%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H F Beebe", %%% version = "1.00", %%% date = "01 November 2023", %%% time = "12:08:43 MDT", %%% filename = "birkhoff-garrett.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "https://www.math.utah.edu/~beebe", %%% checksum = "43269 18098 73452 761001", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "algebra; alternating direction implicit (ADI) %%% methods; bibliography; BibTeX; differential %%% equations; Douglas--Rachford method; elliptic %%% problems; fluid dynamics; functional %%% analysis; Garrett Birkhoff; group theory; %%% history of mathematics; hydrodynamics; %%% interpolation; lattice theory; nuclear %%% reactors; numerical analysis; spline %%% approximation; successive overrelaxation %%% (SOR) methods; topology; Verbandstheorie %%% (lattice theory)", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a bibliography of works by, and %%% about, the influential American %%% mathematician, Garrett Birkhoff (19 January %%% 1911--22 November 1996), son of mathematician %%% George David Birkhoff (1884--1944). %%% %%% Garrett Birkhoff was born in Princeton, NJ, %%% USA, and Harvard University in 1928, and %%% received a B.A. degree there in 1932. He %%% next studied at Cambridge University in the %%% UK, but took no degrees, and returned to %%% Harvard in 1933, becoming an instructor there %%% in 1936. He was appointed George Putnam %%% Professor of Pure and Applied Mathematics at %%% Harvard in 1969, and retired there in 1981. %%% %%% During his career, he was awarded six %%% honorary degrees, was elected to the National %%% Academy of Sciences and the American Academy %%% of Arts and Sciences, was a Guggenheim Fellow %%% in 1948--1949, and was President of the %%% Society for Industrial and Applied %%% Mathematics (SIAM) for 1966--1968. His %%% several textbooks were widely used, and %%% translated into other languages. He received %%% the AMS/SIAM George David Birkhoff Prize in %%% 1978. %%% %%% Entry Rota:1987:SPA republishes a selection %%% of Garrett Birkhoff's important works, and %%% includes a list of 209 of his papers from %%% 1933 to 1986. They are identified in this %%% file in GB-number values. The memoriam in %%% entry Young:1997:GBA lists 44 papers by %%% Garrett Birkhoff, and works related to his. %%% Papers from both those lists are all included %%% in this bibliography. %%% %%% At version 1.00 of this file, Part 1 records %%% 364 publications by Garrett Birkhoff, and the %%% final cross reference lists 8 edited volumes. %%% However, no curriculum vitae for Garrett %%% Birkhoff has been found to check against the %%% coverage in this file. %%% %%% Web sites about Garrett Birkhoff include %%% %%% https://en.wikipedia.org/wiki/Garrett_Birkhoff %%% https://mathshistory.st-andrews.ac.uk/Biographies/Birkhoff_Garrett/ %%% https://www.encyclopedia.com/people/science-and-technology/mathematics-biographies/garrett-birkhoff %%% https://www.mathgenealogy.org/id.php?id=16942 %%% %%% The genealogy site reports that he has 53 %%% students and 1298 academic descendants. One %%% of his students, David Young, Jr., is covered %%% in the BibNet Project, and another, Calvin %%% Wilcox, was a Utah long-time colleague of the %%% bibliographer. %%% %%% Books (some with multiple editions and %%% translations) authored or co-authored by %%% Garrett Birkhoff include: %%% %%% A Brief Survey of Modern Algebra %%% Algebra [English, French, German] %%% A Survey of Modern Algebra %%% Hydrodynamic instability %%% Hydrodynamics: A Study in Logic, Fact and %%% Similitude %%% Jets, Wakes, and Cavities [English, Russian] %%% Lattice Theory [English, Russian] %%% Modern Applied Algebra %%% Numerical Solution of Elliptic Problems %%% Ordinary Differential Equations %%% The Numerical Solution of Elliptic Equations %%% Trends in Lattice Theory %%% %%% Conference proceedings edited or co-edited by %%% Garrett Birkhoff include %%% %%% 1961 Nuclear reactor theory %%% 1962 Hydrodynamic Instability %%% 1969 Transport theory %%% 1970 Numerical solution of field problems %%% in continuum physics %%% 1970 Studies in Numerical Analysis, 2 %%% 1971 Computers in Algebra and Number Theory %%% 1984 Elliptic Problem Solvers, II %%% %%% Journals in which Garrett Birkhoff published %%% most frequently include: %%% ---------------------------+------- %%% journal | count %%% ---------------------------+------- %%% j-BULL-AMS | 42 %%% j-PROC-NATL-ACAD-SCI-USA | 14 %%% j-AMER-MATH-MONTHLY | 10 %%% j-ANN-MATH-2 | 10 %%% j-QUART-APPL-MATH | 10 %%% j-TRANS-AM-MATH-SOC | 10 %%% j-J-MATH-ANAL-APPL | 9 %%% j-J-MATH-MECH | 9 %%% j-DUKE-MATH-J | 7 %%% j-J-MATH-PHYS-MIT | 7 %%% j-PROC-CAMBRIDGE-PHIL-SOC | 5 %%% ... %%% ---------------------------+------- %%% %%% At version 1.00, the year coverage looked %%% like this: %%% %%% 1911 ( 1) 1949 ( 6) 1987 ( 5) %%% 1912 ( 0) 1950 ( 7) 1988 ( 8) %%% 1913 ( 0) 1951 ( 1) 1989 ( 4) %%% 1914 ( 0) 1952 ( 5) 1990 ( 8) %%% 1915 ( 0) 1953 ( 6) 1991 ( 3) %%% 1916 ( 0) 1954 ( 14) 1992 ( 7) %%% 1917 ( 0) 1955 ( 3) 1993 ( 5) %%% 1918 ( 1) 1956 ( 5) 1994 ( 2) %%% 1919 ( 0) 1957 ( 5) 1995 ( 3) %%% 1920 ( 0) 1958 ( 6) 1996 ( 5) %%% 1921 ( 0) 1959 ( 5) 1997 ( 4) %%% 1922 ( 0) 1960 ( 7) 1998 ( 4) %%% 1923 ( 0) 1961 ( 8) 1999 ( 2) %%% 1924 ( 0) 1962 ( 14) 2000 ( 5) %%% 1925 ( 0) 1963 ( 12) 2001 ( 5) %%% 1926 ( 0) 1964 ( 7) 2002 ( 3) %%% 1927 ( 0) 1965 ( 11) 2003 ( 5) %%% 1928 ( 0) 1966 ( 8) 2004 ( 4) %%% 1929 ( 0) 1967 ( 11) 2005 ( 4) %%% 1930 ( 0) 1968 ( 4) 2006 ( 4) %%% 1931 ( 0) 1969 ( 13) 2007 ( 4) %%% 1932 ( 0) 1970 ( 13) 2008 ( 6) %%% 1933 ( 5) 1971 ( 14) 2009 ( 3) %%% 1934 ( 26) 1972 ( 6) 2010 ( 7) %%% 1935 ( 26) 1973 ( 11) 2011 ( 9) %%% 1936 ( 15) 1974 ( 12) 2012 ( 5) %%% 1937 ( 13) 1975 ( 17) 2013 ( 4) %%% 1938 ( 3) 1976 ( 13) 2014 ( 3) %%% 1939 ( 4) 1977 ( 7) 2015 ( 6) %%% 1940 ( 3) 1978 ( 4) 2016 ( 9) %%% 1941 ( 2) 1979 ( 10) 2017 ( 6) %%% 1942 ( 2) 1980 ( 9) 2018 ( 8) %%% 1943 ( 2) 1981 ( 6) 2019 ( 5) %%% 1944 ( 2) 1982 ( 9) 2020 ( 2) %%% 1945 ( 1) 1983 ( 8) 2021 ( 4) %%% 1946 ( 9) 1984 ( 11) 2022 ( 4) %%% 1947 ( 1) 1985 ( 6) 2023 ( 3) %%% 1948 ( 7) 1986 ( 6) %%% 19xx ( 1) %%% %%% Article: 472 %%% Book: 60 %%% InCollection: 23 %%% InProceedings: 45 %%% Misc: 1 %%% PhdThesis: 1 %%% Proceedings: 12 %%% TechReport: 8 %%% %%% Total entries: 622 %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ====================================================================

@Preamble{ "\ifx \undefined \booktitle \def \booktitle #1{{{\em #1}}} \fi" # "\ifx \undefined \bud \def \bud {u} \fi" # "\ifx \undefined \cprime \def \cprime{$'$} \fi" # "\ifx \undefined \cyr \let \cyr = \relax \fi" # "\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}} \fi" # "\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}} \fi" }

%%% ==================================================================== %%% Acknowledgement abbreviations:

@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/|"}

%%% ==================================================================== %%% Journal abbreviations:

@String{j-ADV-MATH= "Advances in Mathematics"} @String{j-ALGEBRA-UNIVERS= "Algebra Universalis"} @String{j-AM-J-MATH= "American Journal of Mathematics"} @String{j-AM-SCI= "American Scientist"} @String{j-AMER-MATH-MONTHLY= "American Mathematical Monthly"} @String{j-ANN-INST-HENRI-POINCARE= "Annales de l'Institut Henri Poincar{\'e}"} @String{j-ANN-INST-HENRI-POINCARE-N-S-B-CALC-PROBAB-STAT= "Annales de l'Institut Henri Poincar{\'e}. Nouvelle s{\'e}rie. Section B. Calcul des Probabilit{\'e}s et Statistique"} @String{j-ANN-MATH= "Annals of Mathematics"} @String{j-ANN-MATH-2= "Annals of Mathematics (2)"} @String{j-ANN-MATH-STAT= "Annals of mathematical statistics"} @String{j-ANN-PROBAB= "Annals of Probability"} @String{j-APPL-MATH-COMP= "Applied Mathematics and Computation"} @String{j-APPL-NUM-MATH= "Applied Numerical Mathematics: Transactions of IMACS"} @String{j-ARCH-HIST-EXACT-SCI= "Archive for History of Exact Sciences"} @String{j-BIT= "BIT (Nordisk tidskrift for informationsbehandling)"} @String{j-BIT-NUM-MATH= "BIT Numerical Mathematics"} @String{j-BRITISH-J-HIST-SCI= "British Journal for the History of Science"} @String{j-BULL-AMS= "Bulletin of the American Mathematical Society"} @String{j-C-R-ACAD-SCI-PARIS= "Comptes rendus de l'Acad{\'e}mie des sciences, Paris"} @String{j-CACM= "Communications of the ACM"} @String{j-CAN-J-MATH= "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques"} @String{j-CAN-MATH-BULL= "Canadian