@Preamble{"\input path.sty"}
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|https://www.math.utah.edu/~beebe/|"}
@String{inst-CECM = "Centre for Experimental and Constructive
Mathematics (CECM) at Simon Fraser
University (SFU)"}
@String{inst-CECM:adr = "Burnaby, BC V5A 1S6, Canada"}
@String{j-ACM-COMM-COMP-ALGEBRA = "ACM Communications in Computer Algebra"}
@String{j-AM-SCI = "American Scientist"}
@String{j-AMER-J-PHYSICS = "American Journal of Physics"}
@String{j-ANALYT-BIOCHEM = "Analytical biochemistry"}
@String{j-ANN-PHYS = "Annals of Physics"}
@String{j-APPL-MATH-COMP = "Applied Mathematics and Computation"}
@String{j-BULL-AMS = "Bulletin of the American Mathematical
Society"}
@String{j-COMPUT-PHYS = "Computers in Physics"}
@String{j-EVOLUTION = "Evolution"}
@String{j-EXP-MATH = "Experimental Mathematics"}
@String{j-INTEGERS = "Integers"}
@String{j-J-CHEM-PHYS = "Journal of Chemical Physics"}
@String{j-J-COMPUT-APPL-MATH = "Journal of Computational and Applied
Mathematics"}
@String{j-J-MATH-PHYS = "Journal of Mathematical Physics"}
@String{j-J-PHYS-A = "Journal of Physics A (Mathematical and
General)"}
@String{j-J-SYMBOLIC-COMP = "Journal of Symbolic Computation"}
@String{j-J-PHYS-A-MATH-THEOR = "Journal of Physics A: Mathematical and
Theoretical"}
@String{j-J-VAC-SCI-TECHNOL-B = "Journal of Vacuum Science \& Technology, B:
Microelectronics and Nanometer
Structures--Processing, Measurement,
and Phenomena"}
@String{j-MATH-COMPUT = "Mathematics of Computation"}
@String{j-MATH-MAG = "Mathematics Magazine"}
@String{j-MATHEMATICA-EDUC = "Mathematica in Education"}
@String{j-NAMS = "Notices of the American Mathematical
Society"}
@String{j-NEW-SCIENTIST = "New Scientist"}
@String{j-NUCLEIC-ACIDS-RES = "Nucleic Acids Research"}
@String{j-PHYS-REV-D = "Physical Review D (Particles and Fields)"}
@String{j-PHYS-TODAY = "Physics Today"}
@String{j-RAMANUJAN-J = "The {Ramanujan} Journal"}
@String{j-SCI-AMER = "Scientific American"}
@String{j-SCIENCE = "Science"}
@String{j-SCIENCE-NEWS = "Science News (Washington, DC)"}
@String{j-SIAM-J-NUMER-ANAL = "SIAM Journal on Numerical Analysis"}
@String{j-THEOR-POPUL-BIOL = "Theoretical Population Biology"}
@String{pub-ACADEMIC = "Academic Press"}
@String{pub-ACADEMIC:adr = "New York, USA"}
@String{pub-AW = "Ad{\-d}i{\-s}on-Wes{\-l}ey"}
@String{pub-AW:adr = "Reading, MA, USA"}
@String{pub-SV = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg,
Germany~/ London, UK~/ etc."}
@String{pub-TELOS = "TELOS division of Springer-Verlag"}
@String{pub-TELOS:adr = "Santa Clara, CA, USA and New York, NY, USA"}
@String{pub-TOPPAN = "Toppan"}
@String{pub-TOPPAN:adr = "Tokyo, Japan"}
@String{pub-WILEY = "John Wiley"}
@String{pub-WILEY:adr = "New York, NY, USA"}
@PhdThesis{Crandall:1973:ARL,
author = "Richard Eugene Crandall",
title = "Asymptotic {Regge} Limits for Inclusive Reactions",
type = "{Ph.D.} thesis",
school = "Massachusetts Institute of Technology",
address = "Cambridge, MA, USA",
pages = "81",
month = "????",
year = "1973",
bibdate = "Tue Mar 19 07:26:52 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://search.proquest.com/docview/302648140",
acknowledgement = ack-nhfb,
advisor = "C. Edward Jones",
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
xxadvisor = "Victor Weisskopf",
}
@Misc{Crandall:1973:HPO,
author = "Richard E. Crandall",
title = "High power operational amplifier",
howpublished = "US Patent 3,919,655.",
month = "",
year = "1973",
bibdate = "Tue Mar 19 09:43:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "US Patent Application ?, filed ?.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Misc{Crandall:1974:CSA,
author = "Richard E. Crandall and D. Morgan",
title = "Central station to addressed point communication
system",
howpublished = "US Patent 4,048,620.",
month = "",
year = "1974",
bibdate = "Tue Mar 19 09:43:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "US Patent Application ?, filed ?.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:1976:ELS,
author = "Richard E. Crandall",
title = "Electrical load shedding feasible if survey documents
real savings",
journal = "Real Estate Forum, {New York}",
volume = "??",
number = "??",
pages = "??--??",
month = jul,
year = "1976",
DOI = "",
bibdate = "Tue Mar 19 09:35:07 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:1976:ETR,
author = "R. E. Crandall and O. A. Bloom",
title = "Existing technology reduces energy consumption by
25\%",
journal = "Institutional Management",
volume = "4",
number = "5",
pages = "??--??",
month = may,
year = "1976",
DOI = "",
bibdate = "Tue Mar 19 09:35:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:1977:P,
author = "Richard Crandall and Peter Orno and M. S. Klamkin and
Brian Hogan and G. A. Heuer and Thomas E. Elsner and
Erwin Just and John Z. Hearon and Charles F. White and
Robert S. Fisk and L. van Hamme and L. Carlitz and Mark
Kleiman and Leon Gerber and Alan Wayne and M. G.
Greening and Erwin Schmid and George Berzsenyi and
Huseyin Demir and Clayton W. Dodge",
title = "Problems",
journal = j-MATH-MAG,
volume = "50",
number = "1",
pages = "46--53",
year = "1977",
CODEN = "MAMGA8",
ISSN = "0025-570X",
MRnumber = "1572195",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://www.jstor.org/stable/2689756",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Mathematics Magazine",
journal-URL = "http://www.maa.org/pubs/mathmag.html",
}
@Misc{Crandall:1978:MSI,
author = "Richard E. Crandall and S. Apsell and A. Galvin",
title = "Multiple sensor intrusion detection system",
howpublished = "US Patent 4,321,592.",
month = "",
year = "1978",
bibdate = "Tue Mar 19 09:43:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "US Patent Application ?, filed ?.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:1978:P,
author = "R. E. Crandall",
title = "On the ``$ 3 x + 1 $'' problem",
journal = j-MATH-COMPUT,
volume = "32",
number = "144",
pages = "1281--1292",
month = oct,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "10A99",
MRnumber = "0480321 (58 \#494)",
MRreviewer = "Richard T. Bumby",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
classcodes = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "$3x+1$ problem; Diophantine equation; number theory;
positive odd integer",
treatment = "T Theoretical or Mathematical",
}
@Article{Erdos:1978:P,
author = "Paul Erdos and Edward T. H. Wang and W. R. Utz and A.
K. Austin and F. David Hammer and Peter Orno and Mark
Kleiman and Jordan I. Levy and Bernardo Recaman and
John Hoyt and Richard Crandall and M. S. Klamkin and
Paul Y. H. Yiu and Brian Hogan and Kenneth Klinger and
Philip Straffin",
title = "Problems",
journal = j-MATH-MAG,
volume = "51",
number = "4",
pages = "245--249",
month = sep,
year = "1978",
CODEN = "MAMGA8",
ISSN = "0025-570X",
MRnumber = "1572276",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://www.jstor.org/stable/2689475",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Mathematics Magazine",
journal-URL = "http://www.maa.org/pubs/mathmag.html",
}
@Article{Crandall:1979:SLT,
author = "R. E. Crandall and M. A. Penk",
title = "A Search for Large Twin Prime Pairs",
journal = j-MATH-COMPUT,
volume = "33",
number = "145",
pages = "383--388",
month = jan,
year = "1979",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2006051",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "10A25 (10J10)",
MRnumber = "514834 (81a:10010)",
MRreviewer = "H. J. Godwin",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
classcodes = "C4190 (Other numerical methods)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Hardy Littlewood twin prime conjecture; large twin
prime pairs; Lucas Lehmer; number; number theory;
parameters; primes; search; theory",
treatment = "T Theoretical or Mathematical",
}
@Article{Crandall:1980:RS,
author = "R. E. Crandall",
title = "On the rings of {Saturn}",
journal = "J. Oregon Acad. Sci.",
volume = "??",
number = "??",
pages = "??--??",
month = mar,
year = "1980",
DOI = "",
bibdate = "Tue Mar 19 08:37:22 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:1981:ECD,
author = "R. E. Crandall",
title = "Electronic {Cavendish} device",
journal = j-AMER-J-PHYSICS,
volume = "49",
number = "7",
pages = "700--??",
month = jul,
year = "1981",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.4766298",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Tue Mar 19 08:22:29 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://link.aip.org/link/ajpias/v49/i7/p700/s2",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
}
@Article{Crandall:1981:LDS,
author = "R. E. Crandall and E. H. Wishnow",
title = "Listening to the {Doppler} shift of visible light",
journal = j-AMER-J-PHYSICS,
volume = "49",
number = "5",
pages = "477--??",
month = may,
year = "1981",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.12481",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Tue Mar 19 08:22:29 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://link.aip.org/link/ajpias/v49/i5/p477/s1",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
}
@InCollection{Stearns:1981:BHP,
author = "S. C. Stearns and R. E. Crandall",
editor = "G. G. E. Scudder and J. L. Reveal",
booktitle = "Evolution today",
title = "Bet-hedging and persistence as adaptations of
colonizers",
publisher = "Carnegie-Mellon University",
address = "Pittsburgh, PA, USA",
pages = "371--383",
year = "1981",
DOI = "",
bibdate = "Tue Mar 19 09:25:24 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
series = "Hunt Institute for Botanical Documentation",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Stearns:1981:QPD,
author = "Stephen C. Stearns and Richard E. Crandall",
title = "Quantitative Predictions of Delayed Maturity",
journal = j-EVOLUTION,
volume = "35",
number = "3",
pages = "455--463",
month = may,
year = "1981",
CODEN = "EVOLAO",
ISSN = "0014-3820 (print), 1558-5646 (electronic)",
ISSN-L = "0014-3820",
bibdate = "Tue Mar 19 06:13:18 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://www.jstor.org/stable/pdfplus/2408194.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Evolution",
}
@Article{Buhler:1982:PF,
author = "J. P. Buhler and R. E. Crandall and M. A. Penk",
title = "Primes of the form $ n! \pm 1 $ and $ 2 \cdot 3 \cdot
5 \cdots p \pm 1 $",
journal = j-MATH-COMPUT,
volume = "38",
number = "158",
pages = "639--643",
month = apr,
year = "1982",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2007298",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "10A25 (10A10)",
MRnumber = "645679 (83c:10006)",
MRreviewer = "Duncan A. Buell",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Crandall:1982:EGS,
author = "R. E. Crandall and Mary Hall Reno",
title = "Erratum: ``{Ground} state energy bounds for potentials
$ x^{\nu } $''\ {[J. Math. Phys. {\bf 23} (1982), no.
1, 64--70; MR 82m:81021]}",
journal = j-J-MATH-PHYS,
volume = "23",
number = "9",
pages = "1737--1737",
month = sep,
year = "1982",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.525543",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "81C05",
MRnumber = "668124 (83k:81010)",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1980.bib",
note = "See \cite{Crandall:1982:GSE}.",
URL = "http://jmp.aip.org/resource/1/jmapaq/v23/i9/p1737_s2",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
pagecount = "1",
}
@Article{Crandall:1982:FIP,
author = "Richard E. Crandall and David J. Griffiths and
Nicholas A. Wheeler and Raymond A. Mayer",
title = "Fields of an infinite plane of color",
journal = j-PHYS-REV-D,
volume = "25",
number = "4",
pages = "1143--1145",
month = feb,
year = "1982",
CODEN = "PRVDAQ",
DOI = "https://doi.org/10.1103/PhysRevD.25.1143",
ISSN = "0556-2821 (print), 1089-4918 (electronic), 1538-4500
(CD-ROM)",
ISSN-L = "0556-2821",
bibdate = "Mon Mar 18 12:18:52 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevD.25.1143;
http://prd.aps.org/abstract/PRD/v25/i4/p1143_1",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Physical Review D (Particles and Fields)",
journal-URL = "http://prd.aps.org/browse",
}
@Article{Crandall:1982:GSE,
author = "R. E. Crandall and Mary Hall Reno",
title = "Ground state energy bounds for potentials $ x^\nu $",
journal = j-J-MATH-PHYS,
volume = "23",
number = "1",
pages = "64--70",
month = jan,
year = "1982",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.525207",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "81C15",
MRnumber = "640372 (82m:81021)",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://jmp.aip.org/;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/jmathphys1980.bib",
note = "See erratum \cite{Crandall:1982:EGS}.",
URL = "http://jmp.aip.org/resource/1/jmapaq/v23/i1/p64_s1",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
pagecount = "7",
}
@Article{Crandall:1982:MAS,
author = "R. E. Crandall",
title = "Minimal apparatus for the speed-of-light measurement",
journal = j-AMER-J-PHYSICS,
volume = "50",
number = "12",
pages = "1157--??",
month = dec,
year = "1982",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.12912",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Tue Mar 19 08:22:29 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://link.aip.org/link/ajpias/v50/i12/p1157/s1",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
}
@Article{Crandall:1982:VML,
author = "R. E. Crandall and Stephen C. Stearns",
title = "Variational models of life-histories: when do
solutions exist?",
journal = j-THEOR-POPUL-BIOL,
volume = "21",
number = "1",
pages = "11--23",
year = "1982",
CODEN = "TLPBAQ",
DOI = "https://doi.org/10.1016/0040-5809(82)90003-X",
ISSN = "0040-5809 (print), 1096-0325 (electronic)",
ISSN-L = "0040-5809",
MRclass = "92A17",
MRnumber = "662519 (84b:92065)",
MRreviewer = "Alan Hastings",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
ajournal = "Theoret. Population Biol.",
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Theoretical Population Biology",
journal-URL = "http://www.sciencedirect.com/science/journal/00405809",
xxnumber = "5",
}
@Article{Crandall:1983:ECD,
author = "R. E. Crandall",
title = "Electronic {Cavendish} device",
journal = j-AMER-J-PHYSICS,
volume = "51",
number = "4",
pages = "367--??",
month = apr,
year = "1983",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.13251",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Tue Mar 19 08:22:29 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "Abstract of 1981 Competition 1st Prize.",
URL = "http://link.aip.org/link/ajpias/v51/i4/p367/s1",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
}
@Article{Crandall:1983:EPM,
author = "R. E. Crandall",
title = "Exact propagator for motion confined to a sector",
journal = j-J-PHYS-A,
volume = "16",
number = "3",
pages = "513--519",
day = "21",
month = feb,
year = "1983",
CODEN = "JPHAC5",
DOI = "https://doi.org/10.1088/0305-4470/16/3/011",
ISSN = "0305-4470 (print), 1361-6447 (electronic)",
ISSN-L = "0305-4470",
bibdate = "Tue Mar 19 06:42:46 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://stacks.iop.org/0305-4470/16/i=3/a=011",
abstract = "In certain situations the Feynman path integral
'collapses' into a countable sum over classical paths.
