximation are often very far from optimal, while good or optimal methods are often very far from obvious For most functions provably optimal methods are not known, however the gap between what is known and what is possible is often small. A considerable number of open problems are posed and a number of related examples are presented.

entry:
@TechReport{Borwein:19xx:CFF,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "On the Complexity of Familiar Functions and Numbers",
  type =         "Report",
  institution =  "Department of Mathematics, Statistics and Computing
                 Science, Dalhousie University",
  address =      "Halifax, NS B3H 3J5, Canada",
  pages =        "30",
  year =         "19xx",
  MRclass =      "6BC25, 41A30, 1OA30",
  bibdate =      "Fri Nov 11 07:08:04 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  abstract =     "This paper examines low-complexity approximations to
                 familiar functions and numbers. The intent is to
                 suggest that a taxonomy of such functions and numbers
                 based on their computational complexity is possible. A
                 central theme is that traditional methods of
                 approximation are often very far from optimal, while
                 good or optimal methods are often very far from obvious
                 For most functions provably optimal methods are not
                 known, however the gap between what is known and what
                 is possible is often small. A considerable number of
                 open problems are posed and a number of related
                 examples are presented.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "$\pi$; algebraic approximation; computation of digits;
                 Elementary functions; low complexity approximation;
                 open problems; rational approximation; reduced
                 complexity approximation",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Undated report",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:19xx:EIG
author: Jonathan M. Borwein
title: Elliptic Integrals and the Gauss--Salamin formula for $ pi $
pages: 16
year: 19xx
bibdate: Mon Nov 07 07:04:34 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.11.07 07:04:34 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawtitle: Elliptic Integrals and the {Gauss--Salamin} formula for $ \pi $
ORCID: Borwein, Jonathan/0000-0002-1263-0646
note:
Unpublished hand-written lecture slides at Dalhousie University. The slides are undated, and the 10 references on the final slides include a reference to E. Salamin (1976) and to P. Backmann's 1977 book booktitle A History of Pi.

abstract:
$ pi $ was first used by W. Jones (1703) as emph pi (short for periphery). Euler (1733) first popularized it as a replacement for $p$ or $c$.

rawabstract:
$ \pi $ was first used by W. Jones (1703) as \emph{pi} (short for periphery). Euler (1733) first popularized it as a replacement for $p$ or $c$.

rawnote:
Unpublished hand-written lecture slides at Dalhousie University. The slides are undated, and the 10 references on the final slides include a reference to E. Salamin (1976) and to P. Backmann's 1977 book \booktitle{A History of Pi}.

entry:
@Unpublished{Borwein:19xx:EIG,
  author =       "Jonathan M. Borwein",
  title =        "Elliptic Integrals and the {Gauss--Salamin} formula
                 for $ \pi $",
  pages =        "16",
  year =         "19xx",
  bibdate =      "Mon Nov 07 07:04:34 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Unpublished hand-written lecture slides at Dalhousie
                 University. The slides are undated, and the 10
                 references on the final slides include a reference to
                 E. Salamin (1976) and to P. Backmann's 1977 book
                 \booktitle{A History of Pi}.",
  abstract =     "$ \pi $ was first used by W. Jones (1703) as \emph{pi}
                 (short for periphery). Euler (1733) first popularized
                 it as a replacement for $p$ or $c$.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:19xx:EMI
author: Jonathan M. Borwein and Peter B. Borwein and Roland Girgensohn and S. Parnes
pages: 16
year: 19xx
bibdate: Thu Aug 11 09:30:52 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:30:52 ???
note: Unpublished.
remark: Cited in cite Octavio:1996:IT.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Peter B. Borwein and Roland Girgensohn and S. Parnes
rawnote: Unpublished.
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Experimental mathematical investigation of decimal and continued fraction expansions of select constants

rawtitle:
Experimental mathematical investigation of decimal and continued fraction expansions of select constants

entry:
@Unpublished{Borwein:19xx:EMI,
  author =       "Jonathan M. Borwein and Peter B. Borwein and Roland
                 Girgensohn and S. Parnes",
  title =        "Experimental mathematical investigation of decimal and
                 continued fraction expansions of select constants",
  year =         "19xx",
  bibdate =      "Thu Aug 11 09:30:52 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Unpublished.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Cited in \cite{Octavio:1996:IT}.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:19xx:MI
author: J. M. Borwein and P. B. Borwein
title: On the Mean Iteration $ (a, b) leftarrow ((a + 3 b) / 4, (sqrt ab + b) / 2) $
type: Report
institution: Department of Mathematics, Statistics and Computing Science, Dalhousie University
address: Halifax, NS B3H 3J5, Canada
pages: 39
year: 19xx
bibdate: Fri Nov 11 07:10:57 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.11.11 07:10:57 ???
remark: Undated report
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein
rawtitle: On the Mean Iteration $ (a, b) \leftarrow ((a + 3 b) / 4, (\sqrt {ab} + b) / 2) $
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
The iterative process $ a_n + 1 = (a_n + 3 b_n) / 4 $, $ b_n + 1 = (sqrt a_n b_n + b_n) / 2 $ is studied in detail. The limit of this quadratically converging process is explicitly identified, as are the uniformizing parameters. The role of symbolic computation, in discovering these non-trivial identifications, is highlighted.

rawabstract:
The iterative process $ a_{n + 1} = (a_n + 3 b_n) / 4 $, $ b_{n + 1} = (\sqrt {a_n b_n} + b_n) / 2 $ is studied in detail. The limit of this quadratically converging process is explicitly identified, as are the uniformizing parameters. The role of symbolic computation, in discovering these non-trivial identifications, is highlighted.

entry:
@TechReport{Borwein:19xx:MI,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "On the Mean Iteration $ (a, b) \leftarrow ((a + 3 b) /
                 4, (\sqrt {ab} + b) / 2) $",
  type =         "Report",
  institution =  "Department of Mathematics, Statistics and Computing
                 Science, Dalhousie University",
  address =      "Halifax, NS B3H 3J5, Canada",
  pages =        "39",
  year =         "19xx",
  bibdate =      "Fri Nov 11 07:10:57 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  abstract =     "The iterative process $ a_{n + 1} = (a_n + 3 b_n) / 4
                 $, $ b_{n + 1} = (\sqrt {a_n b_n} + b_n) / 2 $ is
                 studied in detail. The limit of this quadratically
                 converging process is explicitly identified, as are the
                 uniformizing parameters. The role of symbolic
                 computation, in discovering these non-trivial
                 identifications, is highlighted.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Undated report",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:19xx:PCT
author: Jonathan M. Borwein and Peter B. Borwein
type: Report
institution: Dalhousie University
address: Halifax, NS, Canada
pages: 21
year: 19xx
bibdate: Mon Nov 07 07:01:20 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.11.07 07:01:20 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Peter B. Borwein
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Pi and its computation: a twenty-two hundred year quest continues: why it is now possible to calculate a billion digits of pi

note:
Undated typeset manuscript intended for booktitle Scientific American, but never published. The latest reference is to a 1987 book.

abstract:
Classical mathematics of Gauss, Ramanujan, and others combines the modern theory of algorithms to dramatically improve our understanding of this ancient problem.

remark:
This paper must have been written between 1987 and 1997, and before the discovery of the BBP algorithm cite Bailey:1997:RCV, because the last paragraph says: ``It is also reasonable to speculate that computing the $n$-th digit of $ pi $ is not very much easier than computing all the first $n$ digits. We think it very probable that computing the $n$-th digit of $ pi $ cannot be of a lower order than multiplication. As a consequence, we conjecture that no one will ever determine the $ 10^1000$-th decimal digit of $ pi $.

rawabstract:
Classical mathematics of Gauss, Ramanujan, and others combines the modern theory of algorithms to dramatically improve our understanding of this ancient problem.

rawnote:
Undated typeset manuscript intended for \booktitle{Scientific American}, but never published. The latest reference is to a 1987 book.

rawtitle:
Pi and its computation: a twenty-two hundred year quest continues: why it is now possible to calculate a billion digits of pi

entry:
@TechReport{Borwein:19xx:PCT,
  author =       "Jonathan M. Borwein and Peter B. Borwein",
  title =        "Pi and its computation: a twenty-two hundred year
                 quest continues: why it is now possible to calculate a
                 billion digits of pi",
  type =         "Report",
  institution =  "Dalhousie University",
  address =      "Halifax, NS, Canada",
  pages =        "21",
  year =         "19xx",
  bibdate =      "Mon Nov 07 07:01:20 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Undated typeset manuscript intended for
                 \booktitle{Scientific American}, but never published.
                 The latest reference is to a 1987 book.",
  abstract =     "Classical mathematics of Gauss, Ramanujan, and others
                 combines the modern theory of algorithms to
                 dramatically improve our understanding of this ancient
                 problem.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "This paper must have been written between 1987 and
                 1997, and before the discovery of the BBP algorithm
                 \cite{Bailey:1997:RCV}, because the last paragraph
                 says: ``It is also reasonable to speculate that
                 computing the $n$-th digit of $ \pi $ is not very much
                 easier than computing all the first $n$ digits. We
                 think it very probable that computing the $n$-th digit
                 of $ \pi $ cannot be of a lower order than
                 multiplication. As a consequence, we conjecture that no
                 one will ever determine the $ 10^{1000}$-th decimal
                 digit of $ \pi $.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:19xx:WMS
author: J. M. Borwein and B. Richmond
title: When is a matrix a square?
type: Research report
number: 5
address: Halifax, NS, Canada and Waterloo, ON, Canada
pages: 22
year: 19xx
bibdate: Mon Nov 07 17:45:04 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.11.07 17:45:04 ???
keywords: asymptotic formulae; Jordan forms; partition functions; square roots
remark: There are only 5 references on the last page, the most recent a book from 1976.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and B. Richmond
rawtitle: When is a matrix a square?
ORCID: Borwein, Jonathan/0000-0002-1263-0646
institution:
Department of Mathematics, Dalhousie University and Department of Combinatorics and Optimization, University of Waterloo

abstract:
Necessary and sufficient conditions for an arbitrary $ n times n $ matrix to possess a $k$-th root are given in terms of the associated Jordan form. These characterizations are used to give asymptotic estimates for the relative frequency of nilpotent matrices possessing square roots. The estimates are entirely combinatorial in genesis.

