# bibtab

bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1992:ASW
author: Jonathan Borwein and Shi Tuo Lou
title: Asymptotics of a sequence of Witt vectors
journal: j-J-APPROX-THEORY
volume: 69
number: 3
pages: 326--337
year: 1992
CODEN: JAXTAZ
DOI: https://doi.org/10.1016/0021-9045(92)90006-A
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
MRclass: 05A16 (05E05 05E10 13K05)
MRnumber: 1164995
MRreviewer: Jiang Zeng
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
fjournal: Journal of Approximation Theory
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: Jonathan Borwein and Shi Tuo Lou
rawtitle: Asymptotics of a sequence of {Witt} vectors
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1565/; http://www.sciencedirect.com/science/article/pii/002190459290006A

abstract:
We provide asymptotic and order information about the Witt vectors and integers dn appearing in prod nle 111 + dn(tnn|)=(1-t)et.

rawabstract:
We provide asymptotic and order information about the Witt vectors and integers dn appearing in \prod n\le 111 + dn(tnn|)=(1-t)et.

entry:
@Article{Borwein:1992:ASW,
  author =       "Jonathan Borwein and Shi Tuo Lou",
  title =        "Asymptotics of a sequence of {Witt} vectors",
  journal =      j-J-APPROX-THEORY,
  volume =       "69",
  number =       "3",
  pages =        "326--337",
  year =         "1992",
  CODEN =        "JAXTAZ",
  DOI =          "https://doi.org/10.1016/0021-9045(92)90006-A",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  MRclass =      "05A16 (05E05 05E10 13K05)",
  MRnumber =     "1164995",
  MRreviewer =   "Jiang Zeng",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1565/;
                 http://www.sciencedirect.com/science/article/pii/002190459290006A",
  abstract =     "We provide asymptotic and order information about the
                 Witt vectors and integers dn appearing in \prod n\le
                 111 + dn(tnn|)=(1-t)et.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1992:BRS
author: Jonathan Borwein
title: Book Review: booktitle Set-valued analysis, J-P. Aubin and H. Frankowska
journal: j-BULL-AMS-N-S
volume: 26
number: 1
pages: 157--160
year: 1992
CODEN: BAMOAD
DOI: https://doi.org/10.1090/S0273-0979-1992-00246-X
ISSN: 0273-0979 (print), 1088-9485 (electronic) OR 02730979 (print), 10889485 (electronic)
ISSNL: 0273-0979 OR 02730979
MRnumber: 1567970
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 Society. Bulletin. New Series
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/journals/bull/all_issues.html
rawauthor: Jonathan Borwein
rawtitle: Book Review: {{\booktitle{Set-valued analysis}}, J-P. Aubin and H. Frankowska}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1992:BRS,
  author =       "Jonathan Borwein",
  title =        "Book Review: {{\booktitle{Set-valued analysis}}, J-P.
                 Aubin and H. Frankowska}",
  journal =      j-BULL-AMS-N-S,
  volume =       "26",
  number =       "1",
  pages =        "157--160",
  year =         "1992",
  CODEN =        "BAMOAD",
  DOI =          "https://doi.org/10.1090/S0273-0979-1992-00246-X",
  ISSN =         "0273-0979 (print), 1088-9485 (electronic)",
  ISSN-L =       "0273-0979",
  MRnumber =     "1567970",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "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 Society. Bulletin. New Series",
  journal-URL =  "http://www.ams.org/journals/bull/all_issues.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1992:DMF
author: Jonathan M. Borwein and Adrian S. Lewis
title: Decomposition of multivariate functions
journal: j-CAN-J-MATH
volume: 44
number: 3
pages: 463--482
year: 1992
CODEN: CJMAAB
DOI: https://doi.org/10.4153/CJM-1992-030-9
ISSN: 0008-414X (print), 1496-4279 (electronic) OR 0008414X (print), 14964279 (electronic)
ISSNL: 0008-414X OR 0008414X
MRclass: 54C05 (05C38 08A45 22C05 26B40 28A20)
MRnumber: 1176365
MRreviewer: Douglass L. Grant
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/1569/
fjournal: Canadian Journal of Mathematics. Journal Canadien de Mathematiques
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://cms.math.ca/cjm/
rawauthor: Jonathan M. Borwein and Adrian S. Lewis
rawtitle: Decomposition of multivariate functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1992:DMF,
  author =       "Jonathan M. Borwein and Adrian S. Lewis",
  title =        "Decomposition of multivariate functions",
  journal =      j-CAN-J-MATH,
  volume =       "44",
  number =       "3",
  pages =        "463--482",
  year =         "1992",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-1992-030-9",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  MRclass =      "54C05 (05C38 08A45 22C05 26B40 28A20)",
  MRnumber =     "1176365",
  MRreviewer =   "Douglass L. Grant",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1569/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Canadian Journal of Mathematics. Journal Canadien de
                 Math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1992:FEG
author: J. M. Borwein and I. J. Zucker
journal: j-IMA-J-NUMER-ANAL
volume: 12
number: 4
pages: 519--526
year: 1992
CODEN: IJNADN
DOI: https://doi.org/10.1093/imanum/12.4.519
ISSN: 0272-4979 (print), 1464-3642 (electronic) OR 02724979 (print), 14643642 (electronic)
ISSNL: 0272-4979 OR 02724979
MRclass: 65D20
MRnumber: 1186733
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: IMA Journal of Numerical Analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://imajna.oxfordjournals.org/content/by/year
rawauthor: J. M. Borwein and I. J. Zucker
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind

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

rawtitle:
Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind

entry:
@Article{Borwein:1992:FEG,
  author =       "J. M. Borwein and I. J. Zucker",
  title =        "Fast evaluation of the gamma function for small
                 rational fractions using complete elliptic integrals of
                 the first kind",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "12",
  number =       "4",
  pages =        "519--526",
  year =         "1992",
  CODEN =        "IJNADN",
  DOI =          "https://doi.org/10.1093/imanum/12.4.519",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65D20",
  MRnumber =     "1186733",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1992:KMI
author: Jonathan Borwein and Simeon Reich and Itai Shafrir
title: Krasnosel'ski--Mann iterations in normed spaces
journal: j-CAN-MATH-BULL
volume: 35
number: 1
pages: 21--28
year: 1992
CODEN: CMBUA3
DOI: https://doi.org/10.4153/CMB-1992-003-0
ISSN: 0008-4395 (print), 1496-4287 (electronic) OR 00084395 (print), 14964287 (electronic)
ISSNL: 0008-4395 OR 00084395
MRclass: 47H09 (47H10 47H17)
MRnumber: 1157459
MRreviewer: Gregory B. Passty
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Canadian Mathematical Bulletin. Bulletin Canadien de Mathematiques
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://cms.math.ca/cmb/
rawauthor: Jonathan Borwein and Simeon Reich and Itai Shafrir
rawtitle: {Krasnosel'ski--Mann} iterations in normed spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1992:KMI,
  author =       "Jonathan Borwein and Simeon Reich and Itai Shafrir",
  title =        "{Krasnosel'ski--Mann} iterations in normed spaces",
  journal =      j-CAN-MATH-BULL,
  volume =       "35",
  number =       "1",
  pages =        "21--28",
  year =         "1992",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-1992-003-0",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  MRclass =      "47H09 (47H10 47H17)",
  MRnumber =     "1157459",
  MRreviewer =   "Gregory B. Passty",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "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 =     "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:1992:MHP
author: Jonathan M. Borwein and Mark A. Limber
title: Maple as a High Precision Calculator
journal: j-MAPLE-TECH-NEWS
volume: 0
number: 8
pages: 39--44
month: Fall
year: 1992
ISSN: 1061-5733 OR 10615733
ISSNL: 1061-5733 OR 10615733
bibdate: Fri May 09 22:33:19 1997
bibtimestamp: 1997.05.09 22:33:19 ???
URL: http://www.can.nl/Systems_and_Packages/Per_Purpose/General/Maple/mtn/mtn8.html
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 M. Borwein and Mark A. Limber
rawtitle: {Maple} as a High Precision Calculator
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:1992:MHP,
  author =       "Jonathan M. Borwein and Mark A. Limber",
  title =        "{Maple} as a High Precision Calculator",
  journal =      j-MAPLE-TECH-NEWS,
  volume =       "0",
  number =       "8",
  pages =        "39--44",
  month =        "Fall",
  year =         "1992",
  ISSN =         "1061-5733",
  ISSN-L =       "1061-5733",
  bibdate =      "Fri May 09 22:33:19 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-tech.bib",
  URL =          "http://www.can.nl/Systems_and_Packages/Per_Purpose/General/Maple/mtn/mtn8.html",
  acknowledgement = ack-nhfb,
  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:1992:PFCa
author: Jonathan M. Borwein and Adrian S. Lewis
title: Partially finite convex programming. I. Quasi relative interiors and duality theory
journal: j-MATH-PROG
volume: 57
number: 1--3
pages: 15--48
year: 1992
CODEN: MHPGA4
DOI: https://doi.org/10.1007/BF01581072
ISSN: 0025-5610 (print), 1436-4646 (electronic) OR 00255610 (print), 14364646 (electronic)
ISSNL: 0025-5610 OR 00255610
MRclass: 90C48 (49J15 65K05 90C25)
MRnumber: 1167406
MRreviewer: M. Teboulle
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/1571/; http://link.springer.com/article/10.1007/BF01581072
fjournal: Mathematical Programming
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/10107
rawauthor: Jonathan M. Borwein and Adrian S. Lewis
rawtitle: Partially finite convex programming. {I}. {Quasi} relative interiors and duality theory
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1992:PFCa,
  author =       "Jonathan M. Borwein and Adrian S. Lewis",
  title =        "Partially finite convex programming. {I}. {Quasi}
                 relative interiors and duality theory",
  journal =      j-MATH-PROG,
  volume =       "57",
  number =       "1--3",
  pages =        "15--48",
  year =         "1992",
  CODEN =        "MHPGA4",
  DOI =          "https://doi.org/10.1007/BF01581072",
  ISSN =         "0025-5610 (print), 1436-4646 (electronic)",
  ISSN-L =       "0025-5610",
  MRclass =      "90C48 (49J15 65K05 90C25)",
  MRnumber =     "1167406",
  MRreviewer =   "M. Teboulle",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1571/;
                 http://link.springer.com/article/10.1007/BF01581072",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematical Programming",
  journal-URL =  "http://link.springer.com/journal/10107",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1992:PFCb
author: Jonathan M. Borwein and Adrian S. Lewis
title: Partially finite convex programming, Part II: Explicit lattice models
journal: j-MATH-PROG
volume: 57
number: 1--3
pages: 49--83
year: 1992
CODEN: MHPGA4
DOI: https://doi.org/10.1007/BF01581073
ISSN: 0025-5610 (print), 1436-4646 (electronic) OR 00255610 (print), 14364646 (electronic)
ISSNL: 0025-5610 OR 00255610
MRclass: 90C48 (49N15 65K05 90C25)
MRnumber: 1167407
MRreviewer: M. Teboulle
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/1572/; http://link.springer.com/article/10.1007/BF01581073
fjournal: Mathematical Programming
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/10107
rawauthor: Jonathan M. Borwein and Adrian S. Lewis
rawtitle: Partially finite convex programming, {Part II}: Explicit lattice models
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1992:PFCb,
  author =       "Jonathan M. Borwein and Adrian S. Lewis",
  title =        "Partially finite convex programming, {Part II}:
                 Explicit lattice models",
  journal =      j-MATH-PROG,
  volume =       "57",
  number =       "1--3",
  pages =        "49--83",
  year =         "1992",
  CODEN =        "MHPGA4",
  DOI =          "https://doi.org/10.1007/BF01581073",
  ISSN =         "0025-5610 (print), 1436-4646 (electronic)",
  ISSN-L =       "0025-5610",
  MRclass =      "90C48 (49N15 65K05 90C25)",
  MRnumber =     "1167407",
  MRreviewer =   "M. Teboulle",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1572/;
                 http://link.springer.com/article/10.1007/BF01581073",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematical Programming",
  journal-URL =  "http://link.springer.com/journal/10107",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:1992:SDP
author: J. M. Borwein
crossref: Ioffe:1992:ONA
pages: 39--52
year: 1992
ISBN: 0-582-08065-7 (paperback), 0-470-21943-2 OR 0582080657 (paperback), 0470219432
ISBN13: 978-0-582-08065-2 (paperback), 978-0-470-21943-0 OR 9780582080652 (paperback), 9780470219430
ISSN: 0269-3674 OR 02693674
ISSNL: 0269-3674 OR 02693674
LCCN: QA402.5 .O6424 1991
MRclass: 49J50 (46B20 46G05 47H99)
MRnumber: 1184630
MRreviewer: Julian Revalski
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: Pitman research notes in mathematics series
ZMnumber: 0745.00050
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Differentiability properties of convex, of Lipschitz, and of semicontinuous mappings on Banach spaces

rawtitle:
Differentiability properties of convex, of {Lipschitz}, and of semicontinuous mappings on {Banach} spaces

entry:
@InProceedings{Borwein:1992:SDP,
  author =       "J. M. Borwein",
  title =        "Differentiability properties of convex, of
                 {Lipschitz}, and of semicontinuous mappings on {Banach}
                 spaces",
  crossref =     "Ioffe:1992:ONA",
  pages =        "39--52",
  year =         "1992",
  ISBN =         "0-582-08065-7 (paperback), 0-470-21943-2",
  ISBN-13 =      "978-0-582-08065-2 (paperback), 978-0-470-21943-0",
  ISSN =         "0269-3674",
  ISSN-L =       "0269-3674",
  LCCN =         "QA402.5 .O6424 1991",
  MRclass =      "49J50 (46B20 46G05 47H99)",
  MRnumber =     "1184630",
  MRreviewer =   "Julian Revalski",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Pitman research notes in mathematics series",
  URL =          "",
  ZMnumber =     "0745.00050",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  xxtitle =      "A survey of differentiability properties of convex,
                 {Lipschitz} and lsc functions",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:1992:SEC
author: J. M. Borwein and A. Ben Tal and M. Teboulle
title: Spectral estimation via convex programming
crossref: Phillips:1992:SMS
pages: 275--290
year: 1992
bibdate: Mon Aug 15 14:57:23 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.15 14:57:23 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and A. {Ben Tal} and M. Teboulle
rawtitle: Spectral estimation via convex programming
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:1992:SEC,
  author =       "J. M. Borwein and A. {Ben Tal} and M. Teboulle",
  title =        "Spectral estimation via convex programming",
  crossref =     "Phillips:1992:SMS",
  pages =        "275--290",
  year =         "1992",
  bibdate =      "Mon Aug 15 14:57:23 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1992:SOC
author: Jonathan Borwein and Peter B. Borwein
title: Some Observations on Computer Aided Analysis
journal: j-NAMS
volume: 39
number: 8
pages: 825--829
month: oct
monthnumber: 10
year: 1992
CODEN: AMNOAN
ISSN: 0002-9920 (print), 1088-9477 (electronic) OR 00029920 (print), 10889477 (electronic)
ISSNL: 0002-9920 OR 00029920
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://www.ams.org/journals/notices/199210/199210FullIssue.pdf
fjournal: Notices of the American Mathematical Society
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/notices/
rawauthor: Jonathan Borwein and Peter B. Borwein
rawtitle: Some Observations on Computer Aided Analysis
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/subjects/acc-stab-num-alg.bib

entry:
@Article{Borwein:1992:SOC,
  author =       "Jonathan Borwein and Peter B. Borwein",
  title =        "Some Observations on Computer Aided Analysis",
  journal =      j-NAMS,
  volume =       "39",
  number =       "8",
  pages =        "825--829",
  month =        oct,
  year =         "1992",
  CODEN =        "AMNOAN",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  URL =          "http://www.ams.org/journals/notices/199210/199210FullIssue.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1992:SSH
author: J. M. Borwein and P. B. Borwein
title: Strange Series and High Precision Fraud
journal: j-AMER-MATH-MONTHLY
volume: 99
number: 7
pages: 622--640
month: aug
monthnumber: 8
year: 1992
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2324993
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 40-01 (40A05 40A25)
MRnumber: 1176589, 93f:40001
MRreviewer: John A. Fridy
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
note: See also subsequent work cite Bradshaw:2024:DIV.
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 P. B. Borwein
rawnote: See also subsequent work \cite{Bradshaw:2024:DIV}.
rawtitle: Strange Series and High Precision Fraud
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib

entry:
@Article{Borwein:1992:SSH,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "Strange Series and High Precision Fraud",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "99",
  number =       "7",
  pages =        "622--640",
  month =        aug # "\slash " # sep,
  year =         "1992",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2324993",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "40-01 (40A05 40A25)",
  MRnumber =     "1176589, 93f:40001",
  MRreviewer =   "John A. Fridy",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib",
  note =         "See also subsequent work \cite{Bradshaw:2024:DIV}.",
  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:1992:STS
author: J. M. Borwein and M. Thera
title: Sandwich theorems for semicontinuous operators
journal: j-CAN-MATH-BULL
volume: 35
number: 4
pages: 463--474
year: 1992
CODEN: CMBUA3
DOI: https://doi.org/10.4153/CMB-1992-061-7
ISSN: 0008-4395 (print), 1496-4287 (electronic) OR 00084395 (print), 14964287 (electronic)
ISSNL: 0008-4395 OR 00084395
MRclass: 54C08 (46A99 54C60 54C65 54F05)
MRnumber: 1191505
MRreviewer: P. Maritz
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
fjournal: Canadian 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 M. Th{\'e}ra
rawtitle: Sandwich theorems for semicontinuous operators
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1992:STS,
  author =       "J. M. Borwein and M. Th{\'e}ra",
  title =        "Sandwich theorems for semicontinuous operators",
  journal =      j-CAN-MATH-BULL,
  volume =       "35",
  number =       "4",
  pages =        "463--474",
  year =         "1992",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-1992-061-7",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  MRclass =      "54C08 (46A99 54C60 54C65 54F05)",
  MRnumber =     "1191505",
  MRreviewer =   "P. Maritz",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "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 =     "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: Cook:1992:PSS
author: Matthew Cook and Walther Janous and Marcin E. Kuczma and David Borwein
title: Problems and Solutions: Solutions of Elementary Problems: E3388
journal: j-AMER-MATH-MONTHLY
volume: 99
number: 1
pages: 69--70
month: jan
monthnumber: 1
year: 1992
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2324561
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
note: See also cite Sturm:1990:PSE.
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Matthew Cook and Walther Janous and Marcin E. Kuczma and David Borwein
rawnote: See also \cite{Sturm:1990:PSE}.
rawtitle: Problems and Solutions: Solutions of Elementary Problems: {E3388}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib

entry:
@Article{Cook:1992:PSS,
  author =       "Matthew Cook and Walther Janous and Marcin E. Kuczma
                 and David Borwein",
  title =        "Problems and Solutions: Solutions of Elementary
                 Problems: {E3388}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "99",
  number =       "1",
  pages =        "69--70",
  month =        jan,
  year =         "1992",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2324561",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib",
  note =         "See also \cite{Sturm:1990:PSE}.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bailey:1993:EEE
author: David H. Bailey and Jonathan M. Borwein and Roland Girgensohn
title: Experimental evaluation of Euler sums
type: Technical Report
number: RNR-93-014
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 24
day: 20
month: oct
monthnumber: 10
year: 1993
bibdate: Thu Sep 01 13:58:44 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 13:58:44 ???
URL: http://docserver.carma.newcastle.edu.au/60
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein and Roland Girgensohn
rawtitle: Experimental evaluation of {Euler} sums
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In response to a letter from Goldbach, Euler considered sums of the formpar $$ sum _k = 1^infty big (1 + frac 12^m + cdots + frac 1k^m big ) (k + 1)^-n $$ par for positive integers $m$ and $n$. Euler was able to give explicit values for certain of these sums in terms of the Riemann zeta function. In a recent companion paper, Euler's results were extended to a significantly larger class of sums of this type, including sums with alternating signs.par This research was facilitated by numerical computations using an algorithm that can determine, with high confidence, whether or not a particular numerical value can be expressed as a rational linear combination of several given constants. The present paper presents the numerical techniques used in these computations and lists many of the experimental results that have been obtained.

rawabstract:
In response to a letter from Goldbach, Euler considered sums of the form\par $$ \sum_{k = 1}^\infty \big (1 + \frac {1}{2^m} + \cdots + \frac {1}{k^m} \big) (k + 1)^{-n} $$ \par for positive integers $m$ and $n$. Euler was able to give explicit values for certain of these sums in terms of the Riemann zeta function. In a recent companion paper, Euler's results were extended to a significantly larger class of sums of this type, including sums with alternating signs.\par This research was facilitated by numerical computations using an algorithm that can determine, with high confidence, whether or not a particular numerical value can be expressed as a rational linear combination of several given constants. The present paper presents the numerical techniques used in these computations and lists many of the experimental results that have been obtained.

entry:
@TechReport{Bailey:1993:EEE,
  author =       "David H. Bailey and Jonathan M. Borwein and Roland
                 Girgensohn",
  title =        "Experimental evaluation of {Euler} sums",
  type =         "Technical Report",
  number =       "RNR-93-014",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  pages =        "24",
  day =          "20",
  month =        oct,
  year =         "1993",
  bibdate =      "Thu Sep 01 13:58:44 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/60",
  abstract =     "In response to a letter from Goldbach, Euler
                 considered sums of the form\par

                  $$ \sum_{k = 1}^\infty \big (1 + \frac {1}{2^m} +
                 \cdots + \frac {1}{k^m} \big) (k + 1)^{-n} $$ \par

                 for positive integers $m$ and $n$. Euler was able to
                 give explicit values for certain of these sums in terms
                 of the Riemann zeta function. In a recent companion
                 paper, Euler's results were extended to a significantly
                 larger class of sums of this type, including sums with
                 alternating signs.\par

                 This research was facilitated by numerical computations
                 using an algorithm that can determine, with high
                 confidence, whether or not a particular numerical value
                 can be expressed as a rational linear combination of
                 several given constants. The present paper presents the
                 numerical techniques used in these computations and
                 lists many of the experimental results that have been
                 obtained.",
  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: Bauschke:1993:CNA
author: H. H. Bauschke and J. M. Borwein
title: On the convergence of von Neumann's alternating projection algorithm for two sets
journal: j-SET-VALUED-ANAL
volume: 1
number: 2
pages: 185--212
year: 1993
CODEN: SVANEG
DOI: https://doi.org/10.1007/BF01027691
ISSN: 0927-6947 (print), 1572-932X (electronic) OR 09276947 (print), 1572932X (electronic)
ISSNL: 0927-6947 OR 09276947
MRclass: 65J05 (41A65 47H17 65K10)
MRnumber: 1239403
MRreviewer: F. Deutsch
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/1555/; http://link.springer.com/article/10.1007/BF01027691
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11228
rawauthor: H. H. Bauschke and J. M. Borwein
rawtitle: On the convergence of {von Neumann}'s alternating projection algorithm for two sets
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
fjournal:
Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications

entry:
@Article{Bauschke:1993:CNA,
  author =       "H. H. Bauschke and J. M. Borwein",
  title =        "On the convergence of {von Neumann}'s alternating
                 projection algorithm for two sets",
  journal =      j-SET-VALUED-ANAL,
  volume =       "1",
  number =       "2",
  pages =        "185--212",
  year =         "1993",
  CODEN =        "SVANEG",
  DOI =          "https://doi.org/10.1007/BF01027691",
  ISSN =         "0927-6947 (print), 1572-932X (electronic)",
  ISSN-L =       "0927-6947",
  MRclass =      "65J05 (41A65 47H17 65K10)",
  MRnumber =     "1239403",
  MRreviewer =   "F. Deutsch",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1555/;
                 http://link.springer.com/article/10.1007/BF01027691",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Set-Valued Analysis. An International Journal Devoted
                 to the Theory of Multifunctions and its Applications",
  journal-URL =  "http://link.springer.com/journal/11228",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Beer:1993:MSC
author: Gerald Beer and Jonathan M. Borwein
title: Mosco and Slice Convergence of Level Sets and Graphs of Linear Functionals
journal: j-J-MATH-ANAL-APPL
volume: 175
number: 1
pages: 53--67
year: 1993
CODEN: JMANAK
DOI: https://doi.org/10.1006/jmaa.1993.1151
ISSN: 0022-247X (print), 1096-0813 (electronic) OR 0022247X (print), 10960813 (electronic)
ISSNL: 0022-247X OR 0022247X
MRclass: 46B99 (46N10 49J45 54A20)
MRnumber: 1216744
MRreviewer: Constantin Z{\u{a}}linescu
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: Gerald Beer and Jonathan M. Borwein
rawtitle: {Mosco} and Slice Convergence of Level Sets and Graphs of Linear Functionals
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1562/; http://www.sciencedirect.com/science/article/pii/S0022247X83711510

entry:
@Article{Beer:1993:MSC,
  author =       "Gerald Beer and Jonathan M. Borwein",
  title =        "{Mosco} and Slice Convergence of Level Sets and Graphs
                 of Linear Functionals",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "175",
  number =       "1",
  pages =        "53--67",
  year =         "1993",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1006/jmaa.1993.1151",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "46B99 (46N10 49J45 54A20)",
  MRnumber =     "1216744",
  MRreviewer =   "Constantin Z{\u{a}}linescu",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1562/;
                 http://www.sciencedirect.com/science/article/pii/S0022247X83711510",
  acknowledgement = ack-nhfb,
  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",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:1993:ASS
author: J. M. Borwein
title: Asplund spaces are sequentially reflexive
pages: 53--67
year: 1993
bibdate: Fri Aug 12 14:17:01 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 14:17:01 ???
remark: Research Report CORR 91-14.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein
rawtitle: {Asplund} spaces are sequentially reflexive
ORCID: Borwein, Jonathan/0000-0002-1263-0646
note:
Accepted for publication in the Canadian Journal of Mathematics, but withdrawn and merged with another paper. Jon Borwein recorded that as publication number 121, but because the article numbers changed with each update of his CV, that number has long been incorrect.

rawnote:
Accepted for publication in the Canadian Journal of Mathematics, but withdrawn and merged with another paper. Jon Borwein recorded that as publication number 121, but because the article numbers changed with each update of his CV, that number has long been incorrect.

entry:
@Unpublished{Borwein:1993:ASS,
  author =       "J. M. Borwein",
  title =        "{Asplund} spaces are sequentially reflexive",
  year =         "1993",
  bibdate =      "Fri Aug 12 14:17:01 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Accepted for publication in the Canadian Journal of
                 Mathematics, but withdrawn and merged with another
                 paper. Jon Borwein recorded that as publication number
                 121, but because the article numbers changed with each
                 update of his CV, that number has long been
                 incorrect.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Research Report CORR 91-14.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1993:CDS
author: Jonathan M. Borwein and Adrian S. Lewis
title: Convergence of decreasing sequences of convex sets in nonreflexive Banach spaces
journal: j-SET-VALUED-ANAL
volume: 1
number: 4
pages: 355--363
year: 1993
CODEN: SVANEG
DOI: https://doi.org/10.1007/BF01027825
ISSN: 0927-6947 (print), 1572-932x (electronic) OR 09276947 (print), 1572932x (electronic)
ISSNL: 0927-6947 OR 09276947
MRclass: 49J45 (46N10)
MRnumber: 1267202
MRreviewer: Roberto Lucchetti
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/1551/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11228
rawauthor: Jonathan M. Borwein and Adrian S. Lewis
rawtitle: Convergence of decreasing sequences of convex sets in nonreflexive {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
fjournal:
Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications

entry:
@Article{Borwein:1993:CDS,
  author =       "Jonathan M. Borwein and Adrian S. Lewis",
  title =        "Convergence of decreasing sequences of convex sets in
                 nonreflexive {Banach} spaces",
  journal =      j-SET-VALUED-ANAL,
  volume =       "1",
  number =       "4",
  pages =        "355--363",
  year =         "1993",
  CODEN =        "SVANEG",
  DOI =          "https://doi.org/10.1007/BF01027825",
  ISSN =         "0927-6947 (print), 1572-932x (electronic)",
  ISSN-L =       "0927-6947",
  MRclass =      "49J45 (46N10)",
  MRnumber =     "1267202",
  MRreviewer =   "Roberto Lucchetti",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1551/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Set-Valued Analysis. An International Journal Devoted
                 to the Theory of Multifunctions and its Applications",
  journal-URL =  "http://link.springer.com/journal/11228",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: unpublished
filename: borwein-jonathan-m.bib
label: Borwein:1993:CEU
author: J. M. Borwein and R. K. Goodrich and M. A. Limber
title: A comparison of entropies in the underdetermined moment problem
pages: 355--363
month: may
monthnumber: 5
year: 1993
bibdate: Tue Aug 16 10:06:18 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:06:18 ???
note: Preprint.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and R. K. Goodrich and M. A. Limber
rawnote: Preprint.
rawtitle: A comparison of entropies in the underdetermined moment problem
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Unpublished{Borwein:1993:CEU,
  author =       "J. M. Borwein and R. K. Goodrich and M. A. Limber",
  title =        "A comparison of entropies in the underdetermined
                 moment problem",
  month =        may,
  year =         "1993",
  bibdate =      "Tue Aug 16 10:06:18 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Preprint.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1993:CFH
author: J. M. Borwein and M. Fabian
journal: j-CAN-J-MATH
volume: 45
number: 6
pages: 1121--1134
year: 1993
CODEN: CJMAAB
DOI: https://doi.org/10.4153/CJM-1993-062-8
ISSN: 0008-414X (print), 1496-4279 (electronic) OR 0008414X (print), 14964279 (electronic)
ISSNL: 0008-414X OR 0008414X
MRclass: 46B20 (46B03)
MRnumber: 1247537
MRreviewer: Gilles Godefroy
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/1552/
fjournal: Canadian Journal of Mathematics. Journal Canadien de Mathematiques
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://cms.math.ca/cjm/
rawauthor: J. M. Borwein and M. Fabi{\'a}n
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
On convex functions having points of Gateaux differentiability which are not points of Frechet differentiability

rawtitle:
On convex functions having points of {G{\^a}teaux} differentiability which are not points of {Fr}{\'e}chet differentiability

entry:
@Article{Borwein:1993:CFH,
  author =       "J. M. Borwein and M. Fabi{\'a}n",
  title =        "On convex functions having points of {G{\^a}teaux}
                 differentiability which are not points of {Fr}{\'e}chet
                 differentiability",
  journal =      j-CAN-J-MATH,
  volume =       "45",
  number =       "6",
  pages =        "1121--1134",
  year =         "1993",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-1993-062-8",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  MRclass =      "46B20 (46B03)",
  MRnumber =     "1247537",
  MRreviewer =   "Gilles Godefroy",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1552/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Canadian Journal of Mathematics. Journal Canadien de
                 Math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1993:CNT
author: J. M. Borwein and P. B. Borwein
title: Class number three Ramanujan type series for $ 1 / pi $
journal: j-J-COMPUT-APPL-MATH
volume: 46
number: 1--2
pages: 281--290
day: 14
month: jun
monthnumber: 6
year: 1993
CODEN: JCAMDI
DOI: https://doi.org/10.1016/0377-0427(93)90302-R
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 11Y60 (11R11)
MRnumber: 1222488
MRreviewer: Andrew Granville
bibdate: Sat Feb 25 12:20:57 MST 2017
bibtimestamp: 2017.02.25 12:20:57 MST
note: Computational complex analysis.
fjournal: Journal of Computational and Applied Mathematics
keywords: class number; pi; Ramanujan; series
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: J. M. Borwein and P. B. Borwein
rawnote: Computational complex analysis.
rawtitle: Class number three {Ramanujan} type series for $ 1 / \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/jcomputapplmath1990.bib

URL:
http://docserver.carma.newcastle.edu.au/1560/; http://www.sciencedirect.com/science/article/pii/037704279390302R

abstract:
There is a class of remarkable series for $ 1 / pi $ of the form $ sqrt -C^3 / pi = sum _n = 0^infty frac A + n BC^3 n frac (6n)!(3n)!(n!)^3 $ where $A$, $B$, $C$ are certain algebraic numbers. These were first examined by Ramanujan. These examples arise by computing singular invariants for j and the constants involved will have degree equal to the class number of the associated imaginary quadratic field. Our intention is compute all such class number three examples. The largest such example, with discriminant $ - 907$, adds $ 37$ additional digit accuracy per term. A class number four example with discriminant $ 1555$ gives $ 50$ digits per term.

rawabstract:
There is a class of remarkable series for $ 1 / \pi $ of the form $ \sqrt {-C^3} / \pi = \sum_{n = 0}^\infty \frac {A + n B}{C^{3 n}} \frac {(6n)!}{(3n)!(n!)^3} $ where $A$, $B$, $C$ are certain algebraic numbers. These were first examined by Ramanujan. These examples arise by computing singular invariants for j and the constants involved will have degree equal to the class number of the associated imaginary quadratic field. Our intention is compute all such class number three examples. The largest such example, with discriminant $ - 907$, adds $ 37$ additional digit accuracy per term. A class number four example with discriminant $ 1555$ gives $ 50$ digits per term.