This effect is sought in motion confined to a sector
(in polar coordinates: r>or=0, 0<or= phi <or= alpha ).
The exact space-time propagator is derived as a sum
over a general nonclassical image set, with resulting
structure radically dependent on number-theoretic
properties of pi / alpha . It is shown that collapse
occurs if and only if this number is an integer.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Physics A (Mathematical and General)",
journal-URL = "http://iopscience.iop.org/0305-4470/",
}
@Article{Crandall:1983:EPR,
author = "R. E. Crandall",
title = "Exact propagator for reflectionless potentials",
journal = j-J-PHYS-A,
volume = "16",
number = "13",
pages = "3005--3011",
day = "11",
month = sep,
year = "1983",
CODEN = "JPHAC5",
DOI = "https://doi.org/10.1088/0305-4470/16/13/023",
ISSN = "0305-4470 (print), 1361-6447 (electronic)",
ISSN-L = "0305-4470",
bibdate = "Tue Mar 19 06:42:46 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://stacks.iop.org/0305-4470/16/i=13/a=023",
abstract = "The exact space-time propagation for a general
reflectionless potential is obtained in closed form
involving error functions. It is indicated how bound
states and transmission coefficients may be recovered
from asymptotic behaviour of the propagator. A sum rule
is derived that shows how the leading terms of the
short-time form of the propagator can be used
rigorously in a Feynman path integral formalism.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Physics A (Mathematical and General)",
journal-URL = "http://iopscience.iop.org/0305-4470/",
}
@Article{Crandall:1983:FEA,
author = "R. E. Crandall",
title = "Fast eigenvalue algorithm for central potentials",
journal = j-J-PHYS-A,
volume = "16",
number = "12",
pages = "L395--L399",
day = "21",
month = aug,
year = "1983",
CODEN = "JPHAC5",
DOI = "https://doi.org/10.1088/0305-4470/16/12/001",
ISSN = "0305-4470 (print), 1361-6447 (electronic)",
ISSN-L = "0305-4470",
MRclass = "81C15 (81-08)",
MRnumber = "715717 (85a:81024)",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://stacks.iop.org/0305-4470/16/L395",
abstract = "An algorithm is described that seeks out Schrodinger
eigenvalues E nl for a given central potential V(r).
The algorithm has, in principle, arbitrary precision. A
particular implementation has absolute error mod E-E nl
mod decreasing as T -3 , where T is machine computing
time. The method is tested on the central Gaussian
potential V(r)=-A exp(- lambda r 2 ) of recent
interest.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Physics. A. Mathematical and General",
journal-URL = "http://iopscience.iop.org/0305-4470/",
}
@Article{Crandall:1983:MAD,
author = "R. E. Crandall and J. F. Delord",
title = "Minimal apparatus for determination of {Planck}'s
constant",
journal = j-AMER-J-PHYSICS,
volume = "51",
number = "1",
pages = "90--??",
month = jan,
year = "1983",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.13405",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Tue Mar 19 08:22:29 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://link.aip.org/link/ajpias/v51/i1/p90/s1",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
}
@Article{Crandall:1983:PME,
author = "R. E. Crandall",
title = "Photon mass experiment",
journal = j-AMER-J-PHYSICS,
volume = "51",
number = "8",
pages = "698--702",
month = aug,
year = "1983",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.13149",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Tue Mar 19 08:22:29 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://link.aip.org/link/ajpias/v51/i8/p698/s1",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
remark = "Cited in a list of memorable papers in this journal
\cite{Romer:1991:EMP}.",
}
@Article{Crandall:1983:RTA,
author = "R. E. Crandall and B. R. Litt",
title = "Reassembly and time advance in reflectionless
scattering",
journal = j-ANN-PHYS,
volume = "146",
number = "2",
pages = "458--469",
year = "1983",
CODEN = "ADNYA6",
DOI = "https://doi.org/10.1016/0003-4916(83)90041-6",
ISSN = "0003-4916 (print), 1096-035x (electronic)",
ISSN-L = "0003-4916",
MRclass = "81F05 (47A40)",
MRnumber = "702213 (84m:81155)",
MRreviewer = "T. Sasakawa",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Annals of Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00034916",
}
@Article{Keller:1983:CPF,
author = "Wilfred Keller",
title = "Corrigendum: {``Primes of the form $ n! \pm 1 $ and $
2 \cdot 3 \cdot 5 \cdots p \pm 1 $'' [Math. Comp. {\bf
38} (1982), no. 158, 639--643 and MR 83c:10006] by J.
P. Buhler, R. E. Crandall and M. A. Penk}",
journal = j-MATH-COMPUT,
volume = "40",
number = "162",
pages = "727--727",
month = apr,
year = "1983",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y11 (11A07 11A41)",
MRnumber = "85b:11119",
bibdate = "Wed Jan 15 08:51:30 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Crandall:1984:EST,
author = "R. Crandall and R. Whitnell and R. Bettega",
title = "Exactly soluble two-electron atomic model",
journal = j-AMER-J-PHYSICS,
volume = "52",
number = "5",
pages = "438--??",
month = may,
year = "1984",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.13650",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Tue Mar 19 08:22:29 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://link.aip.org/link/ajpias/v52/i5/p438/s1",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
}
@Article{Crandall:1984:KGR,
author = "R. E. Crandall and N. A. Wheeler",
title = "{Klein--Gordon} radio and the problem of photon mass",
journal = "Il Nuovo Cimento",
volume = "80B",
number = "2",
pages = "??--??",
month = apr,
year = "1984",
DOI = "",
bibdate = "Tue Mar 19 08:40:50 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Book{Crandall:1984:PAS,
author = "Richard E. Crandall",
title = "{Pascal} applications for the sciences",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "x + 246",
year = "1984",
ISBN = "0-471-87242-3 (paperback)",
ISBN-13 = "978-0-471-87242-9 (paperback)",
LCCN = "Q183.9 .C73 1984",
bibdate = "Tue Mar 19 08:16:20 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$16.95",
series = "A Self-teaching guide",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
subject = "Science; Data processing; Programmed instruction;
Pascal (Computer program language); Computer
programming",
}
@Article{McPhee:1984:PCG,
author = "N. McPhee and R. E. Crandall",
title = "{Pascal-86} color graphics package developed at {Reed
College}",
journal = "Intel Innovator Publication",
volume = "5",
number = "2",
pages = "??--??",
month = jun # "\slash " # jul,
year = "1984",
DOI = "",
bibdate = "Tue Mar 19 09:33:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Russell:1984:GPI,
author = "P. J. Russell and Richard E. Crandall and R.
Feinbaum",
title = "{GELYSIS}: {Pascal}-implemented analysis of
one-dimensional electrophoresis gels",
journal = j-NUCLEIC-ACIDS-RES,
volume = "12",
number = "1",
pages = "493--498",
year = "1984",
CODEN = "NARHAD",
ISSN = "0305-1048",
ISSN-L = "0305-1048",
bibdate = "Tue Mar 19 07:02:35 2013",
bibsource = "http://dblp.uni-trier.de/db/journals/nar/nar12.html#RussellCF84;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Nucleic Acids Research",
xxnote = "Is this a different R E Crandall??",
}
@InCollection{Stearns:1984:PAS,
author = "S. C. Stearns and R. E. Crandall",
editor = "G. Potts and R. J. Wootton",
booktitle = "Fish Reproduction",
title = "Plasticity for age and size at sexual maturity: a
life-history response to unavoidable stress",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "13--33",
year = "1984",
DOI = "",
bibdate = "Tue Mar 19 09:23:02 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:1985:CES,
author = "R. Crandall and R. Bettega and R. Whitnell",
title = "A class of exactly soluble three-body problems",
journal = j-J-CHEM-PHYS,
volume = "83",
number = "2",
pages = "698--702",
day = "15",
month = jul,
year = "1985",
CODEN = "JCPSA6",
DOI = "https://doi.org/10.1063/1.449483",
ISSN = "0021-9606 (print), 1089-7690 (electronic)",
ISSN-L = "0021-9606",
MRclass = "81C05 (81G45 81G55)",
MRnumber = "794975 (86h:81014)",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Chemical Physics",
journal-URL = "http://scitation.aip.org/content/aip/journal/jcp/browse",
}
@Book{Crandall:1986:SPM,
author = "Richard E. Crandall and Marianne M. Colgrove",
title = "Scientific programming with {Macintosh Pascal}",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "vii + 279",
year = "1986",
ISBN = "0-471-82176-4 (paperback)",
ISBN-13 = "978-0-471-82176-2 (paperback)",
LCCN = "QA76.8.M3 C73 1986",
bibdate = "Tue Mar 19 08:10:14 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$18.95",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
subject = "Macintosh (Computer); Programming; Pascal (Computer
program language); Science; Data processing",
}
@Article{Crandall:1987:EFE,
author = "R. E. Crandall and J. P. Buhler",
title = "Elementary function expansions for {Madelung}
constants",
journal = j-J-PHYS-A,
volume = "20",
number = "16",
pages = "5497--5510",
day = "11",
month = nov,
year = "1987",
CODEN = "JPHAC5",
DOI = "https://doi.org/10.1088/0305-4470/20/16/024",
ISSN = "0305-4470 (print), 1361-6447 (electronic)",
ISSN-L = "0305-4470",
MRclass = "82A60 (82-08)",
MRnumber = "MR924725 (88m:82034)",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://stacks.iop.org/0305-4470/20/5497",
abstract = "The Madelung constant-essentially the Coulomb energy
density of a crystal-is usually calculated via Ewald
error function expansions or, for the simpler cubic
structures, by the 'cosech' series of modern vintage.
By considering generalised functional equations for
multidimensional zeta functions, the authors provide
explicit expansions for the spatial potential and
energy density of three-dimensional periodic
structures. These formulae, involving only elementary
functions, are suitable for systematic calculation of
Madelung constants of arbitrary point-charge crystals.
They indicate how zeta function relations may be used
for dimensional reduction of certain multiple sums
arising in the special cubic cases.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Physics. A. Mathematical and General",
journal-URL = "http://iopscience.iop.org/0305-4470/",
}
@Article{Crandall:1987:IDM,
author = "R. Crandall and M. McClellan and S. Arch and J.
Doenias and R. Piper",
title = "Inverse diffusion methods for data peak separation",
journal = j-ANALYT-BIOCHEM,
volume = "167",
number = "??",
pages = "15--22",
month = "????",
year = "1987",
CODEN = "ANBCA2",
DOI = "",
ISSN = "0003-2697 (print), 1096-0309 (electronic)",
ISSN-L = "0003-2697",
bibdate = "Tue Mar 19 09:21:49 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Analytical biochemistry",
}
@Article{Crandall:1987:PWC,
author = "R. E. Crandall and J. F. Delord",
title = "The potential within a crystal lattice",
journal = j-J-PHYS-A,
volume = "20",
number = "9",
pages = "2279--2292",
day = "21",
month = jun,
year = "1987",
CODEN = "JPHAC5",
DOI = "https://doi.org/10.1088/0305-4470/20/9/016",
ISSN = "0305-4470 (print), 1361-6447 (electronic)",
ISSN-L = "0305-4470",
MRclass = "78A30 (65B20)",
MRnumber = "895057 (88g:78006)",
MRreviewer = "M. Lawrence Glasser",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://stacks.iop.org/0305-4470/20/2279",
abstract = "The generalised Madelung problem, that of finding the
spatial electric potential within a crystal lattice, is
often approached via analytic function theory. But new
results can be achieved through careful application of
standard theorems from classical electrostatics. In
this way the authors show that the celebrated Madelung
constant for the NaCl crystal can be rigorously bounded
through symmetry arguments devoid of summations. They
derive new expansions of Madelung constants of general
crystals: an absolutely convergent 'sine' series which
has the advantage of non-alternating summands, and an
'exponential' series which agrees in the simple cubic
cases with the 'cosech' expansions of previous authors.
Finally, the authors show how the NaCl Coulomb
singularity may be removed to yield a regular power
series expansion for the potential well at the
origin.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Physics. A. Mathematical and General",
journal-URL = "http://iopscience.iop.org/0305-4470/",
}
@Article{Crandall:1987:WRB,
author = "R. E. Crandall and S. G. Gillespie",
title = "Welcome to the {Rascal Billiard Parlour}",
journal = "MacA.P.P.L.E.",
volume = "??",
number = "??",
pages = "??--??",
month = mar,
year = "1987",
DOI = "",
bibdate = "Tue Mar 19 09:31:25 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:1988:BRM,
author = "R. E. Crandall",
title = "Book Review: {{\booktitle{The Media Lab: Inventing the
Future at MIT}, by Stewart Brand}}",
journal = j-COMPUT-PHYS,
volume = "2",
number = "1",
pages = "91--??",
month = jan,
year = "1988",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.4822669",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Mon Mar 18 12:29:27 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/computphys.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.4822669",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Article{Crandall:1988:NSR,
author = "Richard E. Crandall",
title = "Notes on Simulation and Reality [editorial]",
journal = j-COMPUT-PHYS,
volume = "2",
number = "3",
pages = "102--??",
month = may # "\slash " # jun,
year = "1988",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.4822714",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Mon Mar 18 12:30:53 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/computphys.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.4822714",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Article{Crandall:1989:HMC,
author = "R. E. Crandall and T. G. Dunne",
title = "Heuristic methods for counting and sizing of molecules
in the liquid state",
journal = j-AMER-J-PHYSICS,
volume = "57",
pages = "346--351",
year = "1989",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.16045",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Tue Mar 19 08:22:29 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://link.aip.org/link/ajpias/v57/i4/p346/s1",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
}
@Article{Buhler:1990:CPL,
author = "J. P. Buhler and R. E. Crandall",
title = "On the convergence problem for lattice sums",
journal = j-J-PHYS-A,
volume = "23",
number = "12",
pages = "2523--2528",
day = "21",
month = jun,
year = "1990",
CODEN = "JPHAC5",
DOI = "https://doi.org/10.1088/0305-4470/23/12/029",
ISSN = "0305-4470 (print), 1361-6447 (electronic)",
ISSN-L = "0305-4470",
MRclass = "82B20 (11P21)",
MRnumber = "1063575 (91h:82008)",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://stacks.iop.org/0305-4470/23/2523",
abstract = "Three-dimensional lattice sums Sigma +or-r -s , where
r is the distance to a +or- charged lattice point,
arise in classical lattice point problems (s=0) and the
Madelung problem of physics and chemistry (s=1). In the
latter case the sum over an infinite lattice is purely
formal and the value of the Madelung constant must be
defined precisely, e.g., via related convergent sums or
analytic continuation in s. Indeed, the partial sum
over the sphere r(R) does not converge as R becomes
large. The authors verify a conjecture of J F Delord
(1988) that convergence can be obtained by neutralising
each sphere with an appropriate surface charge.