rawabstract:
Necessary and sufficient conditions for an arbitrary $ n \times n $ matrix to possess a $k$-th root are given in terms of the associated Jordan form. These characterizations are used to give asymptotic estimates for the relative frequency of nilpotent matrices possessing square roots. The estimates are entirely combinatorial in genesis.

entry:
@TechReport{Borwein:19xx:WMS,
  author =       "J. M. Borwein and B. Richmond",
  title =        "When is a matrix a square?",
  type =         "Research report",
  number =       "5",
  institution =  "Department of Mathematics, Dalhousie University and
                 Department of Combinatorics and Optimization,
                 University of Waterloo",
  address =      "Halifax, NS, Canada and Waterloo, ON, Canada",
  pages =        "22",
  year =         "19xx",
  bibdate =      "Mon Nov 07 17:45:04 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  abstract =     "Necessary and sufficient conditions for an arbitrary $
                 n \times n $ matrix to possess a $k$-th root are given
                 in terms of the associated Jordan form. These
                 characterizations are used to give asymptotic estimates
                 for the relative frequency of nilpotent matrices
                 possessing square roots. The estimates are entirely
                 combinatorial in genesis.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "asymptotic formulae; Jordan forms; partition
                 functions; square roots",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "There are only 5 references on the last page, the most
                 recent a book from 1976.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:2000:BLR
author: Heinz H. Bauschke and Jonathan M. Borwein and Paul Tseng
title: Bounded linear regularity, strong CHIP, and CHIP are distinct properties
journal: j-J-CONVEX-ANAL
volume: 7
number: 2
pages: 395--412
year: 2000
ISSN: 0944-6532 (print), 2363-6394 (electronic) OR 09446532 (print), 23636394 (electronic)
MRclass: 90C48 (41A65 49J53 52A15 52A20)
MRnumber: 1811687
MRreviewer: Wu Li
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://www.heldermann.de/JCA/JCA07/JCA072/jca07020.htm
fjournal: Journal of Convex Analysis
remark: CECM Preprint 98:112.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.heldermann.de/JCA/jcacon.htm
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein and Paul Tseng
rawtitle: Bounded linear regularity, strong {CHIP}, and {CHIP} are distinct properties
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
abstract:
Bounded linear regularity, the strong conical hull intersection property (strong CHIP), and the conical hull intersection property (CHIP) are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. It was shown recently that these properties are fundamental in several branches of convex optimization, including convex feasibility problems, error bounds, Fenchel duality, and constrained approximation. It was known that regularity implies strong CHIP. which ill turn implies CHIP; moreover, the three properties always hold for subspaces. The question whether or not converse implications are true for general convex sets was open.

rawabstract:
Bounded linear regularity, the strong conical hull intersection property (strong CHIP), and the conical hull intersection property (CHIP) are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. It was shown recently that these properties are fundamental in several branches of convex optimization, including convex feasibility problems, error bounds, Fenchel duality, and constrained approximation. It was known that regularity implies strong CHIP. which ill turn implies CHIP; moreover, the three properties always hold for subspaces. The question whether or not converse implications are true for general convex sets was open.

entry:
@Article{Bauschke:2000:BLR,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein and Paul
                 Tseng",
  title =        "Bounded linear regularity, strong {CHIP}, and {CHIP}
                 are distinct properties",
  journal =      j-J-CONVEX-ANAL,
  volume =       "7",
  number =       "2",
  pages =        "395--412",
  year =         "2000",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "90C48 (41A65 49J53 52A15 52A20)",
  MRnumber =     "1811687",
  MRreviewer =   "Wu Li",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.heldermann.de/JCA/JCA07/JCA072/jca07020.htm",
  abstract =     "Bounded linear regularity, the strong conical hull
                 intersection property (strong CHIP), and the conical
                 hull intersection property (CHIP) are properties of a
                 collection of finitely many closed convex intersecting
                 sets in Euclidean space. It was shown recently that
                 these properties are fundamental in several branches of
                 convex optimization, including convex feasibility
                 problems, error bounds, Fenchel duality, and
                 constrained approximation. It was known that regularity
                 implies strong CHIP. which ill turn implies CHIP;
                 moreover, the three properties always hold for
                 subspaces. The question whether or not converse
                 implications are true for general convex sets was
                 open.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Convex Analysis",
  journal-URL =  "http://www.heldermann.de/JCA/jcacon.htm",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 98:112.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009 Bauschke,
                 Heinz/D-5582-2009",
  unique-id =    "Bauschke:2000:BLR",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bauschke:2000:ESE
author: Heinz H. Bauschke and Jonathan M. Borwein and Patrick L. Combettes
title: Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 32
year: 2000
MRclass: 52A41 (46G05, 46N10, 49J50, 90C25)
bibdate: Thu Sep 01 09:53:22 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 09:53:22 ???
note: Published in cite Bauschke:2001:ESE.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein and Patrick L. Combettes
rawnote: Published in \cite{Bauschke:2001:ESE}.
rawtitle: Essential smoothness, essential strict convexity, and {Legendre} functions in {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
The classical notions of essential smoothness, essential strict convexity, and Legendreness for convex functions are extended from Euclidean to Banach spaces. A pertinent duality theory is developed and several useful characterizations are given. The proofs rely on new results on the more subtle behavior of subdifferentials and directional derivatives at boundary points of the domain. In weak Asplund spaces, a new formula allows the recovery of the subdifferential from nearby gradients. Finally, it is shown that every Legendre function on a reflexive Banach space is zone consistent, a fundamental property in the analysis of optimization algorithms based on Bregman distances. Numerous illustrating examples are provided.

keywords:
Bregman distance; Bregman projection; coercive; cofinite function; convex function of Legendre type; essentially smooth; essentially strictly convex; Legendre function; Schur property; Schur space; subdifferential; supercoercive; weak Asplund space; zone consistent.

rawabstract:
The classical notions of essential smoothness, essential strict convexity, and Legendreness for convex functions are extended from Euclidean to Banach spaces. A pertinent duality theory is developed and several useful characterizations are given. The proofs rely on new results on the more subtle behavior of subdifferentials and directional derivatives at boundary points of the domain. In weak Asplund spaces, a new formula allows the recovery of the subdifferential from nearby gradients. Finally, it is shown that every Legendre function on a reflexive Banach space is zone consistent, a fundamental property in the analysis of optimization algorithms based on Bregman distances. Numerous illustrating examples are provided.

entry:
@TechReport{Bauschke:2000:ESE,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein and Patrick
                 L. Combettes",
  title =        "Essential smoothness, essential strict convexity, and
                 {Legendre} functions in {Banach} spaces",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "32",
  year =         "2000",
  MRclass =      "52A41 (46G05, 46N10, 49J50, 90C25)",
  bibdate =      "Thu Sep 01 09:53:22 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Bauschke:2001:ESE}.",
  abstract =     "The classical notions of essential smoothness,
                 essential strict convexity, and Legendreness for convex
                 functions are extended from Euclidean to Banach spaces.
                 A pertinent duality theory is developed and several
                 useful characterizations are given. The proofs rely on
                 new results on the more subtle behavior of
                 subdifferentials and directional derivatives at
                 boundary points of the domain. In weak Asplund spaces,
                 a new formula allows the recovery of the
                 subdifferential from nearby gradients. Finally, it is
                 shown that every Legendre function on a reflexive
                 Banach space is zone consistent, a fundamental property
                 in the analysis of optimization algorithms based on
                 Bregman distances. Numerous illustrating examples are
                 provided.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Bregman distance; Bregman projection; coercive;
                 cofinite function; convex function of Legendre type;
                 essentially smooth; essentially strictly convex;
                 Legendre function; Schur property; Schur space;
                 subdifferential; supercoercive; weak Asplund space;
                 zone consistent.",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bauschke:2000:JSC
author: Heinz H. Bauschke and Jonathan M. Borwein
title: Joint and separate convexity of the Bregman distance
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 17
year: 2000
bibdate: Thu Sep 01 09:08:34 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 09:08:34 ???
URL: http://docserver.carma.newcastle.edu.au/227/
keywords: ,convex function; Bregman distance; joint convexity; separate convexity
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein
rawtitle: Joint and separate convexity of the {Bregman} distance
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Algorithms involving Bregman projections for solving optimization problems have been receiving much attention lately. Several of these methods rely crucially on the joint convexity of the Bregman distance. In this note, we study joint and separate convexity of Bregman distances.par To bring out the main ideas more clearly, we consider first functions defined on an open interval. Our main result states that the Bregman distance of a given function is jointly convex if and only if the reciprocal of its second derivative is concave. We observe that Bregman distances induced by the two most popular choices --- the energy and the Boltzmann-Shannon entropy --- are limiting cases in a profound sense. This result is generalized by weakening assumptions on differentiability and strict convexity.par We then consider general, not necessarily separable, convex functions. The characterization of joint convexity has a natural and beautiful analog. Finally, we discuss spectral functions, where the situation is less clear. Throughout, we provide numerous examples to illustrate our results.