entry:
@Article{Borwein:1993:CNT,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "Class number three {Ramanujan} type series for $ 1 /
                 \pi $",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "46",
  number =       "1--2",
  pages =        "281--290",
  day =          "14",
  month =        jun,
  year =         "1993",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(93)90302-R",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "11Y60 (11R11)",
  MRnumber =     "1222488",
  MRreviewer =   "Andrew Granville",
  bibdate =      "Sat Feb 25 12:20:57 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  note =         "Computational complex analysis.",
  URL =          "http://docserver.carma.newcastle.edu.au/1560/;
                 http://www.sciencedirect.com/science/article/pii/037704279390302R",
  abstract =     "There is a class of remarkable series for $ 1 / \pi $
                 of the form $ \sqrt {-C^3} / \pi = \sum_{n = 0}^\infty
                 \frac {A + n B}{C^{3 n}} \frac {(6n)!}{(3n)!(n!)^3} $
                 where $A$, $B$, $C$ are certain algebraic numbers.
                 These were first examined by Ramanujan. These examples
                 arise by computing singular invariants for j and the
                 constants involved will have degree equal to the class
                 number of the associated imaginary quadratic field. Our
                 intention is compute all such class number three
                 examples. The largest such example, with discriminant $
                 - 907$, adds $ 37$ additional digit accuracy per term.
                 A class number four example with discriminant $ 1555$
                 gives $ 50$ digits per term.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "class number; pi; Ramanujan; series",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1993:DKK
author: J. M. Borwein and J. Vanderwerff
title: Dual Kadec--Klee norms and the relationships between Wijsman, slice and Mosco convergence
journal: ArXiv Mathematics e-prints
pages: 281--290
month: feb
monthnumber: 2
year: 1993
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/1993math......2212B
keywords: Mathematics - Functional Analysis, 46B
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and J. Vanderwerff
rawtitle: Dual {Kadec--Klee} norms and the relationships between {Wijsman}, slice and {Mosco} convergence
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper, we completely settle several of the open questions regarding the relationships between the three most fundamental forms of set convergence. In particular, it is shown that Wijsman and slice convergence coincide precisely when the weak star and norm topologies agree on the dual sphere. Consequently, a weakly compactly generated Banach space admits a dense set of norms for which Wijsman and slice convergence coincide if and only if it is an Asplund space. We also show that Wijsman convergence implies Mosco convergence precisely when the weak star and Mackey topologies coincide on the dual sphere. A corollary of these results is that given a fixed norm on an Asplund space, Wijsman and slice convergence coincide if and only if Wijsman convergence implies Mosco convergence.

rawabstract:
In this paper, we completely settle several of the open questions regarding the relationships between the three most fundamental forms of set convergence. In particular, it is shown that Wijsman and slice convergence coincide precisely when the weak star and norm topologies agree on the dual sphere. Consequently, a weakly compactly generated Banach space admits a dense set of norms for which Wijsman and slice convergence coincide if and only if it is an Asplund space. We also show that Wijsman convergence implies Mosco convergence precisely when the weak star and Mackey topologies coincide on the dual sphere. A corollary of these results is that given a fixed norm on an Asplund space, Wijsman and slice convergence coincide if and only if Wijsman convergence implies Mosco convergence.

entry:
@Article{Borwein:1993:DKK,
  author =       "J. M. Borwein and J. Vanderwerff",
  title =        "Dual {Kadec--Klee} norms and the relationships between
                 {Wijsman}, slice and {Mosco} convergence",
  journal =      "ArXiv Mathematics e-prints",
  month =        feb,
  year =         "1993",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/1993math......2212B",
  abstract =     "In this paper, we completely settle several of the
                 open questions regarding the relationships between the
                 three most fundamental forms of set convergence. In
                 particular, it is shown that Wijsman and slice
                 convergence coincide precisely when the weak star and
                 norm topologies agree on the dual sphere. Consequently,
                 a weakly compactly generated Banach space admits a
                 dense set of norms for which Wijsman and slice
                 convergence coincide if and only if it is an Asplund
                 space. We also show that Wijsman convergence implies
                 Mosco convergence precisely when the weak star and
                 Mackey topologies coincide on the dual sphere. A
                 corollary of these results is that given a fixed norm
                 on an Asplund space, Wijsman and slice convergence
                 coincide if and only if Wijsman convergence implies
                 Mosco convergence.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "math/9302212",
  keywords =     "Mathematics - Functional Analysis, 46B",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1993:FAS
author: Jon Borwein and Jon Vanderwerff
title: Further arguments for slice convergence in nonreflexive spaces
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 18
day: 6
month: nov
monthnumber: 11
year: 1993
MRclass: 52A41 (40A30, 46A55, 46B20)
bibdate: Thu Sep 01 14:11:31 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 14:11:31 ???
URL: http://docserver.carma.newcastle.edu.au/62
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jon Borwein and Jon Vanderwerff
rawtitle: Further arguments for slice convergence in nonreflexive spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
It is shown that no notion of set convergence at least as strong as Wijsman convergence but not as strong as slice convergence can be preserved in superspaces. We also show that such intermediate notions of convergence do not always admit representations analogous to those given by Attouch and Beer for slice convergence, and provide a valid reformulation. Some connections between bornologies and the relationships between certain gap convergences for nonconvex sets are also observed.

rawabstract:
It is shown that no notion of set convergence at least as strong as Wijsman convergence but not as strong as slice convergence can be preserved in superspaces. We also show that such intermediate notions of convergence do not always admit representations analogous to those given by Attouch and Beer for slice convergence, and provide a valid reformulation. Some connections between bornologies and the relationships between certain gap convergences for nonconvex sets are also observed.

entry:
@TechReport{Borwein:1993:FAS,
  author =       "Jon Borwein and Jon Vanderwerff",
  title =        "Further arguments for slice convergence in
                 nonreflexive spaces",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  pages =        "18",
  day =          "6",
  month =        nov,
  year =         "1993",
  MRclass =      "52A41 (40A30, 46A55, 46B20)",
  bibdate =      "Thu Sep 01 14:11:31 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/62",
  abstract =     "It is shown that no notion of set convergence at least
                 as strong as Wijsman convergence but not as strong as
                 slice convergence can be preserved in superspaces. We
                 also show that such intermediate notions of convergence
                 do not always admit representations analogous to those
                 given by Attouch and Beer for slice convergence, and
                 provide a valid reformulation. Some connections between
                 bornologies and the relationships between certain gap
                 convergences for nonconvex sets are also observed.",
  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:1993:FME
author: Jonathan M. Borwein
title: On the failure of maximum entropy reconstruction for Fredholm equations and other infinite systems
journal: j-MATH-PROG
volume: 61
number: 2, Ser. A
pages: 251--261
year: 1993
CODEN: MHPGA4
DOI: https://doi.org/10.1007/BF01582150
ISSN: 0025-5610 (print), 1436-4646 (electronic) OR 00255610 (print), 14364646 (electronic)
ISSNL: 0025-5610 OR 00255610
MRclass: 94A12 (45B05 47N99 90C48)
MRnumber: 1240460
MRreviewer: Henry Wolkowicz
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/1559/
fjournal: Mathematical Programming
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/10107
rawauthor: Jonathan M. Borwein
ORCID: Borwein, Jonathan/0000-0002-1263-0646
rawtitle:
On the failure of maximum entropy reconstruction for {Fredholm} equations and other infinite systems

entry:
@Article{Borwein:1993:FME,
  author =       "Jonathan M. Borwein",
  title =        "On the failure of maximum entropy reconstruction for
                 {Fredholm} equations and other infinite systems",
  journal =      j-MATH-PROG,
  volume =       "61",
  number =       "2, Ser. A",
  pages =        "251--261",
  year =         "1993",
  CODEN =        "MHPGA4",
  DOI =          "https://doi.org/10.1007/BF01582150",
  ISSN =         "0025-5610 (print), 1436-4646 (electronic)",
  ISSN-L =       "0025-5610",
  MRclass =      "94A12 (45B05 47N99 90C48)",
  MRnumber =     "1240460",
  MRreviewer =   "Henry Wolkowicz",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1559/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematical Programming",
  journal-URL =  "http://link.springer.com/journal/10107",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1993:GFI
author: J. M. Borwein and P. B. Borwein
title: On the generating function of the integer part: $ [n alpha + gamma ] $
journal: j-J-NUMBER-THEORY
volume: 43
number: 3
pages: 293--318
year: 1993
CODEN: JNUTA9
DOI: https://doi.org/10.1006/jnth.1993.1023
ISSN: 0022-314X (print), 1096-1658 (electronic) OR 0022314X (print), 10961658 (electronic)
ISSNL: 0022-314X OR 0022314X
MRclass: 11J70 (11J91)
MRnumber: 1212686
MRreviewer: A. J. van der Poorten
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 Number Theory
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/0022314X
rawauthor: J. M. Borwein and P. B. Borwein
rawtitle: On the generating function of the integer part: $ [n \alpha + \gamma] $
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1564/; http://www.sciencedirect.com/science/article/pii/S0022314X83710231

abstract:
We show that [long displayed formula]. Here $ p_n $ and $ q_n $ are the numerators and denominators of the convergents of the continued fraction expansion of $ alpha $ and $ t^n $ and $ s^n $ are particular algorithmically generated sequences of best approximates for the non-homogeneous Diophantine approximation problem of minimizing $ |n alpha + gamma - m| $. This generalizes results of Bohmer and Mahler, who considered the special case where $ gamma = 0 $. This representation allows us to easily derive various transcendence results. For example, $ sum ^infty _n = 1 [n e + 12] / (2 n) $ is a Liouville number. Indeed the first series is Liouville for rational $z$, $ w subset [ - 1, 1]$ with $ |z w| neq 1$ provided $ alpha $ has unbounded continued fraction expansion. A second application, which generalizes a theorem originally due to Lord Raleigh, is to give a new proof of a theorem of Fraenkel, namely $ [n alpha + gamma ]^infty _n = 1$ and $ [n alpha prime + gamma prime ]^infty _n = 1$ partition the non-negative integers if and only if $ 1 / alpha + 1 / alpha prime = 1$ and $ gamma / alpha + gamma prime / alpha prime = 0$ (provided some sign and integer independence conditions are placed on $ alpha $, $ beta $, $ gamma $, $ gamma prime $). The analysis which leads to the results is quite delicate and rests heavily on a functional equation for $G$. For this a natural generalization of the simple continued fraction to Kronecker's forms $ |n alpha + gamma - m|$ is required.

rawabstract:
We show that [long displayed formula]. Here $ p_n $ and $ q_n $ are the numerators and denominators of the convergents of the continued fraction expansion of $ \alpha $ and $ t^n $ and $ s^n $ are particular algorithmically generated sequences of best approximates for the non-homogeneous Diophantine approximation problem of minimizing $ |n \alpha + \gamma - m| $. This generalizes results of B{\"o}hmer and Mahler, who considered the special case where $ \gamma = 0 $. This representation allows us to easily derive various transcendence results. For example, $ \sum^\infty_{n = 1} [n e + 12] / (2 n) $ is a Liouville number. Indeed the first series is Liouville for rational $z$, $ w \subset [ - 1, 1]$ with $ |z w| \neq 1$ provided $ \alpha $ has unbounded continued fraction expansion. A second application, which generalizes a theorem originally due to Lord Raleigh, is to give a new proof of a theorem of Fraenkel, namely $ [n \alpha + \gamma]^\infty_{n = 1}$ and $ [n \alpha \prime + \gamma \prime]^\infty_{n = 1}$ partition the non-negative integers if and only if $ 1 / \alpha + 1 / \alpha \prime = 1$ and $ \gamma / \alpha + \gamma \prime / \alpha \prime = 0$ (provided some sign and integer independence conditions are placed on $ \alpha $, $ \beta $, $ \gamma $, $ \gamma \prime $). The analysis which leads to the results is quite delicate and rests heavily on a functional equation for $G$. For this a natural generalization of the simple continued fraction to Kronecker's forms $ |n \alpha + \gamma - m|$ is required.

entry:
@Article{Borwein:1993:GFI,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "On the generating function of the integer part: $ [n
                 \alpha + \gamma] $",
  journal =      j-J-NUMBER-THEORY,
  volume =       "43",
  number =       "3",
  pages =        "293--318",
  year =         "1993",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1006/jnth.1993.1023",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  MRclass =      "11J70 (11J91)",
  MRnumber =     "1212686",
  MRreviewer =   "A. J. van der Poorten",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1564/;
                 http://www.sciencedirect.com/science/article/pii/S0022314X83710231",
  abstract =     "We show that [long displayed formula]. Here $ p_n $
                 and $ q_n $ are the numerators and denominators of the
                 convergents of the continued fraction expansion of $
                 \alpha $ and $ t^n $ and $ s^n $ are particular
                 algorithmically generated sequences of best
                 approximates for the non-homogeneous Diophantine
                 approximation problem of minimizing $ |n \alpha +
                 \gamma - m| $. This generalizes results of B{\"o}hmer
                 and Mahler, who considered the special case where $
                 \gamma = 0 $. This representation allows us to easily
                 derive various transcendence results. For example, $
                 \sum^\infty_{n = 1} [n e + 12] / (2 n) $ is a Liouville
                 number. Indeed the first series is Liouville for
                 rational $z$, $ w \subset [ - 1, 1]$ with $ |z w| \neq
                 1$ provided $ \alpha $ has unbounded continued fraction
                 expansion. A second application, which generalizes a
                 theorem originally due to Lord Raleigh, is to give a
                 new proof of a theorem of Fraenkel, namely $ [n \alpha
                 + \gamma]^\infty_{n = 1}$ and $ [n \alpha \prime +
                 \gamma \prime]^\infty_{n = 1}$ partition the
                 non-negative integers if and only if $ 1 / \alpha + 1 /
                 \alpha \prime = 1$ and $ \gamma / \alpha + \gamma
                 \prime / \alpha \prime = 0$ (provided some sign and
                 integer independence conditions are placed on $ \alpha
                 $, $ \beta $, $ \gamma $, $ \gamma \prime $). The
                 analysis which leads to the results is quite delicate
                 and rests heavily on a functional equation for $G$. For
                 this a natural generalization of the simple continued
                 fraction to Kronecker's forms $ |n \alpha + \gamma -
                 m|$ is required.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1993:GSO
author: J. M. Borwein and M. Fabian
title: On generic second-order Gateaux differentiability
journal: j-NONLINEAR-ANAL
volume: 20
number: 12
pages: 1373--1382
year: 1993
CODEN: NOANDD
DOI: https://doi.org/10.1016/0362-546X(93)90166-P
ISSN: 0362-546x (print), 1873-5215 (electronic) OR 0362546x (print), 18735215 (electronic)
ISSNL: 0362-546X OR 0362546X
MRclass: 46G05 (26E15 49J50 58C20)
MRnumber: 1225345
MRreviewer: Marcin Studniarski
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: residual space; second-order difference quotient; Separable space; twice Gateaux differentiability
remark: Research Report CORR 91-18.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.sciencedirect.com/journal/nonlinear-analysis
rawauthor: J. M. Borwein and M. Fabi{\'a}n
rawtitle: On generic second-order {G{\^a}teaux} differentiability
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1563/; http://www.sciencedirect.com/science/article/pii/0362546X9390166P

entry:
@Article{Borwein:1993:GSO,
  author =       "J. M. Borwein and M. Fabi{\'a}n",
  title =        "On generic second-order {G{\^a}teaux}
                 differentiability",
  journal =      j-NONLINEAR-ANAL,
  volume =       "20",
  number =       "12",
  pages =        "1373--1382",
  year =         "1993",
  CODEN =        "NOANDD",
  DOI =          "https://doi.org/10.1016/0362-546X(93)90166-P",
  ISSN =         "0362-546x (print), 1873-5215 (electronic)",
  ISSN-L =       "0362-546X",
  MRclass =      "46G05 (26E15 49J50 58C20)",
  MRnumber =     "1225345",
  MRreviewer =   "Marcin Studniarski",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1563/;
                 http://www.sciencedirect.com/science/article/pii/0362546X9390166P",
  acknowledgement = ack-nhfb,
  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 =     "residual space; second-order difference quotient;
                 Separable space; twice G{\^a}teaux differentiability",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Research Report CORR 91-18.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1993:HAA
author: J. Borwein and P. Borwein and F. Garvan
title: Hypergeometric analogues of the arithmetic--geometric mean iteration
journal: j-CONST-APPROX
volume: 9
number: 4
pages: 509--523
year: 1993
DOI: https://doi.org/10.1007/BF01204654
ISSN: 0176-4276 (print), 1432-0940 (electronic) OR 01764276 (print), 14320940 (electronic)
ISSNL: 0176-4276 OR 01764276
MRclass: 33C05
MRnumber: 1237931
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 ???
URL: http://docserver.carma.newcastle.edu.au/1556/; http://link.springer.com/article/10.1007/BF01204654
fjournal: Constructive Approximation. An International Journal for Approximations and Expansions
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/365
rawauthor: J. Borwein and P. Borwein and F. Garvan
rawtitle: Hypergeometric analogues of the arithmetic--geometric mean iteration
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1993:HAA,
  author =       "J. Borwein and P. Borwein and F. Garvan",
  title =        "Hypergeometric analogues of the arithmetic--geometric
                 mean iteration",
  journal =      j-CONST-APPROX,
  volume =       "9",
  number =       "4",
  pages =        "509--523",
  year =         "1993",
  DOI =          "https://doi.org/10.1007/BF01204654",
  ISSN =         "0176-4276 (print), 1432-0940 (electronic)",
  ISSN-L =       "0176-4276",
  MRclass =      "33C05",
  MRnumber =     "1237931",
  MRreviewer =   "Bruce C. Berndt",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1556/;
                 http://link.springer.com/article/10.1007/BF01204654",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Constructive Approximation. An International Journal
                 for Approximations and Expansions",
  journal-URL =  "http://link.springer.com/journal/365",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1993:ICM
author: Jonathan M. Borwein and Peter B. Borwein
title: Inequalities for Compound Mean Iterations with Logarithmic Asymptotes
journal: j-J-MATH-ANAL-APPL
volume: 177
number: 2
pages: 572--582
year: 1993
CODEN: JMANAK
DOI: https://doi.org/10.1006/jmaa.1993.1278
ISSN: 0022-247X (print), 1096-0813 (electronic) OR 0022247X (print), 10960813 (electronic)
ISSNL: 0022-247X OR 0022247X
MRclass: 33B99
MRnumber: 1231502
MRreviewer: P. Anandani
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 Peter B. Borwein
rawtitle: Inequalities for Compound Mean Iterations with Logarithmic Asymptotes
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1553/; http://www.sciencedirect.com/science/article/pii/S0022247X83712783

abstract:
We consider the compound means arising as limits from the arithmetic--geometric mean iteration and related iterations. Each of these iterations possesses a logarithmic asymptote. We show that these limit means satisfy very precise inequalities. These can be deduced in a quite uniform fashion from a `comparison lemma' for compound means.

rawabstract:
We consider the compound means arising as limits from the arithmetic--geometric mean iteration and related iterations. Each of these iterations possesses a logarithmic asymptote. We show that these limit means satisfy very precise inequalities. These can be deduced in a quite uniform fashion from a `comparison lemma' for compound means.

entry:
@Article{Borwein:1993:ICM,
  author =       "Jonathan M. Borwein and Peter B. Borwein",
  title =        "Inequalities for Compound Mean Iterations with
                 Logarithmic Asymptotes",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "177",
  number =       "2",
  pages =        "572--582",
  year =         "1993",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1006/jmaa.1993.1278",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "33B99",
  MRnumber =     "1231502",
  MRreviewer =   "P. Anandani",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1553/;
                 http://www.sciencedirect.com/science/article/pii/S0022247X83712783",
  abstract =     "We consider the compound means arising as limits from
                 the arithmetic--geometric mean iteration and related
                 iterations. Each of these iterations possesses a
                 logarithmic asymptote. We show that these limit means
                 satisfy very precise inequalities. These can be deduced
                 in a quite uniform fashion from a `comparison lemma'
                 for compound means.",
  acknowledgement = ack-nhfb,
  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",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1993:LLFa
author: J. M. Borwein and M. Fabian and J. Vanderwerff
title: Locally Lipschitz Functions and Bornological Derivatives
journal: ArXiv Mathematics e-prints
pages: 13
month: feb
monthnumber: 2
year: 1993
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/1993math......2211B; http://docserver.carma.newcastle.edu.au/69/
keywords: Mathematics - Functional Analysis, 46B
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and M. Fabian and J. Vanderwerff
rawtitle: Locally {Lipschitz} Functions and Bornological Derivatives
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We study the relationships between Gateaux, weak Hadamard and Frechet differentiability and their bornologies for Lipschitz and for convex functions. In particular, Frechet and weak Hadamard differentiability coincide for all Lipschitz functions if and only if the space is reflexive (an earlier paper of the first two authors shows that these two notions of differentiability coincide for continuous convex functions if and only if the space does not contain a copy of $ ell _1$). We also examine when Gateaux and weak Hadamard differentiability coincide for continuous convex functions. For instance, spaces with the Dunford--Pettis (Schur) property can be characterized by the coincidence of Gateaux and weak Hadamard (Frechet) differentiability for dual norms.

rawabstract:
We study the relationships between G{\^a}teaux, weak Hadamard and Frechet differentiability and their bornologies for Lipschitz and for convex functions. In particular, Frechet and weak Hadamard differentiability coincide for all Lipschitz functions if and only if the space is reflexive (an earlier paper of the first two authors shows that these two notions of differentiability coincide for continuous convex functions if and only if the space does not contain a copy of $ \ell_1$). We also examine when G{\^a}teaux and weak Hadamard differentiability coincide for continuous convex functions. For instance, spaces with the Dunford--Pettis (Schur) property can be characterized by the coincidence of G{\^a}teaux and weak Hadamard (Frechet) differentiability for dual norms.

entry:
@Article{Borwein:1993:LLFa,
  author =       "J. M. Borwein and M. Fabian and J. Vanderwerff",
  title =        "Locally {Lipschitz} Functions and Bornological
                 Derivatives",
  journal =      "ArXiv Mathematics e-prints",
  pages =        "13",
  month =        feb,
  year =         "1993",
  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/1993math......2211B;
                 http://docserver.carma.newcastle.edu.au/69/",
  abstract =     "We study the relationships between G{\^a}teaux, weak
                 Hadamard and Frechet differentiability and their
                 bornologies for Lipschitz and for convex functions. In
                 particular, Frechet and weak Hadamard differentiability
                 coincide for all Lipschitz functions if and only if the
                 space is reflexive (an earlier paper of the first two
                 authors shows that these two notions of
                 differentiability coincide for continuous convex
                 functions if and only if the space does not contain a
                 copy of $ \ell_1$). We also examine when G{\^a}teaux
                 and weak Hadamard differentiability coincide for
                 continuous convex functions. For instance, spaces with
                 the Dunford--Pettis (Schur) property can be
                 characterized by the coincidence of G{\^a}teaux and
                 weak Hadamard (Frechet) differentiability for dual
                 norms.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "math/9302211",
  keywords =     "Mathematics - Functional Analysis, 46B",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1993:LLFb
author: Jonathan M. Borwein and Marian Fabian and Jon Vanderwerff
title: Locally Lipschitz functions and bornological derivatives
type: CECM Research Report
number: 93:012
institution: inst-CECM
address: inst-CECM:adr
pages: 13
day: 15
month: dec
monthnumber: 12
year: 1993
MRclass: 46A17, 46G05, 58C20 (46B20)
bibdate: Tue Aug 16 10:06:43 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:06:43 ???
URL: http://docserver.carma.newcastle.edu.au/69/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Marian Fabian and Jon Vanderwerff
rawtitle: Locally {Lipschitz} functions and bornological derivatives
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We study the relationships between Gateaux, Weak Hadamard and Frechet differentiability and their bornologies for Lipschitz and for convex functions.

rawabstract:
We study the relationships between Gateaux, Weak Hadamard and Fr{\'e}chet differentiability and their bornologies for Lipschitz and for convex functions.

entry:
@TechReport{Borwein:1993:LLFb,
  author =       "Jonathan M. Borwein and Marian Fabian and Jon
                 Vanderwerff",
  title =        "Locally {Lipschitz} functions and bornological
                 derivatives",
  type =         "CECM Research Report",
  number =       "93:012",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "13",
  day =          "15",
  month =        dec,
  year =         "1993",
  MRclass =      "46A17, 46G05, 58C20 (46B20)",
  bibdate =      "Tue Aug 16 10:06:43 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/69/",
  abstract =     "We study the relationships between Gateaux, Weak
                 Hadamard and Fr{\'e}chet differentiability and their
                 bornologies for Lipschitz and for convex functions.",
  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:1993:MMB
author: Jonathan M. Borwein and Peter B. Borwein
journal: j-SCIENCE
volume: 259
number: 5103
pages: 1928--1930
day: 26
month: mar
monthnumber: 3
year: 1993
CODEN: SCIEAS
DOI: https://doi.org/10.1126/science.259.5103.1928.a
ISSN: 0036-8075 (print), 1095-9203 (electronic) OR 00368075 (print), 10959203 (electronic)
ISSNL: 0036-8075 OR 00368075
bibdate: Sat Sep 03 09:11:44 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.09.03 09:11:44 ???
fjournal: Science (New York, N.Y.)
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencemag.org/archive/
rawauthor: Jonathan M. Borwein and Peter B. Borwein
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Mathematical Malaises: Book Review: booktitle Pi in the sky: counting, thinking and being, John D. Barrow. Clarendon (Oxford University Press), New York, 1992. xii, 317 pp., illus. $25

URL:
http://www.ncbi.nlm.nih.gov/pubmed/17836254; https://www.science.org/doi/10.1126/science.259.5103.1928.a

rawtitle:
Mathematical Malaises: Book Review: {{\booktitle{Pi in the sky: counting, thinking and being}}, John D. Barrow. Clarendon (Oxford University Press), New York, 1992. xii, 317 pp., illus. \$25}

entry:
@Article{Borwein:1993:MMB,
  author =       "Jonathan M. Borwein and Peter B. Borwein",
  title =        "Mathematical Malaises: Book Review: {{\booktitle{Pi in
                 the sky: counting, thinking and being}}, John D.
                 Barrow. Clarendon (Oxford University Press), New York,
                 1992. xii, 317 pp., illus. \$25}",
  journal =      j-SCIENCE,
  volume =       "259",
  number =       "5103",
  pages =        "1928--1930",
  day =          "26",
  month =        mar,
  year =         "1993",
  CODEN =        "SCIEAS",
  DOI =          "https://doi.org/10.1126/science.259.5103.1928.a",
  ISSN =         "0036-8075 (print), 1095-9203 (electronic)",
  ISSN-L =       "0036-8075",
  bibdate =      "Sat Sep 03 09:11:44 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.ncbi.nlm.nih.gov/pubmed/17836254;
                 https://www.science.org/doi/10.1126/science.259.5103.1928.a",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Science (New York, N.Y.)",
  journal-URL =  "http://www.sciencemag.org/archive/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  report-number = "Borwein, Jonathan/A-6082-2009",
  xxDOI =        "https://doi.org/10.1126/science.259.5103.1928",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1993:PFP
author: Jonathan M. Borwein and Adrian S. Lewis
title: Partially-finite programming in $ L_1 $ and the existence of maximum entropy estimates
journal: j-SIAM-J-OPT
volume: 3
number: 2
pages: 248--267
year: 1993
CODEN: SJOPE8
DOI: https://doi.org/10.1137/0803012
ISSN: 1052-6234 (print), 1095-7189 (electronic) OR 10526234 (print), 10957189 (electronic)
ISSNL: 1052-6234 OR 10526234
MRclass: 90C48 (49N15 65K05)
MRnumber: 1215444
MRreviewer: M. Teboulle
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/1558/
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 Adrian S. Lewis
rawtitle: Partially-finite programming in {$ L_1 $} and the existence of maximum entropy estimates
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1993:PFP,
  author =       "Jonathan M. Borwein and Adrian S. Lewis",
  title =        "Partially-finite programming in {$ L_1 $} and the
                 existence of maximum entropy estimates",
  journal =      j-SIAM-J-OPT,
  volume =       "3",
  number =       "2",
  pages =        "248--267",
  year =         "1993",
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  DOI =          "https://doi.org/10.1137/0803012",
  ISSN =         "1052-6234 (print), 1095-7189 (electronic)",
  ISSN-L =       "1052-6234",
  MRclass =      "90C48 (49N15 65K05)",
  MRnumber =     "1215444",
  MRreviewer =   "M. Teboulle",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1558/",
  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:1993:PSPa
author: Jonathan M. Borwein
title: Problems and Solutions: Problems: 10281
journal: j-AMER-MATH-MONTHLY
volume: 100
number: 1
pages: 76--77
month: jan
monthnumber: 1
year: 1993
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2324828
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Wed Aug 10 11:09:47 2016
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.htm
rawauthor: Jonathan M. Borwein
rawtitle: Problems and Solutions: Problems: 10281
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib

entry:
@Article{Borwein:1993:PSPa,
  author =       "Jonathan M. Borwein",
  title =        "Problems and Solutions: Problems: 10281",
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  number =       "1",
  pages =        "76--77",
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  bibdate =      "Wed Aug 10 11:09:47 2016",
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  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
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  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
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bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1993:PSPb
author: David Borwein and Jonathan Borwein
title: Problems and Solutions: Problems: 10335
journal: j-AMER-MATH-MONTHLY
volume: 100
number: 8
pages: 796--798
month: oct
monthnumber: 10
year: 1993
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2324793
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Wed Aug 10 11:09:47 2016
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.htm
rawauthor: David Borwein and Jonathan Borwein
rawtitle: Problems and Solutions: Problems: 10335
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1993:PSPb,
  author =       "David Borwein and Jonathan Borwein",
  title =        "Problems and Solutions: Problems: 10335",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "100",
  number =       "8",
  pages =        "796--798",
  month =        oct,
  year =         "1993",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2324793",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.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.htm",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:1993:SCR
author: Jonathan M. Borwein and Adrian S. Lewis
editor: A. Mohammad-Djafari and G. Demoments
booktitle: Maximum entropy and Bayesian methods (Paris, 1992)
title: A Survey of Convergence Results for Maximum Entropy Methods
volume: 53
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: 39--48
year: 1993
DOI: https://doi.org/10.1007/978-94-017-2217-9_5
MRclass: 49J45 (41A30 42A10)
MRnumber: 1269789
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:36:22 MDT
series: Fund. Theories Phys.
URL: http://link.springer.com/chapter/10.1007/978-94-017-2217-9_5
remark: Research Report CORR 92-32.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Adrian S. Lewis
rawbooktitle: Maximum entropy and {Bayesian} methods ({Paris}, 1992)
raweditor: A. Mohammad-Djafari and G. Demoments
rawtitle: A Survey of Convergence Results for Maximum Entropy Methods
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InProceedings{Borwein:1993:SCR,
  author =       "Jonathan M. Borwein and Adrian S. Lewis",
  editor =       "A. Mohammad-Djafari and G. Demoments",
  booktitle =    "Maximum entropy and {Bayesian} methods ({Paris},
                 1992)",
  title =        "A Survey of Convergence Results for Maximum Entropy
                 Methods",
  volume =       "53",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "39--48",
  year =         "1993",
  DOI =          "https://doi.org/10.1007/978-94-017-2217-9_5",
  MRclass =      "49J45 (41A30 42A10)",
  MRnumber =     "1269789",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Fund. Theories Phys.",
  URL =          "http://link.springer.com/chapter/10.1007/978-94-017-2217-9_5",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Research Report CORR 92-32.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1993:SEV
author: J. M. Borwein and D. Zhuang
title: Super efficiency in vector optimization
journal: j-TRANS-AM-MATH-SOC
volume: 338
number: 1
pages: 105--122
year: 1993
CODEN: TAMTAM
DOI: https://doi.org/10.2307/2154446
ISSN: 0002-9947 (print), 1088-6850 (electronic) OR 00029947 (print), 10886850 (electronic)
ISSNL: 0002-9947 OR 00029947
MRclass: 90C29 (52A41)
MRnumber: 1098432
MRreviewer: Bernard Lemaire
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: 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: J. M. Borwein and D. Zhuang
rawtitle: Super efficiency in vector optimization
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1993:SEV,
  author =       "J. M. Borwein and D. Zhuang",
  title =        "Super efficiency in vector optimization",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "338",
  number =       "1",
  pages =        "105--122",
  year =         "1993",
  CODEN =        "TAMTAM",
  DOI =          "https://doi.org/10.2307/2154446",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "90C29 (52A41)",
  MRnumber =     "1098432",
  MRreviewer =   "Bernard Lemaire",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "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 =     "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:1993:WHS
author: Jonathan M. Borwein and Simon Fitzpatrick
title: A weak Hadamard smooth renorming of $ L_1 (Omega , mu ) $
journal: j-CAN-MATH-BULL
volume: 36
number: 4
pages: 407--413
year: 1993
CODEN: CMBUA3
DOI: https://doi.org/10.4153/CMB-1993-055-5
ISSN: 0008-4395 (print), 1496-4287 (electronic) OR 00084395 (print), 14964287 (electronic)
ISSNL: 0008-4395 OR 00084395
MRclass: 46B25 (46B03 46B20 46E30)
MRnumber: 1245313
MRreviewer: W. A. J. Luxemburg
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://cms.math.ca/10.4153/CMB-1993-055-5; http://docserver.carma.newcastle.edu.au/1554/
fjournal: Canadian Mathematical Bulletin. Bulletin Canadien de Mathematiques
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://cms.math.ca/cmb/
rawauthor: Jonathan M. Borwein and Simon Fitzpatrick
rawtitle: A weak {Hadamard} smooth renorming of {$ L_1 (\Omega, \mu) $}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1993:WHS,
  author =       "Jonathan M. Borwein and Simon Fitzpatrick",
  title =        "A weak {Hadamard} smooth renorming of {$ L_1 (\Omega,
                 \mu) $}",
  journal =      j-CAN-MATH-BULL,
  volume =       "36",
  number =       "4",
  pages =        "407--413",
  year =         "1993",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-1993-055-5",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  MRclass =      "46B25 (46B03 46B20 46E30)",
  MRnumber =     "1245313",
  MRreviewer =   "W. A. J. Luxemburg",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://cms.math.ca/10.4153/CMB-1993-055-5;
                 http://docserver.carma.newcastle.edu.au/1554/",
  acknowledgement = ack-nhfb,
  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:1993:WSC
author: Jonathan Borwein and Simon Fitzpatrick
title: Weak sequential compactness and bornological limit derivatives
type: Report
institution: Department of Mathematics and Statistics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 10
day: 7
month: sep
monthnumber: 9
year: 1993
bibdate: Thu Sep 01 13:54:08 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 13:54:08 ???
URL: http://docserver.carma.newcastle.edu.au/58/2/93_001-Borwein-Borwein-Girgensohn.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein and Simon Fitzpatrick
rawtitle: Weak sequential compactness and bornological limit derivatives
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this note we give a self-contained account of the relationship between the sequential and topological constructions of bornological limit derivatives for locally Lipschitzian real-valued functions on Banach spaces.