Specifically, if L R (s) is the sum over the lattice
points in the sphere r(R) then, for neutrally charged
lattices, they show that as R goes to infinity the
difference L R (s)-R -s L R (0) approaches L(s), where
L(s) is defined by analytic continuation. When s=1 the
term L(1) is the Madelung constant and L R (0)/R is the
Coulombic correction term.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Physics. A. Mathematical and General",
journal-URL = "http://iopscience.iop.org/0305-4470/",
}
@Article{Crandall:1990:NCP,
author = "Richard E. Crandall",
title = "The {NeXT} Computer as Physics Machine",
journal = j-COMPUT-PHYS,
volume = "4",
number = "2",
pages = "132--141",
month = mar # "--" # apr,
year = "1990",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.4822897",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Sat Sep 28 20:21:01 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/mach.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.4822897",
acknowledgement = ack-ble # " \slash" # ack-nhfb,
ajournal = "Comput. Phys",
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
classification = "C7320 (Physics and Chemistry)",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
keywords = "Application interfaces; Application Kit; Computational
physics; Debugging tools; Dense graphics; Displayed
graphics; Experiment; Interface Builder; Mach
UNIX-compatible operating system; Mathematica
application; Messaging; Multitasking; NeXT Computer;
Object-oriented interface; Objective-C compiler;
Physics machine; Physics modeling; PostScript imaging
model; Printed graphics; Profiling tools; Theory;
Window environment",
thesaurus = "Digital simulation; Microcomputer applications;
Microcomputers; Physics computing",
}
@Article{Crandall:1991:ICH,
author = "Richard E. Crandall",
title = "{'Idle'} computers hunt for big primes",
journal = j-NEW-SCIENTIST,
volume = "??",
number = "??",
pages = "??--??",
day = "2",
month = mar,
year = "1991",
CODEN = "NWSCAL",
DOI = "",
ISSN = "0262-4079 (print), 1364-8500 (electronic)",
ISSN-L = "0262-4079",
bibdate = "Tue Mar 19 09:28:44 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "New Scientist",
journal-URL = "http://www.sciencedirect.com/science/journal/02624079",
}
@Book{Crandall:1991:MSa,
author = "Richard E. Crandall",
title = "{Mathematica} for the Sciences",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xiii + 300",
year = "1991",
ISBN = "0-201-51001-4",
ISBN-13 = "978-0-201-51001-0",
LCCN = "Q172 .C73 1991",
bibdate = "Sun May 02 07:59:43 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
note = "See \cite{Crandall:1991:MSb}.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
keywords = "Mathematica (Computer file); Science --- Mathematics
--- Data processing; Science --- Use of --- Software",
}
@Book{Crandall:1991:MSb,
author = "Richard E. Crandall",
title = "{Mathematica} for the Sciences",
publisher = pub-AW # " and " # pub-TOPPAN,
address = pub-AW:adr # " and " # pub-TOPPAN:adr,
pages = "315",
year = "1991",
ISBN = "4-8101-8036-0",
ISBN-13 = "978-4-8101-8036-7",
LCCN = "????",
bibdate = "Sun Apr 07 08:58:17 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
note = "Japanese translation of \cite{Crandall:1991:MSa}.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:1991:SPH,
author = "Richard E. Crandall",
title = "Symbolic processors help physics",
journal = j-COMPUT-PHYS,
volume = "??",
number = "??",
pages = "??--??",
month = oct,
year = "1991",
CODEN = "CPHYE2",
DOI = "",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Tue Mar 19 09:29:59 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Article{Crandall:1991:SSS,
author = "Richard E. Crandall",
title = "Symbolic Software Supports New Adventures in Physics",
journal = j-COMPUT-PHYS,
volume = "5",
number = "6",
pages = "576--579",
month = nov # "\slash " # dec,
year = "1991",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.4823027",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Sat Apr 6 16:22:44 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.4823027",
acknowledgement = ack-ble # " \slash" # ack-nhfb,
ajournal = "Comput. Phys",
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Article{Buhler:1992:IPO,
author = "J. P. Buhler and R. E. Crandall and R. W. Sompolski",
title = "Irregular Primes to One Million",
journal = j-MATH-COMPUT,
volume = "59",
number = "200",
pages = "717--722",
month = oct,
year = "1992",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2153086",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y35 (11B68 11D41 65T20)",
MRnumber = "1134717 (93a:11106)",
MRreviewer = "Duncan A. Buell",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
JSTOR database",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Misc{Crandall:1992:MAP,
author = "Richard E. Crandall",
title = "Method and apparatus for public key exchange in a
cryptographic system",
howpublished = "US Patent 5,159,632.",
month = "",
year = "1992",
bibdate = "Tue Mar 19 09:43:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "US Patent Application ?, filed ?.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Buhler:1993:IPC,
author = "J. Buhler and R. Crandall and R. Ernvall and T.
Mets{\"a}nkyl{\"a}",
title = "Irregular primes and cyclotomic invariants to four
million",
journal = j-MATH-COMPUT,
volume = "61",
number = "203",
pages = "151--153",
month = jul,
year = "1993",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2152942",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11B68 (11D41 11R29 11Y35 11Y40)",
MRnumber = "1197511 (93k:11014)",
MRreviewer = "Harvey Cohn",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Crandall:1993:CAF,
author = "Richard E. Crandall",
title = "Combinatorial approach to {Feynman} path integration",
journal = j-J-PHYS-A,
volume = "26",
number = "14",
pages = "3627--3648",
day = "21",
month = jul,
year = "1993",
CODEN = "JPHAC5",
DOI = "https://doi.org/10.1088/0305-4470/26/14/024",
ISSN = "0305-4470 (print), 1361-6447 (electronic)",
ISSN-L = "0305-4470",
MRclass = "81S40 (58D30)",
MRnumber = "1236586 (94e:81157)",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/feynman-richard-p.bib",
URL = "http://stacks.iop.org/0305-4470/26/3627",
abstract = "Combinatorial relations can be used to convert the
non-relativistic time-sliced Feynman path integral into
perturbation expansions. These methods reveal that when
the time interval is sliced into N increments, each
order of perturbation theory sustains an error O(1/
square root N). In this way the author provides exact
path integral results for the following potentials:
delta-function comb, finite well, tunnelling barrier,
and a generalized exponential cusp. For the tunnelling
barrier it is seen how the celebrated (-1) reflection
factor arises in the limit of infinite barrier height.
The one-dimensional Coulomb problem is solved as a
limiting case of the exponential cusp. In addition, for
power potentials the author indicates how this path
integral approach yields sometimes divergent,
nevertheless asymptotic perturbation expansions.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Physics. A. Mathematical and General",
journal-URL = "http://iopscience.iop.org/0305-4470/",
}
@Misc{Crandall:1993:MAP,
author = "Richard E. Crandall",
title = "Method and apparatus for public key exchange in a
cryptographic system",
howpublished = "US Patent 5,271,061.",
month = "",
year = "1993",
bibdate = "Tue Mar 19 09:43:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "US Patent Application ?, filed ?.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Powell:1993:LDS,
author = "J. Powell and R. Crandall",
title = "Lattice Dynamics for a Simplified {DNA} Model",
journal = j-MATHEMATICA-EDUC,
volume = "2",
number = "3",
pages = "15--20",
year = "1993",
ISSN = "1065-2965",
bibdate = "Sat Apr 6 16:22:40 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
acknowledgement = ack-ble,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Mathematica in Education",
}
@Article{Crandall:1994:DWT,
author = "Richard Crandall and Barry Fagin",
title = "Discrete weighted transforms and large-integer
arithmetic",
journal = j-MATH-COMPUT,
volume = "62",
number = "205",
pages = "305--324",
month = jan,
year = "1994",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2153411",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y11 (11A51 11Y05)",
MRnumber = "1185244 (94c:11123)",
MRreviewer = "Duncan A. Buell",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
URL = "http://www.jstor.org/stable/pdfplus/2153411.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Crandall:1994:EES,
author = "Richard E. Crandall and Joe P. Buhler",
title = "On the evaluation of {Euler} sums",
journal = j-EXP-MATH,
volume = "3",
number = "4",
pages = "275--285",
month = "????",
year = "1994",
CODEN = "????",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11M41 (11Y35)",
MRnumber = "1341720 (96e:11113)",
MRreviewer = "D. R. Heath-Brown",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://projecteuclid.org/euclid.em;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://projecteuclid.org/euclid.em/1048515810",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
}
@Misc{Crandall:1994:MAP,
author = "Richard E. Crandall",
title = "Method and apparatus for public key exchange in a
cryptographic system",
howpublished = "US Patent 5,463,690.",
month = "",
year = "1994",
bibdate = "Tue Mar 19 09:43:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "US Patent Application ?, filed ?.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Book{Crandall:1994:PSC,
author = "Richard E. Crandall",
title = "Projects in Scientific Computation",
publisher = pub-TELOS,
address = pub-TELOS:adr,
pages = "xxiv + 470",
year = "1994",
DOI = "https://doi.org/10.1007/978-1-4612-4324-3",
ISBN = "0-387-97808-9",
ISBN-13 = "978-0-387-97808-6",
LCCN = "Q183.9.P733 1994",
MRclass = "65-00 (34-04 42-04 65-01)",
MRnumber = "1258083 (95d:65001)",
MRreviewer = "G. Opfer",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
note = "With one Macintosh/IBM-PC floppy disk (3.5 inch)",
price = "US\$49.95",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
xxpages = "xvi + 470",
}
@Article{Crandall:1995:TSF,
author = "R. Crandall and J. Doenias and C. Norrie and J.
Young",
title = "The twenty-second {Fermat} number is composite",
journal = j-MATH-COMPUT,
volume = "64",
number = "210",
pages = "863--868",
month = apr,
year = "1995",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2153456",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y11 (11A51)",
MRnumber = "1277765 (95f:11104)",
MRreviewer = "Duncan A. Buell",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
acknowledgement = ack-nhfb,
affiliation = "NeXT Comput. Inc., Redwood City, CA, USA",
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
classcodes = "C4240 (Programming and algorithm theory); C1160
(Combinatorial mathematics)",
corpsource = "NeXT Comput. Inc., Redwood City, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "composite; extant cofactors; Fermat number; machine
proof; number theory; theorem proving",
treatment = "T Theoretical or Mathematical",
}
@Misc{Crandall:1996:MAD,
author = "Richard E. Crandall",
title = "Method and apparatus for {Digital Signature
Authentication}",
howpublished = "US Patent 5,581,616.",
month = "",
year = "1996",
bibdate = "Tue Mar 19 09:43:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "US Patent Application ?, filed ?.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:1996:QZF,
author = "Richard E. Crandall",
title = "On the quantum zeta function",
journal = j-J-PHYS-A,
volume = "29",
number = "21",
pages = "6795--6816",
day = "7",
month = nov,
year = "1996",
CODEN = "JPHAC5",
DOI = "https://doi.org/10.1088/0305-4470/29/21/014",
ISSN = "0305-4470 (print), 1361-6447 (electronic)",
ISSN-L = "0305-4470",
MRclass = "81Q10 (58G26 58Z05)",
MRnumber = "1421901 (97k:81042)",
MRreviewer = "Alfred Actor",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Physics. A. Mathematical and General",
journal-URL = "http://iopscience.iop.org/0305-4470/",
}
@Book{Crandall:1996:TAS,
author = "Richard E. Crandall",
title = "Topics in Advanced Scientific Computation",
publisher = pub-TELOS,
address = pub-TELOS:adr,
pages = "ix + 340",
year = "1996",
DOI = "https://doi.org/10.1007/978-1-4612-2334-4",
ISBN = "0-387-94473-7",
ISBN-13 = "978-0-387-94473-9",
LCCN = "QA9.58.C73 1996",
MRclass = "65-02 (68-02 68Q40)",
MRnumber = "1392472 (97g:65005)",
MRreviewer = "Ian Gladwell",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
note = "Includes programs in C and Mathematica.",
price = "US\$39.95",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
tableofcontents = "1: Selected numerical algorithms \\
Variants of the Newton method / 1 \\
Fast divide and mod algorithms / 7 \\
Fast multiplication / 11 \\
Matrix algebra / 16 \\
Polynomial arithmetic / 21 \\
2: Evaluation of constants and functions \\
Celebrated constants / 37 \\
Riemann zeta function / 49 \\
Multidimensional sums / 68 \\
Examples of special function evaluation /82 \\
3: Number-theoretical algorithms \\
Primes / 89 \\
Bernoulli numbers / 116 \\
Factoring / 125 \\
Fermat numbers / 140 \\
4: Transforms \\
FFT and related algorithms / 149 \\
Walsh--Hadamard transform / 167 \\
Wavelets / 171 \\
Convolution / 179 \\
5: Nonlinear and complex systems \\
N-body problems and chaos / 215 \\
Nonlinear differential systems / 222 \\
Fractal analysis / 229 \\
Learning algorithms / 233 \\
An old and beautiful nonlinear system / 238 \\
6: Data manipulation \\
Signal synthesis, detection and modeling / 249 \\
General data compression / 267 \\
Sound and image compression / 275 \\
Appendix / 285 \\
References / 319 \\
Index / 331",
xxpages = "xii + 340",
}
@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",
month = jan,
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 (97c:11119)",
MRreviewer = "T. Mets{\"a}nkyl{\"a}",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://www.ams.org/mcom/1997-66-217;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00800-4&u=/mcom/1997-66-217/;
http://www.jstor.org/stable/pdfplus/2153664.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Brent:1997:TNF,
author = "Richard P. Brent and Richard E. Crandall and Karl
Dilcher",
title = "Two New Factors of {Fermat} Numbers",
number = "TR-CS-97-11",
institution = "Department of Computer Science, The Australian
National University",
address = "Canberra 0200, ACT, Australia",
pages = "9",
month = may,
year = "1997",
bibdate = "Tue Mar 19 07:08:43 2013",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Techreports/ANU.bib;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://cs.anu.edu.au/techreports/1997/TR-CS-97-11.pdf;
http://cs.anu.edu.au/techreports/1997/TR-CS-97-11.ps.gz",
abstract = "We report the discovery of new 27-decimal digit
factors of the thirteenth and sixteenth Fermat numbers.