rawabstract:
Algorithms involving Bregman projections for solving optimization problems have been receiving much attention lately. Several of these methods rely crucially on the joint convexity of the Bregman distance. In this note, we study joint and separate convexity of Bregman distances.\par To bring out the main ideas more clearly, we consider first functions defined on an open interval. Our main result states that the Bregman distance of a given function is jointly convex if and only if the reciprocal of its second derivative is concave. We observe that Bregman distances induced by the two most popular choices --- the energy and the Boltzmann-Shannon entropy --- are limiting cases in a profound sense. This result is generalized by weakening assumptions on differentiability and strict convexity.\par We then consider general, not necessarily separable, convex functions. The characterization of joint convexity has a natural and beautiful analog. Finally, we discuss spectral functions, where the situation is less clear. Throughout, we provide numerous examples to illustrate our results.

entry:
@TechReport{Bauschke:2000:JSC,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein",
  title =        "Joint and separate convexity of the {Bregman}
                 distance",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "17",
  year =         "2000",
  bibdate =      "Thu Sep 01 09:08:34 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/227/",
  abstract =     "Algorithms involving Bregman projections for solving
                 optimization problems have been receiving much
                 attention lately. Several of these methods rely
                 crucially on the joint convexity of the Bregman
                 distance. In this note, we study joint and separate
                 convexity of Bregman distances.\par

                 To bring out the main ideas more clearly, we consider
                 first functions defined on an open interval. Our main
                 result states that the Bregman distance of a given
                 function is jointly convex if and only if the
                 reciprocal of its second derivative is concave. We
                 observe that Bregman distances induced by the two most
                 popular choices --- the energy and the
                 Boltzmann-Shannon entropy --- are limiting cases in a
                 profound sense. This result is generalized by weakening
                 assumptions on differentiability and strict
                 convexity.\par

                 We then consider general, not necessarily separable,
                 convex functions. The characterization of joint
                 convexity has a natural and beautiful analog. Finally,
                 we discuss spectral functions, where the situation is
                 less clear. Throughout, we provide numerous examples to
                 illustrate our results.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     ",convex function; Bregman distance; joint convexity;
                 separate convexity",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2000:AGM
author: J. M. Borwein and P. B. Borwein
title: The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions
crossref: Berggren:2000:PSB
pages: 537--552
year: 2000
DOI: https://doi.org/10.1007/978-1-4757-3240-5_56
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibtimestamp: 2016.08.11 09:36:22 MDT
note: Reprint of cite Borwein:1984:AGM.
URL: http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_56
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein
rawnote: Reprint of \cite{Borwein:1984:AGM}.
rawtitle: The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InCollection{Borwein:2000:AGM,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:2000:PSB",
  pages =        "537--552",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-1-4757-3240-5_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Borwein:1984:AGM}.",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_56",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2000:AIR
author: Jonathan M. Borwein and Petr Lisonek
title: Applications of integer relation algorithms
journal: j-DISCRETE-MATH
volume: 217
number: 1--3
pages: 65--82
year: 2000
CODEN: DSMHA4
DOI: https://doi.org/10.1016/S0012-365X(99)00256-3
ISSN: 0012-365x (print), 1872-681x (electronic) OR 0012365x (print), 1872681x (electronic)
ISSNL: 0012-365X OR 0012365X
MRclass: 65Y15 (68W99)
MRnumber: 1766260
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
note: Formal power series and algebraic combinatorics (Vienna, 1997).
fjournal: Discrete Mathematics
remark: CECM Research Report 97:104.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Petr Lison{\v{e}}k
rawnote: Formal power series and algebraic combinatorics (Vienna, 1997).
rawtitle: Applications of integer relation algorithms
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/198/; http://www.sciencedirect.com/science/article/pii/S0012365X99002563

abstract:
Let $a$ be a vector of real numbers. By an integer relation for $a$ we mean a non-zero integer vector $c$ such that $ c a^T = 0$. We discuss the algorithms for finding such integer relations from the user's point of view, by presenting examples of their applications and by reviewing the available software implementations.

entry:
@Article{Borwein:2000:AIR,
  author =       "Jonathan M. Borwein and Petr Lison{\v{e}}k",
  title =        "Applications of integer relation algorithms",
  journal =      j-DISCRETE-MATH,
  volume =       "217",
  number =       "1--3",
  pages =        "65--82",
  year =         "2000",
  CODEN =        "DSMHA4",
  DOI =          "https://doi.org/10.1016/S0012-365X(99)00256-3",
  ISSN =         "0012-365x (print), 1872-681x (electronic)",
  ISSN-L =       "0012-365X",
  MRclass =      "65Y15 (68W99)",
  MRnumber =     "1766260",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Formal power series and algebraic combinatorics
                 (Vienna, 1997).",
  URL =          "http://docserver.carma.newcastle.edu.au/198/;
                 http://www.sciencedirect.com/science/article/pii/S0012365X99002563",
  abstract =     "Let $a$ be a vector of real numbers. By an integer
                 relation for $a$ we mean a non-zero integer vector $c$
                 such that $ c a^T = 0$. We discuss the algorithms for
                 finding such integer relations from the user's point of
                 view, by presenting examples of their applications and
                 by reviewing the available software implementations.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Discrete Mathematics",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Research Report 97:104.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2000:ANB
author: J. M. Borwein and M. Jimenez-Sevilla and J. P. Moreno
title: Antiproximinal norms in Banach spaces
institution: inst-CECM
address: inst-CECM:adr
pages: 13
month: oct
monthnumber: 10
year: 2000
MRclass: 46B20
bibdate: Thu Sep 01 09:56:52 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 09:56:52 ???
URL: http://docserver.carma.newcastle.edu.au/233/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and M. Jim{\'e}nez-Sevilla and J. P. Moreno
rawtitle: Antiproximinal norms in {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We prove that every Banach space containing a complemented copy of $ c_0 $ has an antiproximinal body for a suitable norm. If, in addition, the space is separable, there is a pair of antiproximinal norms. In particular, in a separable polyhedral space $X$, the set of all (equivalent) norms on $X$ having an isomorphic antiproximinal norm is dense. In contrast, it is shown that there are no antiproximinal norms in Banach spaces with the Convex Point of Continuity Property (CPCP). Other questions related to the existence of antiproximinal bodies are also discussed.

rawabstract:
We prove that every Banach space containing a complemented copy of $ c_0 $ has an antiproximinal body for a suitable norm. If, in addition, the space is separable, there is a pair of antiproximinal norms. In particular, in a separable polyhedral space $X$, the set of all (equivalent) norms on $X$ having an isomorphic antiproximinal norm is dense. In contrast, it is shown that there are no antiproximinal norms in Banach spaces with the Convex Point of Continuity Property (CPCP). Other questions related to the existence of antiproximinal bodies are also discussed.

entry:
@TechReport{Borwein:2000:ANB,
  author =       "J. M. Borwein and M. Jim{\'e}nez-Sevilla and J. P.
                 Moreno",
  title =        "Antiproximinal norms in {Banach} spaces",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "13",
  month =        oct,
  year =         "2000",
  MRclass =      "46B20",
  bibdate =      "Thu Sep 01 09:56:52 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/233/",
  abstract =     "We prove that every Banach space containing a
                 complemented copy of $ c_0 $ has an antiproximinal body
                 for a suitable norm. If, in addition, the space is
                 separable, there is a pair of antiproximinal norms. In
                 particular, in a separable polyhedral space $X$, the
                 set of all (equivalent) norms on $X$ having an
                 isomorphic antiproximinal norm is dense. In contrast,
                 it is shown that there are no antiproximinal norms in
                 Banach spaces with the Convex Point of Continuity
                 Property (CPCP). Other questions related to the
                 existence of antiproximinal bodies are also
                 discussed.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borwein:2000:CAN
author: Jonathan M. Borwein and Adrian S. Lewis
title: Convex Analysis and Nonlinear Optimization
publisher: pub-SV
address: pub-SV:adr
pages: x + 273
year: 2000
DOI: https://doi.org/10.1007/978-1-4757-9859-3
ISBN: 0-387-98940-4 OR 0387989404
ISBN13: 978-0-387-98940-2 OR 9780387989402
MRclass: 49-01 (46N10 47N10 49-02 49J53 90-01)
MRnumber: 1757448
MRreviewer: John R. Giles
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: Theory and examples.
series: CMS Books in Mathematics/Ouvrages de Mathematiques de la SMC, 3
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Adrian S. Lewis
rawnote: Theory and examples.
rawtitle: Convex Analysis and Nonlinear Optimization
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
This book is a concise account of convex analysis, its applications and extensions, for a broad audience. Blurring as it does the distinctions between mathematical optimization and modern analysis, the elegant language of convexity and duality is indispensable both in computational optimization and for understanding variational properties of functions and multifunctions. Primarily aimed at first-year graduate students, the text consists of short, self-contained sections, each followed by an extensive set of exercises, many of which are guided. The book is thus appropriate either as a class text or for self-study.