mathematical bulletin = Bulletin canadien de math{\'e}matiques"} @String{j-COMM-PURE-APPL-MATH= "Communications on Pure and Applied Mathematics (New York)"} @String{j-COMMUN-MATH-STAT= "Communications in Mathematics and Statistics"} @String{j-COMP-PHYS-COMM= "Computer Physics Communications"} @String{j-COMPOS-MATH= "Compositio Mathematica"} @String{j-COMPUT-MATH-APPL= "Computers and Mathematics with Applications"} @String{j-COMPUTING= "Computing: Archiv f{\"u}r Informatik und Numerik"} @String{j-DUKE-MATH-J= "Duke Mathematical Journal"} @String{j-ECONOMETRICA= "Econometrica"} @String{j-ELECTR-ENG= "Electrical Engineering (American Institute of Electrical Engineers)"} @String{j-ELECTRON-J-LINEAR-ALGEBRA= "Electronic Journal of Linear Algebra"} @String{j-EXP-MATH= "Experimental Mathematics"} @String{j-FORM-ASP-COMPUT= "Formal Aspects of Computing"} @String{j-FOUND-PHYS= "Foundations of Physics"} @String{j-FUND-INFO= "Fundamenta Informaticae"} @String{j-FUNDAM-MATH= "Fundamenta mathematicae"} @String{j-HIST-MATH= "Historia Mathematica"} @String{j-IEEE-COMPUT-ARCHIT-LETT= "IEEE Computer Architecture Letters"} @String{j-IEEE-TRANS-NETWORKING= "IEEE\slash ACM Transactions on Networking"} @String{j-IMA-J-NUMER-ANAL= "IMA Journal of Numerical Analysis"} @String{j-INDIAN-J-MATH= "Indian Journal of Mathematics"} @String{j-INDIANA-UNIV-MATH-J= "Indiana University Mathematics Journal"} @String{j-ISIS= "Isis"} @String{j-J-ALG= "Journal of Algorithms"} @String{j-J-ANAL-MATH= "Journal d'analyse math{\'e}matique"} @String{j-J-APPL-PHYS= "Journal of Applied Physics"} @String{j-J-APPROX-THEORY= "Journal of Approximation Theory"} @String{j-J-COMB-THEORY= "Journal of Combinatorial Theory"} @String{j-J-COMPUT-APPL-MATH= "Journal of Computational and Applied Mathematics"} @String{j-J-COMPUT-PHYS= "Journal of Computational Physics"} @String{j-J-DIFFER-EQU= "Journal of Differential Equations"} @String{j-J-HYDRAULICS-DIV= "Journal of the Hydraulics Division"} @String{j-J-MATH-ANAL-APPL= "Journal of Mathematical Analysis and Applications"} @String{j-J-MATH-MECH= "Journal of Mathematics and Mechanics"} @String{j-J-MATH-PHYS= "Journal of Mathematical Physics"} @String{j-J-MATH-PHYS-MIT= "Journal of Mathematics and Physics (MIT)"} @String{j-J-NUMBER-THEORY= "Journal of Number Theory"} @String{j-J-SCI-COMPUT= "Journal of Scientific Computing"} @String{j-J-SIAM= "Journal of the Society for Industrial and Applied Mathematics"} @String{j-J-STAT-PHYS= "Journal of Statistical Physics"} @String{j-J-SYMBOLIC-COMP= "Journal of Symbolic Computation"} @String{j-LECT-NOTES-COMP-SCI= "Lecture Notes in Computer Science"} @String{j-LECT-NOTES-MATH= "Lecture Notes in Mathematics"} @String{j-LIN-MULT-ALGEBRA= "Linear Multilinear Algebra"} @String{j-LINEAR-ALGEBRA-APPL= "Linear Algebra and its Applications"} @String{j-MATH-COMP-SIM= "Mathematics and Computers in Simulation"} @String{j-MATH-COMPUT= "Mathematics of Computation"} @String{j-MATH-COMPUT-SCI= "Mathematics in Computer Science"} @String{j-MATH-GAZ= "Mathematical Gazette"} @String{j-MATH-INTEL= "The Mathematical Intelligencer"} @String{j-MATH-MAG= "Mathematics Magazine"} @String{j-MATH-TABLES-OTHER-AIDS-COMPUT= "Mathematical Tables and Other Aids to Computation"} @String{j-MATH-Z= "Mathematische Zeitschrift"} @String{j-NAMS= "Notices of the American Mathematical Society"} @String{j-NUM-MATH= "Numerische Mathematik"} @String{j-NUMER-ALGORITHMS= "Numerical Algorithms"} @String{j-NY-TIMES= "New York Times"} @String{j-ORDER-DORDRECHT= "Order (Dordrecht)"} @String{j-OSIRIS= "Osiris"} @String{j-PHILOS-TRANS-R-SOC-LOND-SER-A= "Philosophical Transactions of the Royal Society A: Mathematical, Physical, and Engineering Sciences"} @String{j-PHYS-FLUIDS= "The Physics of Fluids"} @String{j-POKROKY-MAT-FYS-ASTRON= "Pokroky Matematiky, Fyziky a Astronomie"} @String{j-PROC-AM-MATH-SOC= "Proceedings of the American Mathematical Society"} @String{j-PROC-AMER-PHIL-SOC= "Proceedings of the {American Philosophical Society} held at {Philadelphia} for promoting useful knowledge"} @String{j-PROC-CAMBRIDGE-PHIL-SOC= "Proceedings of the Cambridge Philosophical Society. Mathematical and physical sciences"} @String{j-PROC-LONDON-MATH-SOC-2= "Proceedings of the London Mathematical Society. Second Series"} @String{j-PROC-NATL-ACAD-SCI-USA= "Proceedings of the National Academy of Sciences of the United States of America"} @String{j-QUART-APPL-MATH= "Quarterly of Applied Mathematics"} @String{j-REV-HIST-MATH= "Revue d'Histoire des Math{'e}matiques = Journal for the History of Mathematics"} @String{j-SIAM-J-APPL-MATH= "SIAM Journal on Applied Mathematics"} @String{j-SIAM-J-COMPUT= "SIAM Journal on Computing"} @String{j-SIAM-J-CONTROL-OPTIM= "SIAM Journal on Control and Optimization"} @String{j-SIAM-J-DISCR-MATH= "SIAM Journal on Discrete Mathematics"} @String{j-SIAM-J-MAT-ANA-APPL= "SIAM Journal on Matrix Analysis and Applications"} @String{j-SIAM-J-MATH-ANA= "SIAM Journal on Mathematical Analysis"} @String{j-SIAM-J-NUMER-ANAL= "SIAM Journal on Numerical Analysis"} @String{j-SIAM-J-SCI-STAT-COMP= "SIAM Journal on Scientific and Statistical Computing"} @String{j-SIAM-REVIEW= "SIAM Review"} @String{j-SIGMETRICS= "ACM SIGMETRICS Performance Evaluation Review"} @String{j-SIGSAM= "SIGSAM Bulletin"} @String{j-STUD-APPL-MATH= "Studies in Applied Mathematics"} @String{j-SYNTHESE= "Synthese"} @String{j-THEOR-COMP-SCI= "Theoretical Computer Science"} @String{j-TOMS= "ACM Transactions on Mathematical Software"} @String{j-TRANS-AM-MATH-SOC= "Transactions of the American Mathematical Society"} @String{j-TRANS-AM-NUCL-SOC= "Transactions of the American Nuclear Society"} @String{j-TWO-YEAR-COLL-MATH-J= "Two-Year College Mathematics Journal"} @String{j-Z-ANGE-MATH-MECH= "{Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik}"} @String{j-Z-ANGE-MATH-PHYS= "{Zeitschrift f{\"u}r Angewandte Mathematik und Physik = Journal of Applied Mathematics and Physics}"}

%%% ==================================================================== %%% Publisher abbreviations:

@String{pub-A-K-PETERS= "A. K. Peters, Ltd."} @String{pub-A-K-PETERS:adr= "Wellesley, MA, USA"} @String{pub-ACADEMIC= "Academic Press"} @String{pub-ACADEMIC:adr= "New York, USA"} @String{pub-ACM= "ACM Press"} @String{pub-ACM:adr= "New York, NY 10036, USA"} @String{pub-AMS= "American Mathematical Society"} @String{pub-AMS:adr= "Providence, RI, USA"} @String{pub-AW= "Ad{\-d}i{\-s}on-Wes{\-l}ey"} @String{pub-AW:adr= "Reading, MA, USA"} @String{pub-BIRKHAUSER= "Birkh{{\"a}}user"} @String{pub-BIRKHAUSER:adr= "Cambridge, MA, USA; Berlin, Germany; Basel, Switzerland"} @String{pub-BIRKHAUSER-BOSTON= "Birkh{\"a}user Boston Inc."} @String{pub-BIRKHAUSER-BOSTON:adr= "Cambridge, MA, USA"} @String{pub-BLAISDELL= "Blaisdell Pub. Co."} @String{pub-BLAISDELL:adr= "Waltham, MA, USA"} @String{pub-DEKKER= "Marcel Dekker, Inc."} @String{pub-DEKKER:adr= "New York, NY, USA"} @String{pub-DOVER= "Dover Publications, Inc."} @String{pub-DOVER:adr= "New York, NY, USA"} @String{pub-DUNOD= "Dunod"} @String{pub-DUNOD:adr= "Paris, France"} @String{pub-ELSEVIER= "Elsevier"} @String{pub-ELSEVIER:adr= "Amsterdam, The Netherlands"} @String{pub-GAUTHIER-VILLARS= "Gauthier-Villars et cie"} @String{pub-GAUTHIER-VILLARS:adr= "Paris, France"} @String{pub-GREENWOOD= "Greenwood Press"} @String{pub-GREENWOOD:adr= "88 Post Road West, Westport, CT 06881, USA"} @String{pub-GRUYTER= "Walter de Gruyter"} @String{pub-GRUYTER:adr= "Berlin, Germany"} @String{pub-HARVARD= "Harvard University Press"} @String{pub-HARVARD:adr= "Cambridge, MA, USA"} @String{pub-INTERSCIENCE= "Interscience Publishers"} @String{pub-INTERSCIENCE:adr= "New York, NY, USA"} @String{pub-MACMILLAN= "Macmillan Publishing Company"} @String{pub-MACMILLAN:adr= "New York, NY, USA"} @String{pub-MATH-ASSOC-AMER= "Mathematical Association of America"} @String{pub-MATH-ASSOC-AMER:adr= "Washington, DC, USA"} @String{pub-MCGRAW-HILL= "Mc{\-}Graw-Hill"} @String{pub-MCGRAW-HILL:adr= "New York, NY, USA"} @String{pub-NBS= "U.S. National Bureau of Standards"} @String{pub-NBS:adr= "Gaithersburg, MD, USA"} @String{pub-NORTH-HOLLAND= "North-Holland Publishing Co."