rawabstract:
In this note we give a self-contained account of the relationship between the sequential and topological constructions of bornological limit derivatives for locally Lipschitzian real-valued functions on Banach spaces.

entry:
@TechReport{Borwein:1993:WSC,
  author =       "Jonathan Borwein and Simon Fitzpatrick",
  title =        "Weak sequential compactness and bornological limit
                 derivatives",
  type =         "Report",
  institution =  "Department of Mathematics and Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "10",
  day =          "7",
  month =        sep,
  year =         "1993",
  bibdate =      "Thu Sep 01 13:54:08 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/58/2/93_001-Borwein-Borwein-Girgensohn.pdf",
  abstract =     "In this note we give a self-contained account of the
                 relationship between the sequential and topological
                 constructions of bornological limit derivatives for
                 locally Lipschitzian real-valued functions on Banach
                 spaces.",
  acknowledgement = ack-nhfb,
  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: Byerly:1993:PSP
title: Problems and Solutions: Problems: 10274--10281
journal: j-AMER-MATH-MONTHLY
volume: 100
number: 1
pages: 75--77
year: 1993
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2324823
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRnumber: 1542259
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: 10274--10281
ORCID: Borwein, Jonathan/0000-0002-1263-0646
author:
Robert E. Byerly and Murray S. Klamkin and A. Liu and Stephen M. Gagola, Jr. and L. E. Mattics and Raphael M. Robinson and M. Al-Ahmar and Donald E. Knuth and Jonathan M. Borwein

rawauthor:
Robert E. Byerly and Murray S. Klamkin and A. Liu and Stephen M. {Gagola, Jr.} and L. E. Mattics and Raphael M. Robinson and M. Al-Ahmar and Donald E. Knuth and Jonathan M. Borwein

entry:
@Article{Byerly:1993:PSP,
  author =       "Robert E. Byerly and Murray S. Klamkin and A. Liu and
                 Stephen M. {Gagola, Jr.} and L. E. Mattics and Raphael
                 M. Robinson and M. Al-Ahmar and Donald E. Knuth and
                 Jonathan M. Borwein",
  title =        "Problems and Solutions: Problems: 10274--10281",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "100",
  number =       "1",
  pages =        "75--77",
  year =         "1993",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2324823",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRnumber =     "1542259",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "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: Hirschhorn:1993:CAJ
author: Michael Hirschhorn and Frank Garvan and Jon Borwein
title: Cubic analogues of the Jacobian theta function $ theta (z, q) $
journal: j-CAN-J-MATH
volume: 45
number: 4
pages: 673--694
year: 1993
CODEN: CJMAAB
DOI: https://doi.org/10.4153/CJM-1993-038-2
ISSN: 0008-414X (print), 1496-4279 (electronic) OR 0008414X (print), 14964279 (electronic)
ISSNL: 0008-414X OR 0008414X
MRclass: 33D10 (11F27)
MRnumber: 1227653
MRreviewer: Bruce C. Berndt
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1557/
fjournal: Canadian Journal of Mathematics = Journal canadien de mathematiques
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://cms.math.ca/cjm/
rawauthor: Michael Hirschhorn and Frank Garvan and Jon Borwein
rawtitle: Cubic analogues of the {Jacobian} theta function $ \theta (z, q) $
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
http://cms.math.ca/cjm/v45/; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/canjmath1990.bib

entry:
@Article{Hirschhorn:1993:CAJ,
  author =       "Michael Hirschhorn and Frank Garvan and Jon Borwein",
  title =        "Cubic analogues of the {Jacobian} theta function $
                 \theta (z, q) $",
  journal =      j-CAN-J-MATH,
  volume =       "45",
  number =       "4",
  pages =        "673--694",
  month =        "????",
  year =         "1993",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-1993-038-2",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  MRclass =      "33D10 (11F27)",
  MRnumber =     "1227653",
  MRreviewer =   "Bruce C. Berndt",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://cms.math.ca/cjm/v45/;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/canjmath1990.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1557/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Canadian Journal of Mathematics = Journal canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Richter:1993:PSP
title: Problems and Solutions: Problems: 10330--10337
journal: j-AMER-MATH-MONTHLY
volume: 100
number: 8
pages: 796--798
year: 1993
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2324792
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRnumber: 1542408
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: 10330--10337
ORCID: Borwein, Jonathan/0000-0002-1263-0646
author:
R. Bruce Richter and Josef Siran and Carl Pomerance and Kiran S. Kedlaya and Michael Golomb and John Sarli and David Borwein and Jonathan Borwein and Ignacy I. Kotlarski and Horst Alzer

rawauthor:
R. Bruce Richter and Josef Siran and Carl Pomerance and Kiran S. Kedlaya and Michael Golomb and John Sarli and David Borwein and Jonathan Borwein and Ignacy I. Kotlarski and Horst Alzer

entry:
@Article{Richter:1993:PSP,
  author =       "R. Bruce Richter and Josef Siran and Carl Pomerance
                 and Kiran S. Kedlaya and Michael Golomb and John Sarli
                 and David Borwein and Jonathan Borwein and Ignacy I.
                 Kotlarski and Horst Alzer",
  title =        "Problems and Solutions: Problems: 10330--10337",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "100",
  number =       "8",
  pages =        "796--798",
  year =         "1993",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2324792",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRnumber =     "1542408",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "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: Bailey:1994:EEEb
author: David H. Bailey and Jonathan M. Borwein and Roland Girgensohn
title: Experimental evaluation of Euler sums
journal: j-EXP-MATH
volume: 3
number: 1
pages: 17--30
year: 1994
DOI: https://doi.org/10.1080/10586458.1994.10504573
ISSN: 1058-6458 (print), 1944-950X (electronic) OR 10586458 (print), 1944950X (electronic)
ISSNL: 1058-6458 OR 10586458
MRclass: 11Y60
MRnumber: 1302815
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/60/; http://projecteuclid.org/euclid.em/1062621000
fjournal: Experimental Mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.tandfonline.com/loi/uexm20
rawauthor: David H. Bailey and Jonathan M. Borwein and Roland Girgensohn
rawtitle: Experimental evaluation of {Euler} sums
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
bibsource:
http://projecteuclid.org/euclid.em; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/expmath.bib

entry:
@Article{Bailey:1994:EEEb,
  author =       "David H. Bailey and Jonathan M. Borwein and Roland
                 Girgensohn",
  title =        "Experimental evaluation of {Euler} sums",
  journal =      j-EXP-MATH,
  volume =       "3",
  number =       "1",
  pages =        "17--30",
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.1994.10504573",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11Y60",
  MRnumber =     "1302815",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 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/60/;
                 http://projecteuclid.org/euclid.em/1062621000",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bauschke:1994:DAP
author: H. H. Bauschke and J. M. Borwein
title: Dykstra's alternating projection algorithm for two sets
journal: j-J-APPROX-THEORY
volume: 79
number: 3
pages: 418--443
year: 1994
CODEN: JAXTAZ
DOI: https://doi.org/10.1006/jath.1994.1136
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
MRclass: 41A65 (46N10 47N10)
MRnumber: 1305442
MRreviewer: F. Deutsch
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
fjournal: Journal of Approximation Theory
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: H. H. Bauschke and J. M. Borwein
rawtitle: {Dykstra}'s alternating projection algorithm for two sets
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1543/; http://www.sciencedirect.com/science/article/pii/S0021904584711361

abstract:
We analyze Dykstra's algorithm for two arbitrary closed convex sets in a Hilbert space. Our technique also applies to von Neumann's algorithm. Various convergence results follow. An example allows one to compare qualitative and quantitative behaviour of the two algorithms. We discuss the case of finitely many sets.

rawabstract:
We analyze Dykstra's algorithm for two arbitrary closed convex sets in a Hilbert space. Our technique also applies to von Neumann's algorithm. Various convergence results follow. An example allows one to compare qualitative and quantitative behaviour of the two algorithms. We discuss the case of finitely many sets.

entry:
@Article{Bauschke:1994:DAP,
  author =       "H. H. Bauschke and J. M. Borwein",
  title =        "{Dykstra}'s alternating projection algorithm for two
                 sets",
  journal =      j-J-APPROX-THEORY,
  volume =       "79",
  number =       "3",
  pages =        "418--443",
  year =         "1994",
  CODEN =        "JAXTAZ",
  DOI =          "https://doi.org/10.1006/jath.1994.1136",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  MRclass =      "41A65 (46N10 47N10)",
  MRnumber =     "1305442",
  MRreviewer =   "F. Deutsch",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1543/;
                 http://www.sciencedirect.com/science/article/pii/S0021904584711361",
  abstract =     "We analyze Dykstra's algorithm for two arbitrary
                 closed convex sets in a Hilbert space. Our technique
                 also applies to von Neumann's algorithm. Various
                 convergence results follow. An example allows one to
                 compare qualitative and quantitative behaviour of the
                 two algorithms. We discuss the case of finitely many
                 sets.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bauschke:1994:MCP
author: H. H. Bauschke and J. M. Borwein and A. S. Lewis
title: On the method of cyclic projections for convex sets in Hilbert space
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 51
day: 10
month: feb
monthnumber: 2
year: 1994
bibdate: Thu Sep 01 14:51:27 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 14:51:27 ???
URL: http://docserver.carma.newcastle.edu.au/77
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: H. H. Bauschke and J. M. Borwein and A. S. Lewis
rawtitle: On the method of cyclic projections for convex sets in {Hilbert} space
ORCID: Borwein, Jonathan/0000-0002-1263-0646
MRclass:
47H09, 4OM45, 65-02, 65J05, 90C25 (26B25, 41A65, 46C99, 46N10, 47N10, 52A05, 52A41, 65F10, 65KO05, 90C90, 92C55)

abstract:
The method of cyclic projections 1s a powerful tool for solving convex feasibility problems in Hilbert space. Although in many applications, in particular in the field of image reconstruction (electron microscopy, computed tomography), the convex constraint sets do not necessarily intersect, the method of cyclic projections is still employed. Results on the behaviour of the algorithm for this general case are improved, unified, and reviewed. The analysis relies on key concepts from convex analysis and the theory of nonexpansive mappings. The notion of the angle of a tuple of subspaces is introduced. New linear convergence results follow for the case when the constraint sets are closed subspaces whose orthogonal complements have a closed sum; this holds, in particular, for hyperplanes or in Euclidean space.

keywords:
angle; computerized tomography; convex feasibility problem; convex polyhedron; convex set; Fejer monotone sequence; Hilbert space; image reconstruction; Kaczmarz s method; method of cyclic projections; nearest point mapping; nonexpansive map

rawabstract:
The method of cyclic projections 1s a powerful tool for solving convex feasibility problems in Hilbert space. Although in many applications, in particular in the field of image reconstruction (electron microscopy, computed tomography), the convex constraint sets do not necessarily intersect, the method of cyclic projections is still employed. Results on the behaviour of the algorithm for this general case are improved, unified, and reviewed. The analysis relies on key concepts from convex analysis and the theory of nonexpansive mappings. The notion of the angle of a tuple of subspaces is introduced. New linear convergence results follow for the case when the constraint sets are closed subspaces whose orthogonal complements have a closed sum; this holds, in particular, for hyperplanes or in Euclidean space.

entry:
@TechReport{Bauschke:1994:MCP,
  author =       "H. H. Bauschke and J. M. Borwein and A. S. Lewis",
  title =        "On the method of cyclic projections for convex sets in
                 {Hilbert} space",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "51",
  day =          "10",
  month =        feb,
  year =         "1994",
  MRclass =      "47H09, 4OM45, 65-02, 65J05, 90C25 (26B25, 41A65,
                 46C99, 46N10, 47N10, 52A05, 52A41, 65F10, 65KO05,
                 90C90, 92C55)",
  bibdate =      "Thu Sep 01 14:51:27 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/77",
  abstract =     "The method of cyclic projections 1s a powerful tool
                 for solving convex feasibility problems in Hilbert
                 space. Although in many applications, in particular in
                 the field of image reconstruction (electron microscopy,
                 computed tomography), the convex constraint sets do not
                 necessarily intersect, the method of cyclic projections
                 is still employed. Results on the behaviour of the
                 algorithm for this general case are improved, unified,
                 and reviewed. The analysis relies on key concepts from
                 convex analysis and the theory of nonexpansive
                 mappings. The notion of the angle of a tuple of
                 subspaces is introduced. New linear convergence results
                 follow for the case when the constraint sets are closed
                 subspaces whose orthogonal complements have a closed
                 sum; this holds, in particular, for hyperplanes or in
                 Euclidean space.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "angle; computerized tomography; convex feasibility
                 problem; convex polyhedron; convex set; Fej{\'e}r
                 monotone sequence; Hilbert space; image reconstruction;
                 Kaczmarz s method; method of cyclic projections;
                 nearest point mapping; nonexpansive map",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1994:BSA
author: J. M. Borwein and J. D. Vanderwerff
title: Banach spaces that admit support sets
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 6
day: 10
month: jul
monthnumber: 7
year: 1994
bibdate: Thu Sep 01 15:46:06 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 15:46:06 ???
URL: http://docserver.carma.newcastle.edu.au/87
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and J. D. Vanderwerff
rawtitle: {Banach} spaces that admit support sets
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
It is shown that the existence of a closed convex set all of whose points are properly supported in a Banach space is equivalent to the existence of a certain type of uncountable ordered one-sided biorthogonal system. Under the continuum hypothesis, we deduce that this notion is weaker than the existence of an uncountable biorthogonal system.

rawabstract:
It is shown that the existence of a closed convex set all of whose points are properly supported in a Banach space is equivalent to the existence of a certain type of uncountable ordered one-sided biorthogonal system. Under the continuum hypothesis, we deduce that this notion is weaker than the existence of an uncountable biorthogonal system.

entry:
@TechReport{Borwein:1994:BSA,
  author =       "J. M. Borwein and J. D. Vanderwerff",
  title =        "{Banach} spaces that admit support sets",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  pages =        "6",
  day =          "10",
  month =        jul,
  year =         "1994",
  bibdate =      "Thu Sep 01 15:46:06 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/87",
  abstract =     "It is shown that the existence of a closed convex set
                 all of whose points are properly supported in a Banach
                 space is equivalent to the existence of a certain type
                 of uncountable ordered one-sided biorthogonal system.
                 Under the continuum hypothesis, we deduce that this
                 notion is weaker than the existence of an uncountable
                 biorthogonal system.",
  acknowledgement = ack-nhfb,
  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:1994:CCS
author: Jonathan Borwein and Simon Fitzpatrick
title: Characterization of Clarke subgradients among one-dimensional multifunctions
type: Report
institution: Department of Mathematics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 14
day: 2
month: feb
monthnumber: 2
year: 1994
bibdate: Thu Sep 01 09:17:17 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 09:17:17 ???
note: Published in cite Borwein:1995:CCS.
URL: http://docserver.carma.newcastle.edu.au/23/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan Borwein and Simon Fitzpatrick
rawnote: Published in \cite{Borwein:1995:CCS}.
rawtitle: Characterization of {Clarke} subgradients among one-dimensional multifunctions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We introduce the notions of an robustly lower semicontinuous and an robustly upper semicontinuous function of a real variable. The Clarke subgradients of locally Lipschitz functions on an open interval $I$ are shown to be exactly those multifunctions on $I$ of the form $ [alpha (x), beta (x)]$ where $ alpha $ is robustly lower semicontinuous and $ beta $ is robustly upper semicontinuous on $I$. The approximate and symmetric subgradients of locally Lipschitz functions on $I$ are also characterized.

rawabstract:
We introduce the notions of an robustly lower semicontinuous and an robustly upper semicontinuous function of a real variable. The Clarke subgradients of locally Lipschitz functions on an open interval $I$ are shown to be exactly those multifunctions on $I$ of the form $ [\alpha (x), \beta (x)]$ where $ \alpha $ is robustly lower semicontinuous and $ \beta $ is robustly upper semicontinuous on $I$. The approximate and symmetric subgradients of locally Lipschitz functions on $I$ are also characterized.

entry:
@TechReport{Borwein:1994:CCS,
  author =       "Jonathan Borwein and Simon Fitzpatrick",
  title =        "Characterization of {Clarke} subgradients among
                 one-dimensional multifunctions",
  type =         "Report",
  institution =  "Department of Mathematics, Simon Fraser University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "14",
  day =          "2",
  month =        feb,
  year =         "1994",
  bibdate =      "Thu Sep 01 09:17:17 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:1995:CCS}.",
  URL =          "http://docserver.carma.newcastle.edu.au/23/",
  abstract =     "We introduce the notions of an robustly lower
                 semicontinuous and an robustly upper semicontinuous
                 function of a real variable. The Clarke subgradients of
                 locally Lipschitz functions on an open interval $I$ are
                 shown to be exactly those multifunctions on $I$ of the
                 form $ [\alpha (x), \beta (x)]$ where $ \alpha $ is
                 robustly lower semicontinuous and $ \beta $ is robustly
                 upper semicontinuous on $I$. The approximate and
                 symmetric subgradients of locally Lipschitz functions
                 on $I$ are also characterized.",
  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:1994:CFS
author: Jon Borwein and Jon Vanderwerff
title: Convex Functions on ``Sequentially Reflexive'' Banach Spaces
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 11
day: 14
month: sep
monthnumber: 9
year: 1994
bibdate: Wed Aug 31 09:48:34 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 09:48:34 ???
URL: http://docserver.carma.newcastle.edu.au/115/2/95_050-Borwein-Vanderwerff.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jon Borwein and Jon Vanderwerff
rawtitle: Convex Functions on ``Sequentially Reflexive'' {Banach} Spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
There is a sizeable class of results precisely relating boundedness, convergence and differentiability properties of continuous convex functions on Banach spaces to whether or not the space contains an isomorphic copy of $ ell _1 $. In this note, we provide constructions showing that the main such results do not extend to natural broader classes of functions.

rawabstract:
There is a sizeable class of results precisely relating boundedness, convergence and differentiability properties of continuous convex functions on Banach spaces to whether or not the space contains an isomorphic copy of $ \ell_1 $. In this note, we provide constructions showing that the main such results do not extend to natural broader classes of functions.

entry:
@TechReport{Borwein:1994:CFS,
  author =       "Jon Borwein and Jon Vanderwerff",
  title =        "Convex Functions on ``Sequentially Reflexive''
                 {Banach} Spaces",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  pages =        "11",
  day =          "14",
  month =        sep,
  year =         "1994",
  bibdate =      "Wed Aug 31 09:48:34 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/115/2/95_050-Borwein-Vanderwerff.pdf",
  abstract =     "There is a sizeable class of results precisely
                 relating boundedness, convergence and differentiability
                 properties of continuous convex functions on Banach
                 spaces to whether or not the space contains an
                 isomorphic copy of $ \ell_1 $. In this note, we provide
                 constructions showing that the main such results do not
                 extend to natural broader classes of functions.",
  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:1994:CMI
author: Jonathan Borwein
journal: j-AEQUATIONES-MATHEMATICAE
volume: 47
number: 1
pages: 115--118
year: 1994
CODEN: AEMABN
DOI: https://doi.org/10.1007/BF01838145
ISSN: 0001-9054 (print), 1420-8903 (electronic) OR 00019054 (print), 14208903 (electronic)
ISSNL: 0001-9054 OR 00019054
MRclass: 39B12
MRnumber: 1251136
MRreviewer: Shigeru Haruki
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/1541/
fjournal: Aequationes Mathematicae
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/10
rawauthor: Jonathan Borwein
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
A convergent mean iteration: a proof that $ x_n coloneq M(x_n - 1, x_n - 2, cdots , x_n - k) $ converges

rawtitle:
A convergent mean iteration: a proof that {$ x_n \coloneq M(x_{n - 1}, x_{n - 2}, \cdots, x_{n - k}) $} converges

entry:
@Article{Borwein:1994:CMI,
  author =       "Jonathan Borwein",
  title =        "A convergent mean iteration: a proof that {$ x_n
                 \coloneq M(x_{n - 1}, x_{n - 2}, \cdots, x_{n - k}) $}
                 converges",
  journal =      j-AEQUATIONES-MATHEMATICAE,
  volume =       "47",
  number =       "1",
  pages =        "115--118",
  year =         "1994",
  CODEN =        "AEMABN",
  DOI =          "https://doi.org/10.1007/BF01838145",
  ISSN =         "0001-9054 (print), 1420-8903 (electronic)",
  ISSN-L =       "0001-9054",
  MRclass =      "39B12",
  MRnumber =     "1251136",
  MRreviewer =   "Shigeru Haruki",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1541/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Aequationes Mathematicae",
  journal-URL =  "http://link.springer.com/journal/10",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1994:DKK
author: Jon Borwein and Jon Vanderwerff
title: Dual Kadec--Klee norms and the relationships between Wijsman, slice, and Mosco convergence
journal: j-MICH-MATH-J
volume: 41
number: 2
pages: 371--387
year: 1994
CODEN: MIMJA5
DOI: https://doi.org/10.1307/mmj/1029005003
ISSN: 0026-2285 (print), 1945-2365 (electronic) OR 00262285 (print), 19452365 (electronic)
ISSNL: 0026-2285 OR 00262285
MRclass: 46B10 (46B20 46N10 49J45 54B20)
MRnumber: 1278442
MRreviewer: Simon Fitzpatrick
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 Michigan Mathematical Journal
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://projecteuclid.org/all/euclid.mmj
rawauthor: Jon Borwein and Jon Vanderwerff
rawtitle: Dual {Kadec--Klee} norms and the relationships between {Wijsman}, slice, and {Mosco} convergence
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1994:DKK,
  author =       "Jon Borwein and Jon Vanderwerff",
  title =        "Dual {Kadec--Klee} norms and the relationships between
                 {Wijsman}, slice, and {Mosco} convergence",
  journal =      j-MICH-MATH-J,
  volume =       "41",
  number =       "2",
  pages =        "371--387",
  year =         "1994",
  CODEN =        "MIMJA5",
  DOI =          "https://doi.org/10.1307/mmj/1029005003",
  ISSN =         "0026-2285 (print), 1945-2365 (electronic)",
  ISSN-L =       "0026-2285",
  MRclass =      "46B10 (46B20 46N10 49J45 54B20)",
  MRnumber =     "1278442",
  MRreviewer =   "Simon Fitzpatrick",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "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 Michigan Mathematical Journal",
  journal-URL =  "https://projecteuclid.org/all/euclid.mmj",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  xxtitle =      "{Mosco}, {Wijsman} and slice convergence in
                 nonreflexive {Banach} spaces",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1994:ECFc
author: Jon Borwein and Simon Fitzpatrick and Jon Vanderwerff
title: Examples of convex functions and classifications of normed spaces
journal: j-J-CONVEX-ANAL
volume: 1
number: 1
pages: 61--73
year: 1994
ISSN: 0944-6532 (print), 2363-6394 (electronic) OR 09446532 (print), 23636394 (electronic)
MRclass: 46B20 (26B25 46B10 46N10 52A41)
MRnumber: 1326942
MRreviewer: Roland Durier
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/64/; http://www.heldermann-verlag.de/jca/jca01/jca01004.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: Jon Borwein and Simon Fitzpatrick and Jon Vanderwerff
rawtitle: Examples of convex functions and classifications of normed spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1994:ECFc,
  author =       "Jon Borwein and Simon Fitzpatrick and Jon
                 Vanderwerff",
  title =        "Examples of convex functions and classifications of
                 normed spaces",
  journal =      j-J-CONVEX-ANAL,
  volume =       "1",
  number =       "1",
  pages =        "61--73",
  year =         "1994",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "46B20 (26B25 46B10 46N10 52A41)",
  MRnumber =     "1326942",
  MRreviewer =   "Roland Durier",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/64/;
                 http://www.heldermann-verlag.de/jca/jca01/jca01004.pdf",
  acknowledgement = ack-nhfb,
  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:1994:EEEa
author: David Borwein and Jonathan M. Borwein and Roland Girgensohn
title: Explicit evaluation of Euler sums
type: Report
institution: Department of Mathematics and Statistics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 21
day: 18
month: mar
monthnumber: 3
year: 1994
MRclass: 40A25, 40B05 (11M99, 33E99)
bibdate: Thu Sep 01 11:00:10 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 11:00:10 ???
URL: http://docserver.carma.newcastle.edu.au/58
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David Borwein and Jonathan M. Borwein and Roland Girgensohn
rawtitle: Explicit evaluation of {Euler} sums
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In response to a letter from Goldbach, Euler considered sums of the formpar $$ sigma _h(s, t) = sum _n = 1^infty big (1 + frac 12^s + cdots + frac 1(n - 1)^s big ) n^-t, $$ par where $s$ and $t$ are positive integers.par As Euler discovered by a process of extrapolation (from $ s + t leq 13$), $ sigma _h(s, t)$ can be evaluated in terms of Riemann $ zeta $-functions when $ s + t$ is odd. We provide a rigorous proof of Euler's discovery and then give analogous evaluations with proofs for corresponding alternating sums. Relatedly we give a formula for the seriespar $$ sum _n = 1^infty big (1 + frac 12 + cdots + frac 1n big )^2 (n + 1)^-m $$ par This evaluation involves $ zeta $-functions and $ sigma _h(2, m)$.

keywords:
beta function; generating functions; harmonic numbers; polylogarithms; psi function; Riemann zeta function

rawabstract:
In response to a letter from Goldbach, Euler considered sums of the form\par $$ \sigma_h(s, t) = \sum_{n = 1}^\infty \big (1 + \frac {1}{2^s} + \cdots + \frac {1}{(n - 1)^s} \big) n^{-t}, $$ \par where $s$ and $t$ are positive integers.\par As Euler discovered by a process of extrapolation (from $ s + t \leq 13$), $ \sigma_h(s, t)$ can be evaluated in terms of Riemann $ \zeta $-functions when $ s + t$ is odd. We provide a rigorous proof of Euler's discovery and then give analogous evaluations with proofs for corresponding alternating sums. Relatedly we give a formula for the series\par $$ \sum_{n = 1}^\infty \big (1 + \frac {1}{2} + \cdots + \frac {1}{n} \big)^2 (n + 1)^{-m} $$ \par This evaluation involves $ \zeta $-functions and $ \sigma_h(2, m)$.

entry:
@TechReport{Borwein:1994:EEEa,
  author =       "David Borwein and Jonathan M. Borwein and Roland
                 Girgensohn",
  title =        "Explicit evaluation of {Euler} sums",
  type =         "Report",
  institution =  "Department of Mathematics and Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "21",
  day =          "18",
  month =        mar,
  year =         "1994",
  MRclass =      "40A25, 40B05 (11M99, 33E99)",
  bibdate =      "Thu Sep 01 11:00:10 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/58",
  abstract =     "In response to a letter from Goldbach, Euler
                 considered sums of the form\par

                  $$ \sigma_h(s, t) = \sum_{n = 1}^\infty \big (1 +
                 \frac {1}{2^s} + \cdots + \frac {1}{(n - 1)^s} \big)
                 n^{-t}, $$ \par

                 where $s$ and $t$ are positive integers.\par

                 As Euler discovered by a process of extrapolation (from
                 $ s + t \leq 13$), $ \sigma_h(s, t)$ can be evaluated
                 in terms of Riemann $ \zeta $-functions when $ s + t$
                 is odd. We provide a rigorous proof of Euler's
                 discovery and then give analogous evaluations with
                 proofs for corresponding alternating sums. Relatedly we
                 give a formula for the series\par $$ \sum_{n =
                 1}^\infty \big (1 + \frac {1}{2} + \cdots + \frac
                 {1}{n} \big)^2 (n + 1)^{-m} $$ \par

                 This evaluation involves $ \zeta $-functions and $
                 \sigma_h(2, m)$.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "beta function; generating functions; harmonic numbers;
                 polylogarithms; psi function; Riemann zeta function",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1994:EML
author: Jonathan M. Borwein and Adrian S. Lewis and Mark A. Limber
title: Entropy Minimization with Lattice Bounds
journal: j-J-APPROX-THEORY
volume: 79
number: 1
pages: 1--16
year: 1994
CODEN: JAXTAZ
DOI: https://doi.org/10.1006/jath.1994.1110
ISSN: 0021-9045 (print), 1096-0430 (electronic) OR 00219045 (print), 10960430 (electronic)
ISSNL: 0021-9045 OR 00219045
MRclass: 41A46 (41A29 90C48)
MRnumber: 1294317
MRreviewer: Dominikus Noll
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
fjournal: Journal of Approximation Theory
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.sciencedirect.com/science/journal/00219045
rawauthor: Jonathan M. Borwein and Adrian S. Lewis and Mark A. Limber
rawtitle: Entropy Minimization with Lattice Bounds
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1545/; http://www.sciencedirect.com/science/article/pii/S0021904584711105

abstract:
We characterize solutions to the problem of minimizing a convex integral objective function subject to a finite number of linear constraints and requiring that the feasible functions lie in a strip $ [alpha , beta ] $ where $ alpha $ and $ beta $ are extended real valued measurable functions. We use the duality theory of J. M. Borwein and A. S. Lewis (Math. Programming, Series B57 (1992), 15-48, 49-84) to show that the solutions are of the usual form, but truncated where they leave the strip.

rawabstract:
We characterize solutions to the problem of minimizing a convex integral objective function subject to a finite number of linear constraints and requiring that the feasible functions lie in a strip $ [\alpha, \beta] $ where $ \alpha $ and $ \beta $ are extended real valued measurable functions. We use the duality theory of J. M. Borwein and A. S. Lewis (Math. Programming, Series \{B57\} (1992), 15-48, 49-84) to show that the solutions are of the usual form, but truncated where they leave the strip.

entry:
@Article{Borwein:1994:EML,
  author =       "Jonathan M. Borwein and Adrian S. Lewis and Mark A.
                 Limber",
  title =        "Entropy Minimization with Lattice Bounds",
  journal =      j-J-APPROX-THEORY,
  volume =       "79",
  number =       "1",
  pages =        "1--16",
  year =         "1994",
  CODEN =        "JAXTAZ",
  DOI =          "https://doi.org/10.1006/jath.1994.1110",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  MRclass =      "41A46 (41A29 90C48)",
  MRnumber =     "1294317",
  MRreviewer =   "Dominikus Noll",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1545/;
                 http://www.sciencedirect.com/science/article/pii/S0021904584711105",
  abstract =     "We characterize solutions to the problem of minimizing
                 a convex integral objective function subject to a
                 finite number of linear constraints and requiring that
                 the feasible functions lie in a strip $ [\alpha, \beta]
                 $ where $ \alpha $ and $ \beta $ are extended real
                 valued measurable functions. We use the duality theory
                 of J. M. Borwein and A. S. Lewis (Math. Programming,
                 Series \{B57\} (1992), 15-48, 49-84) to show that the
                 solutions are of the usual form, but truncated where
                 they leave the strip.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1994:EMPa
author: Jonathan M. Borwein and Adrian S. Lewis and Roger D. Nussbaum
title: Entropy Minimization, $ D A D $ Problems, and Doubly Stochastic Kernels
journal: j-J-FUNCT-ANAL
volume: 123
number: 2
pages: 264--307
year: 1994
CODEN: JFUAAW
DOI: https://doi.org/10.1006/jfan.1994.1089
ISSN: 0022-1236 (print), 1096-0783 (electronic) OR 00221236 (print), 10960783 (electronic)
ISSNL: 0022-1236 OR 00221236
MRclass: 47N10 (47B99 47H15 49N15 90C30)
MRnumber: 1283029
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 Adrian S. Lewis and Roger D. Nussbaum
rawtitle: Entropy Minimization, {$ D A D $} Problems, and Doubly Stochastic Kernels
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1546/; http://www.sciencedirect.com/science/article/pii/S0022123684710895

abstract:
The classical $ D A D $ problem asks, for a square matrix $A$ with nonnegative entries, when it is possible to find positive diagonal matrices $ D_1$ and $ D_2$ with $ D_1 A D_2$ doubly stochastic. We consider various continuous and measurable generalizations of this problem. Through a fusion of variational and fixed point techniques we obtain strong analogues of the classical results. Our extensions appear inaccessible by either technique separately.

rawabstract:
The classical $ D A D $ problem asks, for a square matrix $A$ with nonnegative entries, when it is possible to find positive diagonal matrices $ D_1$ and $ D_2$ with $ D_1 A D_2$ doubly stochastic. We consider various continuous and measurable generalizations of this problem. Through a fusion of variational and fixed point techniques we obtain strong analogues of the classical results. Our extensions appear inaccessible by either technique separately.