TOC:
1: Background 1.1: Euclidean Spaces 1.2: Symmetric Matrices 2: Inequality Constraints 2.1: Optimality Conditions 2.2: Theorems of the Alternative 2.3: Max-functions 3: Fenchel Duality 3.1: Subgradients and Convex Functions 3.2: The Value Function 3.3: The Fenchel Conjugate 4: Convex Analysis 4.1: Continuity of Convex Functions 4.2: Fenchel Biconjugation 4.3: Lagrangian Duality 5: Special Cases 5.1: Polyhedral Convex Sets and Functions 5.2: Functions of Eigenvalues 5.3: Duality for Linear and Semidefinite Programming 5.4: Convex Process Duality 6: Nonsmooth Optimization 6.1: Generalized Derivatives 6.2: Regularity and Strict Differentiability 6.3: Tangent Cones

rawabstract:
This book is a concise account of convex analysis, its applications and extensions, for a broad audience. Blurring as it does the distinctions between mathematical optimization and modern analysis, the elegant language of convexity and duality is indispensable both in computational optimization and for understanding variational properties of functions and multifunctions. Primarily aimed at first-year graduate students, the text consists of short, self-contained sections, each followed by an extensive set of exercises, many of which are guided. The book is thus appropriate either as a class text or for self-study.

rawTOC:
1: Background \\ 1.1: Euclidean Spaces \\ 1.2: Symmetric Matrices \\ 2: Inequality Constraints \\ 2.1: Optimality Conditions \\ 2.2: Theorems of the Alternative \\ 2.3: Max-functions \\ 3: Fenchel Duality \\ 3.1: Subgradients and Convex Functions \\ 3.2: The Value Function \\ 3.3: The Fenchel Conjugate \\ 4: Convex Analysis \\ 4.1: Continuity of Convex Functions \\ 4.2: Fenchel Biconjugation \\ 4.3: Lagrangian Duality \\ 5: Special Cases \\ 5.1: Polyhedral Convex Sets and Functions \\ 5.2: Functions of Eigenvalues \\ 5.3: Duality for Linear and Semidefinite Programming \\ 5.4: Convex Process Duality \\ 6: Nonsmooth Optimization \\ 6.1: Generalized Derivatives \\ 6.2: Regularity and Strict Differentiability \\ 6.3: Tangent Cones

entry:
@Book{Borwein:2000:CAN,
  author =       "Jonathan M. Borwein and Adrian S. Lewis",
  title =        "Convex Analysis and Nonlinear Optimization",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 273",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-1-4757-9859-3",
  ISBN =         "0-387-98940-4",
  ISBN-13 =      "978-0-387-98940-2",
  MRclass =      "49-01 (46N10 47N10 49-02 49J53 90-01)",
  MRnumber =     "1757448",
  MRreviewer =   "John R. Giles",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Theory and examples.",
  series =       "CMS Books in Mathematics/Ouvrages de Math{\'e}matiques
                 de la SMC, 3",
  abstract =     "This book is a concise account of convex analysis, its
                 applications and extensions, for a broad audience.
                 Blurring as it does the distinctions between
                 mathematical optimization and modern analysis, the
                 elegant language of convexity and duality is
                 indispensable both in computational optimization and
                 for understanding variational properties of functions
                 and multifunctions. Primarily aimed at first-year
                 graduate students, the text consists of short,
                 self-contained sections, each followed by an extensive
                 set of exercises, many of which are guided. The book is
                 thus appropriate either as a class text or for
                 self-study.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  tableofcontents = "1: Background \\
                 1.1: Euclidean Spaces \\
                 1.2: Symmetric Matrices \\
                 2: Inequality Constraints \\
                 2.1: Optimality Conditions \\
                 2.2: Theorems of the Alternative \\
                 2.3: Max-functions \\
                 3: Fenchel Duality \\
                 3.1: Subgradients and Convex Functions \\
                 3.2: The Value Function \\
                 3.3: The Fenchel Conjugate \\
                 4: Convex Analysis \\
                 4.1: Continuity of Convex Functions \\
                 4.2: Fenchel Biconjugation \\
                 4.3: Lagrangian Duality \\
                 5: Special Cases \\
                 5.1: Polyhedral Convex Sets and Functions \\
                 5.2: Functions of Eigenvalues \\
                 5.3: Duality for Linear and Semidefinite Programming
                 \\
                 5.4: Convex Process Duality \\
                 6: Nonsmooth Optimization \\
                 6.1: Generalized Derivatives \\
                 6.2: Regularity and Strict Differentiability \\
                 6.3: Tangent Cones",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2000:CBC
author: J. M. Borwein and J. D. Vanderwerff
title: On the continuity of biconjugate convex functions
type: Report
institution: Department of Mathematics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 10
year: 2000
bibdate: Thu Sep 01 09:43:33 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 09:43:33 ???
note: Published in cite Borwein:2002:CBC.
URL: http://docserver.carma.newcastle.edu.au/230/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and J. D. Vanderwerff
rawnote: Published in \cite{Borwein:2002:CBC}.
rawtitle: On the continuity of biconjugate convex functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We show that a Banach space is a Grothendieck space if and only if every continuous convex function on $X$ has a continuous biconjugate function on $ X**$, thus also answering a question raised by S. Simons. Related characterizations and examples are given.

rawabstract:
We show that a Banach space is a Grothendieck space if and only if every continuous convex function on $X$ has a continuous biconjugate function on $ X**$, thus also answering a question raised by S. Simons. Related characterizations and examples are given.

entry:
@TechReport{Borwein:2000:CBC,
  author =       "J. M. Borwein and J. D. Vanderwerff",
  title =        "On the continuity of biconjugate convex functions",
  type =         "Report",
  institution =  "Department of Mathematics, Simon Fraser University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "10",
  year =         "2000",
  bibdate =      "Thu Sep 01 09:43:33 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2002:CBC}.",
  URL =          "http://docserver.carma.newcastle.edu.au/230/",
  abstract =     "We show that a Banach space is a Grothendieck space if
                 and only if every continuous convex function on $X$ has
                 a continuous biconjugate function on $ X**$, thus also
                 answering a question raised by S. Simons. Related
                 characterizations and examples are given.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2000:CBSa
author: Jonathan M. Borwein and David J. Broadhurst and Joel Kamnitzer
title: Central Binomial Sums, Multiple Clausen Values and Zeta Values
journal: ArXiv High Energy Physics --- Theory e-prints
pages: 10
month: apr
monthnumber: 4
year: 2000
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/2000hep.th....4153B; http://docserver.carma.newcastle.edu.au/243/
keywords: High Energy Physics - Theory, Mathematics - Classical Analysis and ODEs
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David J. Broadhurst and Joel Kamnitzer
rawtitle: Central Binomial Sums, Multiple {Clausen} Values and Zeta Values
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apery sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio. In the non-alternating case, there is a strong connection to polylogarithms of the sixth root of unity, encountered in the 3-loop Feynman diagrams of url hep-th/9803091 and subsequently in url hep-ph/9910223, url hep-ph/9910224, url cond-mat/9911452 and url hep-th/0004010.

rawabstract:
We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Ap{\'e}ry sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio. In the non-alternating case, there is a strong connection to polylogarithms of the sixth root of unity, encountered in the 3-loop Feynman diagrams of \url{hep-th/9803091} and subsequently in \url{hep-ph/9910223}, \url{hep-ph/9910224}, \url{cond-mat/9911452} and \url{hep-th/0004010}.

entry:
@Article{Borwein:2000:CBSa,
  author =       "Jonathan M. Borwein and David J. Broadhurst and Joel
                 Kamnitzer",
  title =        "Central Binomial Sums, Multiple {Clausen} Values and
                 Zeta Values",
  journal =      "ArXiv High Energy Physics --- Theory e-prints",
  month =        apr,
  year =         "2000",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/2000hep.th....4153B;
                 http://docserver.carma.newcastle.edu.au/243/",
  abstract =     "We find and prove relationships between Riemann zeta
                 values and central binomial sums. We also investigate
                 alternating binomial sums (also called Ap{\'e}ry sums).
                 The study of non-alternating sums leads to an
                 investigation of different types of sums which we call
                 multiple Clausen values. The study of alternating sums
                 leads to a tower of experimental results involving
                 polylogarithms in the golden ratio. In the
                 non-alternating case, there is a strong connection to
                 polylogarithms of the sixth root of unity, encountered
                 in the 3-loop Feynman diagrams of \url{hep-th/9803091}
                 and subsequently in \url{hep-ph/9910223},
                 \url{hep-ph/9910224}, \url{cond-mat/9911452} and
                 \url{hep-th/0004010}.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "hep-th/0004153",
  keywords =     "High Energy Physics - Theory, Mathematics - Classical
                 Analysis and ODEs",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2000:CBSb
author: Jonathan Michael Borwein and David J. Broadhurst and Joel Kamnitzer
title: Central binomial sums, multiple Clausen values, and zeta values
type: Report
institution: Department of Mathematics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 17
day: 4
month: nov
monthnumber: 11
year: 2000
bibdate: Thu Sep 01 10:15:29 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 10:15:29 ???
note: Published in cite Borwein:2001:CBS.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Michael Borwein and David J. Broadhurst and Joel Kamnitzer
rawnote: Published in \cite{Borwein:2001:CBS}.
rawtitle: Central binomial sums, multiple {Clausen} values, and zeta values
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apery sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio.

rawabstract:
We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Ap{\'e}ry sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio.