} @String{pub-NORTH-HOLLAND:adr= "Amsterdam, The Netherlands"} @String{pub-OLDENBOURG= "R. Oldenbourg"} @String{pub-OLDENBOURG:adr= "M{\"{u}}nchen, Germany"} @String{pub-OLIVER-BOYD= "Oliver and Boyd"} @String{pub-OLIVER-BOYD:adr= "Edinburgh, UK; London, UK"} @String{pub-OXFORD= "Oxford University Press"} @String{pub-OXFORD:adr= "Walton Street, Oxford OX2 6DP, UK"} @String{pub-PERGAMON= "Pergamon Press"} @String{pub-PERGAMON:adr= "New York, NY, USA"} @String{pub-PH= "Pren{\-}tice-Hall"} @String{pub-PH:adr= "Upper Saddle River, NJ 07458, USA"} @String{pub-PRINCETON= "Princeton University Press"} @String{pub-PRINCETON:adr= "Princeton, NJ, USA"} @String{pub-REIDEL= "D. Reidel"} @String{pub-REIDEL:adr= "Dordrecht, The Netherlands; Boston, MA, USA; Lancaster, UK; Tokyo, Japan"} @String{pub-SIAM= "SIAM Press"} @String{pub-SIAM:adr= "Philadelphia, PA, USA"} @String{pub-SV= "Springer-Verlag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-TEUBNER= "Teubner"} @String{pub-TEUBNER:adr= "Stuttgart, Germany; Leipzig, Germany"} @String{pub-U-MINNESOTA= "University of Minnesota Press"} @String{pub-U-MINNESOTA:adr= "Minneapolis, MN, USA"} @String{pub-U-TORONTO= "University of Toronto Press"} @String{pub-U-TORONTO:adr= "Toronto, ON, Canada"} @String{pub-USGPO= "United States Government Printing Office"} @String{pub-USGPO:adr= "Washington, DC, USA"} @String{pub-VAN-NOSTRAND-REINHOLD= "Van Nostrand Reinhold"} @String{pub-VAN-NOSTRAND-REINHOLD:adr= "New York, NY, USA"} @String{pub-WILEY= "Wiley"} @String{pub-WILEY:adr= "New York, NY, USA"} @String{pub-WORLD-SCI= "World Scientific Publishing Co."} @String{pub-WORLD-SCI:adr= "Singapore; Philadelphia, PA, USA; River Edge, NJ, USA"}

%%% ==================================================================== %%% Series abbreviations:

@String{ser-LECT-NOTES-MATH= "Lecture Notes in Mathematics"}

%%% ==================================================================== %%% Part 1: Publications by Garrett Birkhoff %%% %%% Bibliography entries, sorted by year, and then by citation label:

@Article{Birkhoff:1933:ADP, author = "Garrett Birkhoff", title = "Axiomatic definitions of perfectly separable metric spaces", journal = j-BULL-AMS, volume = "39", number = "8", pages = "601--607", month = aug, year = "1933", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1933-05693-8", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0007.36901", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "2", jfm = "59.1259.02", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", remark = "From the title footnote: ``Adapted from a Harvard Undergraduate Honors Thesis.'' This is Garrett Birkhoff's second published work.", ZBmath = "2547038, 3010639", } @Article{Birkhoff:1933:CS, author = "Garrett Birkhoff", title = "On the combination of subalgebras", journal = j-PROC-CAMBRIDGE-PHIL-SOC, volume = "29", number = "4", pages = "441--464", day = "30", month = oct, year = "1933", CODEN = "PCPSA4", DOI = "https://doi.org/10.1017/S0305004100011464", ISSN = "0008-1981", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0007.39502", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the Cambridge Philosophical Society", GB-number = "3", jfm = "59.0154.02", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP", keywords = "06-XX", ZBmath = "2542994, 3010765", } @Article{Birkhoff:1933:OGA, author = "Garrett Birkhoff", title = "The order of groups of automorphisms", journal = j-BULL-AMS, volume = "39", pages = "871--871", year = "1933", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "59.0167.10", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2543038", } @Article{Birkhoff:1933:TTG, author = "Garrett Birkhoff", title = "A theorem on transitive groups", journal = j-PROC-CAMBRIDGE-PHIL-SOC, volume = "29", number = "2", pages = "257--259", month = may, year = "1933", CODEN = "PCPSA4", DOI = "https://doi.org/10.1017/S0305004100011051", ISSN = "0008-1981", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0006.39202", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the Cambridge Philosophical Society", GB-number = "1", jfm = "59.0151.02", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP", received = "Received 15 May 1933. Read 30 October 1933.", remark = "This is Garrett Birkhoff's first published work, done while he was at Cambridge University working under Philip Hall.", ZBmath = "2542984, 3009053", } @Article{Birkhoff:1934:AAG, author = "Garrett Birkhoff", title = "On the automorphisms of {Abelian} groups", journal = j-BULL-AMS, volume = "40", pages = "390--391", year = "1934", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "60.0112.09", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2537344", } @Article{Birkhoff:1934:AGP, author = "Garrett Birkhoff", title = "On the automorphismus of groups of prime-order", journal = j-BULL-AMS, volume = "40", pages = "391--391", year = "1934", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1934-05856-7", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "60.0112.05", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2537340", } @Article{Birkhoff:1934:ALA, author = "Garrett Birkhoff", title = "Applications of lattice algebra", journal = j-PROC-CAMBRIDGE-PHIL-SOC, volume = "30", number = "2", pages = "115--122", day = "30", month = apr, year = "1934", CODEN = "PCPSA4", DOI = "https://doi.org/10.1017/S0305004100016522", ISSN = "0008-1981", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0009.05501", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the Cambridge Philosophical Society", GB-number = "4", jfm = "60.0092.03", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP", ZBmath = "2537285, 3012912", } @Article{Birkhoff:1934:CRF, author = "Garrett Birkhoff", title = "Combinatorial relations in finite projektive geometies", journal = j-BULL-AMS, volume = "40", pages = "209--209", year = "1934", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1934-05818-X", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "60.0496.04", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2538417", } @Article{Birkhoff:1934:HGa, author = "Garrett Birkhoff", title = "{Hausdorff} groupoids", journal = j-ANN-MATH-2, volume = "35", number = "2", pages = "351--360", month = apr, year = "1934", CODEN = "ANMAAH", DOI = "https://doi.org/10.2307/1968437", ISSN = "0003-486X (print), 1939-8980 (electronic)", ISSN-L = "0003-486X", MRclass = "99-04", MRnumber = "1503167", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0009.20301", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Annals of Mathematics. Second Series", journal-URL = "https://annals.math.princeton.edu/; https://www.jstor.org/journal/annamath", } @Article{Birkhoff:1934:HGb, author = "Garrett Birkhoff", title = "{Hausdorff} groupoids", journal = j-BULL-AMS, volume = "40", pages = "48--48", year = "1934", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "5", jfm = "60.0536.10", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2538530", } @Article{Birkhoff:1934:IARa, author = "Garrett Birkhoff", title = "Ideals in algebraic rings", journal = j-BULL-AMS, volume = "40", pages = "801--801", year = "1934", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "60.0935.07", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2540093", } @Article{Birkhoff:1934:IARb, author = "Garrett Birkhoff", title = "Ideals in algebraic rings", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "20", number = "11", pages = "571--573", day = "1", month = nov, year = "1934", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.20.11.571", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "www.ncbi.nlm.nih.gov/pmc/articles/PMC1076485", ZMnumber = "0010.19302", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the National Academy of Sciences of the United States of America", GB-number = "7", jfm = "60.0931.01", journal-URL = "http://www.pnas.org/content/by/year", ZBmath = "2540069; 3015156", } @Article{Birkhoff:1934:IFV, author = "G. Birkhoff", title = "Integration of functions with values in a {Banach} space", journal = j-BULL-AMS, volume = "40", pages = "664--664", year = "1934", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "60.0224.08", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2537694", } @Article{Birkhoff:1934:LEC, author = "Garrett Birkhoff", title = "Linear extensions of complex-valued linear functions in {Banach} space", journal = j-BULL-AMS, volume = "40", pages = "798--798", year = "1934", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "60.1086.05", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2540569", } @Article{Birkhoff:1934:LER, author = "Garrett Birkhoff", title = "Lattices of equivalence relations", journal = j-BULL-AMS, volume = "40", pages = "797--797", year = "1934", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "60.0916.08", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2539986", } @Article{Birkhoff:1934:LTI, author = "Garrett Birkhoff", title = "On the lattice theory of ideals", journal = j-BULL-AMS, volume = "40", number = "8", pages = "613--619", month = aug, year = "1934", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1934-05928-7", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0009.39402", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "6", jfm = "60.0093.01; 60.0113.10", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2537286, 2537354, 3014220", } @Article{Birkhoff:1934:MEL, author = "Garrett Birkhoff", title = "On monogenic extensions of linear functionals", journal = j-BULL-AMS, volume = "40", pages = "798--798", year = "1934", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "60.1086.06", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2540570", } @Article{Birkhoff:1934:NPC, author = "Garrett Birkhoff", title = "Note on the paper ``{On} the combination of subalgebras''", journal = j-PROC-CAMBRIDGE-PHIL-SOC, volume = "30", number = "2", pages = "200--200", day = "30", month = apr, year = "1934", CODEN = "PCPSA4", DOI = "https://doi.org/10.1017/S0305004100016625", ISSN = "0008-1981", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0009.04905", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the Cambridge Philosophical Society", GB-number = "3a", jfm = "60.0092.02", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP", remark = "The author reports a connection to previous work of Dedekind (Collected Works, 1931).", ZBmath = "2537284; 3012899", } @Article{Birkhoff:1934:OIP, author = "Garrett Birkhoff", title = "Operational identities on points sets", journal = j-BULL-AMS, volume = "40", pages = "800--801", year = "1934", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "60.1086.07", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2540571", } @Article{Birkhoff:1934:ONV, author = "Garrett Birkhoff", title = "Orthogonality in normed vector spaces", journal = j-BULL-AMS, volume = "40", pages = "798--799", year = "1934", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "60.0688.03", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2539003", } @Article{Birkhoff:1934:PSA, author = "Garrett Birkhoff", title = "Problems and Solutions: Advanced Problems: Problems for Solution: 3674", journal = j-AMER-MATH-MONTHLY, volume = "41", number = "4", pages = "269--270", month = apr, year = "1934", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:22 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "See also \cite{Birkhoff:1935:PSA,Dunkel:1935:PSAb,Escott:1935:PSA,Gaines:1935:PSS,Grossman:1935:PSAc,Jones:1935:PSAb}.", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", xxnote = "Check pages??", } @Article{Birkhoff:1934:SAG, author = "Garrett Birkhoff", title = "Subgroups of {Abelian} groups", journal = j-PROC-LONDON-MATH-SOC-2, volume = "38", pages = "385--401", year = "1934", CODEN = "PLMTAL", DOI = "https://doi.org/10.1112/plms/s2-38.1.385", ISSN = "0024-6115 (print), 1460-244x (electronic)", ISSN-L = "0024-6115", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0010.34304", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the London Mathematical Society. Second Series", GB-number = "10", jfm = "60.0893.03", journal-URL = "https://londmathsoc.onlinelibrary.wiley.com/journal/1460244x", ZBmath = "2539925, 3015767", } @Article{Birkhoff:1934:TEJ, author = "Garrett Birkhoff", title = "Transfinite extensions of the {Jordan--H{\"o}lder} theorem", journal = j-BULL-AMS, volume = "40", pages = "391--391", year = "1934", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1934-05856-7", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "60.0112.06", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2537341", } @Article{Birkhoff:1934:TSS, author = "Garrett Birkhoff", title = "Transfinite subgroup series", journal = j-BULL-AMS, volume = "40", number = "12", pages = "847--850", month = dec, year = "1934", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1934-05982-2", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0010.34303", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "9", jfm = "60.0892.02", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2539919; 3015766", } @Article{Birkhoff:1934:TTSa, author = "Garrett Birkhoff", title = "The topology of transformation-sets", journal = j-ANN-MATH-2, volume = "35", number = "4", pages = "861--875", month = oct, year = "1934", CODEN = "ANMAAH", DOI = "https://doi.org/10.2307/1968499", ISSN = "0003-486X (print), 1939-8980 (electronic)", ISSN-L = "0003-486X", MRclass = "54A20 99-04", MRnumber = "1503201", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0010.13304", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Annals of Mathematics. Second Series", GB-number = "8", jfm = "60.1088.01", journal-URL = "https://annals.math.princeton.edu/; https://www.jstor.org/journal/annamath", ZBmath = "3014922; 2540574", } @Article{Birkhoff:1934:TTSb, author = "Garrett Birkhoff", title = "The topology of transformation-sets", journal = j-BULL-AMS, volume = "40", pages = "48--48", year = "1934", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "60.0536.11", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2538531", } @Article{Birkhoff:1935:ACGa, author = "Garrett Birkhoff", title = "Abstract continuous groups. {I}: {Linear} spaces", journal = j-BULL-AMS, volume = "41", pages = "483--483", year = "1935", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1935-06131-2", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "61.0479.04", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2532509", } @Article{Birkhoff:1935:ACGb, author = "Garrett Birkhoff", title = "Abstract continuous groups", journal = j-BULL-AMS, volume = "41", pages = "189--189", year = "1935", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "61.0479.03", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2532508", } @Article{Birkhoff:1935:ALD, author = "Garrett Birkhoff", title = "Abstract linear dependence and lattices", journal = j-AM-J-MATH, volume = "57", pages = "800--804", year = "1935", CODEN = "AJMAAN", DOI = "https://doi.org/10.2307/2371015", ISSN = "0002-9327 (print), 1080-6377 (electronic)", ISSN-L = "0002-9327", MRclass = "05B35 06B05 15A03", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0013.00104", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "American Journal of Mathematics", GB-number = "16", jfm = "61.1027.01", journal-URL = "https://www.jstor.org/journal/amerjmath", ZBmath = "3019694; 2534482", } @Article{Birkhoff:1935:CMA, author = "Garrett Birkhoff", title = "The composition of modular algebras", journal = j-BULL-AMS, volume = "41", pages = "782--782", year = "1935", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1935-06194-4", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "61.1044.06", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2534544", } @Article{Birkhoff:1935:CRP, author = "Garrett Birkhoff", title = "Combinatorial relations in projective geometries", journal = j-ANN-MATH-2, volume = "36", number = "3", pages = "743--748", month = jul, year = "1935", CODEN = "ANMAAH", DOI = "https://doi.org/10.2307/1968656", ISSN = "0003-486X (print), 1939-8980 (electronic)", ISSN-L = "0003-486X", MRclass = "99-04", MRnumber = "1503250", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0012.08205", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Annals of Mathematics. Second Series", GB-number = "12", jfm = "61.0593.01", journal-URL = "https://annals.math.princeton.edu/; https://www.jstor.org/journal/annamath", ZBmath = "3018249; 2532914", } @Article{Birkhoff:1935:CT, author = "Garrett Birkhoff", title = "On the combination of topologies", journal = j-BULL-AMS, volume = "41", pages = "349--349", year = "1935", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "61.0641.21", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2533055", } @Article{Birkhoff:1935:ED, author = "Garrett Birkhoff", title = "Sur les espaces discrets", journal = j-C-R-ACAD-SCI-PARIS, volume = "201", pages = "19--20", year = "1935", ISSN = "0001-4036 (print), 2419-6304 (electronic)", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0012.22702", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Comptes Rendus