Each of the new factors was found by the elliptic curve
method. After division by the new factors and other
known factors, the quotients are seen to be composite
numbers with 2,391 and 19,694 decimal digits
respectively.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:1997:BRC,
author = "Richard E. Crandall",
title = "Book Review: {{\booktitle{Computation of Special
Functions}}, by Shanjie Zhang and Jianming Jin}",
journal = j-AMER-J-PHYSICS,
volume = "65",
number = "4",
pages = "355--355",
month = apr,
year = "1997",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.18543",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Mon Mar 18 12:32:24 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://ajp.aapt.org/resource/1/ajpias/v65/i4/p355_s1",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
}
@Article{Crandall:1997:CLN,
author = "Richard E. Crandall",
title = "The Challenge of Large Numbers",
journal = j-SCI-AMER,
volume = "276",
number = "2",
pages = "74--78",
month = feb,
year = "1997",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican0297-74",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Sat Nov 11 18:07:43 MST 2000",
bibsource = "http://www.sciam.com/1997/0207issue/0207quicksummary.html;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://www.nature.com/scientificamerican/journal/v276/n2/pdf/scientificamerican0297-74.pdf;
http://www.sciam.com/0297issue/0297currentissue.html",
abstract = "In the third century B.C., Archimedes calculated the
sum of all the sand grains it would take to fill the
then known universe. That's a pretty good-size number,
but it's small potatoes compared with mathematicians'
ever expanding notions of how large meaningful numbers
can be.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@TechReport{Crandall:1997:FPC,
author = "Richard E. Crandall",
title = "Floating-point convolutions of length $ 3 \times 2^k
$",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "4",
year = "1997",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/con32k.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@TechReport{Crandall:1997:OTD,
author = "Richard E. Crandall and J. Farrell",
title = "Optimization of two dimensional real convolutions",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "6",
year = "1997",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/con2d.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:1997:SWW,
author = "Richard Crandall and Karl Dilcher and Carl Pomerance",
title = "A search for {Wieferich} and {Wilson} primes",
journal = j-MATH-COMPUT,
volume = "66",
number = "217",
pages = "433--449",
month = jan,
year = "1997",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-97-00791-6",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11A07 (11Y35)",
MRnumber = "1372002 (97c:11004)",
MRreviewer = "Fran{\c{c}}ois Morain",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://www.ams.org/mcom/1997-66-217;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00791-6&u=/mcom/1997-66-217/;
http://www.jstor.org/stable/pdfplus/2153665.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Borwein:1998:CSR,
author = "Jonathan M. Borwein and David M. Bradley and Richard
E. Crandall",
title = "Computational Strategies for the {Riemann} Zeta
Function",
type = "Report",
number = "CECM-98-118",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "68",
day = "30",
month = oct,
year = "1998",
bibdate = "Mon Oct 24 11:29:15 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Published in \cite{Borwein:2000:CSR}.",
URL = "http://docserver.carma.newcastle.edu.au/211;
http://people.reed.edu/~crandall/papers/attach01.pdf",
abstract = "We provide a compendium of evaluation methods for the
Riemann zeta function, presenting formulae ranging from
historical attempts to recently found convergent series
to curious oddities old and new. We concentrate
primarily on practical computational issues, such
issues depending on the domain of the argument, the
desired speed of computation, and the incidence of what
we call ``value recycling.''",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August 2016);
Richard Eugene Crandall (29 December 1947--20 December
2012)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@InProceedings{Crandall:1998:ACA,
author = "Richard E. Crandall",
editor = "????",
booktitle = "{Proceedings of the RSA Conference, San Francisco, CA,
January 1998}",
title = "Advances in Cryptographic Algorithms: New
Discoveries",
publisher = "????",
address = "????",
pages = "",
year = "1998",
DOI = "",
ISBN = "",
ISBN-13 = "",
LCCN = "",
bibdate = "Tue Mar 19 10:06:31 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@TechReport{Crandall:1998:ASF,
author = "Richard E. Crandall",
title = "Applications of space-filling curves",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
year = "1998",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@TechReport{Crandall:1998:FEE,
author = "Richard E. Crandall",
title = "Fast evaluation of {Epstein} zeta functions",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "11",
year = "1998",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/epstein.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:1998:FEM,
author = "Richard E. Crandall",
title = "Fast evaluation of multiple zeta sums",
journal = j-MATH-COMPUT,
volume = "67",
number = "223",
pages = "1163--1172",
month = jul,
year = "1998",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-98-00950-8",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11M41 (11Y60)",
MRnumber = "1459385 (98j:11066)",
MRreviewer = "Dirk Kreimer",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://www.ams.org/mcom/1998-67-223;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00950-8&u=/mcom/1998-67-223/;
http://www.jstor.org/stable/pdfplus/2585176.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Crandall:1998:KSB,
author = "Richard E. Crandall",
editor = "????",
booktitle = "{Worldwide Mathematica Conference, Chicago, IL, June
1998}",
title = "Keynote Speech: Breaking Numerical Records with
{Mathematica}",
volume = "??",
publisher = "????",
address = "????",
pages = "??--??",
year = "1998",
bibdate = "Tue Mar 19 09:52:32 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
keywords = "Richard E. Crandall",
}
@Book{Crandall:1998:NOL,
author = "Richard E. Crandall and Marvin Levich",
title = "A network orange: logic and responsibility in the
{Computer Age}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 130",
year = "1998",
ISBN = "0-387-94647-0",
ISBN-13 = "978-0-387-94647-4",
LCCN = "QA76.9.C66 C73 1998",
bibdate = "Tue Mar 19 08:07:46 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
z3950.loc.gov:7090/Voyager",
note = "With a foreword by Howard Rheingold.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
subject = "Computers and civilization; Computers; Moral and
ethical aspects",
}
@Article{Crandall:1999:CLE,
author = "Richard Crandall and Uli Hofmann and Richard L.
Lozes",
title = "Contrast limitations in electron-beam lithography",
journal = j-J-VAC-SCI-TECHNOL-B,
volume = "17",
number = "6",
pages = "2945--2947",
month = nov # "\slash " # dec,
year = "1999",
CODEN = "JVSTBM",
DOI = "https://doi.org/10.1116/1.590930",
ISSN = "1071-1023 (print), 1520-8567 (electronic)",
ISSN-L = "0734-2101",
bibdate = "Tue Mar 19 09:10:24 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://scitation.aip.org/content/avs/journal/jvstb/17/6/10.1116/1.590930",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Vacuum Science \& Technology, B:
Microelectronics and Nanometer Structures--Processing,
Measurement, and Phenomena",
journal-URL = "http://scitation.aip.org/content/avs/journal/jvstb",
}
@TechReport{Crandall:1999:ICS,
author = "Richard E. Crandall",
title = "Integer convolution via split-radix fast {Galois}
transform",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "4",
year = "1999",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/confgt.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:1999:NRM,
author = "Richard E. Crandall",
title = "New representations for the {Madelung} constant",
journal = j-EXP-MATH,
volume = "8",
number = "4",
pages = "367--379",
month = "????",
year = "1999",
CODEN = "????",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11Y60 (11E45 11M35 33E20 33F05)",
MRnumber = "1737232 (2000m:11125)",
MRreviewer = "David Bradley",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://projecteuclid.org/euclid.em;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://projecteuclid.org/euclid.em/1047262358",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
}
@TechReport{Crandall:1999:PPR,
author = "Richard E. Crandall",
title = "Parallelization of {Pollard}-rho factorization",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "14",
year = "1999",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/parrho.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:1999:SPK,
author = "Richard E. Crandall and Steve Jobs",
title = "Seybold Publisher's Keynote on educational
supercomputing",
journal = "????",
volume = "??",
number = "??",
pages = "??--??",
month = "",
year = "1999",
DOI = "",
bibdate = "Tue Mar 19 09:52:32 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://www.youtube.com/watch?v=89Y8bjVEZ8E",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
keywords = "Richard E. Crandall",
}
@Misc{Crandall:1999:ULC,
author = "Richard E. Crandall",
title = "Universal lossless compressor for digitized analog
data",
howpublished = "US Patent 6,433,707.",
month = "",
year = "1999",
bibdate = "Tue Mar 19 09:43:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "US Patent Application ?, filed ?.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@TechReport{Crandall:1999:VIC,
author = "R. E. Crandall and J. Klivington",
title = "Vector implementation of color-image wavelet
transform",
type = "Report",
institution = "Advanced Computation Group, Apple Computer",
address = "Cupertino, CA, USA",
pages = "15",
day = "25",
month = oct,
year = "1999",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://images.apple.com/acg/pdf/g4wavelet.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@TechReport{Crandall:1999:VIM,
author = "Richard E. Crandall and Jason Klivington",
title = "Vector implementation of multiprecision arithmetic",
type = "Report",
institution = "Advanced Computation Group, Apple Computer",
address = "Cupertino, CA, USA",
pages = "11",
day = "25",
month = oct,
year = "1999",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://images.apple.com/acg/pdf/G4multiprecision.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Hofmann:1999:FPS,
author = "U. Hofmann and R. Crandall and L. Johnson",
title = "Fundamental performance of state-of the-art proximity
effect correction methods",
journal = j-J-VAC-SCI-TECHNOL-B,
volume = "17",
number = "6",
pages = "2940--2944",
month = nov # "\slash " # dec,
year = "1999",
CODEN = "JVSTBM",
DOI = "",
ISSN = "1071-1023 (print), 1520-8567 (electronic)",
ISSN-L = "0734-2101",
bibdate = "Tue Mar 19 09:11:21 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Vacuum Science \& Technology, B:
Microelectronics and Nanometer Structures--Processing,
Measurement, and Phenomena",
journal-URL = "http://scitation.aip.org/content/avs/journal/jvstb",
}
@TechReport{Bailey:199x:KC,
author = "David H. Bailey and Jonathan M. Borwein and Richard E.
Crandall",
title = "On the {Khintchine} constant",
type = "Report",
institution = inst-CECM,
address = inst-CECM:adr,
pages = "19",
year = "199x",
bibdate = "Wed Aug 31 08:55:14 2022",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "Published in \cite{Bailey:1997:KC}",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August 2016);
Richard Eugene Crandall (29 December 1947--20 December
2012)",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "Undated.",
}
@Article{Borwein:2000:CSR,
author = "Jonathan M. Borwein and David M. Bradley and Richard
E. Crandall",
title = "Computational Strategies for the {Riemann} Zeta
Function",
journal = j-J-COMPUT-APPL-MATH,
volume = "121",
number = "1--2",
pages = "247--296",
month = sep,
year = "2000",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(00)00336-8",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "11M06 (11Y35 33F05)",
MRnumber = "1780051 (2001h:11110)",
MRreviewer = "Cem Y. Y{\i}ld{\i}r{\i}m",
bibdate = "Mon Oct 24 11:41:28 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Numerical analysis in the 20th century, Vol. I,
Approximation theory",
URL = "http://people.reed.edu/~crandall/papers/attach01.pdf",
abstract = "We provide a compendium of evaluation methods for the
Riemann zeta function, presenting formulae ranging from
historical attempts to recently found convergent series
to curious oddities old and new. We concentrate
primarily on practical computational issues, such
issues depending on the domain of the argument, the
desired speed of computation, and the incidence of what
we call ``value recycling''.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August 2016);
Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
remark = "CECM Preprint 98:118.",
}
@Article{Brent:2000:TNF,
author = "R. P. Brent and R. E. Crandall and K. Dilcher and C.