entry:
@TechReport{Borwein:2000:CBSb,
  author =       "Jonathan Michael Borwein and David J. Broadhurst and
                 Joel Kamnitzer",
  title =        "Central binomial sums, multiple {Clausen} values, and
                 zeta values",
  type =         "Report",
  institution =  "Department of Mathematics, Simon Fraser University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "17",
  day =          "4",
  month =        nov,
  year =         "2000",
  bibdate =      "Thu Sep 01 10:15:29 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2001:CBS}.",
  abstract =     "We find and prove relationships between Riemann zeta
                 values and central binomial sums. We also investigate
                 alternating binomial sums (also called Ap{\'e}ry sums).
                 The study of non-alternating sums leads to an
                 investigation of different types of sums which we call
                 multiple Clausen values. The study of alternating sums
                 leads to a tower of experimental results involving
                 polylogarithms in the golden ratio.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2000:CDA
author: Jonathan M. Borwein and Pierre Marechal and David Naugler
title: A convex dual approach to the computation of NMR complex spectra
journal: Math. Methods Oper. Res.
volume: 51
number: 1
pages: 91--102
year: 2000
DOI: https://doi.org/10.1007/s001860050004
ISSN: 1432-2994 (print), 1432-5217 (electronic) OR 14322994 (print), 14325217 (electronic)
ISSNL: 1432-2994 OR 14322994
MRclass: 90C30
MRnumber: 1742398
MRreviewer: Massimo Pappalardo
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/207/
fjournal: Mathematical Methods of Operations Research
remark: CECM Research Report 98:114.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Pierre Mar{\'e}chal and David Naugler
rawtitle: A convex dual approach to the computation of {NMR} complex spectra
ORCID: Naugler, David/0000-0001-5485-0498; Borwein, Jonathan/0000-0002-1263-0646
abstract:
The particular entropy method proposed by Hoch et al. [7] for the computation of NMR complex spectra allows an elegant application of the concepts of duality theory. Correspondingly, duality theory casts new light on their choice of entropy. The purpose of this paper is to present the relevant theoretical developments together with some numerical illustrations.

rawabstract:
The particular entropy method proposed by Hoch et al. [7] for the computation of NMR complex spectra allows an elegant application of the concepts of duality theory. Correspondingly, duality theory casts new light on their choice of entropy. The purpose of this paper is to present the relevant theoretical developments together with some numerical illustrations.

entry:
@Article{Borwein:2000:CDA,
  author =       "Jonathan M. Borwein and Pierre Mar{\'e}chal and David
                 Naugler",
  title =        "A convex dual approach to the computation of {NMR}
                 complex spectra",
  journal =      "Math. Methods Oper. Res.",
  volume =       "51",
  number =       "1",
  pages =        "91--102",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/s001860050004",
  ISSN =         "1432-2994 (print), 1432-5217 (electronic)",
  ISSN-L =       "1432-2994",
  MRclass =      "90C30",
  MRnumber =     "1742398",
  MRreviewer =   "Massimo Pappalardo",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/207/",
  abstract =     "The particular entropy method proposed by Hoch et al.
                 [7] for the computation of NMR complex spectra allows
                 an elegant application of the concepts of duality
                 theory. Correspondingly, duality theory casts new light
                 on their choice of entropy. The purpose of this paper
                 is to present the relevant theoretical developments
                 together with some numerical illustrations.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematical Methods of Operations Research",
  ORCID-numbers = "Naugler, David/0000-0001-5485-0498; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "CECM Research Report 98:114.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2000:CDA",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2000:CEL
author: Jonathan Borwein and Yves Lucet and Boris Mordukhovich
title: Compactly epi-Lipschitzian convex sets and functions in normed spaces
journal: j-J-CONVEX-ANAL
volume: 7
number: 2
pages: 375--393
year: 2000
ISSN: 0944-6532 (print), 2363-6394 (electronic) OR 09446532 (print), 23636394 (electronic)
MRclass: 49J53 (46B20 46N10 90C48)
MRnumber: 1811686
MRreviewer: Abderrahim Jourani
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Journal of Convex Analysis
remark: CECM Preprint 98:113.
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 Yves Lucet and Boris Mordukhovich
rawtitle: Compactly epi-{Lipschitzian} convex sets and functions in normed spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/210/; http://www.heldermann.de/JCA/JCA07/JCA072/jca07019.htm

abstract:
We provide several characterizations of compact epi-Lipschitzness for closed convex sets in normed vector spaces. In particular, we show that a closed convex set is compactly epi-Lipschitzian if and only if it has nonempty relative interior, finite codimension, and spans a closed subspace.par Next, we establish that all boundary points of compactly epi-Lipschitzian sets are proper support points. We provide the corresponding results for functions hy using inf-convolutions and the Legendre Fenchel transform. We also give an application to constrained optimization with compactly epi-Lipschitzian data via a generalized Slater condition involving relative interiors.

rawabstract:
We provide several characterizations of compact epi-Lipschitzness for closed convex sets in normed vector spaces. In particular, we show that a closed convex set is compactly epi-Lipschitzian if and only if it has nonempty relative interior, finite codimension, and spans a closed subspace.\par Next, we establish that all boundary points of compactly epi-Lipschitzian sets are proper support points. We provide the corresponding results for functions hy using inf-convolutions and the Legendre Fenchel transform. We also give an application to constrained optimization with compactly epi-Lipschitzian data via a generalized Slater condition involving relative interiors.

entry:
@Article{Borwein:2000:CEL,
  author =       "Jonathan Borwein and Yves Lucet and Boris
                 Mordukhovich",
  title =        "Compactly epi-{Lipschitzian} convex sets and functions
                 in normed spaces",
  journal =      j-J-CONVEX-ANAL,
  volume =       "7",
  number =       "2",
  pages =        "375--393",
  year =         "2000",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "49J53 (46B20 46N10 90C48)",
  MRnumber =     "1811686",
  MRreviewer =   "Abderrahim Jourani",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/210/;
                 http://www.heldermann.de/JCA/JCA07/JCA072/jca07019.htm",
  abstract =     "We provide several characterizations of compact
                 epi-Lipschitzness for closed convex sets in normed
                 vector spaces. In particular, we show that a closed
                 convex set is compactly epi-Lipschitzian if and only if
                 it has nonempty relative interior, finite codimension,
                 and spans a closed subspace.\par

                 Next, we establish that all boundary points of
                 compactly epi-Lipschitzian sets are proper support
                 points. We provide the corresponding results for
                 functions hy using inf-convolutions and the Legendre
                 Fenchel transform. We also give an application to
                 constrained optimization with compactly
                 epi-Lipschitzian data via a generalized Slater
                 condition involving relative interiors.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Convex Analysis",
  journal-URL =  "http://www.heldermann.de/JCA/jcacon.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 98:113.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2000:CEL",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2000:CFL
author: Jonathan M. Borwein and Jon D. Vanderwerff
title: Convex functions of Legendre type in general Banach spaces
type: Report
institution: Department of Mathematics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 14
year: 2000
MRclass: 46B20,46G05,49J50,52A41
bibdate: Thu Sep 01 09:13:15 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 09:13:15 ???
note: Published in cite Borwein:2001:CFL.
URL: http://docserver.carma.newcastle.edu.au/228/
remark: Undated, but PDF metadata says 00:151-Borwein-Vanderwerff.dvi.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Jon D. Vanderwerff
rawnote: Published in \cite{Borwein:2001:CFL}.
rawtitle: Convex functions of {Legendre} type in general {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Convex functions of Legendre type are constructed on arbitrary open convex sets in Banach spaces that satisfy appropriate rotundity and smoothness conditions. A simple direct proof of the existence of ``universal'' barriers on arbitrary open convex sets in $ mathbb R^n $ is given.

keywords:
$beta $-differentiability; barrier function; essentially smooth; Legendre function; strict convexity

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

entry:
@TechReport{Borwein:2000:CFL,
  author =       "Jonathan M. Borwein and Jon D. Vanderwerff",
  title =        "Convex functions of {Legendre} type in general
                 {Banach} spaces",
  type =         "Report",
  institution =  "Department of Mathematics, Simon Fraser University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "14",
  year =         "2000",
  MRclass =      "46B20,46G05,49J50,52A41",
  bibdate =      "Thu Sep 01 09:13:15 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2001:CFL}.",
  URL =          "http://docserver.carma.newcastle.edu.au/228/",
  abstract =     "Convex functions of Legendre type are constructed on
                 arbitrary open convex sets in Banach spaces that
                 satisfy appropriate rotundity and smoothness
                 conditions. A simple direct proof of the existence of
                 ``universal'' barriers on arbitrary open convex sets in
                 $ \mathbb {R}^n $ is given.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "$\beta$-differentiability; barrier function;
                 essentially smooth; Legendre function; strict
                 convexity",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Undated, but PDF metadata says
                 00:151-Borwein-Vanderwerff.dvi.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2000:CSF
author: Jonathan M. Borwein and John Read and Adrian S. Lewis and Qiji Zhu
title: Convex spectral functions of compact operators
journal: j-J-NONLINEAR-CONVEX-ANAL
volume: 1
number: 1
pages: 17--35
year: 2000
ISSN: 1345-4773 (print), 1880-5221 (electronic) OR 13454773 (print), 18805221 (electronic)
ISSNL: 1345-4773 OR 13454773
MRclass: 49N15 (47N10 49J52 90C25)
MRnumber: 1751726
MRreviewer: Mihai Turinici
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://www.ybook.co.jp/online2/jncav1.html
fjournal: Journal of Nonlinear and Convex Analysis. An International Journal
remark: CECM Preprint 99:130.
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 John Read and Adrian S. Lewis and Qiji Zhu
rawtitle: Convex spectral functions of compact operators
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:2000:CSF,
  author =       "Jonathan M. Borwein and John Read and Adrian S. Lewis
                 and Qiji Zhu",
  title =        "Convex spectral functions of compact operators",
  journal =      j-J-NONLINEAR-CONVEX-ANAL,
  volume =       "1",
  number =       "1",
  pages =        "17--35",
  year =         "2000",
  ISSN =         "1345-4773 (print), 1880-5221 (electronic)",
  ISSN-L =       "1345-4773",
  MRclass =      "49N15 (47N10 49J52 90C25)",
  MRnumber =     "1751726",
  MRreviewer =   "Mihai Turinici",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.ybook.co.jp/online2/jncav1.html",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Nonlinear and Convex Analysis. An
                 International Journal",
  journal-URL =  "http://www.ybook.co.jp/jnca.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 99:130.",
  xxauthor =     "Jon Borwein and Adrian Lewis and John Read and Qiji
                 Zhu",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2000:CSR
author: Jonathan M. Borwein and David M. Bradley and Richard E. Crandall
title: Computational Strategies for the Riemann Zeta Function
journal: j-J-COMPUT-APPL-MATH
volume: 121
number: 1--2
pages: 247--296
month: sep
monthnumber: 9
year: 2000
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(00)00336-8
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 11M06 (11Y35 33F05)
MRnumber: 1780051 (2001h:11110)
MRreviewer: Cem Y. Y{\i}ld{\i}r{\i}m
bibdate: Mon Oct 24 11:41:28 2011
bibtimestamp: 2011.10.24 11:41:28 ???
note: Numerical analysis in the 20th century, Vol. I, Approximation theory
URL: http://people.reed.edu/~crandall/papers/attach01.pdf
fjournal: Journal of Computational and Applied Mathematics
remark: CECM Preprint 98:118.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Jonathan M. Borwein and David M. Bradley and Richard E. Crandall
rawnote: Numerical analysis in the 20th century, Vol. I, Approximation theory
rawtitle: Computational Strategies for the {Riemann} Zeta Function
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/bibnet/authors/c/crandall-richard-e.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the incidence of what we call ``value recycling''.