entry:
@Article{Borwein:1994:EMPa,
  author =       "Jonathan M. Borwein and Adrian S. Lewis and Roger D.
                 Nussbaum",
  title =        "Entropy Minimization, {$ D A D $} Problems, and Doubly
                 Stochastic Kernels",
  journal =      j-J-FUNCT-ANAL,
  volume =       "123",
  number =       "2",
  pages =        "264--307",
  year =         "1994",
  CODEN =        "JFUAAW",
  DOI =          "https://doi.org/10.1006/jfan.1994.1089",
  ISSN =         "0022-1236 (print), 1096-0783 (electronic)",
  ISSN-L =       "0022-1236",
  MRclass =      "47N10 (47B99 47H15 49N15 90C30)",
  MRnumber =     "1283029",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1546/;
                 http://www.sciencedirect.com/science/article/pii/S0022123684710895",
  abstract =     "The classical $ D A D $ problem asks, for a square
                 matrix $A$ with nonnegative entries, when it is
                 possible to find positive diagonal matrices $ D_1$ and
                 $ D_2$ with $ D_1 A D_2$ doubly stochastic. We consider
                 various continuous and measurable generalizations of
                 this problem. Through a fusion of variational and fixed
                 point techniques we obtain strong analogues of the
                 classical results. Our extensions appear inaccessible
                 by either technique separately.",
  acknowledgement = ack-nhfb,
  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: article
filename: borwein-jonathan-m.bib
label: Borwein:1994:FAS
author: Jon Borwein and Jon Vanderwerff
title: Further arguments for slice convergence in nonreflexive spaces
journal: j-SET-VALUED-ANAL
volume: 2
number: 4
pages: 529--544
year: 1994
CODEN: SVANEG
DOI: https://doi.org/10.1007/BF01033070
ISSN: 0927-6947 (print), 1572-932x (electronic) OR 09276947 (print), 1572932x (electronic)
ISSNL: 0927-6947 OR 09276947
MRclass: 49J45 (46N10 54B20)
MRnumber: 1308483
MRreviewer: Gerald Beer
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/62/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11228
rawauthor: Jon Borwein and Jon Vanderwerff
rawtitle: Further arguments for slice convergence in nonreflexive spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
fjournal:
Set-Valued Analysis. An International Journal Devoted to the Theory of Multifunctions and its Applications

entry:
@Article{Borwein:1994:FAS,
  author =       "Jon Borwein and Jon Vanderwerff",
  title =        "Further arguments for slice convergence in
                 nonreflexive spaces",
  journal =      j-SET-VALUED-ANAL,
  volume =       "2",
  number =       "4",
  pages =        "529--544",
  year =         "1994",
  CODEN =        "SVANEG",
  DOI =          "https://doi.org/10.1007/BF01033070",
  ISSN =         "0927-6947 (print), 1572-932x (electronic)",
  ISSN-L =       "0927-6947",
  MRclass =      "49J45 (46N10 54B20)",
  MRnumber =     "1308483",
  MRreviewer =   "Gerald Beer",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/62/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Set-Valued Analysis. An International Journal Devoted
                 to the Theory of Multifunctions and its Applications",
  journal-URL =  "http://link.springer.com/journal/11228",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1994:FEDa
author: Jonathan M. Borwein and Roland Girgensohn
title: Functional equations and distribution functions
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 10
day: 15
month: jul
monthnumber: 7
year: 1994
bibdate: Thu Sep 01 15:54:10 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 15:54:10 ???
note: Dedicated to Professor Janos Aczel's on the occasion of his 70th birthday.
URL: http://docserver.carma.newcastle.edu.au/90
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Roland Girgensohn
rawnote: Dedicated to Professor J{\'a}nos Acz{\'e}l's on the occasion of his 70th birthday.
rawtitle: Functional equations and distribution functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Wee consider the functional equationpar $$ f(t) = frac 1b sum _nu = 0^b - 1 f big (frac t - beta _nua big ) mbox for all $ t in mathbb R$ , qquad (F) $$ par where $ 0 < a < 1 $ , $ b in mathbb N backslash 1 $ and $ - 1 = beta _0 leq beta _1 leq beta _2 leq cdots leq beta _p - 1 = 1 $ are given parameters, $ f color mathbb R to mathbb R $ is the unknown. We show that there is a unique bounded function $f$ which solves (F) and satisfies $ f(t) = 0$ for $ t < - 1 / (1 - a)$, $ f(t) = 1$ for $ t > 1 / (1 - a)$. This solution can be interpreted as the distribution function of a certain random series. It 1s known to be either singular or absolutely continuous, but the problem for which parameters it 1s absolutely continuous 1s largely open. We collect some previously established partial answers and generalize them. We also point out an interesting connection to the so-called Schilling equation.

rawabstract:
Wee consider the functional equation\par $$ f(t) = \frac {1}{b} \sum_{\nu = 0}^{b - 1} f \big (\frac {t - \beta_nu}{a} \big) \mbox {for all $ t \in \mathbb{R}$ }, \qquad (F) $$ \par where $ 0 < a < 1 $ , $ b \in \mathbb {N} \backslash \{ 1 \} $ and $ - 1 = \beta_0 \leq \beta_1 \leq \beta_2 \leq \cdots \leq \beta_{p - 1} = 1 $ are given parameters, $ f \color \mathbb {R} \to \mathbb {R} $ is the unknown. We show that there is a unique bounded function $f$ which solves (F) and satisfies $ f(t) = 0$ for $ t < - 1 / (1 - a)$, $ f(t) = 1$ for $ t > 1 / (1 - a)$. This solution can be interpreted as the distribution function of a certain random series. It 1s known to be either singular or absolutely continuous, but the problem for which parameters it 1s absolutely continuous 1s largely open. We collect some previously established partial answers and generalize them. We also point out an interesting connection to the so-called Schilling equation.

entry:
@TechReport{Borwein:1994:FEDa,
  author =       "Jonathan M. Borwein and Roland Girgensohn",
  title =        "Functional equations and distribution functions",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  pages =        "10",
  day =          "15",
  month =        jul,
  year =         "1994",
  bibdate =      "Thu Sep 01 15:54:10 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Dedicated to Professor J{\'a}nos Acz{\'e}l's on the
                 occasion of his 70th birthday.",
  URL =          "http://docserver.carma.newcastle.edu.au/90",
  abstract =     "Wee consider the functional equation\par

                  $$ f(t) = \frac {1}{b} \sum_{\nu = 0}^{b - 1} f \big
                 (\frac {t - \beta_nu}{a} \big) \mbox {for all $ t \in
                 \mathbb{R}$ }, \qquad (F) $$ \par

                 where $ 0 < a < 1 $ , $ b \in \mathbb {N} \backslash \{
                 1 \} $ and $ - 1 = \beta_0 \leq \beta_1 \leq \beta_2
                 \leq \cdots \leq \beta_{p - 1} = 1 $ are given
                 parameters, $ f \color \mathbb {R} \to \mathbb {R} $ is
                 the unknown. We show that there is a unique bounded
                 function $f$ which solves (F) and satisfies $ f(t) = 0$
                 for $ t < - 1 / (1 - a)$, $ f(t) = 1$ for $ t > 1 / (1
                 - a)$. This solution can be interpreted as the
                 distribution function of a certain random series. It 1s
                 known to be either singular or absolutely continuous,
                 but the problem for which parameters it 1s absolutely
                 continuous 1s largely open. We collect some previously
                 established partial answers and generalize them. We
                 also point out an interesting connection to the
                 so-called Schilling equation.",
  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:1994:FEDb
author: Jonathan M. Borwein and Roland Girgensohn
title: Functional equations and distribution functions
journal: Results in Mathematics. Resultate der Mathematik
volume: 26
number: 3--4
pages: 229--237
year: 1994
DOI: https://doi.org/10.1007/BF03323043
ISSN: 0378-6218 OR 03786218
ISSNL: 0378-6218 OR 03786218
MRclass: 39B22 (39B62 60E05 62E15)
MRnumber: 1300602
MRreviewer: K. Lajk{\'o}
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: For Janos Aczel's 70th birthday.
URL: http://docserver.carma.newcastle.edu.au/90/
fjournal: Results in Mathematics. Resultate der Mathematik
acknowledgement: ack-nhfb
ajournal: Results Math.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Roland Girgensohn
rawnote: For J{\'a}nos Acz{\'e}l's 70th birthday.
rawtitle: Functional equations and distribution functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1994:FEDb,
  author =       "Jonathan M. Borwein and Roland Girgensohn",
  title =        "Functional equations and distribution functions",
  journal =      "Results in Mathematics. Resultate der Mathematik",
  volume =       "26",
  number =       "3--4",
  pages =        "229--237",
  year =         "1994",
  DOI =          "https://doi.org/10.1007/BF03323043",
  ISSN =         "0378-6218",
  ISSN-L =       "0378-6218",
  MRclass =      "39B22 (39B62 60E05 62E15)",
  MRnumber =     "1300602",
  MRreviewer =   "K. Lajk{\'o}",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "For J{\'a}nos Acz{\'e}l's 70th birthday.",
  URL =          "http://docserver.carma.newcastle.edu.au/90/",
  acknowledgement = ack-nhfb,
  ajournal =     "Results Math.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Results in Mathematics. Resultate der Mathematik",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1994:MER
author: J. M. Borwein and A. S. Lewis and D. Noll
type: Report
institution: Department of Combinatorics and Optimization University of Waterloo
address: Waterloo, ON N2L 3G1, Canada
pages: 31
day: 14
month: dec
monthnumber: 12
year: 1994
bibdate: Thu Sep 01 15:39:54 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 15:39:54 ???
URL: http://docserver.carma.newcastle.edu.au/82
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and A. S. Lewis and D. Noll
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Maximum entropy reconstruction using derivative information. Part 1: Fisher information and convex duality

abstract:
Maximum entropy spectral density estimation is a technique for reconstructing an unknown density function from some known measurements by maximizing a given measure of entropy of the estimate. Here we present a variety of new entropy measures which attempt to control derivative values of the densities. Our models apply among others to the inference problem based on the averaged Fisher information measure. The duality theory we develop resembles models used in convex optimal control problems. We present a variety of examples, including relaxed moment matching with Fisher information and best interpolation on a strip.

keywords:
duality; Fisher information; generalized solutions; Maximum Entropy method; optimal control; Partially finite convex programming; Spectral Density estimation

rawabstract:
Maximum entropy spectral density estimation is a technique for reconstructing an unknown density function from some known measurements by maximizing a given measure of entropy of the estimate. Here we present a variety of new entropy measures which attempt to control derivative values of the densities. Our models apply among others to the inference problem based on the averaged Fisher information measure. The duality theory we develop resembles models used in convex optimal control problems. We present a variety of examples, including relaxed moment matching with Fisher information and best interpolation on a strip.

rawtitle:
Maximum entropy reconstruction using derivative information. {Part 1}: {Fisher} information and convex duality

entry:
@TechReport{Borwein:1994:MER,
  author =       "J. M. Borwein and A. S. Lewis and D. Noll",
  title =        "Maximum entropy reconstruction using derivative
                 information. {Part 1}: {Fisher} information and convex
                 duality",
  type =         "Report",
  institution =  "Department of Combinatorics and Optimization
                 University of Waterloo",
  address =      "Waterloo, ON N2L 3G1, Canada",
  pages =        "31",
  day =          "14",
  month =        dec,
  year =         "1994",
  bibdate =      "Thu Sep 01 15:39:54 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/82",
  abstract =     "Maximum entropy spectral density estimation is a
                 technique for reconstructing an unknown density
                 function from some known measurements by maximizing a
                 given measure of entropy of the estimate. Here we
                 present a variety of new entropy measures which attempt
                 to control derivative values of the densities. Our
                 models apply among others to the inference problem
                 based on the averaged Fisher information measure. The
                 duality theory we develop resembles models used in
                 convex optimal control problems. We present a variety
                 of examples, including relaxed moment matching with
                 Fisher information and best interpolation on a strip.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "duality; Fisher information; generalized solutions;
                 Maximum Entropy method; optimal control; Partially
                 finite convex programming; Spectral Density
                 estimation",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1994:MES
author: J. M. Borwein and A. S. Lewis and M. N. Limber and D. Noll
title: Maximum Entropy Spectral Analysis Using Derivative Information Part 2: Computational Results
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 19
day: 10
month: jan
monthnumber: 1
year: 1994
bibdate: Thu Sep 01 14:47:08 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 14:47:08 ???
URL: http://docserver.carma.newcastle.edu.au/71
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and A. S. Lewis and M. N. Limber and D. Noll
rawtitle: Maximum Entropy Spectral Analysis Using Derivative Information Part 2: Computational Results
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Maximum entropy density estimation, a technique for reconstructing an unknown density function on the basis of certain measurements, has applications in various areas of applied physical sciences and engineering. Here we present concrete results for the maximum entropy inversion program based on a new class of information measures which are designed to control derivative values of the unknown densities.

keywords:
Convex duality; Fisher information; Optimal Control; Primal dual program; Runge--Kutta methods; Spectral density estimation

rawabstract:
Maximum entropy density estimation, a technique for reconstructing an unknown density function on the basis of certain measurements, has applications in various areas of applied physical sciences and engineering. Here we present concrete results for the maximum entropy inversion program based on a new class of information measures which are designed to control derivative values of the unknown densities.

entry:
@TechReport{Borwein:1994:MES,
  author =       "J. M. Borwein and A. S. Lewis and M. N. Limber and D.
                 Noll",
  title =        "Maximum Entropy Spectral Analysis Using Derivative
                 Information Part 2: Computational Results",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "19",
  day =          "10",
  month =        jan,
  year =         "1994",
  bibdate =      "Thu Sep 01 14:47:08 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/71",
  abstract =     "Maximum entropy density estimation, a technique for
                 reconstructing an unknown density function on the basis
                 of certain measurements, has applications in various
                 areas of applied physical sciences and engineering.
                 Here we present concrete results for the maximum
                 entropy inversion program based on a new class of
                 information measures which are designed to control
                 derivative values of the unknown densities.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Convex duality; Fisher information; Optimal Control;
                 Primal dual program; Runge--Kutta methods; Spectral
                 density estimation",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1994:NRS
author: Jonathan M. Borwein and Marian Fabian
title: A note on regularity of sets and of distance functions in Banach space
journal: j-J-MATH-ANAL-APPL
volume: 182
number: 2
pages: 566--570
year: 1994
CODEN: JMANAK
DOI: https://doi.org/10.1006/jmaa.1994.1104
ISSN: 0022-247X (print), 1096-0813 (electronic) OR 0022247X (print), 10960813 (electronic)
ISSNL: 0022-247X OR 0022247X
MRclass: 49J52
MRnumber: 1269478
MRreviewer: Doug Ward
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
URL: http://www.sciencedirect.com/science/article/pii/S0022247X84711048
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 Mari{\'a}n Fabi{\'a}n
rawtitle: A note on regularity of sets and of distance functions in {Banach} space
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We show that in every infinite dimensional Banach space there is a compact set C and x in C such that C is regular at x (in the sense of nonsmooth analysis) but such that the associated distance function dC is not regular at x and neither is -dC.

rawabstract:
We show that in every infinite dimensional Banach space there is a compact set C and x in C such that C is regular at x (in the sense of nonsmooth analysis) but such that the associated distance function dC is not regular at x and neither is -dC.

entry:
@Article{Borwein:1994:NRS,
  author =       "Jonathan M. Borwein and Mari{\'a}n Fabi{\'a}n",
  title =        "A note on regularity of sets and of distance functions
                 in {Banach} space",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "182",
  number =       "2",
  pages =        "566--570",
  year =         "1994",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1006/jmaa.1994.1104",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "49J52",
  MRnumber =     "1269478",
  MRreviewer =   "Doug Ward",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X84711048",
  abstract =     "We show that in every infinite dimensional Banach
                 space there is a compact set C and x in C such that C
                 is regular at x (in the sense of nonsmooth analysis)
                 but such that the associated distance function dC is
                 not regular at x and neither is -dC.",
  acknowledgement = ack-nhfb,
  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",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1994:SCM
author: J. M. Borwein and P. B. Borwein and F. G. Garvan
title: Some cubic modular identities of Ramanujan
journal: j-TRANS-AM-MATH-SOC
volume: 343
number: 1
pages: 35--47
month: may
monthnumber: 5
year: 1994
CODEN: TAMTAM
DOI: https://doi.org/10.2307/2154520
ISSN: 0002-9947 (print), 1088-6850 (electronic) OR 00029947 (print), 10886850 (electronic)
ISSNL: 0002-9947 OR 00029947
MRclass: 11B65 (11F27 33D10)
MRnumber: 1243610
MRreviewer: George E. Andrews
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/1547/; https://www.jstor.org/stable/2154520
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: J. M. Borwein and P. B. Borwein and F. G. Garvan
rawtitle: Some cubic modular identities of {Ramanujan}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1994:SCM,
  author =       "J. M. Borwein and P. B. Borwein and F. G. Garvan",
  title =        "Some cubic modular identities of {Ramanujan}",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "343",
  number =       "1",
  pages =        "35--47",
  month =        may,
  year =         "1994",
  CODEN =        "TAMTAM",
  DOI =          "https://doi.org/10.2307/2154520",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "11B65 (11F27 33D10)",
  MRnumber =     "1243610",
  MRreviewer =   "George E. Andrews",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1547/;
                 https://www.jstor.org/stable/2154520",
  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: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1994:SEC
author: Jonathan M. Borwein
title: A survey of examples of convex functions and classifications of normed spaces
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 13
day: 1
month: dec
monthnumber: 12
year: 1994
MRclass: 46B20, 46N10 (46B10)
bibdate: Thu Sep 01 16:26:49 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 16:26:49 ???
note: Revised 22 January 1995. Published in cite Borwein:1995:SEC.
URL: http://docserver.carma.newcastle.edu.au/92; http://docserver.carma.newcastle.edu.au/93
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
rawnote: Revised 22 January 1995. Published in \cite{Borwein:1995:SEC}.
rawtitle: A survey of examples of convex functions and classifications of normed spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
This paper represents a slightly extended version of the eponymous talk given at the VII Colloque Franco-Allemand d'Optimisation. My aim is to illustrate the tight connection between the sequential properties of a Banach space and the corresponding properties of the convex functions and sets which may or may not be defined on that space.

keywords:
classical Banach spaces; convex functions; differentiability; Haar-null sets.; nearest points; sequential properties

rawabstract:
This paper represents a slightly extended version of the eponymous talk given at the VII Colloque Franco-Allemand d'Optimisation. My aim is to illustrate the tight connection between the sequential properties of a Banach space and the corresponding properties of the convex functions and sets which may or may not be defined on that space.

entry:
@TechReport{Borwein:1994:SEC,
  author =       "Jonathan M. Borwein",
  title =        "A survey of examples of convex functions and
                 classifications of normed spaces",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  pages =        "13",
  day =          "1",
  month =        dec,
  year =         "1994",
  MRclass =      "46B20, 46N10 (46B10)",
  bibdate =      "Thu Sep 01 16:26:49 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Revised 22 January 1995. Published in
                 \cite{Borwein:1995:SEC}.",
  URL =          "http://docserver.carma.newcastle.edu.au/92;
                 http://docserver.carma.newcastle.edu.au/93",
  abstract =     "This paper represents a slightly extended version of
                 the eponymous talk given at the VII Colloque
                 Franco-Allemand d'Optimisation. My aim is to illustrate
                 the tight connection between the sequential properties
                 of a Banach space and the corresponding properties of
                 the convex functions and sets which may or may not be
                 defined on that space.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "classical Banach spaces; convex functions;
                 differentiability; Haar-null sets.; nearest points;
                 sequential properties",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1994:SOD
author: Jonathan M. Borwein and Dominikus Noll
title: Second order differentiability of convex functions in Banach spaces
journal: j-TRANS-AM-MATH-SOC
volume: 342
number: 1
pages: 43--81
month: mar
monthnumber: 3
year: 1994
CODEN: TAMTAM
DOI: https://doi.org/10.2307/2154684
ISSN: 0002-9947 (print), 1088-6850 (electronic) OR 00029947 (print), 10886850 (electronic)
ISSNL: 0002-9947 OR 00029947
MRclass: 46G05 (26E15)
MRnumber: 1145959
MRreviewer: Lud{\v{e}}k Zaj{\'{\i}}{\v{c}}ek
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/1549/; https://www.jstor.org/stable/2154684
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 Dominikus Noll
rawtitle: Second order differentiability of convex functions in {Banach} spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1994:SOD,
  author =       "Jonathan M. Borwein and Dominikus Noll",
  title =        "Second order differentiability of convex functions in
                 {Banach} spaces",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "342",
  number =       "1",
  pages =        "43--81",
  month =        mar,
  year =         "1994",
  CODEN =        "TAMTAM",
  DOI =          "https://doi.org/10.2307/2154684",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "46G05 (26E15)",
  MRnumber =     "1145959",
  MRreviewer =   "Lud{\v{e}}k Zaj{\'{\i}}{\v{c}}ek",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1549/;
                 https://www.jstor.org/stable/2154684",
  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:1994:SRO
author: Jonathan M. Borwein and Adrian S. Lewis
title: Strong rotundity and optimization
journal: j-SIAM-J-OPT
volume: 4
number: 1
pages: 146--158
year: 1994
CODEN: SJOPE8
DOI: https://doi.org/10.1137/0804008
ISSN: 1052-6234 (print), 1095-7189 (electronic) OR 10526234 (print), 10957189 (electronic)
ISSNL: 1052-6234 OR 10526234
MRclass: 49K27 (90C48)
MRnumber: 1260412
MRreviewer: T. Zolezzi
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/1550/
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 Adrian S. Lewis
rawtitle: Strong rotundity and optimization
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1994:SRO,
  author =       "Jonathan M. Borwein and Adrian S. Lewis",
  title =        "Strong rotundity and optimization",
  journal =      j-SIAM-J-OPT,
  volume =       "4",
  number =       "1",
  pages =        "146--158",
  year =         "1994",
  CODEN =        "SJOPE8",
  DOI =          "https://doi.org/10.1137/0804008",
  ISSN =         "1052-6234 (print), 1095-7189 (electronic)",
  ISSN-L =       "1052-6234",
  MRclass =      "49K27 (90C48)",
  MRnumber =     "1260412",
  MRreviewer =   "T. Zolezzi",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1550/",
  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:1994:STE
author: David Borwein and Jonathan M. Borwein
title: On Some Trigonometric and Exponential Lattice Sums
journal: j-J-MATH-ANAL-APPL
volume: 188
number: 1
pages: 209--218
year: 1994
CODEN: JMANAK
DOI: https://doi.org/10.1006/jmaa.1994.1422
ISSN: 0022-247X (print), 1096-0813 (electronic) OR 0022247X (print), 10960813 (electronic)
ISSNL: 0022-247X OR 0022247X
MRclass: 11L03 (11L07)
MRnumber: 1301727
MRreviewer: Gunter Dufner
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: David Borwein and Jonathan M. Borwein
rawtitle: On Some Trigonometric and Exponential Lattice Sums
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1542/; http://www.sciencedirect.com/science/article/pii/S0022247X84714223

abstract:
Certain two-dimensional trigonometric lattice series, the ordinary convergence of which involves unresolved questions of a deep and delicate number-theoretic nature, are shown to be summable by a special Abelian method and their Abelian sums are obtained. This is done by first evaluating an absolutely convergent exponential lattice series and then analytically extending its sum.

rawabstract:
Certain two-dimensional trigonometric lattice series, the ordinary convergence of which involves unresolved questions of a deep and delicate number-theoretic nature, are shown to be summable by a special Abelian method and their Abelian sums are obtained. This is done by first evaluating an absolutely convergent exponential lattice series and then analytically extending its sum.

entry:
@Article{Borwein:1994:STE,
  author =       "David Borwein and Jonathan M. Borwein",
  title =        "On Some Trigonometric and Exponential Lattice Sums",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "188",
  number =       "1",
  pages =        "209--218",
  year =         "1994",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1006/jmaa.1994.1422",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "11L03 (11L07)",
  MRnumber =     "1301727",
  MRreviewer =   "Gunter Dufner",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1542/;
                 http://www.sciencedirect.com/science/article/pii/S0022247X84714223",
  abstract =     "Certain two-dimensional trigonometric lattice series,
                 the ordinary convergence of which involves unresolved
                 questions of a deep and delicate number-theoretic
                 nature, are shown to be summable by a special Abelian
                 method and their Abelian sums are obtained. This is
                 done by first evaluating an absolutely convergent
                 exponential lattice series and then analytically
                 extending its sum.",
  acknowledgement = ack-nhfb,
  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",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1994:UCMa
author: J. M. Borwein and W. Huang
title: Uniform convergence for moment problems with Fermi--Dirac type entropies
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 11
day: 7
month: jan
monthnumber: 1
year: 1994
MRclass: 49M39, 41A10, 44A60
bibdate: Thu Sep 01 14:42:30 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 14:42:30 ???
URL: http://docserver.carma.newcastle.edu.au/70/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and W. Huang
rawtitle: Uniform convergence for moment problems with {Fermi--Dirac} type entropies
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We consider the best entropic estimation to a unknown density $ bar x $, given some of its algebraic or trigonometric moments. A uniform convergence theorem is established in this paper for such problems using Fermi--Dirac type entropic objectives

keywords:
best approximation; Fenchel duality; Fermi--Dirac entropy; linear constrained optimization; moment problems; uniform convergence

rawabstract:
We consider the best entropic estimation to a unknown density $ \bar {x} $, given some of its algebraic or trigonometric moments. A uniform convergence theorem is established in this paper for such problems using Fermi--Dirac type entropic objectives

entry:
@TechReport{Borwein:1994:UCMa,
  author =       "J. M. Borwein and W. Huang",
  title =        "Uniform convergence for moment problems with
                 {Fermi--Dirac} type entropies",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  pages =        "11",
  day =          "7",
  month =        jan,
  year =         "1994",
  MRclass =      "49M39, 41A10, 44A60",
  bibdate =      "Thu Sep 01 14:42:30 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/70/",
  abstract =     "We consider the best entropic estimation to a unknown
                 density $ \bar {x} $, given some of its algebraic or
                 trigonometric moments. A uniform convergence theorem is
                 established in this paper for such problems using
                 Fermi--Dirac type entropic objectives",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "best approximation; Fenchel duality; Fermi--Dirac
                 entropy; linear constrained optimization; moment
                 problems; uniform convergence",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1994:UCMb
author: J. M. Borwein and W. Huang
title: Uniform convergence for moment problems with Fermi--Dirac type entropies
journal: j-ZOR-MATH-METHODS-OPER-RES
volume: 40
number: 3
pages: 239--252
year: 1994
CODEN: ZMRREP
DOI: https://doi.org/10.1007/BF01432968
ISSN: 0340-9422 OR 03409422
MRclass: 90C45 (44A60)
MRnumber: 1316390
MRreviewer: Dominikus Noll
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/70/; http://link.springer.com/article/10.1007/BF01432968
fjournal: Zeitschrift fur Operations Research. Mathematical Methods of Operations Research
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/186
rawauthor: J. M. Borwein and W. Huang
rawtitle: Uniform convergence for moment problems with {Fermi--Dirac} type entropies
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1994:UCMb,
  author =       "J. M. Borwein and W. Huang",
  title =        "Uniform convergence for moment problems with
                 {Fermi--Dirac} type entropies",
  journal =      j-ZOR-MATH-METHODS-OPER-RES,
  volume =       "40",
  number =       "3",
  pages =        "239--252",
  year =         "1994",
  CODEN =        "ZMRREP",
  DOI =          "https://doi.org/10.1007/BF01432968",
  ISSN =         "0340-9422",
  MRclass =      "90C45 (44A60)",
  MRnumber =     "1316390",
  MRreviewer =   "Dominikus Noll",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/70/;
                 http://link.springer.com/article/10.1007/BF01432968",
  acknowledgement = ack-nhfb,
  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",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1994:UMP
author: J. M. Borwein and M. A. Limber
title: Underdetermined moment problems: a case for convex analysis
journal: SIAG/OPT
number: 5
pages: 9--13
month: Fall
year: 1994
bibdate: Mon Aug 15 14:52:57 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.15 14:52:57 ???
note: Invited talk at 1994 SIAM Conference on Optimization.
remark: Which journal is this??
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and M. A. Limber
rawnote: Invited talk at 1994 SIAM Conference on Optimization.
rawtitle: Underdetermined moment problems: a case for convex analysis
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1994:UMP,
  author =       "J. M. Borwein and M. A. Limber",
  title =        "Underdetermined moment problems: a case for convex
                 analysis",
  journal =      "SIAG/OPT",
  volume =       "??",
  number =       "5",
  pages =        "9--13",
  month =        "Fall",
  year =         "1994",
  DOI =          "",
  bibdate =      "Mon Aug 15 14:52:57 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Invited talk at 1994 SIAM Conference on
                 Optimization.",
  URL =          "",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Which journal is this??",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1994:VAN
author: Jonathan M. Borwein and Qiji J. Zhu
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 40
day: 2
month: may
monthnumber: 5
year: 1994
bibdate: Thu Sep 01 14:58:07 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 14:58:07 ???
URL: http://docserver.carma.newcastle.edu.au/78
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
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

abstract:
We provide a refined sensitivity analysis for finite and infinite horizon control problems where in both cases the perturbation space is $ L^1 $. Our underlying technique relies on a recent sequential description of both the generalized gradient of Clarke and of the approximate $G$-subdifferential of functions defined on a smooth Banach space. We also show that the proximal limit formula for the generalized gradient and its $ L^p$ analogue are direct consequences of these sequential formulas. Related characterizations of Lipschitzness of a function on a smooth space are given.

rawabstract:
We provide a refined sensitivity analysis for finite and infinite horizon control problems where in both cases the perturbation space is $ L^1 $. Our underlying technique relies on a recent sequential description of both the generalized gradient of Clarke and of the approximate $G$-subdifferential of functions defined on a smooth Banach space. We also show that the proximal limit formula for the generalized gradient and its $ L^p$ analogue are direct consequences of these sequential formulas. Related characterizations of Lipschitzness of a function on a smooth space are given.