{Van Halewyn}",
title = "Three new factors of {Fermat} numbers",
journal = j-MATH-COMPUT,
volume = "69",
number = "231",
pages = "1297--1304",
month = jul,
year = "2000",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-00-01207-2",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y05 (11A51)",
MRnumber = "1697645 (2000j:11194)",
MRreviewer = "Samuel S. Wagstaff, Jr.",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://www.ams.org/mcom/2000-69-231;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2000.bib",
URL = "http://www.ams.org/journal-getitem?pii=S0025-5718-00-01207-2;
http://www.ams.org/mcom/2000-69-231/S0025-5718-00-01207-2/S0025-5718-00-01207-2.dvi;
http://www.ams.org/mcom/2000-69-231/S0025-5718-00-01207-2/S0025-5718-00-01207-2.pdf;
http://www.ams.org/mcom/2000-69-231/S0025-5718-00-01207-2/S0025-5718-00-01207-2.ps;
http://www.ams.org/mcom/2000-69-231/S0025-5718-00-01207-2/S0025-5718-00-01207-2.tex",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Crandall:2000:ALD,
author = "Richard E. Crandall",
title = "Algorithms for localized dart-throwing",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "9",
year = "2000",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/darts.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Misc{Crandall:2000:CSU,
author = "Richard E. Crandall",
title = "Cryptographic system using chaotic dynamics",
howpublished = "US Patent 6,587,563.",
month = "",
year = "2000",
bibdate = "Tue Mar 19 09:43:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "US Patent Application ?, filed ?.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@TechReport{Crandall:2000:FEC,
author = "Richard E. Crandall",
title = "Fast evaluation for a certain class of lattice sums",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "5",
year = "2000",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/zeta2D.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@TechReport{Crandall:2000:FMA,
author = "Richard E. Crandall",
title = "Fast matrix algebra on {Apple G4}",
type = "Report",
institution = "Advanced Computation Group, Apple Computer",
address = "Cupertino, CA, USA",
pages = "14",
day = "29",
month = feb,
year = "2000",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://images.apple.com/acg/pdf/g4_matrix072804.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Misc{Crandall:2000:MAS,
author = "Richard E. Crandall",
title = "Method and apparatus for simultaneously encrypting and
compressing data",
howpublished = "US Patent 6,154,542.",
month = "????",
year = "2000",
bibdate = "Tue Mar 19 09:43:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "US Patent Application ?, filed ?.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@TechReport{Crandall:2000:PGE,
author = "Richard E. Crandall",
title = "{PowerPC G4} for Engineering, Science, and Education",
type = "Report",
institution = "Advanced Computation Group, Apple Computer",
address = "Cupertino, CA, USA",
year = "2000",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@TechReport{Crandall:2000:SSF,
author = "R. E. Crandall and J. Klivington",
title = "Supercomputer-style {FFT} library for {Apple G4}",
type = "Report",
institution = "Advanced Computation Group, Apple Computer",
address = "Cupertino, CA, USA",
pages = "24",
day = "6",
month = jan,
year = "2000",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://images.apple.com/acg/pdf/g4fft.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Bailey:2001:RCF,
author = "David H. Bailey and Richard E. Crandall",
title = "On the Random Character of Fundamental Constant
Expansions",
journal = j-EXP-MATH,
volume = "10",
number = "2",
pages = "175--190",
month = jun,
year = "2001",
CODEN = "????",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11K16 (37A45)",
MRnumber = "1837669 (2002h:11067)",
MRreviewer = "Greg Martin",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://projecteuclid.org/euclid.em;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/expmath.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://projecteuclid.org/euclid.em/999188630",
abstract = "We propose a theory to explain random behavior for the
digits in the expansions of fundamental mathematical
constants. At the core of our approach is a general
hypothesis concerning the distribution of the iterates
generated by dynamical maps. On this main hypothesis,
one obtains proofs of base-2 normality---namely bit
randomness in a specific technical sense---for a
collection of celebrated constants, including $ \pi $,
$ \log 2 $, $ \zeta (3) $, and others. Also on the
hypothesis, the number $ \zeta (5) $ is either rational
or normal to base 2. We indicate a research connection
between our dynamical model and the theory of
pseudorandom number generators.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
}
@Article{Buhler:2001:IPC,
author = "Joe Buhler and Richard Crandall and Reijo Ernvall and
Tauno Mets{\"a}nkyl{\"a} and M. Amin Shokrollahi",
title = "Irregular Primes and Cyclotomic Invariants to $ 12 $
Million",
journal = j-J-SYMBOLIC-COMP,
volume = "31",
number = "1--2",
pages = "89--96",
month = jan # "/" # feb,
year = "2001",
CODEN = "JSYCEH",
DOI = "https://doi.org/10.1006/jsco.1999.1011",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
MRclass = "11Y40 (11R18)",
MRnumber = "1806208 (2001m:11220)",
MRreviewer = "Xavier-Fran{\c{c}}ois Roblot",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://www.idealibrary.com/cgi-bin/links/toc/sy;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
note = "Computational algebra and number theory (Milwaukee,
WI, 1996)",
URL = "http://www.idealibrary.com/links/doi/10.1006/jsco.1999.1011;
http://www.idealibrary.com/links/doi/10.1006/jsco.1999.1011/pdf;
http://www.idealibrary.com/links/doi/10.1006/jsco.1999.1011/ref",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
}
@Misc{Crandall:2001:MAF,
author = "Richard E. Crandall and B. Garst",
title = "Method and apparatus for Fast Elliptic Encryption with
Direct Embedding",
howpublished = "US Patent 6,307,935.",
month = "",
year = "2001",
bibdate = "Tue Mar 19 09:43:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "US Patent Application ?, filed ?.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Book{Crandall:2001:PNC,
author = "Richard Crandall and Carl Pomerance",
title = "Prime Numbers: a Computational Perspective",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 545",
year = "2001",
DOI = "https://doi.org/10.1007/978-1-4684-9316-0",
ISBN = "0-387-94777-9",
ISBN-13 = "978-0-387-94777-8",
LCCN = "QA246 .C74 2001",
MRclass = "11A41 (11-02 11A51 11Y05 11Y11 11Y16 11Y35)",
MRnumber = "1821158 (2002a:11007)",
MRreviewer = "Samuel S. Wagstaff, Jr.",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
remark = "While not strictly about pseudorandom numbers, Chapter
8 of this book discusses applications of prime numbers
to cryptography, random-number generation, and
quasi-Monte Carlo methods.",
xxpages = "xvi + 545",
}
@Article{Bailey:2002:RGN,
author = "David H. Bailey and Richard E. Crandall",
title = "Random Generators and Normal Numbers",
journal = j-EXP-MATH,
volume = "11",
number = "4",
pages = "527--546 (2003)",
month = "????",
year = "2002",
CODEN = "????",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11K16 (11K45)",
MRnumber = "1969644 (2004c:11135)",
MRreviewer = "Arne Winterhof",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://projecteuclid.org/euclid.em;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/expmath.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://projecteuclid.org/euclid.em/1057864662",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
}
@TechReport{Crandall:2002:OPF,
author = "R. E. Crandall and J. Papadopoulos",
title = "Octuple-precision floating point on {Apple G4}",
type = "Report",
institution = "Advanced Computation Group, Apple Computer",
address = "Cupertino, CA, USA",
pages = "8",
day = "8",
month = may,
year = "2002",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://images.apple.com/acg/pdf/oct3a.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Barabasi:2003:LNS,
author = "Albert-L{\'a}szl{\'o} Barab{\'a}si and R. E.
Crandall",
title = "Linked: The New Science of Networks",
journal = j-AMER-J-PHYSICS,
volume = "71",
number = "4",
pages = "409--??",
month = apr,
year = "2003",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.1538577",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Tue Mar 19 08:22:29 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://link.aip.org/link/ajpias/v71/i4/p409/s2",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
}
@TechReport{Crandall:2003:IAC,
author = "R. E. Crandall and J. Papadopoulos",
title = "On the implementation of {AKS}-class primality tests",
type = "Report",
institution = "Advanced Computation Group, Apple Computer",
address = "Cupertino, CA, USA",
pages = "9",
day = "18",
month = mar,
year = "2003",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://images.apple.com/acg/pdf/aks3.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Misc{Crandall:2003:MAF,
author = "Richard E. Crandall",
title = "Method and apparatus for fast convolution using spline
kernel",
howpublished = "US Patent 6,701,028.",
month = "",
year = "2003",
bibdate = "Tue Mar 19 09:43:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "US Patent Application ?, filed ?.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Crandall:2003:TFF,
author = "Richard E. Crandall and Ernst W. Mayer and Jason S.
Papadopoulos",
title = "The twenty-fourth {Fermat} number is composite",
journal = j-MATH-COMPUT,
volume = "72",
number = "243",
pages = "1555--1572 (electronic)",
month = jul,
year = "2003",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-02-01479-5",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y11 (11A51 68Q25)",
MRnumber = "1972753 (2004c:11236)",
MRreviewer = "T. Mets{\"a}nkyl{\"a}",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://www.ams.org/mcom/2003-72-243;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2000.bib",
URL = "http://www.ams.org/journal-getitem?pii=S0025-5718-02-01479-5;
http://www.ams.org/mcom/2003-72-243/S0025-5718-02-01479-5/S0025-5718-02-01479-5.dvi;
http://www.ams.org/mcom/2003-72-243/S0025-5718-02-01479-5/S0025-5718-02-01479-5.pdf;
http://www.ams.org/mcom/2003-72-243/S0025-5718-02-01479-5/S0025-5718-02-01479-5.ps;
http://www.ams.org/mcom/2003-72-243/S0025-5718-02-01479-5/S0025-5718-02-01479-5.tex;
http://www.jstor.org/stable/pdfplus/4099850.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Bailey:2004:BEA,
author = "David H. Bailey and Jonathan M. Borwein and Richard E.
Crandall and Carl Pomerance",
title = "On the Binary Expansions of Algebraic Numbers",
journal = "Journal of Number Theory {Bordeaux}",
volume = "16",
number = "3",
pages = "487--518",
month = "????",
year = "2004",
CODEN = "????",
ISSN = "1246-7405",
MRclass = "11K16 (11J25 11J91)",
MRnumber = "2144954 (2006f:11088)",
MRreviewer = "John H. Loxton",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
URL = "http://jtnb.cedram.org/item?id=JTNB_2004__16_3_487_0",
acknowledgement = ack-nhfb,
ajournal = "J. Th\'eor. Nombres Bordeaux",
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal de Th\'eorie des Nombres de Bordeaux",
fjournal-2 = "Journal of Number Theory {Bordeaux}",
}
@TechReport{Bedau:2004:CHF,
author = "M. Bedau and R. E. Crandall and M. Raven",
title = "Cryptographic hash functions based on {Artificial
Life}",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "20",
year = "2004",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/hash.bib",
URL = "http://people.reed.edu/~crandall/papers/crypto8.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Borwein:2004:RAFa,
author = "J. Borwein and R. Crandall and G. Fee",
title = "On the {Ramanujan} {AGM} fraction. {I}. {The}
real-parameter case",
journal = j-EXP-MATH,
volume = "13",
number = "3",
pages = "275--285",
month = "????",
year = "2004",
CODEN = "????",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11J70 (11A55 33C05 40A15)",
MRnumber = "2103326 (2005g:11126)",
MRreviewer = "James G. Mc Laughlin",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://projecteuclid.org/euclid.em;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://projecteuclid.org/euclid.em/1103749836",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
}
@Article{Borwein:2004:RAFb,
author = "J. Borwein and R. Crandall",
title = "On the {Ramanujan} {AGM} fraction. {II}. {The}
complex-parameter case",
journal = j-EXP-MATH,
volume = "13",
number = "3",
pages = "287--295",
month = "????",
year = "2004",
CODEN = "????",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11J70 (11A55 33C05)",
MRnumber = "2103327 (2005h:11149)",
MRreviewer = "James G. Mc Laughlin",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://projecteuclid.org/euclid.em;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://projecteuclid.org/euclid.em/1103749837",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
}
@TechReport{Crandall:2004:BIJ,
author = "Richard E. Crandall",
title = "On a {Bessel}-integral of {J. Borwein}",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "2",
month = aug,
year = "2004",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/borweinJ.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@TechReport{Crandall:2004:GFA,
author = "R. E. Crandall and J. Klivington and D. Kramer",
title = "Gigaelement {FFTs} on {Apple G5} clusters",
type = "Report",
institution = "Advanced Computation Group, Apple Computer",
address = "Cupertino, CA, USA",
pages = "7",
day = "27",
month = aug,
year = "2004",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://images.apple.com/acg/pdf/FFTdistIntel20070816.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@TechReport{Crandall:2004:IPL,
author = "R. Crandall and G. Oxman and M. Helman and A.
Sullivan",
title = "Intuitive physics leads to epidemic models: Focus on
smallpox",
type = "Report",
institution = "Center for Advanced Computation, Reed College",
address = "Portland, OR, USA",
pages = "29",
day = "1",
month = jun,
year = "2004",
bibdate = "Tue Mar 19 10:56:44 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@TechReport{Crandall:2005:FEW,
author = "Richard E. Crandall",
title = "Fast evaluation of the {Witten} zeta function",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "3",
month = aug,
year = "2005",
bibdate = "Tue Mar 19 09:05:22 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/Witten2.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@TechReport{Crandall:2005:FEZ,
author = "Richard E. Crandall",
title = "Fast evaluation of {Zucker} moment-sums",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "3",
month = sep,
year = "2005",
bibdate = "Tue Mar 19 09:04:14 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/Zucker.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Misc{Crandall:2005:MAF,
author = "Richard E. Crandall",
title = "Method and apparatus for fast convolution using
separated spline kernel",
howpublished = "US Patent 6,912,323.",
month = "",
year = "2005",
bibdate = "Tue Mar 19 09:43:57 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "US Patent Application ?, filed ?.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Book{Crandall:2005:PNC,
author = "Richard Crandall and Carl Pomerance",
title = "Prime Numbers: a Computational Perspective",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xvi + 597",
year = "2005",
ISBN = "0-387-25282-7",
ISBN-13 = "978-0-387-25282-7",
MRclass = "11A41 (11A51 11Y05 11Y11 11Y35)",
MRnumber = "2156291 (2006a:11005)",
MRreviewer = "Robert Juricevic",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Bailey:2006:IIC,
author = "D. H. Bailey and J. M. Borwein and R. E. Crandall",
title = "Integrals of the {Ising} class",
journal = j-J-PHYS-A,
volume = "39",
number = "40",
pages = "12271--12302",
month = oct,
year = "2006",
CODEN = "JPHAC5",
DOI = "https://doi.org/10.1088/0305-4470/39/40/001",
ISSN = "0305-4470 (print), 1361-6447 (electronic)",
ISSN-L = "0305-4470",
MRclass = "33F05 (33F10 65D30 82B20 82B80)",
MRnumber = "2261886",
MRreviewer = "Syamal K. Sen",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://adsabs.harvard.edu/abs/2006JPhA...39..001B;
http://iopscience.iop.org/article/10.1088/0305-4470/39/40/001;
http://stacks.iop.org/0305-4470/39/i=40/a=001",
abstract = "From an experimental-mathematical perspective we
analyse 'Ising-class' integrals. These are structurally
related $n$-dimensional integrals we call $ C_n$, $
D_n$, $ E_n$, where $ D_n$ is a magnetic susceptibility
integral central to the Ising theory of solid-state
physics. We first analyse $ C_n \coloneq \frac {4}{n!}
\int_0^\infty \cdots \int_0^\infty \frac { 1 } { \big
(\sum_{ j = 1 }^n (u_j + 1 / u_j) \big)^2 } \frac { d
u_1 } { u_1 } \cdots \frac { d u_n } { u_n }$.
We had conjectured --- on the basis of
extreme-precision numerical quadrature --- that $ C_n $
has a finite large-$n$ limit, namely $ C_\infty = 2
e^{-2} $, with $ \gamma $ being the Euler constant. On
such a numerological clue we are able to prove the
conjecture. We then show that integrals $ D_n $ and $
E_n $ both decay exponentially with $n$, in a certain
rigorous sense. While $ C_n $, $ D_n $ remain
unresolved for $ n \geq 5 $, we were able to conjecture
a closed form for $ E_5 $. Our experimental results
involved extreme-precision, multidimensional quadrature
on intricate integrands; thus, a highly parallel
computation was required.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Physics A (Mathematical and General)",
journal-URL = "http://iopscience.iop.org/1751-8121",
onlinedate = "19 September 2006",
}
@InProceedings{Cahill:2006:STI,
author = "E. Cahill and R. Crandall and L. Rude and A.