rawabstract:
We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the incidence of what we call ``value recycling''.

entry:
@Article{Borwein:2000:CSR,
  author =       "Jonathan M. Borwein and David M. Bradley and Richard
                 E. Crandall",
  title =        "Computational Strategies for the {Riemann} Zeta
                 Function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "121",
  number =       "1--2",
  pages =        "247--296",
  month =        sep,
  year =         "2000",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00336-8",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "11M06 (11Y35 33F05)",
  MRnumber =     "1780051 (2001h:11110)",
  MRreviewer =   "Cem Y. Y{\i}ld{\i}r{\i}m",
  bibdate =      "Mon Oct 24 11:41:28 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Numerical analysis in the 20th century, Vol. I,
                 Approximation theory",
  URL =          "http://people.reed.edu/~crandall/papers/attach01.pdf",
  abstract =     "We provide a compendium of evaluation methods for the
                 Riemann zeta function, presenting formulae ranging from
                 historical attempts to recently found convergent series
                 to curious oddities old and new. We concentrate
                 primarily on practical computational issues, such
                 issues depending on the domain of the argument, the
                 desired speed of computation, and the incidence of what
                 we call ``value recycling''.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 98:118.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2000:LFM
author: Jonathan M. Borwein and Xianfu Wang
title: Lipschitz functions with maximal Clarke subdifferentials are generic
journal: j-PROC-AM-MATH-SOC
volume: 128
number: 11
pages: 3221--3229
year: 2000
CODEN: PAMYAR
DOI: https://doi.org/10.1090/S0002-9939-00-05914-1
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 49J52 (26B25 58C20)
MRnumber: 1777577
MRreviewer: Jean-No{\"e}l Corvellec
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/206/
fjournal: Proceedings of the American Mathematical Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/journals/proc
rawauthor: Jonathan M. Borwein and Xianfu Wang
rawtitle: {Lipschitz} functions with maximal {Clarke} subdifferentials are generic
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We show that on a separable Banach space most Lipschitz functions have maximal Clarke subdifferential mappings. In particular, the generic nonexpansive function has the dual unit ball as its Clarke subdifferential at every point. Diverse corollaries are given.

entry:
@Article{Borwein:2000:LFM,
  author =       "Jonathan M. Borwein and Xianfu Wang",
  title =        "{Lipschitz} functions with maximal {Clarke}
                 subdifferentials are generic",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "128",
  number =       "11",
  pages =        "3221--3229",
  year =         "2000",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/S0002-9939-00-05914-1",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "49J52 (26B25 58C20)",
  MRnumber =     "1777577",
  MRreviewer =   "Jean-No{\"e}l Corvellec",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/206/",
  abstract =     "We show that on a separable Banach space most
                 Lipschitz functions have maximal Clarke subdifferential
                 mappings. In particular, the generic nonexpansive
                 function has the dual unit ball as its Clarke
                 subdifferential at every point. Diverse corollaries are
                 given.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2000:LFM",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:2000:NCMa
author: J. M. Borwein and T. Stanway
editor: Bruce Cload and Tom Jenkyns
title: Numerical and computational mathematics (at the undergraduate level)
publisher: Brock University Press
address: St. Catharines, ON, L2S 3A1 Canada
pages: 20--37
year: 2000
bibdate: Mon Aug 15 14:24:05 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.15 14:24:05 ???
URL: http://docserver.carma.newcastle.edu.au/246/
remark: Also appeared in Cubo.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and T. Stanway
raweditor: Bruce Cload and Tom Jenkyns
rawtitle: Numerical and computational mathematics (at the undergraduate level)
ORCID: Borwein, Jonathan/0000-0002-1263-0646
booktitle:
Proceedings of the Conference on Technology in Mathematics Education at the Secondary and Tertiary Levels, June 2--4, 1999 at Brock University

rawbooktitle:
{Proceedings of the Conference on Technology in Mathematics Education at the Secondary and Tertiary Levels, June 2--4, 1999 at Brock University}

entry:
@InProceedings{Borwein:2000:NCMa,
  author =       "J. M. Borwein and T. Stanway",
  editor =       "Bruce Cload and Tom Jenkyns",
  booktitle =    "{Proceedings of the Conference on Technology in
                 Mathematics Education at the Secondary and Tertiary
                 Levels, June 2--4, 1999 at Brock University}",
  title =        "Numerical and computational mathematics (at the
                 undergraduate level)",
  publisher =    "Brock University Press",
  address =      "St. Catharines, ON, L2S 3A1 Canada",
  pages =        "20--37",
  year =         "2000",
  bibdate =      "Mon Aug 15 14:24:05 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/246/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Also appeared in Cubo.",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2000:PEN
author: J. M. Borwein and P. B. Borwein and K. Dilcher
title: Pi, Euler Numbers, and Asymptotic Expansions
crossref: Berggren:2000:PSB
pages: 642--648
year: 2000
DOI: https://doi.org/10.1007/978-1-4757-3240-5_65
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:36:22 MDT
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein and K. Dilcher
rawtitle: Pi, {Euler} Numbers, and Asymptotic Expansions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1583/; http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_65

entry:
@InCollection{Borwein:2000:PEN,
  author =       "J. M. Borwein and P. B. Borwein and K. Dilcher",
  title =        "Pi, {Euler} Numbers, and Asymptotic Expansions",
  crossref =     "Berggren:2000:PSB",
  pages =        "642--648",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-1-4757-3240-5_65",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1583/;
                 http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_65",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2000:R
author: Jonathan Borwein and Kwok-Kwong Stephen Choi
title: On the representations of $ x y + y z + z x $
journal: j-EXP-MATH
volume: 9
number: 1
pages: 153--158
year: 2000
DOI: https://doi.org/10.1080/10586458.2000.10504642
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 11D85
MRnumber: 1758806
MRreviewer: Mao Hua Le
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/212/; http://projecteuclid.org/euclid.em/1046889597
fjournal: Experimental Mathematics
remark: CECM Preprint 98:119.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.tandfonline.com/loi/uexm20
rawauthor: Jonathan Borwein and Kwok-Kwong Stephen Choi
rawtitle: On the representations of $ x y + y z + z x $
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

abstract:
We show that there are at most 19 integers that are not of the form $ x y + y z + x z $ with $ x, y, z geq 1 $. Eighteen of them are small and easily found. The remaining possibility must be greater than $ 10^11 $ and cannot occur if we assume the Generalized Riemann Hypothesis.

rawabstract:
We show that there are at most 19 integers that are not of the form $ x y + y z + x z $ with $ x, y, z \geq 1 $. Eighteen of them are small and easily found. The remaining possibility must be greater than $ 10^{11} $ and cannot occur if we assume the Generalized Riemann Hypothesis.

entry:
@Article{Borwein:2000:R,
  author =       "Jonathan Borwein and Kwok-Kwong Stephen Choi",
  title =        "On the representations of $ x y + y z + z x $",
  journal =      j-EXP-MATH,
  volume =       "9",
  number =       "1",
  pages =        "153--158",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2000.10504642",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11D85",
  MRnumber =     "1758806",
  MRreviewer =   "Mao Hua Le",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/212/;
                 http://projecteuclid.org/euclid.em/1046889597",
  abstract =     "We show that there are at most 19 integers that are
                 not of the form $ x y + y z + x z $ with $ x, y, z \geq
                 1 $. Eighteen of them are small and easily found. The
                 remaining possibility must be greater than $ 10^{11} $
                 and cannot occur if we assume the Generalized Riemann
                 Hypothesis.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 98:119.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2000:RCS
author: David Borwein and Jonathan Borwein and Greg Fee and Roland Girgensohn
title: Refined Convexity and Special Cases of the Blaschke--Santalo Inequality
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 8
day: 3
month: apr
monthnumber: 4
year: 2000
bibdate: Thu Sep 01 09:02:50 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 09:02:50 ???
URL: http://docserver.carma.newcastle.edu.au/222
remark: Modified 6 June 2000.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David Borwein and Jonathan Borwein and Greg Fee and Roland Girgensohn
rawtitle: Refined Convexity and Special Cases of the {Blaschke--Santalo} Inequality
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We derive the $ l_p $ version of the classical Blaschke--Santalo inequality for polar volumes as a consequence of more subtle convexity estimates for the volume of the $p$ ball in Euclidean space. We also give analogs for the $ (p, q)$-substitution norms.