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

entry:
@TechReport{Borwein:1994:VAN,
  author =       "Jonathan M. Borwein and Qiji J. Zhu",
  title =        "Variational analysis in nonreflexive spaces and
                 applications to control problems with {$ L^1 $}
                 perturbations",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  pages =        "40",
  day =          "2",
  month =        may,
  year =         "1994",
  bibdate =      "Thu Sep 01 14:58:07 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/78",
  abstract =     "We provide a refined sensitivity analysis for finite
                 and infinite horizon control problems where in both
                 cases the perturbation space is $ L^1 $. Our underlying
                 technique relies on a recent sequential description of
                 both the generalized gradient of Clarke and of the
                 approximate $G$-subdifferential of functions defined on
                 a smooth Banach space. We also show that the proximal
                 limit formula for the generalized gradient and its $
                 L^p$ analogue are direct consequences of these
                 sequential formulas. Related characterizations of
                 Lipschitzness of a function on a smooth space 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: inproceedings
filename: borwein-jonathan-m.bib
label: Bailey:1995:FNI
author: D. H. Bailey and J. M. Borwein and R. Girgensohn
booktitle: SIAM Conference on Parallel Computing, San Francisco, February 1995
title: Finding new identities with supercomputers
publisher: pub-SIAM
address: pub-SIAM:adr
pages: ??--??
year: 1995
bibdate: Mon Aug 15 14:48:40 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.15 14:48:40 ???
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. H. Bailey and J. M. Borwein and R. Girgensohn
rawbooktitle: {SIAM Conference on Parallel Computing, San Francisco, February 1995}
rawtitle: Finding new identities with supercomputers
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@InProceedings{Bailey:1995:FNI,
  author =       "D. H. Bailey and J. M. Borwein and R. Girgensohn",
  editor =       "????",
  booktitle =    "{SIAM Conference on Parallel Computing, San Francisco,
                 February 1995}",
  title =        "Finding new identities with supercomputers",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "??--??",
  year =         "1995",
  bibdate =      "Mon Aug 15 14:48:40 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bauschke:1995:CLM
author: Heinz H. Bauschke and Jonathan M. Borwein
title: Continuous linear monotone mappings in Banach space
type: CECM Research Report
number: 95:049
institution: inst-CECM
address: inst-CECM:adr
pages: 48
day: 29
month: aug
monthnumber: 8
year: 1995
bibdate: Tue Aug 16 10:12:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:12:47 ???
URL: http://docserver.carma.newcastle.edu.au/114/; https://web.archive.org/web/20110313015539/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Heinz H. Bauschke and Jonathan M. Borwein
rawtitle: Continuous linear monotone mappings in {Banach} space
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
abstract:
The concept of a monotone operator --- which covers both linear positive semi-definite operators and subdifferentials of convex functions --- has turned out to be very powerful in various branches of mathematics. - Over the last few decades, several new notions of monotonicity have been introduced: Gossez' maximal monotone of type (D), Simons' monotone of type (WD) and of type (NI), Fitzpatrick and Phelps' locally maximal monotone. While these monotonicities are automatic for maximal monotone operators in reflexive Banach spaces and for subdifferentials of convex functions, their precise relationship is largely unknown. In view of the origin of the theory of monotone operators, it is very natural to investigate linear monotone (i.e. positive semi-definite) operators. Here, it 1s shown --- within the beautiful framework of Convex Analysis --- that for continuous linear monotone operators, em all these notions coincide and are equivalent to the monotonicity of the conjugate operator. The latter condition is analyzed and illustrated by several examples. Some nonlinear results on regularizations conclude the paper.

rawabstract:
The concept of a monotone operator --- which covers both linear positive semi-definite operators and subdifferentials of convex functions --- has turned out to be very powerful in various branches of mathematics. - Over the last few decades, several new notions of monotonicity have been introduced: Gossez' maximal monotone of type (D), Simons' monotone of type (WD) and of type (NI), Fitzpatrick and Phelps' locally maximal monotone. While these monotonicities are automatic for maximal monotone operators in reflexive Banach spaces and for subdifferentials of convex functions, their precise relationship is largely unknown. In view of the origin of the theory of monotone operators, it is very natural to investigate linear monotone (i.e. positive semi-definite) operators. Here, it 1s shown --- within the beautiful framework of Convex Analysis --- that for continuous linear monotone operators, {\em all these notions coincide and are equivalent to the monotonicity of the conjugate operator}. The latter condition is analyzed and illustrated by several examples. Some nonlinear results on regularizations conclude the paper.

entry:
@TechReport{Bauschke:1995:CLM,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein",
  title =        "Continuous linear monotone mappings in {Banach}
                 space",
  type =         "CECM Research Report",
  number =       "95:049",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "48",
  day =          "29",
  month =        aug,
  year =         "1995",
  bibdate =      "Tue Aug 16 10:12:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/114/;
                 https://web.archive.org/web/20110313015539/",
  abstract =     "The concept of a monotone operator --- which covers
                 both linear positive semi-definite operators and
                 subdifferentials of convex functions --- has turned out
                 to be very powerful in various branches of mathematics.
                 - Over the last few decades, several new notions of
                 monotonicity have been introduced: Gossez' maximal
                 monotone of type (D), Simons' monotone of type (WD) and
                 of type (NI), Fitzpatrick and Phelps' locally maximal
                 monotone. While these monotonicities are automatic for
                 maximal monotone operators in reflexive Banach spaces
                 and for subdifferentials of convex functions, their
                 precise relationship is largely unknown. In view of the
                 origin of the theory of monotone operators, it is very
                 natural to investigate linear monotone (i.e. positive
                 semi-definite) operators. Here, it 1s shown --- within
                 the beautiful framework of Convex Analysis --- that for
                 continuous linear monotone operators, {\em all these
                 notions coincide and are equivalent to the monotonicity
                 of the conjugate operator}. The latter condition is
                 analyzed and illustrated by several examples. Some
                 nonlinear results on regularizations conclude the
                 paper.",
  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",
  xxtitle =      "Continuous Linear Monotone Operators on {Banach}
                 Space",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bauschke:1995:LFM
author: Heinz H. Bauschke and Jonathan M. Borwein
title: Legendre functions and the method of random Bregman projections
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 48
day: 2
month: mar
monthnumber: 3
year: 1995
MRclass: 49M45 (47TH17, 52A41, 65F10, 65K05, 90C25)
bibdate: Thu Sep 01 16:43:37 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 16:43:37 ???
note: Published in cite Bauschke:1997:LFM.
URL: http://docserver.carma.newcastle.edu.au/96
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:1997:LFM}.
rawtitle: {Legendre} functions and the method of random {Bregman} projections
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
The convex feasibility problem, that is, finding a point in the intersection of finitely many closed convex sets in Euclidean space, arises in various areas of mathematics and physical sciences. It can be solved by the classical method of cyclic orthogonal projections, where, by projecting cyclically onto the sets, a sequence is generated that converges to a point in the intersection. In 1967, Bregman extended this method to non-orthogonal projections based on a new notion of distance, now days called ``Bregman distance''. The Bregman distance is induced by a convex function. If this function is a so-called ``zone consistent Bregman function'', then Bregman's method works; however, deciding on this can be difficult. In this paper, Bregman's method is studied within the powerful framework of Convex Analysis. New insights are obtained and the rich class of ``Bregman / Legendre functions'' is introduced. Bregman's method still works, if the underlying function is Bregman / Legendre or more generally if it is Legendre but some constraint qualification holds additionally. The key advantage 1s the broad applicability and verifiability of these concepts. The results presented here are complementary to recent work by Censor and Reich on the method of random Bregman projections (where the sets are projected onto infinitely often --- not necessarily cyclically). Special attention 1s given to examples, some of which connect to Pythagorean means and to Convex Analysis on the Hermitian or symmetric matrices.

keywords:
Bregman function; Bregman projection; convex feasibility problem; convex function; convex set; essentially smooth function; essentially strictly convex function; Hermitian matrix; Legendre function; projection

rawabstract:
The convex feasibility problem, that is, finding a point in the intersection of finitely many closed convex sets in Euclidean space, arises in various areas of mathematics and physical sciences. It can be solved by the classical method of cyclic orthogonal projections, where, by projecting cyclically onto the sets, a sequence is generated that converges to a point in the intersection. In 1967, Bregman extended this method to non-orthogonal projections based on a new notion of distance, now days called ``Bregman distance''. The Bregman distance is induced by a convex function. If this function is a so-called ``zone consistent Bregman function'', then Bregman's method works; however, deciding on this can be difficult. In this paper, Bregman's method is studied within the powerful framework of Convex Analysis. New insights are obtained and the rich class of ``Bregman\slash Legendre functions'' is introduced. Bregman's method still works, if the underlying function is Bregman\slash Legendre or more generally if it is Legendre but some constraint qualification holds additionally. The key advantage 1s the broad applicability and verifiability of these concepts. The results presented here are complementary to recent work by Censor and Reich on the method of random Bregman projections (where the sets are projected onto infinitely often --- not necessarily cyclically). Special attention 1s given to examples, some of which connect to Pythagorean means and to Convex Analysis on the Hermitian or symmetric matrices.

entry:
@TechReport{Bauschke:1995:LFM,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein",
  title =        "{Legendre} functions and the method of random
                 {Bregman} projections",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "48",
  day =          "2",
  month =        mar,
  year =         "1995",
  MRclass =      "49M45 (47TH17, 52A41, 65F10, 65K05, 90C25)",
  bibdate =      "Thu Sep 01 16:43:37 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Bauschke:1997:LFM}.",
  URL =          "http://docserver.carma.newcastle.edu.au/96",
  abstract =     "The convex feasibility problem, that is, finding a
                 point in the intersection of finitely many closed
                 convex sets in Euclidean space, arises in various areas
                 of mathematics and physical sciences. It can be solved
                 by the classical method of cyclic orthogonal
                 projections, where, by projecting cyclically onto the
                 sets, a sequence is generated that converges to a point
                 in the intersection. In 1967, Bregman extended this
                 method to non-orthogonal projections based on a new
                 notion of distance, now days called ``Bregman
                 distance''. The Bregman distance is induced by a convex
                 function. If this function is a so-called ``zone
                 consistent Bregman function'', then Bregman's method
                 works; however, deciding on this can be difficult. In
                 this paper, Bregman's method is studied within the
                 powerful framework of Convex Analysis. New insights are
                 obtained and the rich class of ``Bregman\slash Legendre
                 functions'' is introduced. Bregman's method still
                 works, if the underlying function is Bregman\slash
                 Legendre or more generally if it is Legendre but some
                 constraint qualification holds additionally. The key
                 advantage 1s the broad applicability and verifiability
                 of these concepts. The results presented here are
                 complementary to recent work by Censor and Reich on the
                 method of random Bregman projections (where the sets
                 are projected onto infinitely often --- not necessarily
                 cyclically). Special attention 1s given to examples,
                 some of which connect to Pythagorean means and to
                 Convex Analysis on the Hermitian or symmetric
                 matrices.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Bregman function; Bregman projection; convex
                 feasibility problem; convex function; convex set;
                 essentially smooth function; essentially strictly
                 convex function; Hermitian matrix; Legendre function;
                 projection",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Bauschke:1995:PAS
author: Heinz H. Bauschke and Jonathan M. Borwein
title: On Projection Algorithms for Solving Convex Feasibility Problems
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 99
day: 28
month: apr
monthnumber: 4
year: 1995
bibdate: Wed Aug 31 08:57:40 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 08:57:40 ???
note: Published in cite Bauschke:1996:PAS
URL: http://docserver.carma.newcastle.edu.au/100/2/95_034-Bauschke-Borwein.pdf
remark: Undated, but stored in 1995-labeled directory, and PDF produced Fri Apr 28 14:11:01 1995.
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:1996:PAS}
rawtitle: On Projection Algorithms for Solving Convex Feasibility Problems
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and flexible framework is investigated. Several crucial new concepts which allow a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence are brought out. Numerous examples are given.

rawabstract:
Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and flexible framework is investigated. Several crucial new concepts which allow a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence are brought out. Numerous examples are given.

entry:
@TechReport{Bauschke:1995:PAS,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein",
  title =        "On Projection Algorithms for Solving Convex
                 Feasibility Problems",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "99",
  day =          "28",
  month =        apr,
  year =         "1995",
  bibdate =      "Wed Aug 31 08:57:40 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Bauschke:1996:PAS}",
  URL =          "http://docserver.carma.newcastle.edu.au/100/2/95_034-Bauschke-Borwein.pdf",
  abstract =     "Due to their extraordinary utility and broad
                 applicability in many areas of classical mathematics
                 and modern physical sciences (most notably,
                 computerized tomography), algorithms for solving convex
                 feasibility problems continue to receive great
                 attention. To unify, generalize, and review some of
                 these algorithms, a very broad and flexible framework
                 is investigated. Several crucial new concepts which
                 allow a systematic discussion of questions on behaviour
                 in general Hilbert spaces and on the quality of
                 convergence are brought out. Numerous examples are
                 given.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Undated, but stored in 1995-labeled directory, and PDF
                 produced Fri Apr 28 14:11:01 1995.",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borowski:1995:DCD
author: Ephraim J. Borowski and Jonathan M. Borwein
title: Dizionario Collins della matematica
publisher: Gremese Editore
address: Roma, Italy
pages: 423
year: 1995
ISBN: 88-7605-813-3 OR 8876058133
ISBN13: 978-88-7605-813-4 OR 9788876058134
bibdate: Tue Aug 16 09:08:42 MDT 2016
bibtimestamp: 2016.08.16 09:08:42 MDT
note: Translation to Italian by Andrea Stracca of cite Borowski:1991:HDM.
series: Dizionari Gremese
subject: Matematica - Enciclopedie e dizionari
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Ephraim J. Borowski and Jonathan M. Borwein
rawnote: Translation to Italian by Andrea Stracca of \cite{Borowski:1991:HDM}.
rawtitle: Dizionario {Collins} della matematica
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib

entry:
@Book{Borowski:1995:DCD,
  author =       "Ephraim J. Borowski and Jonathan M. Borwein",
  title =        "Dizionario {Collins} della matematica",
  publisher =    "Gremese Editore",
  address =      "Roma, Italy",
  pages =        "423",
  year =         "1995",
  ISBN =         "88-7605-813-3",
  ISBN-13 =      "978-88-7605-813-4",
  LCCN =         "????",
  bibdate =      "Tue Aug 16 09:08:42 MDT 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Translation to Italian by Andrea Stracca of
                 \cite{Borowski:1991:HDM}.",
  series =       "Dizionari Gremese",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject =      "Matematica - Enciclopedie e dizionari",
}


bibtype: book
filename: borwein-jonathan-m.bib
label: Borowski:1995:SXC
author: Ephraim J. Borowski and Jonathan M. Borwein
title: Shu xue ci dian
volume: 10
publisher: Mao tou ying chu ban
address: Taibei
pages: 879
year: 1995
ISBN: 957-0337-14-1 OR 9570337141
ISBN13: 978-957-0337-14-3 OR 9789570337143
bibdate: Tue Aug 16 09:05:36 MDT 2016
bibtimestamp: 2016.08.16 09:05:36 MDT
note: Chinese edition of cite Borowski:1991:HDM.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Ephraim J. Borowski and Jonathan M. Borwein
rawnote: Chinese edition of \cite{Borowski:1991:HDM}.
rawtitle: Shu xue ci dian
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib

entry:
@Book{Borowski:1995:SXC,
  author =       "Ephraim J. Borowski and Jonathan M. Borwein",
  title =        "Shu xue ci dian",
  volume =       "10",
  publisher =    "Mao tou ying chu ban",
  address =      "Taibei",
  pages =        "879",
  year =         "1995",
  ISBN =         "957-0337-14-1",
  ISBN-13 =      "978-957-0337-14-3",
  LCCN =         "????",
  bibdate =      "Tue Aug 16 09:05:36 MDT 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Chinese edition of \cite{Borowski:1991:HDM}.",
  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:1995:ATB
author: Jonathan M. Borwein and Roland Girgensohn
title: Addition theorems and binary expansions
journal: j-CAN-J-MATH
volume: 47
number: 2
pages: 262--273
year: 1995
CODEN: CJMAAB
DOI: https://doi.org/10.4153/CJM-1995-013-4
ISSN: 0008-414X (print), 1496-4279 (electronic) OR 0008414X (print), 14964279 (electronic)
ISSNL: 0008-414X OR 0008414X
MRclass: 39B62 (11A63)
MRnumber: 1335077
MRreviewer: W. Herget
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/1537/
fjournal: Canadian Journal of Mathematics. Journal Canadien de Mathematiques
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://cms.math.ca/cjm/
rawauthor: Jonathan M. Borwein and Roland Girgensohn
rawtitle: Addition theorems and binary expansions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1995:ATB,
  author =       "Jonathan M. Borwein and Roland Girgensohn",
  title =        "Addition theorems and binary expansions",
  journal =      j-CAN-J-MATH,
  volume =       "47",
  number =       "2",
  pages =        "262--273",
  year =         "1995",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-1995-013-4",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  MRclass =      "39B62 (11A63)",
  MRnumber =     "1335077",
  MRreviewer =   "W. Herget",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1537/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Canadian Journal of Mathematics. Journal Canadien de
                 Math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1995:CCH
author: Jonathan M. Borwein and Simon Fitzpatrick
title: Closed convex Haar null sets
type: CECM Research Report
number: 95:052
institution: inst-CECM
address: inst-CECM:adr
pages: 9
month: aug
monthnumber: 8
year: 1995
bibdate: Tue Aug 16 10:13:27 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:13:27 ???
URL: http://docserver.carma.newcastle.edu.au/117/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Simon Fitzpatrick
rawtitle: Closed convex {Haar} null sets
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
If $E$ is a separable super-reflexive Banach space then every closed convex subset of $E$ with empty interior is a Haar null set.

rawabstract:
If $E$ is a separable super-reflexive Banach space then every closed convex subset of $E$ with empty interior is a Haar null set.

entry:
@TechReport{Borwein:1995:CCH,
  author =       "Jonathan M. Borwein and Simon Fitzpatrick",
  title =        "Closed convex {Haar} null sets",
  type =         "CECM Research Report",
  number =       "95:052",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "9",
  month =        aug,
  year =         "1995",
  bibdate =      "Tue Aug 16 10:13:27 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/117/",
  abstract =     "If $E$ is a separable super-reflexive Banach space
                 then every closed convex subset of $E$ with empty
                 interior is a Haar null set.",
  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:1995:CCS
author: J. M. Borwein and S. Fitzpatrick
booktitle: Proceedings of the Optimization Miniconference II
title: Characterization of Clarke subgradients among one-dimensional multifunctions
publisher: University of Ballarat
address: Ballarat, VI, Australia
pages: 5--12
year: 1995
bibdate: Mon Aug 15 14:41:04 2016
bibsource: 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/23/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and S. Fitzpatrick
rawbooktitle: Proceedings of the Optimization Miniconference II
rawtitle: Characterization of {Clarke} subgradients among one-dimensional multifunctions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InProceedings{Borwein:1995:CCS,
  author =       "J. M. Borwein and S. Fitzpatrick",
  booktitle =    "Proceedings of the Optimization Miniconference II",
  title =        "Characterization of {Clarke} subgradients among
                 one-dimensional multifunctions",
  publisher =    "University of Ballarat",
  address =      "Ballarat, VI, Australia",
  pages =        "5--12",
  year =         "1995",
  bibdate =      "Mon Aug 15 14:41:04 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/23/",
  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:1995:CLR
author: Jonathan M. Borwein and Jon D. Vanderwerff
title: Convergence of Lipschitz regularizations of convex functions
journal: j-J-FUNCT-ANAL
volume: 128
number: 1
pages: 139--162
year: 1995
CODEN: JFUAAW
DOI: https://doi.org/10.1006/jfan.1995.1026
ISSN: 0022-1236 (print), 1096-0783 (electronic) OR 00221236 (print), 10960783 (electronic)
ISSNL: 0022-1236 OR 00221236
MRclass: 49J45 (46N10 49J52)
MRnumber: 1317713
MRreviewer: Lionel Thibault
bibdate: Thu Aug 11 10:27:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 10:27:38 ???
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 Jon D. Vanderwerff
rawtitle: Convergence of {Lipschitz} regularizations of convex functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1540/; http://www.sciencedirect.com/science/article/pii/S0022123685710269

abstract:
For a sequence or net of convex functions on a Banach space, we study pointwise convergence of their Lipschitz regularizations and convergence of their epigraphs. The Lipschitz regularizations we will consider are the infimal convolutions of the functions with appropriate multiples of the norm. For a sequence of convex functions on a separable Banach space we show that both pointwise convergence of their Lipschitz regularizations and Wijsman convergence of their epigraphs are equivalent to variants of two conditions used by Attouch and Beer to characterize slice convergence. Results for nonseparable spaces are obtained by separable reduction arguments. As a by-product, slice convergence for an arbitrary net of convex functions can be deduced from the pointwise convergence of their regularizations precisely when the w* and the norm topologies agree on the dual sphere. This extends some known results and answers an open question.

rawabstract:
For a sequence or net of convex functions on a Banach space, we study pointwise convergence of their Lipschitz regularizations and convergence of their epigraphs. The Lipschitz regularizations we will consider are the infimal convolutions of the functions with appropriate multiples of the norm. For a sequence of convex functions on a separable Banach space we show that both pointwise convergence of their Lipschitz regularizations and Wijsman convergence of their epigraphs are equivalent to variants of two conditions used by Attouch and Beer to characterize slice convergence. Results for nonseparable spaces are obtained by separable reduction arguments. As a by-product, slice convergence for an arbitrary net of convex functions can be deduced from the pointwise convergence of their regularizations precisely when the w* and the norm topologies agree on the dual sphere. This extends some known results and answers an open question.

entry:
@Article{Borwein:1995:CLR,
  author =       "Jonathan M. Borwein and Jon D. Vanderwerff",
  title =        "Convergence of {Lipschitz} regularizations of convex
                 functions",
  journal =      j-J-FUNCT-ANAL,
  volume =       "128",
  number =       "1",
  pages =        "139--162",
  year =         "1995",
  CODEN =        "JFUAAW",
  DOI =          "https://doi.org/10.1006/jfan.1995.1026",
  ISSN =         "0022-1236 (print), 1096-0783 (electronic)",
  ISSN-L =       "0022-1236",
  MRclass =      "49J45 (46N10 49J52)",
  MRnumber =     "1317713",
  MRreviewer =   "Lionel Thibault",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1540/;
                 http://www.sciencedirect.com/science/article/pii/S0022123685710269",
  abstract =     "For a sequence or net of convex functions on a Banach
                 space, we study pointwise convergence of their
                 Lipschitz regularizations and convergence of their
                 epigraphs. The Lipschitz regularizations we will
                 consider are the infimal convolutions of the functions
                 with appropriate multiples of the norm. For a sequence
                 of convex functions on a separable Banach space we show
                 that both pointwise convergence of their Lipschitz
                 regularizations and Wijsman convergence of their
                 epigraphs are equivalent to variants of two conditions
                 used by Attouch and Beer to characterize slice
                 convergence. Results for nonseparable spaces are
                 obtained by separable reduction arguments. As a
                 by-product, slice convergence for an arbitrary net of
                 convex functions can be deduced from the pointwise
                 convergence of their regularizations precisely when the
                 w* and the norm topologies agree on the dual sphere.
                 This extends some known results and answers an open
                 question.",
  acknowledgement = ack-nhfb,
  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: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1995:CML
author: David Borwein and Jonathan M. Borwein and Christopher Pinner
title: Convergence of Madelung-Like Lattice Sums
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 46
month: jun
monthnumber: 6
year: 1995
bibdate: Wed Aug 31 09:30:55 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 09:30:55 ???
URL: http://docserver.carma.newcastle.edu.au/104/2/95_040-Borwein-Borwein-Pinner.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David Borwein and Jonathan M. Borwein and Christopher Pinner
rawtitle: Convergence of {Madelung}-Like Lattice Sums
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We make a general study of the convergence properties of lattice sums, involving potentials, of the form occurring in Mathematical Chemistry and Physics. Many specific examples are studied in detail. The prototype is Madelung's constant for NaCl: $$ sum _- infty ^+ infty frac ( - 1)^n + m + psqrt n^2 + m^2 + p^2 = - 1.74756459 cdots $$ resuming that one appropriately interprets the summation process.

rawabstract:
We make a general study of the convergence properties of lattice sums, involving potentials, of the form occurring in Mathematical Chemistry and Physics. Many specific examples are studied in detail. The prototype is Madelung's constant for NaCl: $$ \sum_{- \infty }^{+ \infty } \frac {( - 1)^{n + m + p}}{\sqrt {n^2 + m^2 + p^2}} = - 1.74756459 \cdots $$ resuming that one appropriately interprets the summation process.

entry:
@TechReport{Borwein:1995:CML,
  author =       "David Borwein and Jonathan M. Borwein and Christopher
                 Pinner",
  title =        "Convergence of {Madelung}-Like Lattice Sums",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "46",
  month =        jun,
  year =         "1995",
  bibdate =      "Wed Aug 31 09:30:55 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/104/2/95_040-Borwein-Borwein-Pinner.pdf",
  abstract =     "We make a general study of the convergence properties
                 of lattice sums, involving potentials, of the form
                 occurring in Mathematical Chemistry and Physics. Many
                 specific examples are studied in detail. The prototype
                 is Madelung's constant for NaCl: $$ \sum_{- \infty }^{+
                 \infty } \frac {( - 1)^{n + m + p}}{\sqrt {n^2 + m^2 +
                 p^2}} = - 1.74756459 \cdots $$ resuming that one
                 appropriately interprets the summation process.",
  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:1995:DDF
author: J. M. Borwein and Xianfu Wang
title: Distinct Differentiable Functions May Share the Same Clarke Subdifferential at all points
type: Report
institution: inst-CARMA
address: inst-CARMA:adr
pages: 10
day: 29
month: jun
monthnumber: 6
year: 1995
bibdate: Wed Aug 31 06:33:16 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 06:33:16 ???
note: Published in cite Borwein:1997:DDF.
URL: https://docserver.carma.newcastle.edu.au/112/2/95_047-Borwein-Wang.pdf
remark: Revised 8 September 1995.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and Xianfu Wang
rawnote: Published in \cite{Borwein:1997:DDF}.
rawtitle: Distinct Differentiable Functions May Share the Same {Clarke} Subdifferential at all points
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We construct, using Zahorski's Theorem, two everywhere differentiable real-valued Lipschitz functions differing by more than a constant but sharing the same Clarke subdifferential and the same approximate subdifferential.

rawabstract:
We construct, using Zahorski's Theorem, two everywhere differentiable real-valued Lipschitz functions differing by more than a constant but sharing the same Clarke subdifferential and the same approximate subdifferential.

entry:
@TechReport{Borwein:1995:DDF,
  author =       "J. M. Borwein and Xianfu Wang",
  title =        "Distinct Differentiable Functions May Share the Same
                 {Clarke} Subdifferential at all points",
  type =         "Report",
  institution =  inst-CARMA,
  address =      inst-CARMA:adr,
  pages =        "10",
  day =          "29",
  month =        jun,
  year =         "1995",
  bibdate =      "Wed Aug 31 06:33:16 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:1997:DDF}.",
  URL =          "https://docserver.carma.newcastle.edu.au/112/2/95_047-Borwein-Wang.pdf",
  abstract =     "We construct, using Zahorski's Theorem, two everywhere
                 differentiable real-valued Lipschitz functions
                 differing by more than a constant but sharing the same
                 Clarke subdifferential and the same approximate
                 subdifferential.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Revised 8 September 1995.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1995:EEEa
author: David Borwein and Jonathan M. Borwein and Roland Girgensohn
title: Explicit evaluation of Euler sums
journal: j-PROC-EDINBURGH-MATH-SOC-2
volume: 38
number: 2
pages: 277--294
month: jun
monthnumber: 6
year: 1995
CODEN: PRMSA3
DOI: https://doi.org/10.1017/S0013091500019088
ISSN: 0013-0915 (print), 1464-3839 (electronic) OR 00130915 (print), 14643839 (electronic)
ISSNL: 0013-0915 OR 00130915
MRclass: 11M06 (11Y60)
MRnumber: 1335874
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 ???
URL: http://docserver.carma.newcastle.edu.au/58/
fjournal: Proceedings of the Edinburgh Mathematical Society (2)
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://journals.cambridge.org/action/displayJournal?jid=PEM
rawauthor: David Borwein and Jonathan M. Borwein and Roland Girgensohn
rawtitle: Explicit evaluation of {Euler} sums
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1995:EEEa,
  author =       "David Borwein and Jonathan M. Borwein and Roland
                 Girgensohn",
  title =        "Explicit evaluation of {Euler} sums",
  journal =      j-PROC-EDINBURGH-MATH-SOC-2,
  volume =       "38",
  number =       "2",
  pages =        "277--294",
  month =        jun,
  year =         "1995",
  CODEN =        "PRMSA3",
  DOI =          "https://doi.org/10.1017/S0013091500019088",
  ISSN =         "0013-0915 (print), 1464-3839 (electronic)",
  ISSN-L =       "0013-0915",
  MRclass =      "11M06 (11Y60)",
  MRnumber =     "1335874",
  MRreviewer =   "Bruce C. Berndt",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/58/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Proceedings of the Edinburgh Mathematical Society
                 (2)",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PEM",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1995:EUC
author: Jonathan M. Borwein and Jon D. Vanderwerff
title: Epigraphical and uniform convergence of convex functions
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 19
day: 17
month: mar
monthnumber: 3
year: 1995
MRclass: 46A55, 46B20, 52A41
bibdate: Thu Sep 01 16:32:28 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 16:32:28 ???
URL: http://docserver.carma.newcastle.edu.au/94/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Jon D. Vanderwerff
rawtitle: Epigraphical and uniform convergence of convex functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We examine when a sequence of lsc convex functions on a Banach space con- verges uniformly on bounded sets (resp. compact sets) provided it converges Attouch-Wets (resp. Painleve--Kuratowski). We also obtain related results for pointwise convergence and uniform convergence on weakly compact sets. Some known results concerning the convergence of sequences of linear functionals are shown to also hold for lsc convex functions. For example, a sequence of lsc convex functions converges uniformly on bounded sets to a continuous affine function provided that the convergence is uniform on weakly compact sets and the space does not contain an isomorphic copy of $ ell _1 $.

keywords:
Attouch-Wets convergence; Epi-convergence; lsc convex function; Mosco convergence.; Painleve--Kuratowski convergence; pointwise convergence; uniform convergence

rawabstract:
We examine when a sequence of lsc convex functions on a Banach space con- verges uniformly on bounded sets (resp. compact sets) provided it converges Attouch-Wets (resp. Painlev{\'e}--Kuratowski). We also obtain related results for pointwise convergence and uniform convergence on weakly compact sets. Some known results concerning the convergence of sequences of linear functionals are shown to also hold for lsc convex functions. For example, a sequence of lsc convex functions converges uniformly on bounded sets to a continuous affine function provided that the convergence is uniform on weakly compact sets and the space does not contain an isomorphic copy of $ \ell_1 $.

entry:
@TechReport{Borwein:1995:EUC,
  author =       "Jonathan M. Borwein and Jon D. Vanderwerff",
  title =        "Epigraphical and uniform convergence of convex
                 functions",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  pages =        "19",
  day =          "17",
  month =        mar,
  year =         "1995",
  MRclass =      "46A55, 46B20, 52A41",
  bibdate =      "Thu Sep 01 16:32:28 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/94/",
  abstract =     "We examine when a sequence of lsc convex functions on
                 a Banach space con- verges uniformly on bounded sets
                 (resp. compact sets) provided it converges Attouch-Wets
                 (resp. Painlev{\'e}--Kuratowski). We also obtain
                 related results for pointwise convergence and uniform
                 convergence on weakly compact sets. Some known results
                 concerning the convergence of sequences of linear
                 functionals are shown to also hold for lsc convex
                 functions. For example, a sequence of lsc convex
                 functions converges uniformly on bounded sets to a
                 continuous affine function provided that the
                 convergence is uniform on weakly compact sets and the
                 space does not contain an isomorphic copy of $ \ell_1
                 $.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Attouch-Wets convergence; Epi-convergence; lsc convex
                 function; Mosco convergence.; Painlev{\'e}--Kuratowski
                 convergence; pointwise convergence; uniform
                 convergence",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1995:FHMa
author: J. M. Borwein and W. Z. Huang
title: A fast heuristic method for polynomial moment problems with Boltzmann--Shannon entropy
journal: j-SIAM-J-OPT
volume: 5
number: 1
pages: 68--99
year: 1995
CODEN: SJOPE8
DOI: https://doi.org/10.1137/0805004
ISSN: 1052-6234 (print), 1095-7189 (electronic) OR 10526234 (print), 10957189 (electronic)
ISSNL: 1052-6234 OR 10526234
MRclass: 90C45 (44A60 65K05)
MRnumber: 1315705
MRreviewer: Dominikus Noll
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/1539/
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: J. M. Borwein and W. Z. Huang
rawtitle: A fast heuristic method for polynomial moment problems with {Boltzmann--Shannon} entropy
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1995:FHMa,
  author =       "J. M. Borwein and W. Z. Huang",
  title =        "A fast heuristic method for polynomial moment problems
                 with {Boltzmann--Shannon} entropy",
  journal =      j-SIAM-J-OPT,
  volume =       "5",
  number =       "1",
  pages =        "68--99",
  year =         "1995",
  CODEN =        "SJOPE8",
  DOI =          "https://doi.org/10.1137/0805004",
  ISSN =         "1052-6234 (print), 1095-7189 (electronic)",
  ISSN-L =       "1052-6234",
  MRclass =      "90C45 (44A60 65K05)",
  MRnumber =     "1315705",
  MRreviewer =   "Dominikus Noll",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1539/",
  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:1995:FHMb
author: J. M. Borwein and M. N. Limber and D. Noll
title: Fast heuristic methods for function reconstruction using derivative information
journal: j-APPL-ANAL
volume: 58
number: 3--4
pages: 241--261
year: 1995
CODEN: APANCC
DOI: https://doi.org/10.1080/00036819508840375
ISSN: 0003-6811 OR 00036811
ISSNL: 0003-6811 OR 00036811
MRclass: 65D15 (49N15 62G05)
MRnumber: 1383191
MRreviewer: Zdzis{\l}aw W. Trzaska
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/1536/
fjournal: Applicable Analysis. An International Journal
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and M. N. Limber and D. Noll
rawtitle: Fast heuristic methods for function reconstruction using derivative information
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1995:FHMb,
  author =       "J. M. Borwein and M. N. Limber and D. Noll",
  title =        "Fast heuristic methods for function reconstruction
                 using derivative information",
  journal =      j-APPL-ANAL,
  volume =       "58",
  number =       "3--4",
  pages =        "241--261",
  year =         "1995",
  CODEN =        "APANCC",
  DOI =          "https://doi.org/10.1080/00036819508840375",
  ISSN =         "0003-6811",
  ISSN-L =       "0003-6811",
  MRclass =      "65D15 (49N15 62G05)",
  MRnumber =     "1383191",
  MRreviewer =   "Zdzis{\l}aw W. Trzaska",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1536/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Applicable Analysis. An International Journal",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1995:GCP
author: D. Borwein and J. M. Borwein and P. B. Borwein and R. Girgensohn
title: Giuga's conjecture on primality
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 16
day: 9
month: jun
monthnumber: 6
year: 1995
MRclass: 11A41, 11Y11 (11Y50)
bibdate: Thu Sep 01 15:48:11 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 15:48:11 ???
note: Published in cite Borwein:1996:GCP.
URL: http://docserver.carma.newcastle.edu.au/88
keywords: Carmichael numbers; Computational number theory; Primality
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: D. Borwein and J. M. Borwein and P. B. Borwein and R. Girgensohn
rawnote: Published in \cite{Borwein:1996:GCP}.
rawtitle: {Giuga}'s conjecture on primality
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
G. Giuga conjectured that if an integer $n$ satisfies $ sum _k = 1^n - 1 k^n - 1 equiv - 1 bmod n$, then $n$ must be a prime. We survey what is known about this interesting and now fairly old conjecture. Giuga proved that $n$ is a counterexample to his conjecture if and only if each prime divisor $p$ of $n$ satisfies $ (p - 1) | (n / p - 1)$ and $ p | (n / p - 1)$. Using this characterization, he proved computationally that any counterexample has at least 1,000 digits; equipped with more computing power, E. Bedocchi later raised this bound to 1,700 digits. By improving on their method, we determine that any counterexample has at least 13,800 digits. We also give some new results on the second of the above conditions. This leads, in our opinion, to some interesting questions about what we call Giuga numbers and Giuga sequences.

rawabstract:
G. Giuga conjectured that if an integer $n$ satisfies $ \sum_{k = 1}^{n - 1} k^{n - 1} \equiv - 1 \bmod n$, then $n$ must be a prime. We survey what is known about this interesting and now fairly old conjecture. Giuga proved that $n$ is a counterexample to his conjecture if and only if each prime divisor $p$ of $n$ satisfies $ (p - 1) | (n / p - 1)$ and $ p | (n / p - 1)$. Using this characterization, he proved computationally that any counterexample has at least 1,000 digits; equipped with more computing power, E. Bedocchi later raised this bound to 1,700 digits. By improving on their method, we determine that any counterexample has at least 13,800 digits. We also give some new results on the second of the above conditions. This leads, in our opinion, to some interesting questions about what we call Giuga numbers and Giuga sequences.

entry:
@TechReport{Borwein:1995:GCP,
  author =       "D. Borwein and J. M. Borwein and P. B. Borwein and R.
                 Girgensohn",
  title =        "{Giuga}'s conjecture on primality",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  pages =        "16",
  day =          "9",
  month =        jun,
  year =         "1995",
  MRclass =      "11A41, 11Y11 (11Y50)",
  bibdate =      "Thu Sep 01 15:48:11 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:1996:GCP}.",
  URL =          "http://docserver.carma.newcastle.edu.au/88",
  abstract =     "G. Giuga conjectured that if an integer $n$ satisfies
                 $ \sum_{k = 1}^{n - 1} k^{n - 1} \equiv - 1 \bmod n$,
                 then $n$ must be a prime. We survey what is known about
                 this interesting and now fairly old conjecture. Giuga
                 proved that $n$ is a counterexample to his conjecture
                 if and only if each prime divisor $p$ of $n$ satisfies
                 $ (p - 1) | (n / p - 1)$ and $ p | (n / p - 1)$. Using
                 this characterization, he proved computationally that
                 any counterexample has at least 1,000 digits; equipped
                 with more computing power, E. Bedocchi later raised
                 this bound to 1,700 digits. By improving on their
                 method, we determine that any counterexample has at
                 least 13,800 digits. We also give some new results on
                 the second of the above conditions. This leads, in our
                 opinion, to some interesting questions about what we
                 call Giuga numbers and Giuga sequences.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Carmichael numbers; Computational number theory;
                 Primality",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1995:IIS
author: David Borwein and Jonathan M. Borwein
title: On an intriguing integral and some series related to $ zeta (4) $
journal: j-PROC-AM-MATH-SOC
volume: 123
number: 4
pages: 1191--1198
year: 1995
CODEN: PAMYAR
DOI: https://doi.org/10.2307/2160718
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 11Y60 (11M06 11Y35 33B15 42A16)
MRnumber: 1231029
MRreviewer: Henri Joris
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/1538/
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: David Borwein and Jonathan M. Borwein
rawtitle: On an intriguing integral and some series related to $ \zeta (4) $
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
An intriguing log-cosine integral is fully analyzed and shown to have value a rational multiple of $ zeta (4) $, $ zeta $ being the Riemann zeta function. From this we deduce by means of generating functions and Parseval's identity the sums of certain series previously established by a completely different method.

rawabstract:
An intriguing log-cosine integral is fully analyzed and shown to have value a rational multiple of $ \zeta (4) $, $ \zeta $ being the Riemann zeta function. From this we deduce by means of generating functions and Parseval's identity the sums of certain series previously established by a completely different method.

entry:
@Article{Borwein:1995:IIS,
  author =       "David Borwein and Jonathan M. Borwein",
  title =        "On an intriguing integral and some series related to
                 $ \zeta (4) $",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "123",
  number =       "4",
  pages =        "1191--1198",
  year =         "1995",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.2307/2160718",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "11Y60 (11M06 11Y35 33B15 42A16)",
  MRnumber =     "1231029",
  MRreviewer =   "Henri Joris",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1538/",
  abstract =     "An intriguing log-cosine integral is fully analyzed
                 and shown to have value a rational multiple of $ \zeta
                 (4) $, $ \zeta $ being the Riemann zeta function. From
                 this we deduce by means of generating functions and
                 Parseval's identity the sums of certain series
                 previously established by a completely different
                 method.",
  acknowledgement = ack-nhfb,
  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: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1995:LFP
author: Jonathan M. Borwein and Warren B. Moors and Xianfu Wang
title: Lipschitz functions with prescribed derivatives and subderivatives
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 16
day: 25
month: jul
monthnumber: 7
year: 1995
MRclass: 49J52 (46N10, 58C20)
bibdate: Thu Sep 01 16:15:30 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 16:15:30 ???
URL: http://docserver.carma.newcastle.edu.au/92
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
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
abstract:
In general it is difficult to construct Lipschitz functions which are not directly built up from either convex or distance functions. One impediment to such constructions is that outside of the real line it 1s difficult to find anti-derivatives. The main result of this paper provides, under suitable circumstances, a technique for constructing such anti-derivatives. More precisely, we show that if $ f_1, f_2, ldots , f_n $ are continuously differentiable real-valued locally Lipschitz functions defined on a non-empty open subset $A$ of a separable Banach space $X$, then there exists a real-valued locally Lipschitz function $g$ defined on $A$ such that at each point $ x in A$ the Clarke subgradient of $g$ at $x$ equals $ mathrm co nabla f_1 (x), nabla f_2 (x), ldots , nabla f_n(x) $.par This same construction also shows that for any finite family $ T_1, T_2, ldots , T_n $ of maximal cyclically monotone mappings from $A$ into non-empty subsets of $ X^star $, there exists a real-valued locally Lipschitz function $g$ defined on $A$ such that at each point $ x in A$ the Clarke subgradient of $g$ at $x$ equals $ mathrm co T_1 (x), T_2 (x), ldots , T_n(x) $. Moreover, we show that $g$ is convex if and only if $ T_1 = T_2 = cdots = T_n$.