Hebdomadaires des S{\'e}ances de l'Acad{\'e}mie des Sciences, Paris", GB-number = "13", jfm = "61.0629.02", journal-URL = "http://gallica.bnf.fr/ark:/12148/cb343481087/date", language = "French", ZBmath = "3018863; 2532990", } @Article{Birkhoff:1935:GMPa, author = "G. D. Birkhoff and M. R. Hestenes", title = "Generalized Minimax Principle in the Calculus of Variations", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "21", number = "2", pages = "96--99", day = "1", month = feb, year = "1935", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.21.2.96", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", bibdate = "Wed Oct 25 10:45:03 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Magnus Rudolf Hestenes (13 February 1906--31 May 1991)", fjournal = "Proceedings of the National Academy of Sciences of the United States of America", journal-URL = "http://www.pnas.org/content/by/year", } @Article{Birkhoff:1935:GMPb, author = "G. D. Birkhoff and M. R. Hestenes", title = "Generalized minimax principle in the calculus of variations", journal = j-DUKE-MATH-J, volume = "1", number = "4", pages = "413--432", month = dec, year = "1935", CODEN = "DUMJAO", DOI = "https://doi.org/10.1215/S0012-7094-35-00128-4", ISSN = "0012-7094 (print), 1547-7398 (electronic)", ISSN-L = "0012-7094", MRclass = "99-04", MRnumber = "1545886", bibdate = "Tue Oct 24 13:24:42 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Magnus Rudolf Hestenes (13 February 1906--31 May 1991)", fjournal = "Duke Mathematical Journal", journal-URL = "http://projecteuclid.org/info/euclid.dmj", } @Article{Birkhoff:1935:IFV, author = "Garrett Birkhoff", title = "Integration of functions with values in a {Banach} space", journal = j-TRANS-AM-MATH-SOC, volume = "38", number = "2", pages = "357--378", month = sep, year = "1935", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/1989687", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "28B05 (46G10)", MRnumber = "1501815", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0013.00803", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Transactions of the American Mathematical Society", GB-number = "14", jfm = "61.0234.01", journal-URL = "http://www.ams.org/journals/tran/", ZBmath = "3019718; 2531862", } @Article{Birkhoff:1935:LTI, author = "Garrett Birkhoff", title = "On the lattice theory of ideals. {II}", journal = j-BULL-AMS, volume = "41", pages = "37--37", year = "1935", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "61.0127.03", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2531535", } @Article{Birkhoff:1935:LTL, author = "Garrett Birkhoff", title = "On the lattice theory of linear dependence", journal = j-BULL-AMS, volume = "41", pages = "332--332", year = "1935", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "61.0997.10", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2534377", } @Article{Birkhoff:1935:NCI, author = "Garrett Birkhoff", title = "Non-commutative integration", journal = j-BULL-AMS, volume = "41", pages = "182--182", year = "1935", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1935-06073-2", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "61.0248.04", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2531906", } @Article{Birkhoff:1935:NDL, author = "Garrett Birkhoff", title = "A new definition of limit", journal = j-BULL-AMS, volume = "41", pages = "636--636", year = "1935", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "61.0641.20", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2533054", } @Article{Birkhoff:1935:NICa, author = "G. D. Birkhoff and M. R. Hestenes", title = "Natural Isoperimetric Conditions in the Calculus of Variations", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "21", number = "2", pages = "99--102", day = "1", month = feb, year = "1935", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.21.2.99", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", bibdate = "Wed Oct 25 10:45:03 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Magnus Rudolf Hestenes (13 February 1906--31 May 1991)", fjournal = "Proceedings of the National Academy of Sciences of the United States of America", journal-URL = "http://www.pnas.org/content/by/year", } @Article{Birkhoff:1935:NICb, author = "G. D. Birkhoff and M. R. Hestenes", title = "Natural Isoperimetric Conditions in the Calculus of Variations", journal = j-DUKE-MATH-J, volume = "1", number = "2", month = jun, year = "1935", CODEN = "DUMJAO", DOI = "https://doi.org/10.1215/s0012-7094-35-00118-1", ISSN = "0012-7094 (print), 1547-7398 (electronic)", ISSN-L = "0012-7094", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Magnus Rudolf Hestenes (13 February 1906--31 May 1991)", fjournal = "Duke Mathematical Journal", journal-URL = "http://projecteuclid.org/info/euclid.dmj", } @Article{Birkhoff:1935:OLM, author = "Garrett Birkhoff", title = "Orthogonality in linear metric spaces", journal = j-DUKE-MATH-J, volume = "1", number = "2", pages = "169--172", month = jun, year = "1935", CODEN = "DUMJAO", DOI = "https://doi.org/10.1215/S0012-7094-35-00115-6", ISSN = "0012-7094 (print), 1547-7398 (electronic)", ISSN-L = "0012-7094", MRclass = "99-04", MRnumber = "1545873", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0012.30604", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Duke Mathematical Journal", GB-number = "11", jfm = "61.0634.01", journal-URL = "http://projecteuclid.org/info/euclid.dmj", ZBmath = "3019176; 2533007", } @Article{Birkhoff:1935:PSA, author = "Garrett Birkhoff and E. D. Rainville and Morgan Ward", title = "Problems and Solutions: Advanced Problems: 3674", journal = j-AMER-MATH-MONTHLY, volume = "42", number = "8", pages = "518--521", month = oct, year = "1935", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:55 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "See also \cite{Escott:1934:PSA}.", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", } @Article{Birkhoff:1935:PSL, author = "Garrett Birkhoff", title = "Postulates systems for {Lie} groups", journal = j-BULL-AMS, volume = "41", pages = "329--329", year = "1935", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "61.0479.02", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2532507", } @Article{Birkhoff:1935:SAA, author = "Garrett Birkhoff", title = "On the structure of abstract algebras", journal = j-PROC-CAMBRIDGE-PHIL-SOC, volume = "31", number = "4", pages = "433--454", month = oct, year = "1935", CODEN = "PCPSA4", DOI = "https://doi.org/10.1017/S0305004100013463", ISSN = "0008-1981", MRclass = "08A05 08A02 08A35 06B05", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0013.00105", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the Cambridge Philosophical Society", GB-number = "15", jfm = "61.1026.07", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP", ZBmath = "3019695; 2534481", } @Article{Birkhoff:1936:CFG, author = "Garrett Birkhoff", title = "Continuous free groups", journal = j-BULL-AMS, volume = "42", pages = "340--340", year = "1936", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1936-06457-8", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "62.0447.04", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2526421", } @Article{Birkhoff:1936:CGL, author = "Garrett Birkhoff", title = "Continuous groups and linear spaces", journal = "Rec. Math. Moscou, n. Ser.", volume = "1", pages = "635--642", year = "1936", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0016.20401", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Recueil Math{\'e}matique. Nouvelle S{\'e}rie", GB-number = "26", jfm = "62.1231.03", xxjournal = "Mat. Sbornik, N.S.", ZBmath = "3025704; 2529312", } @Article{Birkhoff:1936:CT, author = "Garrett Birkhoff", title = "On the combination of topologies", journal = j-FUNDAM-MATH, volume = "26", pages = "156--166", year = "1936", DOI = "https://doi.org/10.4064/fm-26-1-156-166", ISSN = "0016-2736 (print), 1730-6329 (electronic)", ISSN-L = "0016-2736", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0013.36804; 0014.28002", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Fundamenta Mathematicae", GB-number = "18", jfm = "62.0688.05", journal-URL = "https://www.impan.pl/en/publishing-house/journals-and-series/fundamenta-mathematicae/all", ZBmath = "2527200; 3022559; 3021183", } @Article{Birkhoff:1936:EDL, author = "Garrett Birkhoff", title = "The enumeration of distributive lattices", journal = j-BULL-AMS, volume = "42", pages = "487--487", year = "1936", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1936-06457-8", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "62.0048.19", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2525194", } @Article{Birkhoff:1936:FCG, author = "Garrett Birkhoff", title = "Free continuous groups. {II}", journal = j-BULL-AMS, volume = "42", pages = "344--344", year = "1936", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1936-06457-8", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "62.0447.05", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2526422", } @InProceedings{Birkhoff:1936:IDE, author = "Garrett Birkhoff", booktitle = "C. R. Congr. internat. Math., Oslo 1936", title = "Integration of differential equations", volume = "2", publisher = "????", address = "????", pages = "50--51", year = "1936", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "17", jfm = "63.0436.03", ZBmath = "2521040", } @Article{Birkhoff:1936:LGI, author = "Garrett Birkhoff", title = "{Lie} groups isomorphic in the large with no linear groups", journal = j-BULL-AMS, volume = "42", pages = "344--344", year = "1936", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1936-06457-8", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "62.0447.07", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2526424", } @Article{Birkhoff:1936:LGS, author = "Garrett Birkhoff", title = "{Lie} groups simply isomorphic with no linear group", journal = j-BULL-AMS, volume = "42", number = "12", pages = "883--888", month = dec, year = "1936", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1936-06457-8", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", MRclass = "99-04", MRnumber = "1563459", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0016.01502", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "22", jfm = "62.0442.02; 62.0447.08", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2526402; 3024952; 2526425", } @Article{Birkhoff:1936:LQM, author = "Garrett Birkhoff and John von Neumann", title = "The logic of quantum mechanics", journal = j-ANN-MATH-2, volume = "37", number = "4", pages = "823--843", month = oct, year = "1936", CODEN = "ANMAAH", DOI = "https://doi.org/10.2307/1968621", ISSN = "0003-486X (print), 1939-8980 (electronic)", ISSN-L = "0003-486X", MRclass = "03G12 81P10 99-04", MRnumber = "1503312", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/logic.bib", note = "Reprinted in \cite[Paper 7]{Taub:1962:JNC}.", ZMnumber = "0015.14603", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Annals of Mathematics. Second Series", GB-number = "21", jfm = "62.1061.04", journal-URL = "https://annals.math.princeton.edu/; https://www.jstor.org/journal/annamath", ZBmath = "3023737; 2528684", } @Article{Birkhoff:1936:LRN, author = "Garrett Birkhoff", title = "Linear representability of nilpotent {Lie} algebras", journal = j-BULL-AMS, volume = "42", pages = "624--624", year = "1936", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1936-06457-8", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "62.0122.02", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2525440", } @Article{Birkhoff:1936:MSC, author = "Garrett Birkhoff", title = "Moore-{Smith} convergence in general topology", journal = j-BULL-AMS, volume = "42", pages = "44--44", year = "1936", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1936-06457-8", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "62.0695.17", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2527245", } @Article{Birkhoff:1936:NTGa, author = "Garrett Birkhoff", title = "A note on topological groups", journal = j-BULL-AMS, volume = "42", pages = "26--26", year = "1936", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1936-06457-8", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "62.0446.03", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2526416", } @Article{Birkhoff:1936:NTGb, author = "Garrett Birkhoff", title = "A note on topological groups", journal = j-COMPOS-MATH, volume = "3", pages = "427--430", year = "1936", CODEN = "CMPMAF", ISSN = "0010-437x (print), 1570-5846 (electronic)", ISSN-L = "0010-437X", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0015.00702", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Compositio Mathematica", GB-number = "20", jfm = "62.0434.03", ZBmath = "2526385; 3023204", } @Article{Birkhoff:1936:OGA, author = "Garrett Birkhoff and Philip Hall", title = "On the order of groups of automorphisms", journal = j-TRANS-AM-MATH-SOC, volume = "39", number = "3", pages = "496--499", month = may, year = "1936", CODEN = "TAMTAM", DOI = "https://doi.org/10.1090/S0002-9947-1936-1501860-9; https://doi.org/10.2307/1989764", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "20D45", MRnumber = "1501860", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0014.15002", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Transactions of the American Mathematical Society", GB-number = "19", jfm = "62.0082.01", journal-URL = "http://www.ams.org/journals/tran/", ZBmath = "3022066; 2525319", } @Article{Birkhoff:1936:POS, author = "Garrett Birkhoff", title = "Partially ordered sets and the inclusion relation", journal = j-BULL-AMS, volume = "42", pages = "43--44", year = "1936", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1936-06457-8", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", jfm = "62.0048.18", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "2525193", } @Article{Birkhoff:1937:EA, author = "Garrett Birkhoff", title = "An extended arithmetic", journal = j-DUKE-MATH-J, volume = "3", number = "2", pages = "311--316", month = jun, year = "1937", CODEN = "DUMJAO", DOI = "https://doi.org/10.1215/S0012-7094-37-00323-5", ISSN = "0012-7094 (print), 1547-7398 (electronic)", ISSN-L = "0012-7094", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0016.38702", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Duke Mathematical Journal", GB-number = "28", jfm = "63.0030.06", journal-URL = "http://projecteuclid.org/info/euclid.dmj", ZBmath = "3026424; 2519821", } @InProceedings{Birkhoff:1937:GC, author = "Garrett Birkhoff", booktitle = "C. R. Congr. internat. Math., Oslo 1936", title = "Generalized convergence", volume = "2", publisher = "????", address = "????", pages = "152--153", year = "1937", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "17", jfm = "63.0572.08", ZBmath = "2521516", } @Article{Birkhoff:1937:GGT, author = "Garrett Birkhoff", title = "{Galois} and Group Theory", journal = j-OSIRIS, volume = "3", number = "31", pages = "260--268", month = "????", year = "1937", CODEN = "OSIRAX", DOI = "https://doi.org/10.2307/301590", ISSN = "0369-7827 (print), 1933-8287 (electronic)", ISSN-L = "0369-7827", bibdate = "Mon Mar 30 15:08:56 MDT 2015", bibsource = "http://www.jstor.org/action/showPublication?journalCode=osiris; http://www.jstor.org/stable/i213314; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/i/infeld-leopold.bib; https://www.math.utah.edu/pub/tex/bib/osiris.bib", URL = "http://www.jstor.org/stable/301590", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Osiris", GB-number = "31", jfm = "63.0810.04", journal-URL = "http://www.jstor.org/page/journal/osiris/about.html", ZBmath = "2522446", } @Article{Birkhoff:1937:IO, author = "Garrett Birkhoff", title = "On the integration of operators", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "23", number = "1", pages = "11--13", day = "1", month = jan, year = "1937", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.23.1.11", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0016.06103", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the National Academy of Sciences of the United States of America", GB-number = "23", jfm = "63.0423.02", journal-URL = "http://www.pnas.org/content/by/year", ZBmath = "3025146; 2521011", } @Article{Birkhoff:1937:MC, author = "Garrett Birkhoff", title = "The meaning of completeness", journal = j-ANN-MATH-2, volume = "38", number = "1", pages = "57--60", month = jan, year = "1937", CODEN = "ANMAAH", DOI = "https://doi.org/10.2307/1968509", ISSN = "0003-486X (print), 1939-8980 (electronic)", ISSN-L = "0003-486X", MRclass = "99-04", MRnumber = "1503324", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0016.08503", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Annals of Mathematics. Second Series", GB-number = "25", jfm = "63.0568.01", journal-URL = "https://annals.math.princeton.edu/; https://www.jstor.org/journal/annamath", ZBmath = "3025226; 2521493", } @Article{Birkhoff:1937:MSC, author = "Garrett Birkhoff", title = "{Moore--Smith} convergence in general topology", journal = j-ANN-MATH-2, volume = "38", number = "1", pages = "39--56", month = jan, year = "1937", CODEN = "ANMAAH", DOI = "https://doi.org/10.2307/1968508", ISSN = "0003-486X (print), 1939-8980 (electronic)", ISSN-L = "0003-486X", MRclass = "99-04", MRnumber = "1503323", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0016.08502", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Annals of Mathematics. Second Series", GB-number = "24", jfm = "63.0567.06", journal-URL = "https://annals.math.princeton.edu/; https://www.jstor.org/journal/annamath", ZBmath = "3025225; 2521492", } @InProceedings{Birkhoff:1937:OIR, author = "Garrett Birkhoff", booktitle = "C. R. Congr. internat. Math., Oslo 1936", title = "Order and the inclusion relation", publisher = "????", address = "????", pages = "37--37", year = "1937", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "17", jfm = "63.0031.05", ZBmath = "2519826", } @Misc{Birkhoff:1937:OTA, author = "Garrett Birkhoff", title = "Offprints of two articles by {Garrett Birkhoff}", howpublished = "UK National Archives", year = "1937", bibdate = "Sat Nov 04 06:42:15 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Offprints of \cite{Birkhoff:1936:LGS} and \cite{Birkhoff:1937:RLA}.", URL = "https://discovery.nationalarchives.gov.uk/details/r/8e10cc1c-25fa-4793-a52c-583255326a3d", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Birkhoff:1937:PI, author = "Garrett Birkhoff", title = "On Product Integration", journal = j-J-MATH-PHYS-MIT, volume = "16", number = "1--4", pages = "104--132", month = apr, year = "1937", CODEN = "JMPHA9", DOI = "https://doi.org/10.1002/sapm1937161104", ISSN = "0097-1421", ISSN-L = "0097-1421", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib", URL = "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1937161104", ZMnumber = "0018.13402", acknowledgement = ack-nhfb, ajournal = "J. Math. Phys. (MIT)", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematics and Physics (MIT)", GB-number = "30", jfm = "63.1001.03", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590", onlinedate = "April 1937", ZBmath = "3028850; 2523201", } @Article{Birkhoff:1937:RLA, author = "Garrett Birkhoff", title = "Representability of {Lie} algebras and {Lie} groups by matrices", journal = j-ANN-MATH-2, volume = "38", number = "2", pages = "526--532", month = apr, year = "1937", CODEN = "ANMAAH", DOI = "https://doi.org/10.2307/1968569", ISSN = "0003-486X (print), 1939-8980 (electronic)", ISSN-L = "0003-486X", MRclass = "17B35 16S30 17B30 99-04", MRnumber = "1503351", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0016.24402", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Annals of Mathematics. Second Series", GB-number = "27", jfm = "63.0090.01", journal-URL = "https://annals.math.princeton.edu/; https://www.jstor.org/journal/annamath", ZBmath = "3025861; 2520028", } @Article{Birkhoff:1937:RS, author = "Garrett Birkhoff", title = "Rings of sets", journal = j-DUKE-MATH-J, volume = "3", number = "3", pages = "443--454", month = sep, year = "1937", CODEN = "DUMJAO", DOI = "https://doi.org/10.1215/S0012-7094-37-00334-X", ISSN = "0012-7094 (print), 1547-7398 (electronic)", ISSN-L = "0012-7094", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0017.19403", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Duke Mathematical Journal", GB-number = "29", jfm = "63.0832.02", journal-URL = "http://projecteuclid.org/info/euclid.dmj", ZBmath = "3027429; 2522565", } @Article{Birkhoff:1938:AG, author = "Garrett Birkhoff", title = "Analytical groups", journal = j-TRANS-AM-MATH-SOC, volume = "43", number = "1", pages = "61--101", month = jan, year = "1938", CODEN = "TAMTAM", DOI = "https://doi.org/10.1090/S0002-9947-1938-1501934-4; https://doi.org/10.2307/1989902", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "22E15 (22A05 54H11)", MRnumber = "1501934", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0018.20502", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Transactions of the American Mathematical Society", GB-number = "32", jfm = "64.1092.02", journal-URL = "http://www.ams.org/journals/tran/", ZBmath = "3029132; 2518297", } @Article{Birkhoff:1938:DPS, author = "Garrett Birkhoff", title = "Dependent probabilities and spaces {L}", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "24", number = "3", pages = "154--159", day = "1", month = mar, year = "1938", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.24.3.154", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0018.26402", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the National Academy of Sciences of the United States of America", GB-number = "33", jfm = "64.0535.01", journal-URL = "http://www.pnas.org/content/by/year", ZBmath = "3029376; 2516169", } @Article{Birkhoff:1938:LTA, author = "Garrett Birkhoff", title = "Lattices and their applications", journal = j-BULL-AMS, volume = "44", number = "12", pages = "793--800", year = "1938", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1938-06866-8", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", MRclass = "06-02 99-04", MRnumber = "1563879", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0020.00101", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "34", jfm = "64.0071.03", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "3031678; 2514832", } @Article{Alaoglu:1939:GET, author = "L. Alaoglu and G. Birkhoff", title = "General ergodic theorems", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "25", number = "12", pages = "628--630", day = "1", month = dec, year = "1939", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.25.12.628", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", MRclass = "46.3X", MRnumber = "908", MRreviewer = "N. Dunford", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0022.36103", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the National Academy of Sciences of the United States of America", GB-number = "38", jfm = "65.1323.01", journal-URL = "http://www.pnas.org/content/by/year", ZBmath = "3036582; 2513752", } @Article{Birkhoff:1939:CBA, author = "Garrett Birkhoff and Morgan Ward", title = "A characterization of {Boolean} algebras", journal = j-ANN-MATH-2, volume = "40", number = "3", pages = "609--610", month = jul, year = "1939", CODEN = "ANMAAH", DOI = "https://doi.org/10.2307/1968945", ISSN = "0003-486X (print), 1939-8980 (electronic)", ISSN-L = "0003-486X", MRclass = "09.1X", MRnumber = "9", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0021.21301", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Annals of Mathematics. Second Series", GB-number = "36", jfm = "65.0086.05", journal-URL = "https://annals.math.princeton.edu/; https://www.jstor.org/journal/annamath", ZBmath = "3034310; 2509883", } @Article{Birkhoff:1939:ETG, author = "Garrett Birkhoff", title = "An ergodic theorem for general semi-groups", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "25", number = "12", pages = "625--627", day = "1", month = dec, year = "1939", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.25.12.625", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", MRclass = "46.3X", MRnumber = "907", MRreviewer = "N. Dunford", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0022.36102", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the National Academy of Sciences of the United States of America", GB-number = "37", jfm = "65.1323.02", journal-URL = "http://www.pnas.org/content/by/year", ZBmath = "3036581; 2513753", } @Article{Birkhoff:1939:MET, author = "Garrett Birkhoff", title = "The mean ergodic theorem", journal = j-DUKE-MATH-J, volume = "5", number = "1", pages = "19--20", month = mar, year = "1939", CODEN = "DUMJAO", DOI = "https://doi.org/10.1215/S0012-7094-39-00502-8", ISSN = "0012-7094 (print), 1547-7398 (electronic)", ISSN-L = "0012-7094", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0021.23601", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Duke Mathematical Journal", GB-number = "35", jfm = "65.0516.01", journal-URL = "http://projecteuclid.org/info/euclid.dmj", ZBmath = "3034383; 2511063", } @Article{Alaoglu:1940:GET, author = "L. Alaoglu and G. Birkhoff", title = "General ergodic