Sullivan",
editor = "????",
booktitle = "{Proceedings of the 5th Annual Hawaii International
Conference on Mathematics, Statistics, and related
fields}",
title = "Space-time influenza model with demographic, mobility,
and vaccine parameters",
publisher = "????",
address = "????",
pages = "??--??",
year = "2006",
DOI = "",
ISBN = "",
ISBN-13 = "",
LCCN = "",
bibdate = "Tue Mar 19 09:20:45 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://academic.reed.edu/epi/papers/USAfluFINAL.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
pagecount = "25",
}
@TechReport{Crandall:2006:NFP,
author = "Richard E. Crandall",
title = "Note on fast polylogarithm computation",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "6",
month = jan,
year = "2006",
bibdate = "Tue Mar 19 09:03:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://people.reed.edu/~crandall/papers/Polylog.pdf;
https://web.archive.org/web/20120916145721/http://people.reed.edu/~crandall/papers/Polylog.pdf",
abstract = "The polylogarithm function $ \Li_n(z) = \sum_{k =
1}^\infty z^k / k^n $, manifestly convergent for $ |z|
\eq 1 $, integer $ n > 1 $, is sometimes
numerically\slash symbolically relevant for $ |z| > 1
$, i.e., the analytic continuation may be required. By
exploiting analytic symmetry relations, we give, for
integer $n$, simple and efficient algorithms for
complete continuation in complex $z$.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Bailey:2007:BI,
author = "D. H. Bailey and J. M. Borwein and R. E. Crandall",
title = "Box integrals",
journal = j-J-COMPUT-APPL-MATH,
volume = "206",
number = "1",
pages = "196--208",
year = "2007",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2006.06.010",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65D30 (11Y60 33E20 60E05)",
MRnumber = "2337437 (2008i:65036)",
MRreviewer = "Michael J. Evans",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Bailey:2007:HFI,
author = "D. H. Bailey and D. Borwein and J. M. Borwein and R.
E. Crandall",
title = "Hypergeometric Forms for {Ising}-Class Integrals",
journal = j-EXP-MATH,
volume = "16",
number = "3",
pages = "257--276",
month = "????",
year = "2007",
CODEN = "????",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "33E20 (33C05 33F05 33F10 65D30 82B20)",
MRnumber = "2367317 (2009c:33053)",
MRreviewer = "Wadim Zudilin",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.tandfonline.com/toc/uexm20/16/3;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://projecteuclid.org/euclid.em/1204928528",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
}
@Article{Borwein:2007:DCR,
author = "D. Borwein and J. Borwein and R. Crandall and R.
Mayer",
title = "On the dynamics of certain recurrence relations",
journal = j-RAMANUJAN-J,
volume = "13",
number = "1-3",
pages = "63--101",
year = "2007",
CODEN = "RAJOF9",
DOI = "https://doi.org/10.1007/s11139-006-0243-3",
ISSN = "1382-4090 (print), 1572-9303 (electronic)",
ISSN-L = "1382-4090",
MRclass = "11B37 (11A55 11Y16 37C99 37E99 39A10 65Q05)",
MRnumber = "2281157 (2007m:11014)",
MRreviewer = "James G. Mc Laughlin",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "Special issue for Richard Askey's 70th birthday.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "The Ramanujan Journal. An International Journal
Devoted to the Areas of Mathematics Influenced by
Ramanujan",
journal-URL = "http://link.springer.com/journal/11139",
}
@TechReport{Borwein:2007:ELAa,
author = "David Borwein and Jonathan Borwein and Richard
Crandall",
title = "Effective {Laguerre} asymptotics",
type = "Report",
institution = "Department of Computer Science, Dalhousie University",
address = "Halifax, NS, Canada B3H 4R2",
year = "2007",
bibdate = "Thu Aug 11 08:24:07 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://locutus.cs.dal.ca:8088/archive/00000334/;
http://web.archive.org/web/20070208032521/http://locutus.cs.dal.ca:8088/archive/00000334/",
abstract = "It is known that the generalized Laguerre polynomials
can enjoy sub-exponential growth for large primary
index. Specifically, for certain fixed parameter pairs
$ (a, z) $ one has the large-$n$ asymptotic $$ L_n^{( -
a)}( - z) \sim C(a, z) n^{-a / 2 - 1 / 4} e^{2 \sqrt
{nz}}. $$ We introduce a computationally motivated
contour integral that allows highly efficient numerical
evaluation of $ L_n$, yet also leads to general
asymptotic series over the full domain for
sub-exponential behavior. We eventually lay out a fast
algorithm for generation of the rather formidable
expansion coefficients. Along the way we address the
difficult problem of establishing effective (i.e.,
rigorous and explicit) error bounds on the general
expansion. To this end, we avoid classical
stationary-phase and steepest-descent techniques in
favor of an ``exp-arc'' method that amounts to a
natural bridge between converging series and effective
asymptotics. Finally, we exhibit an absolutely
convergent exp-arc series for Bessel-function
evaluation as an alternative to conventional
ascending-asymptotic switching.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Chen:2007:OAR,
author = "Charlie C. Chen and Jiinpo Wu and Richard E.
Crandall",
title = "Obstacles to the adoption of radio frequency
identification technology in the emergency rooms of
hospitals",
journal = "International Journal of Electronic Healthcare
(IJEH)",
volume = "3",
number = "2",
pages = "193--207",
year = "2007",
DOI = "https://doi.org/10.1504/IJEH.2007.013100",
bibdate = "Tue Mar 19 07:06:56 2013",
bibsource = "http://dblp.uni-trier.de/db/journals/ijeh/ijeh3.html#ChenWC07;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
ajournal = "IJEH",
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Journal of Physics A (Mathematical and General)",
journal-URL = "http://iopscience.iop.org/1751-8121",
xxnote = "Is this a different R E Crandall??",
}
@TechReport{Crandall:2007:NSK,
author = "Richard E. Crandall",
title = "Note on sinc-kernel sums and {Poisson}
transformation",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "4",
month = jun,
year = "2007",
bibdate = "Tue Mar 19 09:00:45 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/Sinc.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@TechReport{Crandall:2007:TRW,
author = "Richard E. Crandall",
title = "Theory of {ROOF} walks",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "40",
day = "19",
month = aug,
year = "2007",
bibdate = "Tue Mar 19 09:00:45 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/ROOF.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
keywords = "ROOF (Running out of Fuel) walks",
}
@Article{Borwein:2008:ELA,
author = "David Borwein and Jonathan M. Borwein and Richard E.
Crandall",
title = "Effective {Laguerre} Asymptotics",
journal = j-SIAM-J-NUMER-ANAL,
volume = "46",
number = "6",
pages = "3285--3312",
month = "????",
year = "2008",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/07068031X",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "33C65 (30E20 34E05)",
MRnumber = "2448665 (2010a:33037)",
MRreviewer = "Yu-Qiu Zhao",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://siamdl.aip.org/dbt/dbt.jsp?KEY=SJNAAM&Volume=46&Issue=6;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal2000.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@TechReport{Crandall:2008:TRW,
author = "Richard E. Crandall",
title = "Theory of {ROOF} walks",
type = "Report",
institution = "Reed College",
address = "Portland, OR, USA",
pages = "40",
day = "23",
month = may,
year = "2008",
bibdate = "Tue Mar 19 09:00:45 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/ROOF11.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
keywords = "ROOF (Running out of Fuel) walks",
}
@Article{Bailey:2009:RQR,
author = "D. H. Bailey and J. M. Borwein and R. E. Crandall",
title = "Resolution of the {Quinn--Rand--Strogatz} constant of
nonlinear physics",
journal = j-EXP-MATH,
volume = "18",
number = "1",
pages = "107--116",
month = "????",
year = "2009",
CODEN = "????",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "11Y60 (11M35 11Z05)",
MRnumber = "2548991 (2010k:11192)",
MRreviewer = "Herman J. J. te Riele",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.tandfonline.com/toc/uexm20/18/1;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://projecteuclid.org/euclid.em/1243430534",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
}
@Article{Bailey:2010:ATB,
author = "D. H. Bailey and J. M. Borwein and R. E. Crandall",
title = "Advances in the theory of box integrals",
journal = j-MATH-COMPUT,
volume = "79",
number = "271",
pages = "1839--1866",
month = jul,
year = "2010",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-10-02338-0",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y60 (65D30)",
MRnumber = "2630017 (2011d:11293)",
MRreviewer = "Michael J. Evans",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://www.ams.org/mcom/2010-79-271;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02338-0/;
http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02338-0/S0025-5718-10-02338-0.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Borwein:2010:HDB,
author = "Jonathan M. Borwein and O-Yeat Chan and R. E.
Crandall",
title = "Higher-Dimensional Box Integrals",
journal = j-EXP-MATH,
volume = "19",
number = "4",
pages = "431--446",
month = "????",
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1080/10586458.2010.10390634",
ISSN = "1058-6458 (print), 1944-950X (electronic)",
ISSN-L = "1058-6458",
MRclass = "33B30",
MRnumber = "2778656 (2012c:33012)",
MRreviewer = "Cristinel Mortici",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "http://projecteuclid.org/euclid.em;
http://www.tandfonline.com/toc/uexm20/19/4;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/expmath.bib",
URL = "http://projecteuclid.org/euclid.em/1317758103",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Experimental Mathematics",
journal-URL = "http://www.tandfonline.com/loi/uexm20",
}
@InCollection{Crandall:2010:TLR,
author = "Richard E. Crandall",
booktitle = "Gems in experimental mathematics",
title = "Theory of log-rational integrals",
volume = "517",
publisher = "Amer. Math. Soc.",
address = "Providence, RI",
pages = "127--142",
year = "2010",
DOI = "https://doi.org/10.1090/conm/517/10137",
MRclass = "33B30 (11M06 33E20)",
MRnumber = "2731092 (2011m:33005)",
MRreviewer = "Matilde N. Lal{\'{\i}}n",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
series = "Contemp. Math.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Book{Crandall:2011:SRS,
author = "Richard Crandall",
title = "Scientific Reflections: Selected Multidisciplinary
Works",
publisher = "Perfectly Scientific Press",
address = "Portland, OR, USA",
edition = "Second",
pages = "vi + 385",
year = "2011",
ISBN = "1-935638-08-4",
ISBN-13 = "978-1-935638-08-7",
LCCN = "Q113 .C72 2011",
MRclass = "01A75 (00B60)",
MRnumber = "2961410",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Book{Crandall:2012:ARS,
author = "Richard E. Crandall",
title = "Algorithmic Reflections: Selected Works",
publisher = "PSI Press",
address = "Portland, OR, USA",
edition = "First Perfectly Scientific Press paperback",
pages = "410",
year = "2012",
ISBN = "1-935638-19-X",
ISBN-13 = "978-1-935638-19-3",
LCCN = "QA958 .C736 2012",
bibdate = "Fri Jun 30 11:14:26 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
subject = "Algorithms; Algorithmes",
tableofcontents = "Part I: Number theory \\
On the $ 3 x + 1$ problem \\
On a conjecture of Crandall concerning the $ q n + 1$
problem \\
A search for Wieferich and Wilson primes \\
Parallelization of Pollard-rho factorization \\
Three new factors of Fermat numbers \\
Random generators and normal numbers \\
The googol-th bit of the Erd{\H{o}}s--Borwein constant
\\
Part II: Analytical algorithms \\
Fast evaluation of multiple zeta sums \\
On the Khintchine Constant \\
On the dynamics of certain recurrence relations \\
Effective Laguerre asymptotics \\
Theory of ROOF walks \\
Unified algorithms for polylogarithm, $L$-series, and
zeta variants \\
Part III: Physics, biology, epidemics, and physiology
\\
The potential within a crystal lattice \\
The fractal character of space-time epidemics \\
Mathematical signatures as tools for visual dysfunction
\\
NLA system for medical-data classification \\
On the fractal distribution of brain synapses",
}
@Article{Crandall:2012:GTB,
author = "Richard Crandall",
title = "The googol-th bit of the {Erd{\H{o}}s--Borwein}
constant",
journal = j-INTEGERS,
volume = "12",
number = "5",
pages = "811--840",
month = oct,
year = "2012",
CODEN = "INTEHN",
DOI = "https://doi.org/10.1515/integers-2012-0007",
ISSN = "1867-0652 (print), 1867-0660 (electronic)",
ISSN-L = "1867-0652",
MRclass = "11Y60 (11J72)",
MRnumber = "2988549",
bibdate = "Mon Mar 18 11:54:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Integers",
journal-URL = "http://www.degruyter.com/view/j/integ",
}
@TechReport{Crandall:2012:PEN,
author = "Richard E. Crandall",
title = "The {Poisson} equation and `natural' {Madelung}
constants",
type = "Report",
institution = "Center for Advanced Computation, Reed College",
address = "Portland, OR, USA",
pages = "23",
day = "29",
month = sep,
year = "2012",
bibdate = "Fri Aug 16 16:46:36 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "https://www.davidhbailey.com/dhbpapers/REC-PoissonAnalytic.pdf",
abstract = "Remarkably, the Poisson equation of classical
electrostatics has found recent applications in other
fields, for example in graphics and image processing.
It is of interest to revisit Poisson theory in regard
to what actually happens in arbitrary dimensions. In
either physics or graphics, one seeks solutions of $
\nabla^2 P (r) = - \rho (r) $, where $r$ is an
$n$-dimensional vector. The present treatment involves
solutions $P$ where $ \rho $ is the charge density of
an infinite but $n$-dimensional crystal (NaCl-type).
Because the potentials $P$ being summed are only of the
form $ \pm 1 / |r| $ for $ n = 3 $ dimensions, we have
cause to define `natural' Madelung constants on the
basis of the true behavior $ \P \asymp 1 / r^{n - 2}$
(or $ \asymp \log r $ in $ n = 2 $ dimensions). These
new constants can sometimes be given closed forms; for
example, we show that for $ n = 2 $ dimensions, the
natural Madelung constant --- essentially the binding
energy density of a sheaf of line charges is given
by\par
$$ {\cal N}_2 = (1 / 4 \pi) \log {4 \Gamma^3 (3 / 4) /
\pi^3} $$ \par
Even when a closed form is not available, we do have
for every $ {\cal N}_n$ exponentially fast
computational formulae. We also describe fast
computational algorithms that achieve extreme precision
for various relevant lattice sums.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Misc{Crandall:2012:UAP,
author = "R. E. Crandall",
title = "Unified algorithms for polylogarithm, {$L$}-series,
and zeta variants",
type = "Preprint",
pages = "53",
year = "2012",
bibdate = "Tue Sep 09 11:50:04 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Published in \cite{Crandall:2012:ARS}.",
URL = "http://www.perfscipress.com/papers/universalTOC25.pdf;
https://web.archive.org/web/20130430193005/http://www.perfscipress.com/papers/universalTOC25.pdf",
abstract = "We describe a general computational scheme for
evaluation of a wide class of number-theoretical
functions. We avoid asymptotic expansions in favor of
manifestly convergent series that lend themselves
naturally to rigorous error bounds. By employing three
fundamental series algorithms we achieve a unified
strategy to compute the various functions via parameter
selection. This work amounts to a compendium of methods
to establish extreme-precision results as typify modern
experimental mathematics. A fortuitous byproduct of
this unified approach is automatic analytic
continuation over complex parameters. Another byproduct
is a host of converging series for various fundamental
constants.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
remark-1 = "In memory of gentle colleague Jerry Keiper
(1953--1995).",
remark-2 = "Host in URL field no longer exists; cited in
\cite{Coffey:2014:SRR}.",
}
@Article{Bailey:2013:EFS,
author = "David H. Bailey and Jonathan M. Borwein and Richard E.