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

rawabstract:
In general it is difficult to construct Lipschitz functions which are not directly built up from either convex or distance functions. One impediment to such constructions is that outside of the real line it 1s difficult to find anti-derivatives. The main result of this paper provides, under suitable circumstances, a technique for constructing such anti-derivatives. More precisely, we show that if $ f_1, f_2, \ldots, f_n $ are continuously differentiable real-valued locally Lipschitz functions defined on a non-empty open subset $A$ of a separable Banach space $X$, then there exists a real-valued locally Lipschitz function $g$ defined on $A$ such that at each point $ x \in A$ the Clarke subgradient of $g$ at $x$ equals $ \mathrm {co} \{ \nabla f_1 (x), \nabla f_2 (x), \ldots {}, \nabla f_n(x) \} $.\par This same construction also shows that for any finite family $ \{ T_1, T_2, \ldots {}, T_n \} $ of maximal cyclically monotone mappings from $A$ into non-empty subsets of $ X^\star $, there exists a real-valued locally Lipschitz function $g$ defined on $A$ such that at each point $ x \in A$ the Clarke subgradient of $g$ at $x$ equals $ \mathrm {co} \{ T_1 (x), T_2 (x), \ldots {}, T_n(x) \} $. Moreover, we show that $g$ is convex if and only if $ T_1 = T_2 = \cdots = T_n$.

entry:
@TechReport{Borwein:1995:LFP,
  author =       "Jonathan M. Borwein and Warren B. Moors and Xianfu
                 Wang",
  title =        "{Lipschitz} functions with prescribed derivatives and
                 subderivatives",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  pages =        "16",
  day =          "25",
  month =        jul,
  year =         "1995",
  MRclass =      "49J52 (46N10, 58C20)",
  bibdate =      "Thu Sep 01 16:15:30 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/92",
  abstract =     "In general it is difficult to construct Lipschitz
                 functions which are not directly built up from either
                 convex or distance functions. One impediment to such
                 constructions is that outside of the real line it 1s
                 difficult to find anti-derivatives. The main result of
                 this paper provides, under suitable circumstances, a
                 technique for constructing such anti-derivatives. More
                 precisely, we show that if $ f_1, f_2, \ldots, f_n $
                 are continuously differentiable real-valued locally
                 Lipschitz functions defined on a non-empty open subset
                 $A$ of a separable Banach space $X$, then there exists
                 a real-valued locally Lipschitz function $g$ defined on
                 $A$ such that at each point $ x \in A$ the Clarke
                 subgradient of $g$ at $x$ equals $ \mathrm {co} \{
                 \nabla f_1 (x), \nabla f_2 (x), \ldots {}, \nabla
                 f_n(x) \} $.\par

                 This same construction also shows that for any finite
                 family $ \{ T_1, T_2, \ldots {}, T_n \} $ of maximal
                 cyclically monotone mappings from $A$ into non-empty
                 subsets of $ X^\star $, there exists a real-valued
                 locally Lipschitz function $g$ defined on $A$ such that
                 at each point $ x \in A$ the Clarke subgradient of $g$
                 at $x$ equals $ \mathrm {co} \{ T_1 (x), T_2 (x),
                 \ldots {}, T_n(x) \} $. Moreover, we show that $g$ is
                 convex if and only if $ T_1 = T_2 = \cdots = T_n$.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Clarke subgradient; differentiability; Haar-null set;
                 Lipschitz functions; maximal cyclically monotone
                 operator; minimal cusco",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Borwein:1995:MCF
author: Jonathan M. Borwein and Kenneth R. Davidson
booktitle: Canadian Mathematical Society. 1945--1995
title: Mathematics in Canada: the future of mathematics in Canada 50 years later
volume: 1
publisher: Canadian Mathematical Society
address: Ottawa, ON, Canada
pages: 231--268 (249--268 fran{\c{c}}iai)
year: 1995
MRclass: 01A80 (01A67)
MRnumber: 1661625
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
note: Dual English--French text.
series: CMS Publications
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Kenneth R. Davidson
rawbooktitle: {Canadian Mathematical Society}. 1945--1995
rawnote: Dual English--French text.
rawtitle: Mathematics in {Canada}: the future of mathematics in {Canada} 50 years later
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:1995:MCF,
  author =       "Jonathan M. Borwein and Kenneth R. Davidson",
  booktitle =    "{Canadian Mathematical Society}. 1945--1995",
  title =        "Mathematics in {Canada}: the future of mathematics in
                 {Canada} 50 years later",
  volume =       "1",
  publisher =    "Canadian Mathematical Society",
  address =      "Ottawa, ON, Canada",
  pages =        "231--268 (249--268 fran{\c{c}}iai)",
  year =         "1995",
  MRclass =      "01A80 (01A67)",
  MRnumber =     "1661625",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Dual English--French text.",
  series =       "CMS Publications",
  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:1995:MEMa
author: J. M. Borwein and P. B. Borwein and R. Girgensohn and S. Parnes
title: Mathematical Experimentation and Methodology
pages: 231--268 (249--268 fran{\c{c}}iai)
month: jan
monthnumber: 1
year: 1995
bibdate: Tue Aug 16 10:07:27 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.16 10:07:27 ???
note: Unpublished report.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein and R. Girgensohn and S. Parnes
rawnote: Unpublished report.
rawtitle: Mathematical Experimentation and Methodology
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Unpublished{Borwein:1995:MEMa,
  author =       "J. M. Borwein and P. B. Borwein and R. Girgensohn and
                 S. Parnes",
  title =        "Mathematical Experimentation and Methodology",
  month =        jan,
  year =         "1995",
  bibdate =      "Tue Aug 16 10:07:27 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Unpublished report.",
  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:1995:MER
author: J. M. Borwein and A. S. Lewis and M. N. Limber and D. Noll
title: Maximum entropy reconstruction using derivative information. II. Computational results
journal: j-NUM-MATH
volume: 69
number: 3
pages: 243--256
year: 1995
CODEN: NUMMA7
DOI: https://doi.org/10.1007/s002110050090
ISSN: 0029-599x (print), 0945-3245 (electronic) OR 0029599x (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65K10 (65U05)
MRnumber: 1312779
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/71/; http://link.springer.com/article/10.1007/s002110050090
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 A. S. Lewis and M. N. Limber and D. Noll
rawtitle: Maximum entropy reconstruction using derivative information. {II}. {Computational} results
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1995:MER,
  author =       "J. M. Borwein and A. S. Lewis and M. N. Limber and D.
                 Noll",
  title =        "Maximum entropy reconstruction using derivative
                 information. {II}. {Computational} results",
  journal =      j-NUM-MATH,
  volume =       "69",
  number =       "3",
  pages =        "243--256",
  year =         "1995",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s002110050090",
  ISSN =         "0029-599x (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65K10 (65U05)",
  MRnumber =     "1312779",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/71/;
                 http://link.springer.com/article/10.1007/s002110050090",
  acknowledgement = ack-nhfb,
  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",
  xxtitle =      "Maximum entropy spectral analysis using first order
                 information. {Part 2}: {A} Numerical Algorithm for
                 {Fisher} information duality",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1995:MSE
author: Jonathan M. Borwein and Peter B. Borwein and Roland Girgensohn and S. Parnes
title: Making sense of experimental mathematics
type: CECM preprint
number: 95:032
institution: inst-CECM
address: inst-CECM:adr
pages: 243--256
year: 1995
bibdate: Thu Aug 11 09:31:33 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:31:33 ???
URL: http://docserver.carma.newcastle.edu.au/98/
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
rawtitle: Making sense of experimental mathematics
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@TechReport{Borwein:1995:MSE,
  author =       "Jonathan M. Borwein and Peter B. Borwein and Roland
                 Girgensohn and S. Parnes",
  title =        "Making sense of experimental mathematics",
  type =         "CECM preprint",
  number =       "95:032",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  year =         "1995",
  bibdate =      "Thu Aug 11 09:31:33 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/98/",
  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:1995: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
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 243--256
month: sep
monthnumber: 9
year: 1995
MRclass: 49J52 (49J40, 49J50, 58C20)
bibdate: Wed Aug 31 09:53:05 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 09:53:05 ???
URL: http://docserver.carma.newcastle.edu.au/116/2/95_051-Borwein-Treiman-Zhu.pdf
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
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
abstract:
We consider nonsmooth constrained optimization problems with semicontinuous and continuous data in Banach space and derive necessary conditions without constraint qualification in terms of smooth subderivatives and normal cones. These results, in different versions, are set in reflexive and smooth Banach spaces.

keywords:
Constrained optimization problems; multipliers; nonsmooth analysis; normals and fuzzy calculus.; subderivatives

rawabstract:
We consider nonsmooth constrained optimization problems with semicontinuous and continuous data in Banach space and derive necessary conditions without constraint qualification in terms of smooth subderivatives and normal cones. These results, in different versions, are set in reflexive and smooth Banach spaces.

entry:
@TechReport{Borwein:1995: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",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  month =        sep,
  year =         "1995",
  MRclass =      "49J52 (49J40, 49J50, 58C20)",
  bibdate =      "Wed Aug 31 09:53:05 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/116/2/95_051-Borwein-Treiman-Zhu.pdf",
  abstract =     "We consider nonsmooth constrained optimization
                 problems with semicontinuous and continuous data in
                 Banach space and derive necessary conditions without
                 constraint qualification in terms of smooth
                 subderivatives and normal cones. These results, in
                 different versions, are set in reflexive and smooth
                 Banach spaces.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "Constrained optimization problems; multipliers;
                 nonsmooth analysis; normals and fuzzy calculus.;
                 subderivatives",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1995:PAS
author: Jonathan M. Borwein and Alexander Ioffe
title: Proximal Analysis in Smooth Spaces
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 30
day: 21
month: feb
monthnumber: 2
year: 1995
bibdate: Thu Sep 01 14:05:31 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 14:05:31 ???
URL: http://docserver.carma.newcastle.edu.au/61
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Alexander Ioffe
rawtitle: Proximal Analysis in Smooth Spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We provide a highly-refined sequential description of the generalized gradients of Clarke and approximate $G$-subdifferential of a lower semicontinuous extended-real-valued function defined on a Banach space with a $ beta $-smooth equivalent renorm. In the case of a Frechet differentiable renorm we give a corresponding result for the corresponding singular objects.

keywords:
$G$ subdifferentials; Clarke subdifferentials; distance functions; Lipschitz functions; lower semi continuous functions; normals; smooth renorms; sub-derivatives; tangent cones; variational principles

rawabstract:
We provide a highly-refined sequential description of the generalized gradients of Clarke and approximate $G$-subdifferential of a lower semicontinuous extended-real-valued function defined on a Banach space with a $ \beta $-smooth equivalent renorm. In the case of a Fr{\'e}chet differentiable renorm we give a corresponding result for the corresponding singular objects.

entry:
@TechReport{Borwein:1995:PAS,
  author =       "Jonathan M. Borwein and Alexander Ioffe",
  title =        "Proximal Analysis in Smooth Spaces",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  pages =        "30",
  day =          "21",
  month =        feb,
  year =         "1995",
  bibdate =      "Thu Sep 01 14:05:31 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/61",
  abstract =     "We provide a highly-refined sequential description of
                 the generalized gradients of Clarke and approximate
                 $G$-subdifferential of a lower semicontinuous
                 extended-real-valued function defined on a Banach space
                 with a $ \beta $-smooth equivalent renorm. In the case
                 of a Fr{\'e}chet differentiable renorm we give a
                 corresponding result for the corresponding singular
                 objects.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "$G$ subdifferentials; Clarke subdifferentials;
                 distance functions; Lipschitz functions; lower semi
                 continuous functions; normals; smooth renorms;
                 sub-derivatives; tangent cones; variational
                 principles",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1995:SAD
author: J. M. Borwein and W. Sun
title: The stability analysis of dynamic SPECT systems
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 14
year: 1995
MRclass: 68U10, 41A30, 65F35
bibdate: Thu Sep 01 17:55:00 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 17:55:00 ???
URL: http://docserver.carma.newcastle.edu.au/99
keywords: least squares; medical imaging; SPECT model; stability
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and W. Sun
rawtitle: The stability analysis of dynamic {SPECT} systems
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
SPECT (Single Photon Emission Computed Tomography) techniques have been applied to a wide range of medical studies. The stability of a SPECT model depends strongly upon the data collected. We show that a SPECT model is full rank and well-conditioned (stable) if the projection data are large enough. Condition number estimates for a linear model are given. Numerical results for a class of linear models confirm our theoretical analysis.

remark:
Undated and no date in PDF file metadata, but directory numbering suggests 1995. Newest entry [1] in References list is dated 1994. Reference [7] is published in cite Limber:1995:DRF.

rawabstract:
SPECT (Single Photon Emission Computed Tomography) techniques have been applied to a wide range of medical studies. The stability of a SPECT model depends strongly upon the data collected. We show that a SPECT model is full rank and well-conditioned (stable) if the projection data are large enough. Condition number estimates for a linear model are given. Numerical results for a class of linear models confirm our theoretical analysis.

entry:
@TechReport{Borwein:1995:SAD,
  author =       "J. M. Borwein and W. Sun",
  title =        "The stability analysis of dynamic {SPECT} systems",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "14",
  year =         "1995",
  MRclass =      "68U10, 41A30, 65F35",
  bibdate =      "Thu Sep 01 17:55:00 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/99",
  abstract =     "SPECT (Single Photon Emission Computed Tomography)
                 techniques have been applied to a wide range of medical
                 studies. The stability of a SPECT model depends
                 strongly upon the data collected. We show that a SPECT
                 model is full rank and well-conditioned (stable) if the
                 projection data are large enough. Condition number
                 estimates for a linear model are given. Numerical
                 results for a class of linear models confirm our
                 theoretical analysis.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "least squares; medical imaging; SPECT model;
                 stability",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Undated and no date in PDF file metadata, but
                 directory numbering suggests 1995. Newest entry [1] in
                 References list is dated 1994. Reference [7] is
                 published in \cite{Limber:1995:DRF}.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1995:SCB
author: Jonathan Borwein and Simon Fitzpatrick
title: $ rm Weak^ast $ sequential compactness and bornological limit derivatives
journal: j-J-CONVEX-ANAL
volume: 2
number: 1--2
pages: 59--67
year: 1995
ISSN: 0944-6532 (print), 2363-6394 (electronic) OR 09446532 (print), 23636394 (electronic)
MRclass: 49J52 (46G05 47N10 49J40 58C20)
MRnumber: 1363360
MRreviewer: Nikolay V. Zhivkov
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: Dedicated to R. T. Rockafellar on his 60th birthday.
URL: http://www.heldermann.de/JCA/jcacon.htmvol.2_no.1+2/j4_49.ps.gz
fjournal: Journal of Convex Analysis
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.heldermann.de/JCA/jcacon.htm
rawauthor: Jonathan Borwein and Simon Fitzpatrick
rawnote: Dedicated to R. T. Rockafellar on his 60th birthday.
rawtitle: {$ {\rm Weak}^\ast $} sequential compactness and bornological limit derivatives
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this note we give a self-contained account of the relationship between the sequential and topological constructions of bornological limit derivatives for locally Lipschitzian real-valued functions on Banach spaces.

keywords:
Asplund space; bornological limit derivative; Clarke subgradient; Frechet derivative; Gateaux derivative; subderivative; weak Hadamard derivative; weak* sequential compactness.; weakly compactly generated

entry:
@Article{Borwein:1995:SCB,
  author =       "Jonathan Borwein and Simon Fitzpatrick",
  title =        "{$ {\rm Weak}^\ast $} sequential compactness and
                 bornological limit derivatives",
  journal =      j-J-CONVEX-ANAL,
  volume =       "2",
  number =       "1--2",
  pages =        "59--67",
  year =         "1995",
  ISSN =         "0944-6532 (print), 2363-6394 (electronic)",
  MRclass =      "49J52 (46G05 47N10 49J40 58C20)",
  MRnumber =     "1363360",
  MRreviewer =   "Nikolay V. Zhivkov",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Dedicated to R. T. Rockafellar on his 60th birthday.",
  URL =          "http://www.heldermann.de/JCA/jcacon.htmvol.2_no.1+2/j4_49.ps.gz",
  abstract =     "In this note we give a self-contained account of the
                 relationship between the sequential and topological
                 constructions of bornological limit derivatives for
                 locally Lipschitzian real-valued functions on Banach
                 spaces.",
  acknowledgement = ack-nhfb,
  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",
  keywords =     "Asplund space; bornological limit derivative; Clarke
                 subgradient; Fr{\'e}chet derivative; Gateaux
                 derivative; subderivative; weak Hadamard derivative;
                 weak* sequential compactness.; weakly compactly
                 generated",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  received =     "6 June 1994; revised 15 November 1994",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Borwein:1995:SEC
author: Jonathan M. Borwein
editor: Roland Durier and Chistian Michelot
booktitle: Recent Developments in Optimization: Seventh French--German Conference on Optimization (Dijon 1994)
title: A survey of examples of convex functions and classifications of normed spaces
volume: 429
publisher: pub-SV
address: pub-SV:adr
pages: 60--71
year: 1995
DOI: https://doi.org/10.1007/978-3-642-46823-0_5
ISBN: 3-642-46823-3 OR 3642468233
ISBN13: 978-3-642-46823-0 OR 9783642468230
LCCN: QA402.5
MRclass: 46N10 (46B20 49J50)
MRnumber: 1358388
MRreviewer: A. B. N{\'e}meth
bibdate: Mon Aug 15 14:50:05 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.15 14:50:05 ???
series: Lecture Notes in Economic and Mathematical Systems
URL: http://docserver.carma.newcastle.edu.au/93/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein
raweditor: Roland Durier and Chistian Michelot
rawtitle: A survey of examples of convex functions and classifications of normed spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
rawbooktitle:
Recent Developments in Optimization: Seventh {French--German} Conference on Optimization ({Dijon} 1994)

entry:
@InProceedings{Borwein:1995:SEC,
  author =       "Jonathan M. Borwein",
  editor =       "Roland Durier and Chistian Michelot",
  booktitle =    "Recent Developments in Optimization: Seventh
                 {French--German} Conference on Optimization ({Dijon}
                 1994)",
  title =        "A survey of examples of convex functions and
                 classifications of normed spaces",
  volume =       "429",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "60--71",
  year =         "1995",
  DOI =          "https://doi.org/10.1007/978-3-642-46823-0_5",
  ISBN =         "3-642-46823-3",
  ISBN-13 =      "978-3-642-46823-0",
  LCCN =         "QA402.5",
  MRclass =      "46N10 (46B20 49J50)",
  MRnumber =     "1358388",
  MRreviewer =   "A. B. N{\'e}meth",
  bibdate =      "Mon Aug 15 14:50:05 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Lecture Notes in Economic and Mathematical Systems",
  URL =          "http://docserver.carma.newcastle.edu.au/93/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  xxtitle =      "A survey of examples of convex functions and the
                 classification of {Banach} spaces",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1995:SRR
author: J. M. Borwein and E. Wong
title: A survey of results relating to Giuga's conjecture on primality
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 21
day: 8
month: may
monthnumber: 5
year: 1995
bibdate: Wed Aug 31 08:44:19 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 08:44:19 ???
note: Published in cite Borwein:1997:SRR.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and E. Wong
rawnote: Published in \cite{Borwein:1997:SRR}.
rawtitle: A survey of results relating to {Giuga}'s conjecture on primality
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
This article is an expanded version of the talk given by the first author at the 25th Anniversary Conference of the Centre de Recherches Mathematiques.

rawabstract:
This article is an expanded version of the talk given by the first author at the 25th Anniversary Conference of the Centre de R{\'e}cherches Math{\'e}matiques.

entry:
@TechReport{Borwein:1995:SRR,
  author =       "J. M. Borwein and E. Wong",
  title =        "A survey of results relating to {Giuga}'s conjecture
                 on primality",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "21",
  day =          "8",
  month =        may,
  year =         "1995",
  bibdate =      "Wed Aug 31 08:44:19 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:1997:SRR}.",
  abstract =     "This article is an expanded version of the talk given
                 by the first author at the 25th Anniversary Conference
                 of the Centre de R{\'e}cherches Math{\'e}matiques.",
  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:1995:SRSa
author: Jonathan M. Borwein and Jon D. Vanderwerff
title: A survey on renorming and set convergence
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 19
day: 25
month: mar
monthnumber: 3
year: 1995
MRclass: 46A55, 46B20, 52A41
bibdate: Thu Sep 01 16:51:41 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 16:51:41 ???
note: Published in cite Borwein:1995:SRSb.
URL: http://docserver.carma.newcastle.edu.au/97
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:1995:SRSb}.
rawtitle: A survey on renorming and set convergence
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
This article presents a survey of some recent results relating set convergence and renorming. We focus most of our attention on norms having various Kadec--Klee properties and their interplay with certain forms of set convergence including Wijsman and slice convergence.

keywords:
convex analysis; Kadec--Klee norms; Lipschitz regularizations; Mosco convergence; set convergence; slice convergence; Wijsman convergence

rawabstract:
This article presents a survey of some recent results relating set convergence and renorming. We focus most of our attention on norms having various Kadec--Klee properties and their interplay with certain forms of set convergence including Wijsman and slice convergence.

entry:
@TechReport{Borwein:1995:SRSa,
  author =       "Jonathan M. Borwein and Jon D. Vanderwerff",
  title =        "A survey on renorming and set convergence",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  pages =        "19",
  day =          "25",
  month =        mar,
  year =         "1995",
  MRclass =      "46A55, 46B20, 52A41",
  bibdate =      "Thu Sep 01 16:51:41 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:1995:SRSb}.",
  URL =          "http://docserver.carma.newcastle.edu.au/97",
  abstract =     "This article presents a survey of some recent results
                 relating set convergence and renorming. We focus most
                 of our attention on norms having various Kadec--Klee
                 properties and their interplay with certain forms of
                 set convergence including Wijsman and slice
                 convergence.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "convex analysis; Kadec--Klee norms; Lipschitz
                 regularizations; Mosco convergence; set convergence;
                 slice convergence; Wijsman convergence",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1995:SRSb
author: Jonathan M. Borwein and Jon D. Vanderwerff
title: A survey on renorming and set convergence
journal: Topological Methods in Nonlinear Analysis
volume: 5
number: 2
pages: 211--228
year: 1995
ISSN: 1230-3429 OR 12303429
ISSNL: 1230-3429 OR 12303429
MRclass: 46B20 (46G05 46N10 49J45 54B20)
MRnumber: 1374058
MRreviewer: David Yost
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/97/; https://www.tmna.ncu.pl/static/files/v05n2-01.pdf
fjournal: Topological Methods in Nonlinear Analysis
acknowledgement: ack-nhfb
ajournal: Topol. Methods Nonlinear Anal.
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: https://www.tmna.ncu.pl/static/archives/archives.html
rawauthor: Jonathan M. Borwein and Jon D. Vanderwerff
rawtitle: A survey on renorming and set convergence
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1995:SRSb,
  author =       "Jonathan M. Borwein and Jon D. Vanderwerff",
  title =        "A survey on renorming and set convergence",
  journal =      "Topological Methods in Nonlinear Analysis",
  volume =       "5",
  number =       "2",
  pages =        "211--228",
  year =         "1995",
  ISSN =         "1230-3429",
  ISSN-L =       "1230-3429",
  MRclass =      "46B20 (46G05 46N10 49J45 54B20)",
  MRnumber =     "1374058",
  MRreviewer =   "David Yost",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/97/;
                 https://www.tmna.ncu.pl/static/files/v05n2-01.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Topol. Methods Nonlinear Anal.",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Topological Methods in Nonlinear Analysis",
  journal-URL =  "https://www.tmna.ncu.pl/static/archives/archives.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1995:VSV
author: Jonathan M. Borwein and Qiji J. Zhu
type: Report
institution: Department of Mathematics & Statistics, Simon Fraser University
address: Burnaby, BC V5A 156, Canada
pages: 40
day: 18
month: mar
monthnumber: 3
year: 1995
MRclass: 49J52 (49L25, 49J40, 49J50, 58C20)
bibdate: Thu Sep 01 15:35:07 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 15:35:07 ???
URL: http://docserver.carma.newcastle.edu.au/80
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Qiji J. Zhu
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Viscosity solutions and viscosity subderivatives in smooth Banach spaces with applications to metric regularity

abstract:
In Gateaux or bornologically differentiable spaces there are two natural generalizations of the concept of a Frechet subderivative: In this paper we study the viscosity subderivative (which is the more robust of the two) and establish refined fuzzy sum rules for it in a smooth Banach space. These rules are applied to obtain comparison results for viscosity solutions of Hamilton--Jacobi equations in $ beta $-smooth spaces. A unified treatment of metric regularity in smooth spaces completes the paper. This illustrates the flexibility of viscosity subderivatives as a tool for analysis.

keywords:
fuzzy sum rule; Hamilton--Jacobi equations; metric regularity; smooth spaces; viscosity solutions; Viscosity subderivative

rawabstract:
In Gateaux or bornologically differentiable spaces there are two natural generalizations of the concept of a Fr{\'e}chet subderivative: In this paper we study the viscosity subderivative (which is the more robust of the two) and establish refined fuzzy sum rules for it in a smooth Banach space. These rules are applied to obtain comparison results for viscosity solutions of Hamilton--Jacobi equations in $ \beta $-smooth spaces. A unified treatment of metric regularity in smooth spaces completes the paper. This illustrates the flexibility of viscosity subderivatives as a tool for analysis.

rawtitle:
Viscosity solutions and viscosity subderivatives in smooth {Banach} spaces with applications to metric regularity

entry:
@TechReport{Borwein:1995:VSV,
  author =       "Jonathan M. Borwein and Qiji J. Zhu",
  title =        "Viscosity solutions and viscosity subderivatives in
                 smooth {Banach} spaces with applications to metric
                 regularity",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 156, Canada",
  pages =        "40",
  day =          "18",
  month =        mar,
  year =         "1995",
  MRclass =      "49J52 (49L25, 49J40, 49J50, 58C20)",
  bibdate =      "Thu Sep 01 15:35:07 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/80",
  abstract =     "In Gateaux or bornologically differentiable spaces
                 there are two natural generalizations of the concept of
                 a Fr{\'e}chet subderivative: In this paper we study the
                 viscosity subderivative (which is the more robust of
                 the two) and establish refined fuzzy sum rules for it
                 in a smooth Banach space. These rules are applied to
                 obtain comparison results for viscosity solutions of
                 Hamilton--Jacobi equations in $ \beta $-smooth spaces.
                 A unified treatment of metric regularity in smooth
                 spaces completes the paper. This illustrates the
                 flexibility of viscosity subderivatives as a tool for
                 analysis.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "fuzzy sum rule; Hamilton--Jacobi equations; metric
                 regularity; smooth spaces; viscosity solutions;
                 Viscosity subderivative",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Limber:1995:DRF
author: M. A. Limber and M. N. Limber and A. Celler and J. S. Barney and J. M. Borwein
title: Direct reconstruction of functional parameters for dynamic SPECT
journal: j-IEEE-TRANS-NUCL-SCI
volume: 42
number: 4
pages: 1249--1256
month: aug
monthnumber: 8
year: 1995
CODEN: IRNSAM
DOI: https://doi.org/10.1109/23.467872
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/1995ITNS...42.1249L; http://docserver.carma.newcastle.edu.au/1535/
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: M. A. Limber and M. N. Limber and A. Celler and J. S. Barney and J. M. Borwein
rawtitle: Direct reconstruction of functional parameters for dynamic {SPECT}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Limber:1995:DRF,
  author =       "M. A. Limber and M. N. Limber and A. Celler and J. S.
                 Barney and J. M. Borwein",
  title =        "Direct reconstruction of functional parameters for
                 dynamic {SPECT}",
  journal =      j-IEEE-TRANS-NUCL-SCI,
  volume =       "42",
  number =       "4",
  pages =        "1249--1256",
  month =        aug,
  year =         "1995",
  CODEN =        "IRNSAM",
  DOI =          "https://doi.org/10.1109/23.467872",
  ISSN =         "0018-9499 (print), 1558-1578 (electronic)",
  ISSN-L =       "0018-9499",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/1995ITNS...42.1249L;
                 http://docserver.carma.newcastle.edu.au/1535/",
  acknowledgement = ack-nhfb,
  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:1996:QP
author: David H. Bailey and Jonathan M. Borwein and Peter B. Borwein and Simon Plouffe
title: The quest for pi
institution: inst-CECM
address: inst-CECM:adr
pages: 16
day: 25
month: jun
monthnumber: 6
year: 1996
bibdate: Wed Aug 31 15:23:45 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 15:23:45 ???
note: Published in cite Bailey:1997:QP
URL: http://docserver.carma.newcastle.edu.au/164/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: David H. Bailey and Jonathan M. Borwein and Peter B. Borwein and Simon Plouffe
rawnote: Published in \cite{Bailey:1997:QP}
rawtitle: The quest for pi
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
This article gives a brief history of the analysis and computation of the mathematical constant $ pi = 3.141359 ldots $, including a number of the formulas that have been used to compute $ pi $ through the ages. Recent developments in this area are then discussed in some detail, including the recent computation of $ pi $ to over six billion decimal digits using high-order convergent algorithms, and a newly discovered scheme that permits arbitrary individual hexadecimal digits of $ pi $ to be computed.

rawabstract:
This article gives a brief history of the analysis and computation of the mathematical constant $ \pi = 3.141359 \ldots {} $, including a number of the formulas that have been used to compute $ \pi $ through the ages. Recent developments in this area are then discussed in some detail, including the recent computation of $ \pi $ to over six billion decimal digits using high-order convergent algorithms, and a newly discovered scheme that permits arbitrary individual hexadecimal digits of $ \pi $ to be computed.