rawabstract:
We derive the $ l_p $ version of the classical Blaschke--Santalo inequality for polar volumes as a consequence of more subtle convexity estimates for the volume of the $p$ ball in Euclidean space. We also give analogs for the $ (p, q)$-substitution norms.

entry:
@TechReport{Borwein:2000:RCS,
  author =       "David Borwein and Jonathan Borwein and Greg Fee and
                 Roland Girgensohn",
  title =        "Refined Convexity and Special Cases of the
                 {Blaschke--Santalo} Inequality",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "8",
  day =          "3",
  month =        apr,
  year =         "2000",
  bibdate =      "Thu Sep 01 09:02:50 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/222",
  abstract =     "We derive the $ l_p $ version of the classical
                 Blaschke--Santalo inequality for polar volumes as a
                 consequence of more subtle convexity estimates for the
                 volume of the $p$ ball in Euclidean space. We also give
                 analogs for the $ (p, q)$-substitution norms.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Modified 6 June 2000.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:2000:RGC
author: J. M. Borwein and M. Fabian and I. Kortezov and P. D. Loewen
title: The range of the gradient of a continuously differentiable bump
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 21
day: 12
month: oct
monthnumber: 10
year: 2000
MRclass: 46G05, 58C20
bibdate: Thu Sep 01 09:47:22 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 09:47:22 ???
note: Published in cite Borwein:2001:RGC.
URL: http://docserver.carma.newcastle.edu.au/231/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and M. Fabian and I. Kortezov and P. D. Loewen
rawnote: Published in \cite{Borwein:2001:RGC}.
rawtitle: The range of the gradient of a continuously differentiable bump
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
For a continuously differentiable function with bounded nonempty support, the range of the gradient cannot be locally contained in a hyperplane. However, iterative methods allow the construction of continuously differentiable functions whose gradient ranges have rather general topological features. For example, the gradient range may fail to be simply connected.

rawabstract:
For a continuously differentiable function with bounded nonempty support, the range of the gradient cannot be locally contained in a hyperplane. However, iterative methods allow the construction of continuously differentiable functions whose gradient ranges have rather general topological features. For example, the gradient range may fail to be simply connected.

entry:
@TechReport{Borwein:2000:RGC,
  author =       "J. M. Borwein and M. Fabian and I. Kortezov and P. D.
                 Loewen",
  title =        "The range of the gradient of a continuously
                 differentiable bump",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "21",
  day =          "12",
  month =        oct,
  year =         "2000",
  MRclass =      "46G05, 58C20",
  bibdate =      "Thu Sep 01 09:47:22 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:2001:RGC}.",
  URL =          "http://docserver.carma.newcastle.edu.au/231/",
  abstract =     "For a continuously differentiable function with
                 bounded nonempty support, the range of the gradient
                 cannot be locally contained in a hyperplane. However,
                 iterative methods allow the construction of
                 continuously differentiable functions whose gradient
                 ranges have rather general topological features. For
                 example, the gradient range may fail to be simply
                 connected.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:2000:RME
author: J. M. Borwein and P. B. Borwein and D. H. Bailey
title: Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
crossref: Berggren:2000:PSB
pages: 623--641
year: 2000
DOI: https://doi.org/10.1007/978-1-4757-2736-4_64; https://doi.org/10.1007/978-1-4757-3240-5_64
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:36:22 MDT
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein and D. H. Bailey
rawtitle: {Ramanujan}, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1587/; http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_64; http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_64

entry:
@InCollection{Borwein:2000:RME,
  author =       "J. M. Borwein and P. B. Borwein and D. H. Bailey",
  title =        "{Ramanujan}, Modular Equations, and Approximations to
                 Pi or How to Compute One Billion Digits of Pi",
  crossref =     "Berggren:2000:PSB",
  pages =        "623--641",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-1-4757-2736-4_64;
                 https://doi.org/10.1007/978-1-4757-3240-5_64",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1587/;
                 http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_64;
                 http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_64",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2000:SDI
author: Jonathan M. Borwein and Warren B. Moors
title: Separable determination of integrability and minimality of the Clarke subdifferential mapping
journal: j-PROC-AM-MATH-SOC
volume: 128
number: 1
pages: 215--221
month: jan
monthnumber: 1
year: 2000
CODEN: PAMYAR
DOI: https://doi.org/10.1090/S0002-9939-99-05001-7
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 49J52 (46N10 58C20)
MRnumber: 1622793
MRreviewer: Lionel Thibault
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/196/; https://www.jstor.org/stable/119403
fjournal: Proceedings of the American Mathematical Society
remark: CECM Research Report 97:102.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/journals/proc
rawauthor: Jonathan M. Borwein and Warren B. Moors
rawtitle: Separable determination of integrability and minimality of the {Clarke} subdifferential mapping
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper we show that the study of integrability and D-representability of Lipschitz functions defined on arbitrary Banach spaces reduces to the study of these properties on separable Banach spaces.

rawabstract:
In this paper we show that the study of integrability and D-representability of Lipschitz functions defined on arbitrary Banach spaces reduces to the study of these properties on separable Banach spaces.

entry:
@Article{Borwein:2000:SDI,
  author =       "Jonathan M. Borwein and Warren B. Moors",
  title =        "Separable determination of integrability and
                 minimality of the {Clarke} subdifferential mapping",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "128",
  number =       "1",
  pages =        "215--221",
  month =        jan,
  year =         "2000",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/S0002-9939-99-05001-7",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "49J52 (46N10 58C20)",
  MRnumber =     "1622793",
  MRreviewer =   "Lionel Thibault",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/196/;
                 https://www.jstor.org/stable/119403",
  abstract =     "In this paper we show that the study of integrability
                 and D-representability of Lipschitz functions defined
                 on arbitrary Banach spaces reduces to the study of
                 these properties on separable Banach spaces.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Research Report 97:102.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2000:SDI",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:2000:SM
author: D. Borwein and J. M. Borwein and P. Marechal
title: Surprise maximization
journal: j-AMER-MATH-MONTHLY
volume: 107
number: 6
pages: 517--527
month: jun
monthnumber: 6
year: 2000
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2589347
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 00A08 (03B48 90C90)
MRnumber: 1767060
MRreviewer: S. Kutateladze
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/209/
fjournal: American Mathematical Monthly
remark: CECM Preprint 98:116.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.jstor.org/journals/00029890.html
rawauthor: D. Borwein and J. M. Borwein and P. Mar{\'e}chal
rawtitle: Surprise maximization
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
The Surprise Examination or Unexpected Hanging Paradox has long fascinated mathematicians and philosophers, as the number of publications devoted to it attests. For an exhaustive bibliography on the subject, see [1]. We examine and solve the optimization problems arising from an information theoretic avoidance of the Paradox. These problems provide a very satisfactory application of both the Kuhn-Tucker theory and of various classical inequalities and estimation techniques. We assume some elementary knowledge of optimization but recall the necessary convex analytic concepts in the course of the paper. Readers unfamiliar with this background may simply skip a couple of proofs and a few technical details.