Crandall",
title = "Expectations on fractal sets",
journal = j-APPL-MATH-COMP,
volume = "??",
number = "??",
pages = "??--??",
month = "????",
year = "2013",
CODEN = "AMHCBQ",
DOI = "",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Mar 19 11:50:08 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "To appear.",
URL = "http://www.davidhbailey.com/dhbpapers/fracboxes.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Bailey:2013:LSA,
author = "David H. Bailey and Jonathan M. Borwein and Richard E.
Crandall and John Zucker",
title = "Lattice sums arising from the {Poisson} equation",
journal = j-J-PHYS-A-MATH-THEOR,
volume = "46",
number = "11",
pages = "115201",
month = mar,
year = "2013",
CODEN = "JPAMB5",
DOI = "https://doi.org/10.1088/1751-8113/46/11/115201",
ISSN = "1751-8113 (print), 1751-8121 (electronic)",
ISSN-L = "1751-8113",
MRclass = "35J05 (11Y40 35C05)",
MRnumber = "3030150",
bibdate = "Thu Aug 11 07:19:54 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://adsabs.harvard.edu/abs/2013JPhA...46k5201B;
http://iopscience.iop.org/article/10.1088/1751-8113/46/11/115201;
http://stacks.iop.org/1751-8121/46/i=11/a=115201;
http://www.davidhbailey.com/dhbpapers/PoissonLattice.pdf",
abstract = "In recent times, attention has been directed to the
problem of solving the Poisson equation, either in
engineering scenarios (computational) or in regard to
crystal structure (theoretical). Herein we study a
class of lattice sums that amount to Poisson solutions,
namely the $n$-dimensional forms $ \begin {eqnarray*}
\phi \_ n(r \_ 1, \dots, r \_ n) = \frac \{ 1 \} \{ \ p
i {\^ {}}2 \} \sum \_ \{ m \_ 1, \dots, m \_ n \odd \}
\frac \{ e{\^ {}} \{ i \ p i (m \_ 1 r \_ 1 + \cdots +
m \_ n r \_ n) \} \} \{ m \_ 1 {\^ {}}2 + \cdots + m \_
n{\^ {}}2 \} . \end {eqnarray*} $
By virtue of striking connections with Jacobi $ \thetav
$-function values, we are able to develop new closed
forms for certain values of the coordinates r$_k$, and
extend such analysis to similar lattice sums. A primary
result is that for rational $x$, $y$, the natural
potential $ \phiv_2 (x, y)$ is $ \frac {1}{\pi } \log
A$ where $A$ is an algebraic number. Various extensions
and explicit evaluations are given. Such work is made
possible by number-theoretical analysis, symbolic
computation and experimental mathematics, including
extensive numerical computations using up to
20,000-digit arithmetic.",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
eid = "115201",
fjournal = "Journal of Physics A: Mathematical and Theoretical",
journal-URL = "http://iopscience.iop.org/1751-8121",
pagecount = "31",
}
@Article{Borwein:2013:CFW,
author = "Jonathan M. Borwein and Richard E. Crandall",
title = "Closed forms: What they are and why we care",
journal = j-NAMS,
volume = "60",
number = "1",
pages = "50--65",
month = jan,
year = "2013",
CODEN = "AMNOAN",
DOI = "https://doi.org/10.1090/noti936",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "33F05",
MRnumber = "3052463",
MRreviewer = "Allan J. Mac Leod",
bibdate = "Tue Mar 19 11:53:53 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/nams2010.bib",
URL = "http://www.ams.org/notices/201301/rnoti-p50.pdf",
acknowledgement = ack-nhfb,
ajournal = "Notices Amer. Math. Soc.",
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
}
@InCollection{Crandall:2013:FDB,
author = "Richard Crandall",
title = "On the Fractal Distribution of Brain Synapses",
crossref = "Bailey:2013:CAM",
pages = "325--348",
year = "2013",
bibdate = "Mon Sep 05 08:05:13 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
}
@Article{Wolfram:2013:RRC,
author = "Stephen Wolfram",
title = "Remembering {Richard Crandall} (1947--2012)",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "47",
number = "1/2",
pages = "14--15",
month = mar,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2503697.2503700",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Wed Jul 17 06:23:04 MDT 2013",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
acknowledgement = ack-nhfb,
author-dates = "Richard Eugene Crandall (29 December 1947--20 December
2012)",
fjournal = "ACM Communications in Computer Algebra",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Walker:1983:SVD,
author = "J. Walker",
title = "Simple and vivid demonstrations of advanced concepts
in physics",
journal = j-SCI-AMER,
volume = "??",
number = "??",
pages = "??--??",
month = jan,
year = "1983",
CODEN = "SCAMAC",
DOI = "",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Tue Mar 19 09:34:10 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "Survey of Richard E. Crandall's experimental work.",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Gollub:1986:PC,
author = "Jerry P. Gollub and Neal B. Abraham",
title = "Physics in the colleges",
journal = j-PHYS-TODAY,
volume = "39",
number = "6",
pages = "28--34",
month = jun,
year = "1986",
CODEN = "PHTOAD",
DOI = "https://doi.org/10.1063/1.881029",
ISSN = "0031-9228 (print), 1945-0699 (electronic)",
ISSN-L = "0031-9228",
bibdate = "Tue Mar 19 09:32:23 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://www.physicstoday.org/resource/1/phtoad/v39/i6/p28_s1",
acknowledgement = ack-nhfb,
fjournal = "Physics Today",
journal-URL = "http://www.physicstoday.org/",
keywords = "Richard E. Crandall",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Romer:1991:EMP,
author = "Robert H. Romer",
title = "Editorial: Memorable papers from the
{{\booktitle{American Journal of Physics}}},
1933--1990",
journal = j-AMER-J-PHYSICS,
volume = "59",
number = "3",
pages = "201--207",
month = mar,
year = "1991",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.16562",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Sat Apr 20 15:26:08 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bunge-mario.bib;
https://www.math.utah.edu/pub/bibnet/authors/c/clerk-maxwell-james.bib;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/bibnet/authors/d/dyson-freeman-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/rutherford-ernest.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/slater-john-clarke.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/sommerfeld-arnold.bib;
https://www.math.utah.edu/pub/bibnet/authors/u/uhlenbeck-george-e.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
remark = "The cited papers include \cite{Crandall:1983:PME}.",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Taylor:1992:BRM,
author = "Cyrus Taylor",
title = "Book Reviews: {{\booktitle{Mathematica for the
Sciences}}, by Richard E. Crandall} and
{{\booktitle{Mathematica in Action}}, by Stan Wagon}",
journal = j-PHYS-TODAY,
volume = "45",
number = "1",
pages = "71--71",
month = jan,
year = "1992",
CODEN = "PHTOAD",
DOI = "https://doi.org/10.1063/1.2809498",
ISSN = "0031-9228 (print), 1945-0699 (electronic)",
ISSN-L = "0031-9228",
bibdate = "Mon Mar 18 12:43:24 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
URL = "http://www.physicstoday.org/resource/1/phtoad/v45/i1/p71_s1",
acknowledgement = ack-nhfb,
fjournal = "Physics Today",
journal-URL = "http://www.physicstoday.org/",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Wenes:1994:BRP,
author = "Geert Wenes",
title = "Book Review: {{\booktitle{Projects in Scientific
Computation}}, by Richard E. Crandall} and
{{\booktitle{A Scientist's and Engineer's Guide to
Workstations and Supercomputers}}, by Rubin H. Landau
and Paul J. Fink, Jr.}",
journal = j-COMPUT-PHYS,
volume = "8",
number = "1",
pages = "68--??",
month = "????",
year = "1994",
CODEN = "CPHYE2",
DOI = "",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Mon Mar 18 12:35:18 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/super.bib",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Franco:1995:CCC,
author = "Zachary Franco and Carl Pomerance",
title = "On a conjecture of {Crandall} concerning the $ q x + 1
$ problem",
journal = j-MATH-COMPUT,
volume = "64",
number = "211",
pages = "1333--1336",
month = jul,
year = "1995",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11B83 (11B05)",
MRnumber = "95j:11019",
MRreviewer = "J. C. Lagarias",
bibdate = "Sat Jan 11 13:29:06 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Peterson:2000:GCO,
author = "Ivars Peterson",
title = "Great Computations: Owners of home computers join
researchers in cracking problems and crunch-",
journal = j-SCIENCE-NEWS,
volume = "157",
number = "10",
pages = "152--155",
day = "4",
month = mar,
year = "2000",
CODEN = "SCNEBK",
ISSN = "0036-8423 (print), 1943-0930 (electronic)",
ISSN-L = "0036-8423",
bibdate = "Tue Mar 19 09:52:32 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://www.sciencenews.org/pages/pdfs/data/2000/157-10/15710-12.pdf",
acknowledgement = ack-nhfb,
fjournal = "Science News (Washington, DC)",
journal-URL = "http://www.jstor.org/journals/00368423.html;
http://www.sciencenews.org/view/archives;
http://www3.interscience.wiley.com/journal/122396840/home",
keywords = "Great Internet Mersenne Prime search; Richard E.
Crandall",
remark = "The article credits Richard Crandall for the fast
primality test used in searching for large Mersenne
primes. It also refers to the work in
\cite{Crandall:2003:TFF} that proves that the 24th
Mersenne number, a 5-million digit number, is not a
prime number.",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Peterson:2001:PMM,
author = "Ivars Peterson",
title = "Pi {\`a} la Mode: Mathematicians tackled the seeming
randomness of pi's digits",
journal = j-SCIENCE-NEWS,
volume = "160",
number = "9",
pages = "136--137",
day = "1",
month = sep,
year = "2001",
CODEN = "SCNEBK",
ISSN = "0036-8423 (print), 1943-0930 (electronic)",
ISSN-L = "0036-8423",
bibdate = "Sat Mar 03 15:27:13 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.jstor.org/stable/4012633",
acknowledgement = ack-nhfb,
fjournal = "Science News (Washington, DC)",
journal-URL = "http://www.jstor.org/journals/00368423.html;
http://www.sciencenews.org/view/archives;
http://www3.interscience.wiley.com/journal/122396840/home",
keywords = "Richard E. Crandall",
remark = "See \cite{Bailey:2001:RCF} for the research discussed
by Peterson.",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Preuss:2001:DPR,
author = "Paul Preuss",
title = "Are the Digits of Pi Random? {A} {Berkeley Lab}
Researcher May Hold the Key",
journal = "Energy Science News",
volume = "??",
number = "??",
pages = "??--??",
month = "????",
year = "2001",
DOI = "????",
bibdate = "Tue Mar 19 09:52:32 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
note = "pnl.gov",
URL = "http://web.archive.org/web/20050208141708/http://www.pnl.gov/energyscience/10-01/art3.htm;
http://www.pnl.gov/energyscience/10-01/art3.htm",
acknowledgement = ack-nhfb,
keywords = "David H. Bailey; Richard E. Crandall",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
xxnote = "URL at pnl.gov cannot be found on 19 March 2013;
archive.org has it.",
}
@Article{Seife:2001:MRD,
author = "Charles Seife",
title = "Mathematics: Randomly Distributed Slices of $ \pi $",
journal = j-SCIENCE,
volume = "293",
number = "5531",
pages = "793--??",
day = "3",
month = aug,
year = "2001",
CODEN = "SCIEAS",
DOI = "https://doi.org/10.1126/science.293.5531.793",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Tue Mar 19 09:52:32 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://www.sciencemag.org/content/293/5531/793.summary",
acknowledgement = ack-nhfb,
fjournal = "Science",
journal-URL = "http://www.sciencemag.org/archive/",
keywords = "Richard E. Crandall",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Seife:2001:PKE,
author = "Charles Seife",
title = "Pi Keeps 'Em Guessing",
journal = "Science NOW",
volume = "??",
number = "??",
pages = "??--??",
day = "27",
month = jul,
year = "2001",
DOI = "",
bibdate = "Tue Mar 19 09:52:32 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://news.sciencemag.org/sciencenow/2001/07/27-01.html;
http://sciencenow.sciencemag.org/cgi/content/full/2001/727/1",
acknowledgement = ack-nhfb,
keywords = "BBP formula; David H. Bailey; Jonathan Borwein;
Richard E. Crandall",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Teitelbaum:2002:RPN,
author = "J. Teitelbaum",
title = "Review of {{\booktitle{Prime numbers: A computational
perspective}}, by Crandall, R. and Pomerance, C.}",
journal = j-BULL-AMS,
volume = "39",
number = "3",
pages = "449--454",
month = apr,
year = "2002",
CODEN = "BAMOAD",
DOI = "",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Tue Mar 19 09:57:17 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Wagon:2002:BRM,
author = "Stan Wagon",
title = "Book Review: Mathematics: Prime Time:
{{\booktitle{Prime Numbers: A Computational
Perspective}}. Richard Crandall and Carl Pomerance, xvi
+ 545 pp. Springer-Verlag, 2001. \$49.95}",
journal = j-AM-SCI,
volume = "90",
number = "1",
pages = "84",
month = jan # "\slash " # feb,
year = "2002",
CODEN = "AMSCAC",
ISSN = "0003-0996 (print), 1545-2786 (electronic)",
ISSN-L = "0003-0996",
bibdate = "Tue Mar 19 06:13:18 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
note = "See \cite{Crandall:2001:PNC}.",
URL = "http://www.jstor.org/stable/pdfplus/27857605.pdf",
acknowledgement = ack-nhfb,
fjournal = "American Scientist",
journal-URL = "http://www.americanscientist.org/issues/past.aspx",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Gibbs:2003:DSP,
author = "W. W. Gibbs",
title = "A Digital Slice of Pi. The New Way to do Pure Math:
Experimentally",
journal = j-SCI-AMER,
volume = "288",
number = "5",
pages = "23--24",
month = may,
year = "2003",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican0503-23",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Tue Apr 26 16:23:52 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
URL = "http://crd.lbl.gov/~dhbailey/sciam-2003.pdf;
http://www.nature.com/scientificamerican/journal/v288/n5/pdf/scientificamerican0503-23.pdf;
http://www.scientificamerican.com/article.cfm?id=a-digital-slice-of-pi",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
keywords = "Richard E. Crandall",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{McCartin:2003:AEP,
author = "Brian J. McCartin and Suzanne M. Labadie",
title = "Accurate and efficient pricing of vanilla stock
options via the {Crandall--Douglas} scheme",
journal = j-APPL-MATH-COMP,
volume = "143",
number = "1",
pages = "39--60",
day = "20",
month = oct,
year = "2003",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Jan 9 08:41:07 MST 2004",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
xxnote = "Is this about R E Crandall's work??",
}
@Article{Dworkin:2004:MSD,
author = "Andy Dworkin",
title = "Mathematical Supermodels Define Epidemic Predictions",
journal = "The Oregonian",
volume = "??",
number = "??",
pages = "??--??",
day = "28",
month = apr,
year = "2004",
DOI = "",
bibdate = "Tue Mar 19 09:52:32 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/EpiArticle.pdf",
acknowledgement = ack-nhfb,
keywords = "Richard E. Crandall",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Klarreich:2004:MLC,
author = "Erica Klarreich",
title = "{Math Lab}: Computer experiments are transforming
mathematics",
journal = j-SCIENCE-NEWS,
volume = "165",
number = "17",
pages = "266--??",
day = "24",
month = apr,
year = "2004",
CODEN = "SCNEBK",
DOI = "",
ISSN = "0036-8423 (print), 1943-0930 (electronic)",
ISSN-L = "0036-8423",
bibdate = "Tue Mar 19 09:52:32 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://www.sciencenews.org/articles/20040424/bob9.asp;
http://www.sciencenews.org/view/feature/id/4949/description/Math_Lab;
http://www.sciencenews.org/view/generic/id/5159/description/Letters_from_the_June_26_2004_issue_of_iScience_News-i",
acknowledgement = ack-nhfb,
fjournal = "Science News (Washington, DC)",
journal-URL = "http://www.jstor.org/journals/00368423.html;
http://www.sciencenews.org/view/archives;
http://www3.interscience.wiley.com/journal/122396840/home",
keywords = "Richard E. Crandall",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Landhuis:2005:CGC,
author = "Esther Landhuis",
title = "A case for giving children flu shots: Studies indicate
sweeping benefits",
journal = "The Mercury News",
volume = "??",
number = "??",
pages = "??--??",
day = "20",
month = jan,
year = "2005",
DOI = "",
bibdate = "Tue Mar 19 09:52:32 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://www.mercurynews.com/mld/mercurynews/living/health/10688678.htm",
acknowledgement = ack-nhfb,
keywords = "Richard E. Crandall",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Moody:2005:RPQ,
author = "Robin J. Moody",
title = "{Reed} professor, {Qmedtrix} put together idea",
journal = "Portland Business Journal",
volume = "??",
number = "??",
pages = "??--??",
day = "23",
month = dec,
year = "2005",
DOI = "",
bibdate = "Tue Mar 19 09:52:32 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://people.reed.edu/~crandall/papers/Qmedtrix-Reed.pdf",
acknowledgement = ack-nhfb,
keywords = "Richard E. Crandall",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Misc{Bailey:2012:MPI,
author = "David H. Bailey and Jonathan Borwein",
title = "Mathematician\slash physicist\slash inventor {Richard
Crandall} dies at 64",
howpublished = "Web blog.",
day = "21",
month = dec,
year = "2012",
bibdate = "Mon Mar 18 12:22:22 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://experimentalmath.info/blog/2012/12/mathematicianphysicistinventor-richard-crandall-dies-at-64/",
acknowledgement = ack-nhfb,
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Misc{Wolfram:2012:RRC,
author = "Stephen Wolfram",
title = "Remembering {Richard Crandall} (1947--2012)",
howpublished = "Web blog.",
day = "30",
month = dec,
year = "2012",
bibdate = "Mon Mar 18 14:07:23 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://blog.stephenwolfram.com/2012/12/remembering-richard-crandall-1947-2012/",
acknowledgement = ack-nhfb,
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Bailey:2014:CTE,
author = "David H. Bailey and Jonathan M. Borwein and Richard E.