entry:
@TechReport{Bailey:1996:QP,
  author =       "David H. Bailey and Jonathan M. Borwein and Peter B.
                 Borwein and Simon Plouffe",
  title =        "The quest for pi",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "16",
  day =          "25",
  month =        jun,
  year =         "1996",
  bibdate =      "Wed Aug 31 15:23:45 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Bailey:1997:QP}",
  URL =          "http://docserver.carma.newcastle.edu.au/164/",
  abstract =     "This article gives a brief history of the analysis and
                 computation of the mathematical constant $ \pi =
                 3.141359 \ldots {} $, including a number of the
                 formulas that have been used to compute $ \pi $ through
                 the ages. Recent developments in this area are then
                 discussed in some detail, including the recent
                 computation of $ \pi $ to over six billion decimal
                 digits using high-order convergent algorithms, and a
                 newly discovered scheme that permits arbitrary
                 individual hexadecimal digits of $ \pi $ to be
                 computed.",
  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:1996:MMD
author: Heinz H. Bauschke and Jonathan M. Borwein
type: Report
institution: Department of Combinatorics & Optimization, University of Waterloo
address: Waterloo, Ontario N2L 3G1, Canada
pages: 23
day: 20
month: nov
monthnumber: 11
year: 1996
bibdate: Wed Aug 31 15:38:23 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 15:38:23 ???
note: Published in cite Bauschke:1999:MMD.
URL: http://docserver.carma.newcastle.edu.au/180/
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:MMD}.
ORCID: 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

abstract:
The concept of a monotone operator --- which covers both linear positive semi-definite operators and subdifferentials of convex functions 1s fundamental in various branches of mathematics. Over the last few decades, several stronger notions of monotonicity have been introduced: Gossez's maximal monotonicity of dense type, Fitzpatrick and Phelps's local maximal monotonicity, and Simons's monotonicity of type (NI). While these monotonicities are automatic for maximal monotone operators in reflexive Banach spaces and for subdifferentials of convex functions, their precise relationship is largely unknown. Here, it 1s shown --- within the beautiful framework of Convex Analysis --- that for continuous linear monotone operators, all these notions coincide and are equivalent to the monotonicity of the conjugate operator. This condition is further analyzed and illustrated by examples.

rawabstract:
The concept of a monotone operator --- which covers both linear positive semi-definite operators and subdifferentials of convex functions 1s fundamental in various branches of mathematics. Over the last few decades, several stronger notions of monotonicity have been introduced: Gossez's maximal monotonicity of dense type, Fitzpatrick and Phelps's local maximal monotonicity, and Simons's monotonicity of type (NI). While these monotonicities are automatic for maximal monotone operators in reflexive Banach spaces and for subdifferentials of convex functions, their precise relationship is largely unknown. Here, it 1s shown --- within the beautiful framework of Convex Analysis --- that for continuous linear monotone operators, all these notions coincide and are equivalent to the monotonicity of the conjugate operator. This condition is further analyzed and illustrated by examples.

rawtitle:
Maximal monotonicity of dense type, local maximal monotonicity, and monotonicity of the conjugate are all the same for continuous linear operators

entry:
@TechReport{Bauschke:1996: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",
  type =         "Report",
  institution =  "Department of Combinatorics \& Optimization,
                 University of Waterloo",
  address =      "Waterloo, Ontario N2L 3G1, Canada",
  pages =        "23",
  day =          "20",
  month =        nov,
  year =         "1996",
  bibdate =      "Wed Aug 31 15:38:23 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Bauschke:1999:MMD}.",
  URL =          "http://docserver.carma.newcastle.edu.au/180/",
  abstract =     "The concept of a monotone operator --- which covers
                 both linear positive semi-definite operators and
                 subdifferentials of convex functions 1s fundamental in
                 various branches of mathematics. Over the last few
                 decades, several stronger notions of monotonicity have
                 been introduced: Gossez's maximal monotonicity of dense
                 type, Fitzpatrick and Phelps's local maximal
                 monotonicity, and Simons's monotonicity of type (NI).
                 While these monotonicities are automatic for maximal
                 monotone operators in reflexive Banach spaces and for
                 subdifferentials of convex functions, their precise
                 relationship is largely unknown. Here, it 1s shown ---
                 within the beautiful framework of Convex Analysis ---
                 that for continuous linear monotone operators, all
                 these notions coincide and are equivalent to the
                 monotonicity of the conjugate operator. This condition
                 is further analyzed and illustrated by examples.",
  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: Bauschke:1996:PAS
author: Heinz H. Bauschke and Jonathan M. Borwein
title: On Projection Algorithms for Solving Convex Feasibility Problems
journal: j-SIAM-REVIEW
volume: 38
number: 3
pages: 367--426
month: sep
monthnumber: 9
year: 1996
CODEN: SIREAD
DOI: https://doi.org/10.1137/S0036144593251710
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
MRclass: 90C25 (47N10 49M45 65J10)
MRnumber: 1 409 591
MRreviewer: F. Deutsch
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/100/; http://epubs.siam.org/sam-bin/dbq/article/25171
fjournal: SIAM Review. A Publication of the Society for Industrial and Applied Mathematics
acknowledgement: ack-nhfb
affiliation: Simon Fraser Univ
affiliationaddress: BC, Can
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
corpsource: Dept. of Math. and Stat., Simon Fraser Univ., Burnaby, BC, Canada
journalURL: http://epubs.siam.org/sirev
journalabr: SIAM Rev
onlinedate: September 1996
treatment: T Theoretical or Mathematical
bibsource:
Compendex database; http://epubs.siam.org/toc/siread/38/3; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib; http://www.siam.org/journals/sirev/sirev383.htm

abstract:
Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and flexible framework is investigated. Several crucial new concepts which allow a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence are brought out. Numerous examples are given.

keywords:
Algorithms; Approximation theory; Classical mathematics; computerised tomography; Computerized tomography; computerized tomography; convergence of numerical methods; Convergence of numerical methods; convex feasibility; Convex feasibility problems; Convex inequalities; Convex programming; convex programming; Functions; Hilbert spaces; Image reconstruction; image reconstruction; image recovery; iterative method; Iterative methods; iterative methods; Linear convergence; linear convergence; linear inequality; Mathematical programming; Problem solving; Projection algorithms; projection algorithms; set theory; Subgradient algorithm; subgradient algorithm

remark:
According to the obituary at the AMS Web site, this is Jon Borwein's most-cited paper. Google Scholar shows 1231 citations as of 02 January 2017, fewer than the 1378 noted in cite Barzilai:1988:TPS.

entry:
@Article{Bauschke:1996:PAS,
  author =       "Heinz H. Bauschke and Jonathan M. Borwein",
  title =        "On Projection Algorithms for Solving Convex
                 Feasibility Problems",
  journal =      j-SIAM-REVIEW,
  volume =       "38",
  number =       "3",
  pages =        "367--426",
  month =        sep,
  year =         "1996",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/S0036144593251710",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "90C25 (47N10 49M45 65J10)",
  MRnumber =     "1 409 591",
  MRreviewer =   "F. Deutsch",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "Compendex database;
                 http://epubs.siam.org/toc/siread/38/3;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib;
                 http://www.siam.org/journals/sirev/sirev383.htm",
  URL =          "http://docserver.carma.newcastle.edu.au/100/;
                 http://epubs.siam.org/sam-bin/dbq/article/25171",
  abstract =     "Due to their extraordinary utility and broad
                 applicability in many areas of classical mathematics
                 and modern physical sciences (most notably,
                 computerized tomography), algorithms for solving convex
                 feasibility problems continue to receive great
                 attention. To unify, generalize, and review some of
                 these algorithms, a very broad and flexible framework
                 is investigated. Several crucial new concepts which
                 allow a systematic discussion of questions on behaviour
                 in general Hilbert spaces and on the quality of
                 convergence are brought out. Numerous examples are
                 given.",
  acknowledgement = ack-nhfb,
  affiliation =  "Simon Fraser Univ",
  affiliationaddress = "BC, Can",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  classification = "723.2; 723.5; 921.5; 921.6; B0250 (Combinatorial
                 mathematics); B0260 (Optimisation techniques); B0290F
                 (Interpolation and function approximation); B6140C
                 (Optical information, image and video signal
                 processing); C1160 (Combinatorial mathematics); C1180
                 (Optimisation techniques); C1250 (Pattern recognition);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Dept. of Math. and Stat., Simon Fraser Univ., Burnaby,
                 BC, Canada",
  fjournal =     "SIAM Review. A Publication of the Society for
                 Industrial and Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "Algorithms; Approximation theory; Classical
                 mathematics; computerised tomography; Computerized
                 tomography; computerized tomography; convergence of
                 numerical methods; Convergence of numerical methods;
                 convex feasibility; Convex feasibility problems; Convex
                 inequalities; Convex programming; convex programming;
                 Functions; Hilbert spaces; Image reconstruction; image
                 reconstruction; image recovery; iterative method;
                 Iterative methods; iterative methods; Linear
                 convergence; linear convergence; linear inequality;
                 Mathematical programming; Problem solving; Projection
                 algorithms; projection algorithms; set theory;
                 Subgradient algorithm; subgradient algorithm",
  onlinedate =   "September 1996",
  ORCID-numbers = "Bauschke, Heinz/0000-0002-4155-9930; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "According to the obituary at the AMS Web site, this is
                 Jon Borwein's most-cited paper. Google Scholar shows
                 1231 citations as of 02 January 2017, fewer than the
                 1378 noted in \cite{Barzilai:1988:TPS}.",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1996:ADE
author: J. M. Borwein and F. G. Garvan
title: Approximations to $ pi $ via the Dedekind eta function
type: Report
institution: Department of Mathematics, Simon Fraser University
address: Burnaby, BC V5A 1S6, Canada
pages: 28
day: 27
month: mar
monthnumber: 3
year: 1996
bibdate: Wed Aug 31 14:56:53 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 14:56:53 ???
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
abstract:
Arguably the most efficient algorithm currently known for the extended precision calculation of $ pi $ 1s a quartic iteration due to J. M. and P. B. Borwein. In their paper, the Borwein's show how this iteration and others are intimately connected to the work of Ramanujan. This connection 1s shown utilizing their alpha-function which is defined in terms of theta-functions. They are able to find p-th order iterations based on this function using modular equations for the theta-functions. In this paper we construct an infinite family of functions $ alpha _p $. Each $ alpha _p $ gives rise to a $p$-th order iteration. For $ p = 4$ we obtain a quartic iteration due to the Borweins but not the one that comes from the alpha-function. For $ p = 3$ we obtain a cubic iteration due to the Borweins that does not come from the alpha-function. For $ p = 7$ we find a septic iteration that is analogous to the cubic iteration. For $ p = 9$ we obtain a nonic (ninth order) iteration that does not seem to come from iterating the cubic twice. Our method depends on using the computer and a symbolic algebra package to find and solve certain modular equations.

rawabstract:
Arguably the most efficient algorithm currently known for the extended precision calculation of $ \pi $ 1s a quartic iteration due to J. M. and P. B. Borwein. In their paper, the Borwein's show how this iteration and others are intimately connected to the work of Ramanujan. This connection 1s shown utilizing their alpha-function which is defined in terms of theta-functions. They are able to find p-th order iterations based on this function using modular equations for the theta-functions. In this paper we construct an infinite family of functions $ \alpha_p $. Each $ \alpha_p $ gives rise to a $p$-th order iteration. For $ p = 4$ we obtain a quartic iteration due to the Borweins but not the one that comes from the alpha-function. For $ p = 3$ we obtain a cubic iteration due to the Borweins that does not come from the alpha-function. For $ p = 7$ we find a septic iteration that is analogous to the cubic iteration. For $ p = 9$ we obtain a nonic (ninth order) iteration that does not seem to come from iterating the cubic twice. Our method depends on using the computer and a symbolic algebra package to find and solve certain modular equations.

entry:
@TechReport{Borwein:1996:ADE,
  author =       "J. M. Borwein and F. G. Garvan",
  title =        "Approximations to $ \pi $ via the {Dedekind} eta
                 function",
  type =         "Report",
  institution =  "Department of Mathematics, Simon Fraser University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "28",
  day =          "27",
  month =        mar,
  year =         "1996",
  bibdate =      "Wed Aug 31 14:56:53 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/158/",
  abstract =     "Arguably the most efficient algorithm currently known
                 for the extended precision calculation of $ \pi $ 1s a
                 quartic iteration due to J. M. and P. B. Borwein. In
                 their paper, the Borwein's show how this iteration and
                 others are intimately connected to the work of
                 Ramanujan. This connection 1s shown utilizing their
                 alpha-function which is defined in terms of
                 theta-functions. They are able to find p-th order
                 iterations based on this function using modular
                 equations for the theta-functions. In this paper we
                 construct an infinite family of functions $ \alpha_p $.
                 Each $ \alpha_p $ gives rise to a $p$-th order
                 iteration. For $ p = 4$ we obtain a quartic iteration
                 due to the Borweins but not the one that comes from the
                 alpha-function. For $ p = 3$ we obtain a cubic
                 iteration due to the Borweins that does not come from
                 the alpha-function. For $ p = 7$ we find a septic
                 iteration that is analogous to the cubic iteration. For
                 $ p = 9$ we obtain a nonic (ninth order) iteration that
                 does not seem to come from iterating the cubic twice.
                 Our method depends on using the computer and a symbolic
                 algebra package to find and solve certain modular
                 equations.",
  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:1996:AGM
author: Jonathan A. Borwein and Petr Lisonek and John A. Macdonald
title: Arithmetic--Geometric Means Revisited
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 8
year: 1996
bibdate: Thu Sep 01 10:39:15 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.09.01 10:39:15 ???
URL: http://docserver.carma.newcastle.edu.au/4/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan A. Borwein and Petr Lison{\v{e}}k and John A. Macdonald
rawtitle: Arithmetic--Geometric Means Revisited
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We use Maple's tt gfun library to study the limit formulae for a two-term recurrence (iteration) $ A G_N $, which in the case $ N = 2 $ specializes to the well-known Arithmetic-Geometric Mean iteration of Gauss. Our main aim 1s to independently rediscover and prove the limit formulae for two classical cases ($ N = 2, 3$) in a completely automated manner and to open the way for studying the remaining cases ($ N > 3$).

rawabstract:
We use Maple's {\tt gfun} library to study the limit formulae for a two-term recurrence (iteration) $ A G_N $, which in the case $ N = 2 $ specializes to the well-known Arithmetic-Geometric Mean iteration of Gauss. Our main aim 1s to independently rediscover and prove the limit formulae for two classical cases ($ N = 2, 3$) in a completely automated manner and to open the way for studying the remaining cases ($ N > 3$).

entry:
@TechReport{Borwein:1996:AGM,
  author =       "Jonathan A. Borwein and Petr Lison{\v{e}}k and John A.
                 Macdonald",
  title =        "Arithmetic--Geometric Means Revisited",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "8",
  year =         "1996",
  bibdate =      "Thu Sep 01 10:39:15 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/4/",
  abstract =     "We use Maple's {\tt gfun} library to study the limit
                 formulae for a two-term recurrence (iteration) $ A G_N
                 $, which in the case $ N = 2 $ specializes to the
                 well-known Arithmetic-Geometric Mean iteration of
                 Gauss. Our main aim 1s to independently rediscover and
                 prove the limit formulae for two classical cases ($ N =
                 2, 3$) in a completely automated manner and to open the
                 way for studying the remaining cases ($ N > 3$).",
  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:1996:ASC
author: D. Borwein and J. M. Borwein and Xianfu Wang
title: Approximate subgradients and coderivatives in $ bf R^n $
journal: j-SET-VALUED-ANAL
volume: 4
number: 4
pages: 375--398
year: 1996
CODEN: SVANEG
DOI: https://doi.org/10.1007/BF00436112
ISSN: 0927-6947 (print), 1572-932x (electronic) OR 09276947 (print), 1572932x (electronic)
ISSNL: 0927-6947 OR 09276947
MRclass: 49J52
MRnumber: 1422402
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/152/; http://link.springer.com/article/10.1007/BF00436112
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11228
rawauthor: D. Borwein and J. M. Borwein and Xianfu Wang
rawtitle: Approximate subgradients and coderivatives in {$ {\bf R}^n $}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
We show that in two dimensions or higher the Mordukhovich--Ioffe approximate subgradient and Clarke subgradient may differ almost everywhere for real-valued Lipschitz functions. Uncountably many Frechet differentiable vector-valued Lipschitz functions differing by more than constants can share the same Mordukhovich--Ioffe coderivatives. Moreover, the approximate Jacobian associated with the Mordukhovich--Ioffe coderivative can be nonconvex almost everywhere for Frechet differentiable vector-valued Lipschitz functions. Finally we show that for vector-valued Lipschitz functions the approximate Jacobian associated with the Mordukhovich-Ioffe coderivative can be almost everywhere disconnected.

rawabstract:
We show that in two dimensions or higher the Mordukhovich--Ioffe approximate subgradient and Clarke subgradient may differ almost everywhere for real-valued Lipschitz functions. Uncountably many Fr{\'e}chet differentiable vector-valued Lipschitz functions differing by more than constants can share the same Mordukhovich--Ioffe coderivatives. Moreover, the approximate Jacobian associated with the Mordukhovich--Ioffe coderivative can be nonconvex almost everywhere for Fr{\'e}chet differentiable vector-valued Lipschitz functions. Finally we show that for vector-valued Lipschitz functions the approximate Jacobian associated with the Mordukhovich-Ioffe coderivative can be almost everywhere disconnected.

entry:
@Article{Borwein:1996:ASC,
  author =       "D. Borwein and J. M. Borwein and Xianfu Wang",
  title =        "Approximate subgradients and coderivatives in {$ {\bf
                 R}^n $}",
  journal =      j-SET-VALUED-ANAL,
  volume =       "4",
  number =       "4",
  pages =        "375--398",
  year =         "1996",
  CODEN =        "SVANEG",
  DOI =          "https://doi.org/10.1007/BF00436112",
  ISSN =         "0927-6947 (print), 1572-932x (electronic)",
  ISSN-L =       "0927-6947",
  MRclass =      "49J52",
  MRnumber =     "1422402",
  MRreviewer =   "Doug Ward",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/152/;
                 http://link.springer.com/article/10.1007/BF00436112",
  abstract =     "We show that in two dimensions or higher the
                 Mordukhovich--Ioffe approximate subgradient and Clarke
                 subgradient may differ almost everywhere for
                 real-valued Lipschitz functions. Uncountably many
                 Fr{\'e}chet differentiable vector-valued Lipschitz
                 functions differing by more than constants can share
                 the same Mordukhovich--Ioffe coderivatives. Moreover,
                 the approximate Jacobian associated with the
                 Mordukhovich--Ioffe coderivative can be nonconvex
                 almost everywhere for Fr{\'e}chet differentiable
                 vector-valued Lipschitz functions. Finally we show that
                 for vector-valued Lipschitz functions the approximate
                 Jacobian associated with the Mordukhovich-Ioffe
                 coderivative can be almost everywhere disconnected.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Set-Valued Analysis. An International Journal Devoted
                 to the Theory of Multifunctions and its Applications",
  journal-URL =  "http://link.springer.com/journal/11228",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1996:BRE
author: Jonathan M. Borwein and Rob M. Corless
journal: j-SIAM-REVIEW
volume: 38
number: 2
pages: 333--337
month: jun
monthnumber: 6
year: 1996
CODEN: SIREAD
DOI: https://doi.org/10.1137/1038058
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Wed Aug 31 09:45:28 2016
bibtimestamp: 2016.08.31 09:45:28 ???
URL: https://www.jstor.org/stable/2132886
fjournal: SIAM Review
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://epubs.siam.org/sirev
onlinedate: June 1996
rawauthor: Jonathan M. Borwein and Rob M. Corless
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Book Review: booktitle The Encyclopedia of Integer Sequences, by N. J. A. Sloane and Simon Plouffe. Academic Press, San Diego, CA, 1995. $44.95. xii + 587 pp., hardcover. ISBN 0-12-558630-2

bibsource:
http://epubs.siam.org/toc/siread/38/2; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

rawtitle:
Book Review: {{\booktitle{The Encyclopedia of Integer Sequences}}, by N. J. A. Sloane and Simon Plouffe. Academic Press, San Diego, CA, 1995. \$44.95. xii + 587 pp., hardcover. ISBN 0-12-558630-2}

entry:
@Article{Borwein:1996:BRE,
  author =       "Jonathan M. Borwein and Rob M. Corless",
  title =        "Book Review: {{\booktitle{The Encyclopedia of Integer
                 Sequences}}, by N. J. A. Sloane and Simon Plouffe.
                 Academic Press, San Diego, CA, 1995. \$44.95. xii + 587
                 pp., hardcover. ISBN 0-12-558630-2}",
  journal =      j-SIAM-REVIEW,
  volume =       "38",
  number =       "2",
  pages =        "333--337",
  month =        jun,
  year =         "1996",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1038058",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Wed Aug 31 09:45:28 2016",
  bibsource =    "http://epubs.siam.org/toc/siread/38/2;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "https://www.jstor.org/stable/2132886",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "June 1996",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1996:BSAa
author: J. M. Borwein and J. D. Vanderwerff
title: Banach spaces that admit support sets
journal: j-PROC-AM-MATH-SOC
volume: 124
number: 3
pages: 751--755
year: 1996
CODEN: PAMYAR
DOI: https://doi.org/10.1090/S0002-9939-96-03122-X
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 46B20 (46B03)
MRnumber: 1301010
MRreviewer: Catherine Finet
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/87/
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 J. D. Vanderwerff
rawtitle: {Banach} spaces that admit support sets
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1996:BSAa,
  author =       "J. M. Borwein and J. D. Vanderwerff",
  title =        "{Banach} spaces that admit support sets",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "124",
  number =       "3",
  pages =        "751--755",
  year =         "1996",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/S0002-9939-96-03122-X",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "46B20 (46B03)",
  MRnumber =     "1301010",
  MRreviewer =   "Catherine Finet",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/87/",
  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:1996:BSAb
author: J. M. Borwein and J. D. Vanderwerff
title: Banach spaces that admit support sets
journal: j-PROC-AM-MATH-SOC
volume: 124
number: 3
pages: 751--756
month: mar
monthnumber: 3
year: 1996
CODEN: PAMYAR
DOI: https://doi.org/10.1090/S0002-9939-96-03122-X
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
bibdate: Fri Aug 12 12:16:08 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 12:16:08 ???
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 J. D. Vanderwerff
rawtitle: {Banach} spaces that admit support sets
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/87/; http://www.ams.org/journals/proc/1996-124-03/S0002-9939-96-03122-X/

abstract:
It is shown that the existence of a closed convex set all of whose points are properly supported in a Banach space is equivalent to the existence of a certain type of uncountable ordered one-sided biorthogonal system. Under the continuum hypothesis, we deduce that this notion is weaker than the existence of an uncountable biorthogonal system.

entry:
@Article{Borwein:1996:BSAb,
  author =       "J. M. Borwein and J. D. Vanderwerff",
  title =        "{Banach} spaces that admit support sets",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "124",
  number =       "3",
  pages =        "751--756",
  month =        mar,
  year =         "1996",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/S0002-9939-96-03122-X",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  bibdate =      "Fri Aug 12 12:16:08 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/87/;
                 http://www.ams.org/journals/proc/1996-124-03/S0002-9939-96-03122-X/",
  abstract =     "It is shown that the existence of a closed convex set
                 all of whose points are properly supported in a Banach
                 space is equivalent to the existence of a certain type
                 of uncountable ordered one-sided biorthogonal system.
                 Under the continuum hypothesis, we deduce that this
                 notion is weaker than the existence of an uncountable
                 biorthogonal system.",
  acknowledgement = ack-nhfb,
  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: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1996:CRE
author: Jonathan M. Borwein and Warren B. Moors
title: A chain rule for essentially smooth Lipschitz functions
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 751--756
day: 16
month: jan
monthnumber: 1
year: 1996
bibdate: Wed Aug 31 14:42:53 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 14:42:53 ???
note: Published in cite Borwein:1998:CRE
URL: http://docserver.carma.newcastle.edu.au/151/
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:1998:CRE}
rawtitle: A chain rule for essentially smooth {Lipschitz} functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper we introduce a new class of real-valued locally Lipschitz functions, (that are similar in nature and definition to Valadier's em saine functions) which we call em arc-wise essentially smooth, and we show that if $ g colon R^n to R $ is arc-wise essentially smooth on $ R^n $ and each function $ f_j colon R^m to R $, $ 1 leq j leq n $ is strictly differentiable almost everywhere in $ R^m $, then $ g circ f $ is strictly differentiable almost everywhere in $ R^m $, where $ f equiv (f_1 f_2, ldots , f_n) $. We also show that all the semi-smooth and pseudo-regular functions are arc-wise essentially smooth. Thus, we provide a large and robust lattice algebra of Lipschitz functions whose generalized derivatives are well-behaved.

rawabstract:
In this paper we introduce a new class of real-valued locally Lipschitz functions, (that are similar in nature and definition to Valadier's {\em saine\/} functions) which we call {\em arc-wise essentially smooth}, and we show that if $ g \colon R^n \to R $ is arc-wise essentially smooth on $ R^n $ and each function $ f_j \colon R^m \to R $, $ 1 \leq j \leq n $ is strictly differentiable almost everywhere in $ R^m $, then $ g \circ f $ is strictly differentiable almost everywhere in $ R^m $, where $ f \equiv (f_1 f_2, \ldots, f_n) $. We also show that all the semi-smooth and pseudo-regular functions are arc-wise essentially smooth. Thus, we provide a large and robust lattice algebra of Lipschitz functions whose generalized derivatives are well-behaved.

entry:
@TechReport{Borwein:1996:CRE,
  author =       "Jonathan M. Borwein and Warren B. Moors",
  title =        "A chain rule for essentially smooth {Lipschitz}
                 functions",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  day =          "16",
  month =        jan,
  year =         "1996",
  bibdate =      "Wed Aug 31 14:42:53 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:1998:CRE}",
  URL =          "http://docserver.carma.newcastle.edu.au/151/",
  abstract =     "In this paper we introduce a new class of real-valued
                 locally Lipschitz functions, (that are similar in
                 nature and definition to Valadier's {\em saine\/}
                 functions) which we call {\em arc-wise essentially
                 smooth}, and we show that if $ g \colon R^n \to R $ is
                 arc-wise essentially smooth on $ R^n $ and each
                 function $ f_j \colon R^m \to R $, $ 1 \leq j \leq n $
                 is strictly differentiable almost everywhere in $ R^m
                 $, then $ g \circ f $ is strictly differentiable almost
                 everywhere in $ R^m $, where $ f \equiv (f_1 f_2,
                 \ldots, f_n) $. We also show that all the semi-smooth
                 and pseudo-regular functions are arc-wise essentially
                 smooth. Thus, we provide a large and robust lattice
                 algebra of Lipschitz functions whose generalized
                 derivatives are well-behaved.",
  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:1996:DAM
author: Jonathan M. Borwein and Peter B. Borwein and Stephen Braham and Robert Corless and Loki Jorgenson
title: Digitally Activated Mathematics for a Brave New World Wide Web
journal: Education, Research and Perspectives
volume: 23
number: 2
pages: 28--47
month: dec
monthnumber: 12
year: 1996
ISSN: 0311-2543 (print), 1446-0017 (electronic) OR 03112543 (print), 14460017 (electronic)
ISSNL: 0311-2543 OR 03112543
bibdate: Fri Aug 12 12:03:38 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 12:03:38 ???
note: Special issue on multimedia technologies and education.
remark: The journal Web site has no online archives before year 2000.
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.erpjournal.net/
rawnote: Special issue on multimedia technologies and education.
rawtitle: Digitally Activated Mathematics for a Brave New {World Wide Web}
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/1533/; http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:13132; https://search.informit.com.au/documentSummary%3Bdn=970909729%3Bres=IELAPA

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

entry:
@Article{Borwein:1996:DAM,
  author =       "Jonathan M. Borwein and Peter B. Borwein and Stephen
                 Braham and Robert Corless and Loki J{\"o}rgenson",
  title =        "Digitally Activated Mathematics for a Brave New {World
                 Wide Web}",
  journal =      "Education, Research and Perspectives",
  volume =       "23",
  number =       "2",
  pages =        "28--47",
  month =        dec,
  year =         "1996",
  ISSN =         "0311-2543 (print), 1446-0017 (electronic)",
  ISSN-L =       "0311-2543",
  bibdate =      "Fri Aug 12 12:03:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Special issue on multimedia technologies and
                 education.",
  URL =          "http://docserver.carma.newcastle.edu.au/1533/;
                 http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:13132;
                 https://search.informit.com.au/documentSummary%3Bdn=970909729%3Bres=IELAPA",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  journal-URL =  "http://www.erpjournal.net/",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "The journal Web site has no online archives before
                 year 2000.",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1996:EFEa
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 $k$
number: CECM-96-067, OUT-4102-63, hep-th/9611004
institution: inst-CECM
address: inst-CECM:adr
pages: 21
day: 2
month: sep
monthnumber: 9
year: 1996
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
URL: http://docserver.carma.newcastle.edu.au/161
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and David M. Bradley and David J. Broadhurst
rawtitle: Evaluations of $k$-fold {Euler\slash Zagier} sums: a compendium of results for arbitrary $k$
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theory. There are various conjectures related to these sums whose incompletion is a sign that both the mathematics and physics communities do not yet completely understand the field. Here, we assemble results for Euler / Zagier sums (also known as multidimensional zeta / harmonic sums) of arbitrary depth, including sign alternations. Many of our results were obtained empirically and are apparently new. By carefully compiling and examining a huge data base of high precision numerical evaluations, we can claim with some confidence that certain classes of results are exhaustive. While many proofs are lacking, we have sketched derivations of all results that have so far been proved.

rawabstract:
Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theory. There are various conjectures related to these sums whose incompletion is a sign that both the mathematics and physics communities do not yet completely understand the field. Here, we assemble results for Euler\slash Zagier sums (also known as multidimensional zeta\slash harmonic sums) of arbitrary depth, including sign alternations. Many of our results were obtained empirically and are apparently new. By carefully compiling and examining a huge data base of high precision numerical evaluations, we can claim with some confidence that certain classes of results are exhaustive. While many proofs are lacking, we have sketched derivations of all results that have so far been proved.

entry:
@TechReport{Borwein:1996:EFEa,
  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 $k$",
  number =       "CECM-96-067, OUT-4102-63, hep-th/9611004",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "21",
  day =          "2",
  month =        sep,
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/161",
  abstract =     "Euler sums (also called Zagier sums) occur within the
                 context of knot theory and quantum field theory. There
                 are various conjectures related to these sums whose
                 incompletion is a sign that both the mathematics and
                 physics communities do not yet completely understand
                 the field. Here, we assemble results for Euler\slash
                 Zagier sums (also known as multidimensional zeta\slash
                 harmonic sums) of arbitrary depth, including sign
                 alternations. Many of our results were obtained
                 empirically and are apparently new. By carefully
                 compiling and examining a huge data base of high
                 precision numerical evaluations, we can claim with some
                 confidence that certain classes of results are
                 exhaustive. While many proofs are lacking, we have
                 sketched derivations of all results that have so far
                 been proved.",
  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:1996:EFEb
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: ArXiv High Energy Physics --- Theory e-prints
pages: 21
month: nov
monthnumber: 11
year: 1996
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/1996hep.th...11004B; http://arxiv.org/abs/hep-th/9611004
keywords: High Energy Physics - Theory
remark: Accepted 31 October 1996.
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
rawtitle: Evaluations of $k$-fold {Euler\slash Zagier} sums: a compendium of results for arbitrary $k$
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theory. There are various conjectures related to these sums whose incompletion is a sign that both the mathematics and physics communities do not yet completely understand the field. Here, we assemble results for Euler/Zagier sums (also known as multidimensional zeta/harmonic sums) of arbitrary depth, including sign alternations. Many of our results were obtained empirically and are apparently new. By carefully compiling and examining a huge data base of high precision numerical evaluations, we can claim with some confidence that certain classes of results are exhaustive. While many proofs are lacking, we have sketched derivations of all results that have so far been proved.

rawabstract:
Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theory. There are various conjectures related to these sums whose incompletion is a sign that both the mathematics and physics communities do not yet completely understand the field. Here, we assemble results for Euler/Zagier sums (also known as multidimensional zeta/harmonic sums) of arbitrary depth, including sign alternations. Many of our results were obtained empirically and are apparently new. By carefully compiling and examining a huge data base of high precision numerical evaluations, we can claim with some confidence that certain classes of results are exhaustive. While many proofs are lacking, we have sketched derivations of all results that have so far been proved.