entry:
@Article{Borwein:2000:SM,
  author =       "D. Borwein and J. M. Borwein and P. Mar{\'e}chal",
  title =        "Surprise maximization",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "107",
  number =       "6",
  pages =        "517--527",
  month =        jun # "\slash " # jul,
  year =         "2000",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2589347",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "00A08 (03B48 90C90)",
  MRnumber =     "1767060",
  MRreviewer =   "S. Kutateladze",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/209/",
  abstract =     "The Surprise Examination or Unexpected Hanging Paradox
                 has long fascinated mathematicians and philosophers, as
                 the number of publications devoted to it attests. For
                 an exhaustive bibliography on the subject, see [1]. We
                 examine and solve the optimization problems arising
                 from an information theoretic avoidance of the Paradox.
                 These problems provide a very satisfactory application
                 of both the Kuhn-Tucker theory and of various classical
                 inequalities and estimation techniques. We assume some
                 elementary knowledge of optimization but recall the
                 necessary convex analytic concepts in the course of the
                 paper. Readers unfamiliar with this background may
                 simply skip a couple of proofs and a few technical
                 details.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 98:116.",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2000:SM",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Theodorescu:2000:PSS
author: Radu Theodorescu and Jonathan M. Borwein
title: Problems and Solutions: Solutions: Moments of the Poisson Distribution: 10738
journal: j-AMER-MATH-MONTHLY
volume: 107
number: 7
pages: 659--659
month: aug
monthnumber: 8
year: 2000
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2589135
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRnumber: 1543703
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: https://www.jstor.org/stable/2589135
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.jstor.org/journals/00029890.html
rawauthor: Radu Theodorescu and Jonathan M. Borwein
rawtitle: Problems and Solutions: Solutions: Moments of the {Poisson} Distribution: 10738
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Theodorescu:2000:PSS,
  author =       "Radu Theodorescu and Jonathan M. Borwein",
  title =        "Problems and Solutions: Solutions: Moments of the
                 {Poisson} Distribution: 10738",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "107",
  number =       "7",
  pages =        "659--659",
  month =        aug # "\slash " # sep,
  year =         "2000",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2589135",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRnumber =     "1543703",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "https://www.jstor.org/stable/2589135",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Bailey:2001:EMR
author: David H. Bailey and Jonathan M. Borwein
title: Experimental mathematics: recent developments and future outlook
crossref: Engquist:2001:MUB
pages: 51--66
year: 2001
MRclass: 00A99
MRnumber: 1852153
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/250/
remark: CECM Preprint 99:143.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein
rawtitle: Experimental mathematics: recent developments and future outlook
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Bailey:2001:EMR,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Experimental mathematics: recent developments and
                 future outlook",
  crossref =     "Engquist:2001:MUB",
  pages =        "51--66",
  year =         "2001",
  MRclass =      "00A99",
  MRnumber =     "1852153",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/250/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 99:143.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:2001:ESE
author: Heinz H. Bauschke and Jonathan M. Borwein and Patrick L. Combettes
title: Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces
journal: j-COMMUN-CONTEMP-MATH
volume: 3
number: 4
pages: 615--647
year: 2001
DOI: https://doi.org/10.1142/S0219199701000524
ISSN: 0219-1997 (print), 1793-6683 (electronic) OR 02191997 (print), 17936683 (electronic)
MRclass: 49J53 (46G05 46N10)
MRnumber: 1869107
MRreviewer: S. Simons
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/232/
fjournal: Communications in Contemporary Mathematics
remark: CECM Preprint 00:156.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.worldscientific.com/worldscinet/ccm
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein and Patrick L. Combettes
rawtitle: Essential smoothness, essential strict convexity, and {Legendre} functions in {Banach} spaces
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
abstract:
The classical notions of essential smoothness, essential strict convexity, and Legendreness for convex functions axe extended from Euclidean to Banach spaces. A pertinent duality theory is developed and several useful characterizations are given. The proofs rely on new results on the more subtle behavior of subdifferentials and directional derivatives at boundary points of the domain. In weak Asplund spaces, a new formula allows the recovery of the subdifferential from nearby gradients. Finally, it is shown that every Legendre function on a reflexive Banach space is zone consistent, a fundamental property in the analysis of optimization algorithms based on Bregman distances. Numerous illustrating examples are provided.

rawabstract:
The classical notions of essential smoothness, essential strict convexity, and Legendreness for convex functions axe extended from Euclidean to Banach spaces. A pertinent duality theory is developed and several useful characterizations are given. The proofs rely on new results on the more subtle behavior of subdifferentials and directional derivatives at boundary points of the domain. In weak Asplund spaces, a new formula allows the recovery of the subdifferential from nearby gradients. Finally, it is shown that every Legendre function on a reflexive Banach space is zone consistent, a fundamental property in the analysis of optimization algorithms based on Bregman distances. Numerous illustrating examples are provided.

entry:
@Article{Bauschke:2001:ESE,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein and Patrick
                 L. Combettes",
  title =        "Essential smoothness, essential strict convexity, and
                 {Legendre} functions in {Banach} spaces",
  journal =      j-COMMUN-CONTEMP-MATH,
  volume =       "3",
  number =       "4",
  pages =        "615--647",
  year =         "2001",
  DOI =          "https://doi.org/10.1142/S0219199701000524",
  ISSN =         "0219-1997 (print), 1793-6683 (electronic)",
  MRclass =      "49J53 (46G05 46N10)",
  MRnumber =     "1869107",
  MRreviewer =   "S. Simons",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/232/",
  abstract =     "The classical notions of essential smoothness,
                 essential strict convexity, and Legendreness for convex
                 functions axe extended from Euclidean to Banach spaces.
                 A pertinent duality theory is developed and several
                 useful characterizations are given. The proofs rely on
                 new results on the more subtle behavior of
                 subdifferentials and directional derivatives at
                 boundary points of the domain. In weak Asplund spaces,
                 a new formula allows the recovery of the
                 subdifferential from nearby gradients. Finally, it is
                 shown that every Legendre function on a reflexive
                 Banach space is zone consistent, a fundamental property
                 in the analysis of optimization algorithms based on
                 Bregman distances. Numerous illustrating examples are
                 provided.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Communications in Contemporary Mathematics",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ccm",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 00:156.",
  researcherid-numbers = "Combettes, Patrick/A-2442-2011 Borwein,
                 Jonathan/A-6082-2009 Bauschke, Heinz/D-5582-2009",
  unique-id =    "Bauschke:2001:ESE",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Bauschke:2001:JSC
author: Heinz H. Bauschke and Jonathan M. Borwein
editor: Dan Butnariu and Yair Censor and Simeon Reich
booktitle: Inherently Parallel Algorithms in Feasibility and Optimization and their Applications (Haifa, 2000)
title: Joint and separate convexity of the Bregman distance
volume: 8
publisher: pub-NORTH-HOLLAND
address: pub-NORTH-HOLLAND:adr
pages: 23--36
year: 2001
DOI: https://doi.org/10.1016/S1570-579X(01)80004-5
ISSN: 1570-579X (print), 2212-1145 (electronic) OR 1570579X (print), 22121145 (electronic)
ISSNL: 1570-579X OR 1570579X
MRclass: 90C48 (49J53 65J05 90C30)
MRnumber: 1853214
MRreviewer: Simeon Reich
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
series: Studies in Computational Mathematics
keywords: :Bregman distance; convex function; joint convexity; separate convexity
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein
raweditor: Dan Butnariu and Yair Censor and Simeon Reich
rawtitle: Joint and separate convexity of the {Bregman} distance
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/227/; http://www.sciencedirect.com/science/article/pii/S1570579X01800045

abstract:
Algorithms involving Bregman projections for solving optimization problems have been receiving much attention lately. Several of these methods rely crucially on the joint convexity of the Bregman distance. In this note, we study joint and separate convexity of Bregman distances. To bring out the main ideas more clearly, we consider first functions defined on an open interval. Our main result states that the Bregman distance of a given function is jointly convex if and only if the reciprocal of its second derivative is concave. We observe that Bregman distances induced by the two most popular choices --- the energy and the Boltzmann--Shannon entropy --- are limiting cases in a profound sense. This result is generalized by weakening assumptions on differentiability and strict convexity. We then consider general, not necessarily separable, convex functions. The characterization of joint convexity has a natural and beautiful analog. Finally, we discuss spectral functions, where the situation is less clear. Throughout, we provide numerous examples to illustrate our results.

rawabstract:
Algorithms involving Bregman projections for solving optimization problems have been receiving much attention lately. Several of these methods rely crucially on the joint convexity of the Bregman distance. In this note, we study joint and separate convexity of Bregman distances. To bring out the main ideas more clearly, we consider first functions defined on an open interval. Our main result states that the Bregman distance of a given function is jointly convex if and only if the reciprocal of its second derivative is concave. We observe that Bregman distances induced by the two most popular choices --- the energy and the Boltzmann--Shannon entropy --- are limiting cases in a profound sense. This result is generalized by weakening assumptions on differentiability and strict convexity. We then consider general, not necessarily separable, convex functions. The characterization of joint convexity has a natural and beautiful analog. Finally, we discuss spectral functions, where the situation is less clear. Throughout, we provide numerous examples to illustrate our results.

rawbooktitle:
Inherently Parallel Algorithms in Feasibility and Optimization and their Applications ({Haifa}, 2000)

entry:
@InProceedings{Bauschke:2001:JSC,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein",
  editor =       "Dan Butnariu and Yair Censor and Simeon Reich",
  booktitle =    "Inherently Parallel Algorithms in Feasibility and
                 Optimization and their Applications ({Haifa}, 2000)",
  title =        "Joint and separate convexity of the {Bregman}
                 distance",
  volume =       "8",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "23--36",
  year =         "2001",
  DOI =          "https://doi.org/10.1016/S1570-579X(01)80004-5",
  ISSN =         "1570-579X (print), 2212-1145 (electronic)",
  ISSN-L =       "1570-579X",
  MRclass =      "90C48 (49J53 65J05 90C30)",
  MRnumber =     "1853214",
  MRreviewer =   "Simeon Reich",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Studies in Computational Mathematics",
  URL =          "http://docserver.carma.newcastle.edu.au/227/;
                 http://www.sciencedirect.com/science/article/pii/S1570579X01800045",
  abstract =     "Algorithms involving Bregman projections for solving
                 optimization problems have been receiving much
                 attention lately. Several of these methods rely
                 crucially on the joint convexity of the Bregman
                 distance. In this note, we study joint and separate
                 convexity of Bregman distances. To bring out the main
                 ideas more clearly, we consider first functions defined
                 on an open interval. Our main result states that the
                 Bregman distance of a given function is jointly convex
                 if and only if the reciprocal of its second derivative
                 is concave. We observe that Bregman distances induced
                 by the two most popular choices --- the energy and the
                 Boltzmann--Shannon entropy --- are limiting cases in a
                 profound sense. This result is generalized by weakening
                 assumptions on differentiability and strict convexity.
                 We then consider general, not necessarily separable,
                 convex functions. The characterization of joint
                 convexity has a natural and beautiful analog. Finally,
                 we discuss spectral functions, where the situation is
                 less clear. Throughout, we provide numerous examples to
                 illustrate our results.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     ":Bregman distance; convex function; joint convexity;
                 separate convexity",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