Crandall",
title = "Computation and theory of extended
{Mordell--Tornheim--Witten} sums",
journal = j-MATH-COMPUT,
volume = "83",
number = "288",
pages = "1795--1821",
year = "2014",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-2014-02768-3",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33B15 (11M32 33F05 65D20 65D30)",
MRnumber = "3194130",
MRreviewer = "Mehdi Hassani",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "http://www.ams.org/mcom/2014-83-288;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2014-83-288/S0025-5718-2014-02768-3;
http://www.ams.org/journals/mcom/2014-83-288/S0025-5718-2014-02768-3/S0025-5718-2014-02768-3.pdf",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Coffey:2014:SRR,
author = "Mark W. Coffey",
title = "Series representation of the {Riemann} zeta function
and other results: {Complements} to a paper of
{Crandall}",
journal = j-MATH-COMPUT,
volume = "83",
number = "287",
pages = "1383--1395",
year = "2014",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Sep 9 11:37:49 MDT 2014",
bibsource = "http://www.ams.org/mcom/2014-83-287;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2014-83-287/S0025-5718-2013-02755-X;
http://www.ams.org/journals/mcom/2014-83-287/S0025-5718-2013-02755-X/S0025-5718-2013-02755-X.pdf",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Article{Bailey:2015:CCI,
author = "D. H. Bailey and J. M. Borwein",
title = "{Crandall}'s computation of the incomplete Gamma
function and the {Hurwitz} zeta function, with
applications to {Dirichlet} {$L$}-series",
journal = j-APPL-MATH-COMP,
volume = "268",
number = "??",
pages = "462--477",
day = "1",
month = oct,
year = "2015",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Wed Sep 16 06:56:32 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300315008292",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Misc{Broadhurst:2015:PPH,
author = "David Broadhurst",
title = "A prime puzzle in honor of {Richard Crandall}",
howpublished = "Web site.",
day = "5",
month = oct,
year = "2015",
bibdate = "Mon Oct 05 10:03:31 2015",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib",
URL = "http://experimentalmath.info/blog/2015/10/a-prime-puzzle-in-honor-of-richard-crandall/",
acknowledgement = ack-nhfb,
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
}
@Book{Wolfram:2016:IMP,
author = "Stephen Wolfram",
title = "Idea makers: personal perspectives on the lives and
ideas of some notable people",
publisher = "Wolfram Media, Inc.",
address = "Champaign, IL, USA",
pages = "250 (est.)",
year = "2016",
ISBN = "1-57955-003-7 (hardcover), 1-57955-005-3 (e-book),
1-57955-011-8",
ISBN-13 = "978-1-57955-003-5 (hardcover), 978-1-57955-005-9
(e-book), 978-1-57955-011-0",
LCCN = "Q141 .W678562 2016",
bibdate = "Fri Jul 15 16:08:15 MDT 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/feynman-richard-p.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
URL = "http://www.wolfram-media.com/products/idea-makers.html",
acknowledgement = ack-nhfb,
keywords = "Ada Lovelace; Alan Turing; Beno{\^\i}t Mandelbrot;
Bertrand Russell; Alfred North Whitehead; George Boole;
Gottfried Leibniz; John von Neumann; Kurt G{\"o}del;
Marvin Minsky; Richard Crandall; Richard Feynman;
Russell Towle; Solomon Golomb; Srinivasa Ramanujan;
Steve Jobs",
subject = "Biography; History; Science; Scientists",
subject-dates = "Richard Eugene Crandall (29 December 1947--20
December 2012)",
tableofcontents = "Preface \\
Richard Feynman \\
Kurt G{\"o}del \\
Alan Turing \\
John von Neumann \\
George Boole \\
Ada Lovelace \\
Gottfried Leibniz \\
Beno{\^\i}t Mandelbrot \\
Steve Jobs \\
Marvin Minsky \\
Russell Towle \\
Bertrand Russell \& Alfred Whitehead \\
Richard Crandall \\
Srinivasa Ramanujan \\
Solomon Golomb",
}
@Book{Bailey:2013:CAM,
editor = "David H. Bailey and Heinz H. Bauschke and Peter
Borwein and Frank Garvan and Michel Th{\'e}ra and Jon
D. Vanderwerff and Henry Wolkowicz",
booktitle = "Computational and analytical mathematics: in honor of
{Jonathan Borwein}'s 60th Birthday",
title = "Computational and analytical mathematics: in honor of
{Jonathan Borwein}'s 60th Birthday",
volume = "50",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 701",
year = "2013",
DOI = "https://doi.org/10.1007/978-1-4614-7621-4",
ISBN = "1-4614-7620-8, 1-4614-7621-6 (e-book)",
ISBN-13 = "978-1-4614-7620-7, 978-1-4614-7621-4 (e-book)",
ISSN = "2194-1009",
LCCN = "QA241",
bibdate = "Thu Aug 11 13:32:34 MDT 2016",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wolkowicz-henry.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
series = "Springer proceedings in mathematics and statistics",
URL = "http://public.eblib.com/choice/publicfullrecord.aspx?p=1466708;
http://swb.eblib.com/patron/FullRecord.aspx?p=1466708;
http://www.myilibrary.com?id=547562",
abstract = "The research of Jonathan Borwein has had a profound
impact on optimization, functional analysis, operations
research, mathematical programming, number theory, and
experimental mathematics. Having authored more than a
dozen books and more than 300 publications, Dr. Borwein
is one of the most productive Canadian mathematicians
ever. His research spans pure, applied, and
computational mathematics as well as high performance
computing, and continues to have an enormous impact:
MathSciNet lists more than 2500 citations by more than
1250 authors, and Borwein is one of the 250 most cited
mathematicians of the period 1980--1999. He has served
the Canadian Mathematics Community through his
presidency (2000--2002) as well as his 15 years of
editing the CMS book series. Jonathan Borwein's vision
and initiative have been crucial in initiating and
developing several institutions that provide support
for researchers with a wide range of scientific
interests. A few notable examples include the Centre
for Experimental and Constructive Mathematics and the
IRMACS Centre at Simon Fraser University, the Dalhousie
Distributed Research Institute at Dalhousie University,
the Western Canada Research Grid, and the Centre for
Computer Assisted Research Mathematics and its
Applications, University of Newcastle. The workshops
that were held over the years in Dr. Borwein's honor
attracted high-caliber scientists from a wide range of
mathematical fields. This present volume is an
outgrowth of the workshop entitled Computational and
Analytical Mathematics, held in May 2011 in celebration
of Jonathan Borwein's 60th Birthday. The collection
contains various state-of-the-art research manuscripts
and surveys presenting contributions that have risen
from the conference, and is an excellent opportunity to
survey state-of-the-art research and discuss promising
research directions and approaches.",
acknowledgement = ack-nhfb,
author-dates = "Peter Borwein (10 May 1953--23 August 2020); Richard
Eugene Crandall (29 December 1947--20 December 2012)",
subject = "Number theory; Mathematical analysis; Mathematics;
Functional Analysis; Operator Theory; Operations
Research, Management Science; Algebra; Intermediate.;
Mathematical analysis.; Number theory.",
tableofcontents = "Normal Numbers and Pseudorandom Generators / David
H. Bailey and Jonathan M. Borwein / 1--18 \\
New Demiclosedness Principles for (Firmly) Nonexpansive
Operators / Heinz H. Bauschke / 19--28 \\
Champernowne's Number, Strong Normality, and the X
Chromosome / Adrian Belshaw and Peter B. Borwein /
29--44 \\
Optimality Conditions for Semivectorial Bilevel Convex
Optimal Control Problems / Henri Bonnel and Jacqueline
Morgan / 45--78 \\
Monotone Operators Without Enlargements / Jonathan M.
Borwein and Regina S. Burachik / 79--103 \\
A Br{\o}ndsted--Rockafellar Theorem for Diagonal
Subdifferential Operators / Radu Ioan Bo{\c{t}} and
Ern{\"o} Robert Csetnek / 105--112 \\
A $q$-Analog of Euler's Reduction Formula for the
Double Zeta Function / David M. Bradley and Xia Zhou /
113--126 \\
Fast Computation of Bernoulli, Tangent and Secant
Numbers / Richard P. Brent and David Harvey / 127--142
\\
Monotone Operator Methods for Nash Equilibria in
Non-potential Games / Luis M. Brice{\"a}no-Arias and
Patrick L. Combettes / 143--159 \\
Compactness, Optimality, and Risk / B. Cascales, J.
Orihuela and M. Ruiz Gal{\'a}n / 161--218 \\
Logarithmic and Complex Constant Term Identities / Tom
Chappell, Alain Lascoux and S. Ole Warnaar /
219--250\\
Preprocessing and Regularization for Degenerate
Semidefinite Programs / Yuen-Lam Cheung, Simon Schurr
and Henry Wolkowicz / 251--303 \\
The Largest Roots of the Mandelbrot Polynomials /
Robert M. Corless and Piers W. Lawrence / 305--324 \\
On the Fractal Distribution of Brain Synapses / Richard
Crandall / 325--348 \\
Visible Points in Convex Sets and Best Approximation /
Frank Deutsch, Hein Hundal and Ludmil Zikatanov /
349--364 \\
On Derivative Criteria for Metric Regularity / Asen L.
Dontchev and H{\'e}l{\`e}ne Frankowska / 365--374 \\
Five Classes of Monotone Linear Relations and Operators
/ Mclean R. Edwards / 375--400 \\
Upper Semicontinuity of Duality and Preduality Mappings
/ J. R. Giles / 401--410 \\
Convexity and Variational Analysis / A. D. Ioffe /
411--444 \\
Generic Existence of Solutions and Generic
Well-Posedness of Optimization Problems / P. S.
Kenderov and J. P. Revalski / 445--453 \\
Legendre Functions Whose Gradients Map Convex Sets to
Convex Sets / Alexander Knecht and Jon Vanderwerff /
455--462\\
On the Convergence of Iteration Processes for
Semigroups of Nonlinear Mappings in Banach Spaces / W.
M. Kozlowski and Brailey Sims / 463--484 \\
Techniques and Open Questions in Computational Convex
Analysis / Yves Lucet / 485--500 \\
Existence and Approximation of Fixed Points of Right
Bregman Nonexpansive Operators / Victoria
Mart{\'i}n-M{\'a}rquez and Simeon Reich / 501--520 \\
Primal Lower Nice Functions and Their Moreau Envelopes
/ Marc Mazade and Lionel Thibault / 521--553 \\
Bundle Method for Non-Convex Minimization with Inexact
Subgradients and Function Values / Dominikus Noll /
555--592 \\
Convergence of Linesearch and Trust-Region Methods
Using the Kurdyka--{\L}ojasiewicz Inequality /
Dominikus Noll and Aude Rondepierre / 593--611 \\
Strong Duality in Conic Linear Programming: Facial
Reduction and Extended Duals / G{\'a}bor Pataki /
613--634 \\
Towards a New Era in Subdifferential Analysis? /
Jean-Paul Penot /635--665 \\
Modular Equations and Lattice Sums / Mathew Rogers and
Boonrod Yuttanan / 667--680 \\
An Epigraph-Based Approach to Sensitivity Analysis in
Set-Valued Optimization / Douglas E. Ward and Stephen
E. Wright / 681--701",
}