entry:
@Article{Borwein:1996:EFEb,
  author =       "Jonathan M. Borwein and David M. Bradley and David J.
                 Broadhurst",
  title =        "Evaluations of $k$-fold {Euler\slash Zagier} sums: a
                 compendium of results for arbitrary $k$",
  journal =      "ArXiv High Energy Physics --- Theory e-prints",
  month =        nov,
  year =         "1996",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/1996hep.th...11004B;
                 http://arxiv.org/abs/hep-th/9611004",
  abstract =     "Euler sums (also called Zagier sums) occur within the
                 context of knot theory and quantum field theory. There
                 are various conjectures related to these sums whose
                 incompletion is a sign that both the mathematics and
                 physics communities do not yet completely understand
                 the field. Here, we assemble results for Euler/Zagier
                 sums (also known as multidimensional zeta/harmonic
                 sums) of arbitrary depth, including sign alternations.
                 Many of our results were obtained empirically and are
                 apparently new. By carefully compiling and examining a
                 huge data base of high precision numerical evaluations,
                 we can claim with some confidence that certain classes
                 of results are exhaustive. While many proofs are
                 lacking, we have sketched derivations of all results
                 that have so far been proved.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  eprint =       "hep-th/9611004",
  keywords =     "High Energy Physics - Theory",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Accepted 31 October 1996.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1996:ETE
author: Jonathan M. Borwein and Roland Girgensohn
title: Evaluation of triple Euler sums
journal: j-ELECT-J-COMB
volume: 3
number: 1
pages: Research Paper 23
year: 1996
ISSN: 1077-8926 (print), 1097-1440 (electronic) OR 10778926 (print), 10971440 (electronic)
ISSNL: 1077-8926 OR 10778926
MRclass: 11M99 (11Y60)
MRnumber: 1401442
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 ???
fjournal: Electronic Journal of Combinatorics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Roland Girgensohn
rawtitle: Evaluation of triple {Euler} sums
ORCID: Borwein, Jonathan/0000-0002-1263-0646
URL:
http://docserver.carma.newcastle.edu.au/118/; http://www.combinatorics.org/Volume_3/Abstracts/v3i1r23.html

entry:
@Article{Borwein:1996:ETE,
  author =       "Jonathan M. Borwein and Roland Girgensohn",
  title =        "Evaluation of triple {Euler} sums",
  journal =      j-ELECT-J-COMB,
  volume =       "3",
  number =       "1",
  pages =        "Research Paper 23",
  year =         "1996",
  ISSN =         "1077-8926 (print), 1097-1440 (electronic)",
  ISSN-L =       "1077-8926",
  MRclass =      "11M99 (11Y60)",
  MRnumber =     "1401442",
  MRreviewer =   "Bruce C. Berndt",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/118/;
                 http://www.combinatorics.org/Volume_3/Abstracts/v3i1r23.html",
  acknowledgement = ack-nhfb,
  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 =    "27",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1996:EUC
author: Jonathan M. Borwein and Jon D. Vanderwerff
title: Epigraphical and uniform convergence of convex functions
journal: j-TRANS-AM-MATH-SOC
volume: 348
number: 4
pages: 1617--1631
month: apr
monthnumber: 4
year: 1996
CODEN: TAMTAM
DOI: https://doi.org/10.1090/S0002-9947-96-01581-4
ISSN: 0002-9947 (print), 1088-6850 (electronic) OR 00029947 (print), 10886850 (electronic)
ISSNL: 0002-9947 OR 00029947
MRclass: 49J45 (46A55 46B20 46N10 52A41)
MRnumber: 1344203
MRreviewer: W. W. Breckner
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/94/; https://www.jstor.org/stable/2155155
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 Jon D. Vanderwerff
rawtitle: Epigraphical and uniform convergence of convex functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1996:EUC,
  author =       "Jonathan M. Borwein and Jon D. Vanderwerff",
  title =        "Epigraphical and uniform convergence of convex
                 functions",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "348",
  number =       "4",
  pages =        "1617--1631",
  month =        apr,
  year =         "1996",
  CODEN =        "TAMTAM",
  DOI =          "https://doi.org/10.1090/S0002-9947-96-01581-4",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "49J45 (46A55 46B20 46N10 52A41)",
  MRnumber =     "1344203",
  MRreviewer =   "W. W. Breckner",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/94/;
                 https://www.jstor.org/stable/2155155",
  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:1996:GCP
author: D. Borwein and J. M. Borwein and P. B. Borwein and R. Girgensohn
title: Giuga's conjecture on primality
journal: j-AMER-MATH-MONTHLY
volume: 103
number: 1
pages: 40--50
year: 1996
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2975213
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 11A25
MRnumber: 1369150
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 ???
URL: http://docserver.carma.newcastle.edu.au/88/
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: D. Borwein and J. M. Borwein and P. B. Borwein and R. Girgensohn
rawtitle: {Giuga}'s conjecture on primality
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1996:GCP,
  author =       "D. Borwein and J. M. Borwein and P. B. Borwein and R.
                 Girgensohn",
  title =        "{Giuga}'s conjecture on primality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "103",
  number =       "1",
  pages =        "40--50",
  year =         "1996",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2975213",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11A25",
  MRnumber =     "1369150",
  MRreviewer =   "Andrew Granville",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/88/",
  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:1996:MER
author: J. M. Borwein and A. S. Lewis and D. Noll
journal: j-MATH-OP-RES
volume: 21
number: 2
pages: 442--468
year: 1996
CODEN: MOREDQ
DOI: https://doi.org/10.1287/moor.21.2.442
ISSN: 0364-765x (print), 1526-5471 (electronic) OR 0364765x (print), 15265471 (electronic)
ISSNL: 0364-765X OR 0364765X
MRclass: 90C48 (49N15)
MRnumber: 1397223
MRreviewer: Vaithilingam Jeyakumar
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/82/
fjournal: Mathematics of Operations Research
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://pubsonline.informs.org/loi/moor
rawauthor: J. M. Borwein and A. S. Lewis and D. Noll
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Maximum entropy reconstruction using derivative information. I. Fisher information and convex duality

rawtitle:
Maximum entropy reconstruction using derivative information. {I}. {Fisher} information and convex duality

entry:
@Article{Borwein:1996:MER,
  author =       "J. M. Borwein and A. S. Lewis and D. Noll",
  title =        "Maximum entropy reconstruction using derivative
                 information. {I}. {Fisher} information and convex
                 duality",
  journal =      j-MATH-OP-RES,
  volume =       "21",
  number =       "2",
  pages =        "442--468",
  year =         "1996",
  CODEN =        "MOREDQ",
  DOI =          "https://doi.org/10.1287/moor.21.2.442",
  ISSN =         "0364-765x (print), 1526-5471 (electronic)",
  ISSN-L =       "0364-765X",
  MRclass =      "90C48 (49N15)",
  MRnumber =     "1397223",
  MRreviewer =   "Vaithilingam Jeyakumar",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/82/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematics of Operations Research",
  journal-URL =  "http://pubsonline.informs.org/loi/moor",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1996:MSE
author: Jonathan Borwein and Peter B. Borwein and Roland Girgensohn and S. Parnes
title: Making sense of experimental mathematics
journal: j-MATH-INTEL
volume: 18
number: 4
pages: 12--18
month: Fall
year: 1996
CODEN: MAINDC
DOI: https://doi.org/10.1007/BF03026747
ISSN: 0343-6993 (print), 1866-7414 (electronic) OR 03436993 (print), 18667414 (electronic)
ISSNL: 0343-6993 OR 03436993
MRclass: 00A35
MRnumber: 1413248
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/98/
fjournal: The Mathematical Intelligencer
remark: This entry appears to be contained in cite Octavio:1996:IT. Is it a separate paper??
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/283
rawauthor: Jonathan Borwein and Peter B. Borwein and Roland Girgensohn and S. Parnes
rawtitle: Making sense of experimental mathematics
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1996:MSE,
  author =       "Jonathan Borwein and Peter B. Borwein and Roland
                 Girgensohn and S. Parnes",
  title =        "Making sense of experimental mathematics",
  journal =      j-MATH-INTEL,
  volume =       "18",
  number =       "4",
  pages =        "12--18",
  month =        "Fall",
  year =         "1996",
  CODEN =        "MAINDC",
  DOI =          "https://doi.org/10.1007/BF03026747",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  MRclass =      "00A35",
  MRnumber =     "1413248",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/98/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "The Mathematical Intelligencer",
  journal-URL =  "http://link.springer.com/journal/283",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "This entry appears to be contained in
                 \cite{Octavio:1996:IT}. Is it a separate paper??",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1996:NSE
author: Jonathan M. Borwein and Warren B. Moors
title: Null sets and essentially smooth Lipschitz functions
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 22
day: 4
month: jun
monthnumber: 6
year: 1996
bibdate: Wed Aug 31 15:13:13 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 15:13:13 ???
note: Published in cite Borwein:1998:NSE.
URL: http://docserver.carma.newcastle.edu.au/162/
remark: Revised January 17th 1997.
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:1998:NSE}.
rawtitle: Null sets and essentially smooth {Lipschitz} functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
abstract:
In this paper we extend the notion of a Lebesgue-null set to a notion which is valid in any completely metrizable Abelian topological group. We then use this definition to introduce and study the class of essentially smooth functions. These are, roughly speaking, those Lipschitz functions which are smooth (in each direction) almost everywhere.

rawabstract:
In this paper we extend the notion of a Lebesgue-null set to a notion which is valid in any completely metrizable Abelian topological group. We then use this definition to introduce and study the class of essentially smooth functions. These are, roughly speaking, those Lipschitz functions which are smooth (in each direction) almost everywhere.

entry:
@TechReport{Borwein:1996:NSE,
  author =       "Jonathan M. Borwein and Warren B. Moors",
  title =        "Null sets and essentially smooth {Lipschitz}
                 functions",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "22",
  day =          "4",
  month =        jun,
  year =         "1996",
  bibdate =      "Wed Aug 31 15:13:13 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:1998:NSE}.",
  URL =          "http://docserver.carma.newcastle.edu.au/162/",
  abstract =     "In this paper we extend the notion of a Lebesgue-null
                 set to a notion which is valid in any completely
                 metrizable Abelian topological group. We then use this
                 definition to introduce and study the class of
                 essentially smooth functions. These are, roughly
                 speaking, those Lipschitz functions which are smooth
                 (in each direction) almost everywhere.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "Revised January 17th 1997.",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1996:PAS
author: Jonathan M. Borwein and Alexander Ioffe
title: Proximal analysis in smooth spaces
journal: j-SET-VALUED-ANAL
volume: 4
number: 1
pages: 1--24
year: 1996
CODEN: SVANEG
DOI: https://doi.org/10.1007/BF00419371
ISSN: 0927-6947 (print), 1572-932x (electronic) OR 09276947 (print), 1572932x (electronic)
ISSNL: 0927-6947 OR 09276947
MRclass: 49J52 (46N10 58C20)
MRnumber: 1384247
MRreviewer: Philip D. Loewen
bibdate: Wed Aug 10 11:09:47 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.10 11:09:47 ???
URL: http://docserver.carma.newcastle.edu.au/61/
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://link.springer.com/journal/11228
rawauthor: Jonathan M. Borwein and Alexander Ioffe
rawtitle: Proximal analysis in smooth spaces
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1996:PAS,
  author =       "Jonathan M. Borwein and Alexander Ioffe",
  title =        "Proximal analysis in smooth spaces",
  journal =      j-SET-VALUED-ANAL,
  volume =       "4",
  number =       "1",
  pages =        "1--24",
  year =         "1996",
  CODEN =        "SVANEG",
  DOI =          "https://doi.org/10.1007/BF00419371",
  ISSN =         "0927-6947 (print), 1572-932x (electronic)",
  ISSN-L =       "0927-6947",
  MRclass =      "49J52 (46N10 58C20)",
  MRnumber =     "1384247",
  MRreviewer =   "Philip D. Loewen",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/61/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Set-Valued Analysis. An International Journal Devoted
                 to the Theory of Multifunctions and its Applications",
  journal-URL =  "http://link.springer.com/journal/11228",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1996:PSR
author: Jonathan M. Borwein
title: Problems and Solutions: Revivals: 10281
journal: j-AMER-MATH-MONTHLY
volume: 103
number: 10
pages: 911--912
year: 1996
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRnumber: 1542929
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://links.jstor.org/sici?sici=0002-9890(199612)103:10<911:1>2.0.CO%3B2-5&origin=MSN
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
rawtitle: Problems and Solutions: Revivals: 10281
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1996:PSR,
  author =       "Jonathan M. Borwein",
  title =        "Problems and Solutions: Revivals: 10281",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "103",
  number =       "10",
  pages =        "911--912",
  year =         "1996",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRnumber =     "1542929",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://links.jstor.org/sici?sici=0002-9890(199612)103:10<911:1>2.0.CO%3B2-5&origin=MSN",
  acknowledgement = ack-nhfb,
  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:1996:PSS
author: Jonathan M. Borwein and Donald A. Darling and D. B. Tyler
title: Problems and Solutions: Solutions: 10281
journal: j-AMER-MATH-MONTHLY
volume: 103
number: 2
pages: 181--183
year: 1996
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2975121
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRnumber: 1542802
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 Donald A. Darling and D. B. Tyler
rawtitle: Problems and Solutions: Solutions: 10281
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Borwein:1996:PSS,
  author =       "Jonathan M. Borwein and Donald A. Darling and D. B.
                 Tyler",
  title =        "Problems and Solutions: Solutions: 10281",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "103",
  number =       "2",
  pages =        "181--183",
  year =         "1996",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2975121",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRnumber =     "1542802",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "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:1996:SRZ
author: Jonathan M. Borwein and Peter B. Borwein
title: Srinivasa Ramanujan und die Zahl Pi. (German) [Srinivasa Ramanujan and the number $ pi $]
crossref: Faltings:1996:MM
pages: 60--68
year: 1996
bibdate: Fri Aug 12 14:57:29 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.12 14:57:29 ???
note: Reprint of cite Borwein:1988:RP.
URL: http://docserver.carma.newcastle.edu.au/1379/; https://web.archive.org/web/20170227063951/
language: German
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: Jonathan M. Borwein and Peter B. Borwein
rawnote: Reprint of \cite{Borwein:1988:RP}.
rawtitle: {Srinivasa Ramanujan und die Zahl Pi}. ({German}) [{Srinivasa Ramanujan} and the number $ \pi $]
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Borwein:1996:SRZ,
  author =       "Jonathan M. Borwein and Peter B. Borwein",
  title =        "{Srinivasa Ramanujan und die Zahl Pi}. ({German})
                 [{Srinivasa Ramanujan} and the number $ \pi $]",
  crossref =     "Faltings:1996:MM",
  pages =        "60--68",
  year =         "1996",
  bibdate =      "Fri Aug 12 14:57:29 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Reprint of \cite{Borwein:1988:RP}.",
  URL =          "http://docserver.carma.newcastle.edu.au/1379/;
                 https://web.archive.org/web/20170227063951/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  language =     "German",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  xxtitle =      "{Ramanujan} and {Pi}",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1996:SSA
author: Jonathan Borwein and David Bradley
title: Searching Symbolically for Apery-like Formulae for Values of the Riemann Zeta Function
journal: j-SIGSAM
volume: 30
number: 2
pages: 2--7
month: jun
monthnumber: 6
year: 1996
CODEN: SIGSBZ
DOI: https://doi.org/10.1145/235699.235700
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/170/; http://doi.acm.org/10.1145/235699.235700
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)
classcodes: C7310 (Mathematics computing)
corpsource: Centre for Exp. and Constructive Math., Simon Fraser Univ., Burnaby, BC, Canada
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J1000
treatment: T Theoretical or Mathematical
issue: 116
rawauthor: Jonathan Borwein and David Bradley
rawtitle: Searching Symbolically for {Ap{\'e}ry}-like Formulae for Values of the {Riemann} Zeta Function
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

abstract:
We discuss some aspects of the search for identities using computer algebra and symbolic methods. To keep the discussion as concrete as possible, we shall focus on so-called Apery-like formulae for special values of the Riemann Zeta function. Many of these results are apparently new, and much more work needs to be done before they can be formally proved and properly classified. A first step in this direction can be found in [1].

keywords:
algebra; Apery-like formulae; computer; formal proof; functions; Riemann Zeta function; special values; symbol manipulation; symbolic methods

rawabstract:
We discuss some aspects of the search for identities using computer algebra and symbolic methods. To keep the discussion as concrete as possible, we shall focus on so-called Ap{\'e}ry-like formulae for special values of the Riemann Zeta function. Many of these results are apparently new, and much more work needs to be done before they can be formally proved and properly classified. A first step in this direction can be found in [1].

entry:
@Article{Borwein:1996:SSA,
  author =       "Jonathan Borwein and David Bradley",
  title =        "Searching Symbolically for {Ap{\'e}ry}-like Formulae
                 for Values of the {Riemann} Zeta Function",
  journal =      j-SIGSAM,
  volume =       "30",
  number =       "2",
  pages =        "2--7",
  month =        jun,
  year =         "1996",
  CODEN =        "SIGSBZ",
  DOI =          "https://doi.org/10.1145/235699.235700",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Wed Aug 10 12:08:56 2016",
  bibsource =    "http://portal.acm.org/;
                 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/170/;
                 http://doi.acm.org/10.1145/235699.235700",
  abstract =     "We discuss some aspects of the search for identities
                 using computer algebra and symbolic methods. To keep
                 the discussion as concrete as possible, we shall focus
                 on so-called Ap{\'e}ry-like formulae for special values
                 of the Riemann Zeta function. Many of these results are
                 apparently new, and much more work needs to be done
                 before they can be formally proved and properly
                 classified. A first step in this direction can be found
                 in [1].",
  acknowledgement = ack-nhfb,
  acmid =        "235700",
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  classcodes =   "C7310 (Mathematics computing)",
  corpsource =   "Centre for Exp. and Constructive Math., Simon Fraser
                 Univ., Burnaby, BC, Canada",
  fjournal =     "SIGSAM Bulletin (ACM Special Interest Group on
                 Symbolic and Algebraic Manipulation)",
  issue =        "116",
  issue-date =   "June 1996",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
  keywords =     "algebra; Apery-like formulae; computer; formal proof;
                 functions; Riemann Zeta function; special values;
                 symbol manipulation; symbolic methods",
  numpages =     "6",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Borwein:1996:VSV
author: Jonathan M. Borwein and Qiji J. Zhu
journal: j-SIAM-J-CONTROL-OPTIM
volume: 34
number: 5
pages: 1568--1591
year: 1996
CODEN: SJCODE
DOI: https://doi.org/10.1137/S0363012994268801
ISSN: 0363-0129 (print), 1095-7138 (electronic) OR 03630129 (print), 10957138 (electronic)
ISSNL: 0363-0129 OR 03630129
MRclass: 49L25 (49J52 49N10)
MRnumber: 1404847
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 ???
URL: http://docserver.carma.newcastle.edu.au/80/
fjournal: SIAM Journal on Control and Optimization
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://epubs.siam.org/sicon
rawauthor: Jonathan M. Borwein and Qiji J. Zhu
ORCID: Borwein, Jonathan/0000-0002-1263-0646
title:
Viscosity solutions and viscosity subderivatives in smooth Banach spaces with applications to metric regularity

rawtitle:
Viscosity solutions and viscosity subderivatives in smooth {Banach} spaces with applications to metric regularity

entry:
@Article{Borwein:1996:VSV,
  author =       "Jonathan M. Borwein and Qiji J. Zhu",
  title =        "Viscosity solutions and viscosity subderivatives in
                 smooth {Banach} spaces with applications to metric
                 regularity",
  journal =      j-SIAM-J-CONTROL-OPTIM,
  volume =       "34",
  number =       "5",
  pages =        "1568--1591",
  year =         "1996",
  CODEN =        "SJCODE",
  DOI =          "https://doi.org/10.1137/S0363012994268801",
  ISSN =         "0363-0129 (print), 1095-7138 (electronic)",
  ISSN-L =       "0363-0129",
  MRclass =      "49L25 (49J52 49N10)",
  MRnumber =     "1404847",
  MRreviewer =   "Abderrahim Jourani",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/80/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "SIAM Journal on Control and Optimization",
  journal-URL =  "http://epubs.siam.org/sicon",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: techreport
filename: borwein-jonathan-m.bib
label: Borwein:1996:WOM
title: What is organic mathematics?
type: Report
institution: inst-CECM
address: inst-CECM:adr
pages: 20
day: 24
month: apr
monthnumber: 4
year: 1996
bibdate: Wed Aug 31 14:53:22 2022
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2022.08.31 14:53:22 ???
note: Published in cite Borwein:1997:WOM.
URL: http://docserver.carma.newcastle.edu.au/157/
remark: No abstract in report
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawnote: Published in \cite{Borwein:1997:WOM}.
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:
@TechReport{Borwein:1996: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?",
  type =         "Report",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "20",
  day =          "24",
  month =        apr,
  year =         "1996",
  bibdate =      "Wed Aug 31 14:53:22 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  note =         "Published in \cite{Borwein:1997:WOM}.",
  URL =          "http://docserver.carma.newcastle.edu.au/157/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "No abstract in report",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Octavio:1996:IT
author: Alfredo Octavio and Jonathan Borwein and Peter B. Borwein and Roland Girgensohn and S. Parnes
title: The ``indexed'' theorem
journal: j-MATH-INTEL
volume: 18
number: 4
pages: 9--18
month: sep
monthnumber: 9
year: 1996
CODEN: MAINDC
DOI: https://doi.org/10.1007/bf03026747
ISSN: 0343-6993 (print), 1866-7414 (electronic) OR 03436993 (print), 18667414 (electronic)
ISSNL: 0343-6993 OR 03436993
bibdate: Thu Aug 11 09:28:04 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.11 09:28:04 ???
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: Alfredo Octavio and Jonathan Borwein and Peter B. Borwein and Roland Girgensohn and S. Parnes
rawtitle: The ``indexed'' theorem
ORCID: Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Octavio:1996:IT,
  author =       "Alfredo Octavio and Jonathan Borwein and Peter B.
                 Borwein and Roland Girgensohn and S. Parnes",
  title =        "The ``indexed'' theorem",
  journal =      j-MATH-INTEL,
  volume =       "18",
  number =       "4",
  pages =        "9--18",
  month =        sep,
  year =         "1996",
  CODEN =        "MAINDC",
  DOI =          "https://doi.org/10.1007/bf03026747",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  bibdate =      "Thu Aug 11 09:28:04 2016",
  bibsource =    "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: Bailey:1997:KC
author: David H. Bailey and Jonathan M. Borwein and Richard E. Crandall
title: On the Khintchine constant
journal: j-MATH-COMPUT
volume: 66
number: 217
pages: 417--431
year: 1997
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-97-00800-4
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11Y60 (11K50 11Y65)
MRnumber: 1377659
MRreviewer: T. Mets{\"a}nkyl{\"a}
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/1997MaCom..66..417B; http://docserver.carma.newcastle.edu.au/102/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
journalURL: http://www.ams.org/mcom/
rawauthor: David H. Bailey and Jonathan M. Borwein and Richard E. Crandall
rawtitle: On the {Khintchine} constant
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bailey:1997:KC,
  author =       "David H. Bailey and Jonathan M. Borwein and Richard E.
                 Crandall",
  title =        "On the {Khintchine} constant",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "217",
  pages =        "417--431",
  year =         "1997",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-97-00800-4",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y60 (11K50 11Y65)",
  MRnumber =     "1377659",
  MRreviewer =   "T. Mets{\"a}nkyl{\"a}",
  bibdate =      "Thu Aug 11 07:19:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://adsabs.harvard.edu/abs/1997MaCom..66..417B;
                 http://docserver.carma.newcastle.edu.au/102/",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: borwein-jonathan-m.bib
label: Bailey:1997:QP
author: David H. Bailey and Jonathan M. Borwein and Peter B. Borwein and Simon Plouffe
title: The quest for pi
journal: j-MATH-INTEL
volume: 19
number: 1
pages: 50--57
year: 1997
CODEN: MAINDC
DOI: https://doi.org/10.1007/BF03024340
ISSN: 0343-6993 (print), 1866-7414 (electronic) OR 03436993 (print), 18667414 (electronic)
ISSNL: 0343-6993 OR 03436993
MRclass: 01A99
MRnumber: 1439159
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/164/
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: David H. Bailey and Jonathan M. Borwein and Peter B. Borwein and Simon Plouffe
rawtitle: The quest for pi
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
entry:
@Article{Bailey:1997:QP,
  author =       "David H. Bailey and Jonathan M. Borwein and Peter B.
                 Borwein and Simon Plouffe",
  title =        "The quest for pi",
  journal =      j-MATH-INTEL,
  volume =       "19",
  number =       "1",
  pages =        "50--57",
  year =         "1997",
  CODEN =        "MAINDC",
  DOI =          "https://doi.org/10.1007/BF03024340",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  MRclass =      "01A99",
  MRnumber =     "1439159",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/164/",
  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 = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: inproceedings
filename: borwein-jonathan-m.bib
label: Bailey:1997:RME
author: D. H. Bailey and J. M. Borwein and P. B. Borwein
crossref: Borwein:1997:OMP
pages: 35--71
year: 1997
ISSN: 0731-1036 OR 07311036
ISSNL: 0731-1036 OR 07311036
MRclass: 11Y60 (01A60 11F03 33E20)
MRnumber: 1483913
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
note: Reprint of cite Borwein:1989:RME.
series: CMS Conference Proceedings
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
bookURL: http://www.cecm.sfu.ca/organics
rawauthor: D. H. Bailey and J. M. Borwein and P. B. Borwein
rawnote: Reprint of \cite{Borwein:1989:RME}.
ORCID: Bailey, David H./0000-0002-7574-8342; Borwein, Jonathan/0000-0002-1263-0646
title:
Ramanujan, modular equations, and approximations to pi or How to compute one billion digits of pi [MR0991866 (90d:11143)]

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

URL:
http://docserver.carma.newcastle.edu.au/1587/; http://www.cecm.sfu.ca/organics/papers/borwein/index.html; https://web.archive.org/web/20170328083101/

abstract:
The article underlying our contribution started life in 1986 when David Bailey and Jon and Peter B. Borwein began to write separate pieces on ``Pi and its computation'' for the MAA Monthly. With urging from Herb Wilf (the then editor) the authors joined forces and a joint paper issued forth that was published in 1989. Since 1989, while the computers have continued to improve and the computation of has continued unabated, the underlying mathematical and computational techniques being employed are still much as described in the printed piece.par We opted to use this article as our contribution to Organic Mathematics for several reasons: it is reasonably accessible; it clearly allows for ``enhancement''; it was complete as a written piece and so allowed us to concentrate on the key issues underlying the larger project. Moreover, it tells a 3,000 year story touching many themes (from transcendence theory, to elliptic functions, and the Fast Fourier Transform) and involving many great thinkers (Archimedes, Newton, Gauss, Euler, Ramanujan, Von Neumann, Hilbert). In sum then we felt that the article provided an exellent test-bed to try out what would work in a multi-modal mathematical environment.par A project like this presents several challenges for the mathematician as multi-media author. First, the technology is changing so quickly that tools uninvented when the project began are sure to be obsolete before it is finished. Second, it involves a super-highway to be sure but one running through terra incognita. At many levels one must balance the issues of form and function, speed and scope. The version presently before you looks little like the one of six months ago --- small changes to the interface can greatly enhance or reduce readability.par The opportunities are great. Within this article, you will see the bust of Ramanujan. You can read quotes from many sources and see part of the original documents from Hermite, Shanks, von Neumann and others. You may use ``lattice basis reduction'' over the Web; plot and compute many fascinating functions. If you want to try more examples the opportunities will be there.par On the down side, you may plunge off into secondary links and get lost coming back. You may find the plethora of hypertext links and options distracting, and the present limitations of using Maple over the Internet frustrating.par Our hope is that this article and this collection will play some role in limning the possibilities and flagging the pot-holes of trying to use these new tools to engage, educate and excite students, users and producers of mathematics.

rawabstract:
The article underlying our contribution started life in 1986 when David Bailey and Jon and Peter B. Borwein began to write separate pieces on ``Pi and its computation'' for the MAA Monthly. With urging from Herb Wilf (the then editor) the authors joined forces and a joint paper issued forth that was published in 1989. Since 1989, while the computers have continued to improve and the computation of has continued unabated, the underlying mathematical and computational techniques being employed are still much as described in the printed piece.\par We opted to use this article as our contribution to Organic Mathematics for several reasons: it is reasonably accessible; it clearly allows for ``enhancement''; it was complete as a written piece and so allowed us to concentrate on the key issues underlying the larger project. Moreover, it tells a 3,000 year story touching many themes (from transcendence theory, to elliptic functions, and the Fast Fourier Transform) and involving many great thinkers (Archimedes, Newton, Gauss, Euler, Ramanujan, Von Neumann, Hilbert). In sum then we felt that the article provided an exellent test-bed to try out what would work in a multi-modal mathematical environment.\par A project like this presents several challenges for the mathematician as multi-media author. First, the technology is changing so quickly that tools uninvented when the project began are sure to be obsolete before it is finished. Second, it involves a super-highway to be sure but one running through terra incognita. At many levels one must balance the issues of form and function, speed and scope. The version presently before you looks little like the one of six months ago --- small changes to the interface can greatly enhance or reduce readability.\par The opportunities are great. Within this article, you will see the bust of Ramanujan. You can read quotes from many sources and see part of the original documents from Hermite, Shanks, von Neumann and others. You may use ``lattice basis reduction'' over the Web; plot and compute many fascinating functions. If you want to try more examples the opportunities will be there.\par On the down side, you may plunge off into secondary links and get lost coming back. You may find the plethora of hypertext links and options distracting, and the present limitations of using Maple over the Internet frustrating.\par Our hope is that this article and this collection will play some role in limning the possibilities and flagging the pot-holes of trying to use these new tools to engage, educate and excite students, users and producers of mathematics.

rawtitle:
{Ramanujan}, modular equations, and approximations to pi or {How} to compute one billion digits of pi [{MR0991866} (90d:11143)]

entry:
@InProceedings{Bailey:1997:RME,
  author =       "D. H. Bailey and J. M. Borwein and P. B. Borwein",
  title =        "{Ramanujan}, modular equations, and approximations to
                 pi or {How} to compute one billion digits of pi
                 [{MR0991866} (90d:11143)]",
  crossref =     "Borwein:1997:OMP",
  pages =        "35--71",
  year =         "1997",
  ISSN =         "0731-1036",
  ISSN-L =       "0731-1036",
  MRclass =      "11Y60 (01A60 11F03 33E20)",
  MRnumber =     "1483913",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  note =         "Reprint of \cite{Borwein:1989:RME}.",
  series =       "CMS Conference Proceedings",
  URL =          "http://docserver.carma.newcastle.edu.au/1587/;
                 http://www.cecm.sfu.ca/organics/papers/borwein/index.html;
                 https://web.archive.org/web/20170328083101/",
  abstract =     "The article underlying our contribution started life
                 in 1986 when David Bailey and Jon and Peter B. Borwein
                 began to write separate pieces on ``Pi and its
                 computation'' for the MAA Monthly. With urging from
                 Herb Wilf (the then editor) the authors joined forces
                 and a joint paper issued forth that was published in
                 1989. Since 1989, while the computers have continued to
                 improve and the computation of has continued unabated,
                 the underlying mathematical and computational
                 techniques being employed are still much as described
                 in the printed piece.\par

                 We opted to use this article as our contribution to
                 Organic Mathematics for several reasons: it is
                 reasonably accessible; it clearly allows for
                 ``enhancement''; it was complete as a written piece and
                 so allowed us to concentrate on the key issues
                 underlying the larger project. Moreover, it tells a
                 3,000 year story touching many themes (from
                 transcendence theory, to elliptic functions, and the
                 Fast Fourier Transform) and involving many great
                 thinkers (Archimedes, Newton, Gauss, Euler, Ramanujan,
                 Von Neumann, Hilbert). In sum then we felt that the
                 article provided an exellent test-bed to try out what
                 would work in a multi-modal mathematical
                 environment.\par

                 A project like this presents several challenges for the
                 mathematician as multi-media author. First, the
                 technology is changing so quickly that tools uninvented
                 when the project began are sure to be obsolete before
                 it is finished. Second, it involves a super-highway to
                 be sure but one running through terra incognita. At
                 many levels one must balance the issues of form and
                 function, speed and scope. The version presently before
                 you looks little like the one of six months ago ---
                 small changes to the interface can greatly enhance or
                 reduce readability.\par

                 The opportunities are great. Within this article, you
                 will see the bust of Ramanujan. You can read quotes
                 from many sources and see part of the original
                 documents from Hermite, Shanks, von Neumann and others.
                 You may use ``lattice basis reduction'' over the Web;
                 plot and compute many fascinating functions. If you
                 want to try more examples the opportunities will be
                 there.\par

                 On the down side, you may plunge off into secondary
                 links and get lost coming back. You may find the
                 plethora of hypertext links and options distracting,
                 and the present limitations of using Maple over the
                 Internet frustrating.\par

                 Our hope is that this article and this collection will
                 play some role in limning the possibilities and
                 flagging the pot-holes of trying to use these new tools
                 to engage, educate and excite students, users and
                 producers of mathematics.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  book-URL =     "http://www.cecm.sfu.ca/organics",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: borwein-jonathan-m.bib
label: Bauschke:1997:CSC
author: H. H. Bauschke and J. M. Borwein and A. S. Lewis
editor: Yair Censor and Simeon Reich
booktitle: Recent Developments in Optimization Theory and Nonlinear Analysis
title: Convex sets and the cyclic projection algorithm
volume: 204
publisher: pub-AMS
address: pub-AMS:adr
pages: 1--38
year: 1997
bibdate: Mon Aug 15 14:42:36 2016
bibsource: https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib
bibtimestamp: 2016.08.15 14:42:36 ???
series: Contemporary Mathematics
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: H. H. Bauschke and J. M. Borwein and A. S. Lewis
rawbooktitle: Recent Developments in Optimization Theory and Nonlinear Analysis
raweditor: Yair Censor and Simeon Reich
rawtitle: Convex sets and the cyclic projection algorithm
ORCID: Bauschke, Heinz/0000-0002-4155-9930; Borwein, Jonathan/0000-0002-1263-0646
entry:
@InCollection{Bauschke:1997:CSC,
  author =       "H. H. Bauschke and J. M. Borwein and A. S. Lewis",
  editor =       "Yair Censor and Simeon Reich",
  booktitle =    "Recent Developments in Optimization Theory and
                 Nonlinear Analysis",
  title =        "Convex sets and the cyclic projection algorithm",
  volume =       "204",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "1--38",
  year =         "1997",
  bibdate =      "Mon Aug 15 14:42:36 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib",
  series =       "Contemporary Mathematics",
  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",
}