theorems", journal = j-ANN-MATH-2, volume = "41", number = "2", pages = "293--309", month = apr, year = "1940", CODEN = "ANMAAH", DOI = "https://doi.org/10.2307/1969004", ISSN = "0003-486x (print), 1939-8980 (electronic)", ISSN-L = "0003-486X", MRclass = "46.3X", MRnumber = "2026", MRreviewer = "N. Dunford", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0024.12402", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Annals of Mathematics. Second Series", GB-number = "39", jfm = "66.0559.02", journal-URL = "https://annals.math.princeton.edu/; https://www.jstor.org/journal/annamath", ZBmath = "3038709; 2506868", } @Book{Birkhoff:1940:LT, author = "Garrett Birkhoff", title = "Lattice Theory", volume = "25", publisher = pub-AMS, address = pub-AMS:adr, pages = "v + 155", year = "1940", MRclass = "06-02 09.1X", MRnumber = "1959", MRreviewer = "O. Frink", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "American Mathematical Society Publications", ZMnumber = "0063.00402", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", jfm = "66.0100.04", ZBmath = "2505658; 3103212", } @Article{Birkhoff:1940:NEG, author = "Garrett Birkhoff", title = "Neutral elements in general lattices", journal = j-BULL-AMS, volume = "46", pages = "702--705", year = "1940", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1940-07285-4", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", MRclass = "09.1X", MRnumber = "2846", MRreviewer = "O. Frink", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0024.09903", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "40", jfm = "66.0101.01", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "3038638; 2505659", } @Article{Birkhoff:1941:MFG, author = "Garrett Birkhoff", title = "Metric foundations of geometry", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "27", number = "8", pages = "402--406", day = "15", month = aug, year = "1941", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.27.8.402", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", MRclass = "48.0X", MRnumber = "4472", MRreviewer = "H. Busemann", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0060.32705", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the National Academy of Sciences of the United States of America", GB-number = "41", journal-URL = "http://www.pnas.org/content/by/year", ZBmath = "3097925", } @Book{Birkhoff:1941:SMA, author = "Garrett Birkhoff and Saunders {Mac Lane}", title = "A Survey of Modern Algebra", publisher = pub-MACMILLAN, address = pub-MACMILLAN:adr, pages = "xi + 450", year = "1941", MRclass = "00A05 12-01 13-01 06-01 20-01 09.1X", MRnumber = "5093", MRreviewer = "N. Jacobson", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0061.04802", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", ZBmath = "3099537", } @Article{Birkhoff:1942:GA, author = "Garrett Birkhoff", title = "Generalized arithmetic", journal = j-DUKE-MATH-J, volume = "9", number = "2", pages = "283--302", month = jun, year = "1942", CODEN = "DUMJAO", DOI = "https://doi.org/10.1215/S0012-7094-42-00921-9", ISSN = "0012-7094 (print), 1547-7398 (electronic)", ISSN-L = "0012-7094", MRclass = "27.2X", MRnumber = "7031", MRreviewer = "N. Dunford", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "http://projecteuclid.org/euclid.dmj/1077493225", ZMnumber = "0060.12609", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Duke Mathematical Journal", GB-number = "43", journal-URL = "http://projecteuclid.org/info/euclid.dmj", xxpages = "284--302", ZBmath = "3096323", } @Article{Birkhoff:1942:LOG, author = "Garrett Birkhoff", title = "Lattice-ordered groups", journal = j-ANN-MATH-2, volume = "43", number = "2", pages = "298--331", month = apr, year = "1942", CODEN = "ANMAAH", DOI = "https://doi.org/10.2307/1968871", ISSN = "0003-486x (print), 1939-8980 (electronic)", ISSN-L = "0003-486X", MRclass = "20.0X", MRnumber = "6550", MRreviewer = "H. Wallman", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0060.05808", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Annals of Mathematics. Second Series", GB-number = "42", journal-URL = "https://annals.math.princeton.edu/; https://www.jstor.org/journal/annamath", received = "10 December 1941", ZBmath = "3095752", } @Article{Birkhoff:1943:RGO, author = "Garrett Birkhoff", title = "The radical of a group with operators", journal = j-BULL-AMS, volume = "49", pages = "751--753", year = "1943", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1943-08022-6", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", MRclass = "09.1X 20D45", MRnumber = "9021", MRreviewer = "N. Jacobson", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0061.02902", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "45", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "3099400", } @Article{Birkhoff:1943:WL, author = "Garrett Birkhoff", title = "What is a Lattice?", journal = j-AMER-MATH-MONTHLY, volume = "50", number = "8", pages = "484--487", month = oct, year = "1943", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2304186", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "09.1X", MRnumber = "8597", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0060.05806", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "American Mathematical Monthly", GB-number = "44", journal-URL = "http://www.jstor.org/journals/00029890.html", ZBmath = "3095750", } @Article{Birkhoff:1944:MFG, author = "Garrett Birkhoff", title = "Metric foundations of geometry. {I}", journal = j-TRANS-AM-MATH-SOC, volume = "55", number = "3", pages = "465--492", month = may, year = "1944", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/1990304", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "48.0X", MRnumber = "10393", MRreviewer = "L. M. Blumenthal", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0060.32706", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Transactions of the American Mathematical Society", GB-number = "46", journal-URL = "http://www.ams.org/journals/tran/", ZBmath = "3097926", } @Article{Birkhoff:1944:SUU, author = "Garrett Birkhoff", title = "Subdirect unions in universal algebra", journal = j-BULL-AMS, volume = "50", pages = "764--768", year = "1944", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1944-08235-9", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", MRclass = "09.1X", MRnumber = "10542", MRreviewer = "N. H. McCoy", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0060.05809", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "47", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "3095753", } @InCollection{Birkhoff:1945:LOL, author = "Garrett Birkhoff", booktitle = "{Festschrift zum 60. Geburtstag von Prof. Dr. Andreas Speiser}", title = "Lattice-ordered {Lie} groups", publisher = "Orell F{\"u}ssli", address = "Z{\"u}rich, Switzerland", pages = "209--217", year = "1945", MRclass = "06F25 22E99 17B60 20.0X", MRnumber = "15116", MRreviewer = "P. A. Smith", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0061.04703", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "48", ZBmath = "3099531", } @Article{Birkhoff:1946:DBL, author = "Garrett Birkhoff", title = "{Drei Bemerkungen zur linearen Algebra}. ({German}) [{Three} remarks on linear algebra]", journal = "Rev., Ser. A, Univ. Nac. Tucum{\'a}n", volume = "5", pages = "147--151", year = "1946", ISSN = "0080-2360", ISSN-L = "0080-2360", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0060.07906", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Universidad Nacional de Tucum{\'a}n. Facultad de Ciencias Exactas y Tecnolog{\'\i}a. Revista. Serie A. Matem{\'a}tica y F{\'\i}sica Te{\'o}rica", fjournal-2 = "Revista. Serie A. Matematica y Fisica Teorica", language = "German", ZBmath = "3095897", } @Article{Birkhoff:1946:DPS, author = "George D. Birkhoff and Garrett Birkhoff", title = "Distributive postulates for systems like {Boolean} algebras", journal = j-TRANS-AM-MATH-SOC, volume = "60", number = "1", pages = "3--11", month = jul, year = "1946", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/1990239", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "09.1X", MRnumber = "17735", MRreviewer = "A. L. Foster", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0060.05810", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Transactions of the American Mathematical Society", GB-number = "51", journal-URL = "http://www.ams.org/journals/tran/", ZBmath = "3095754", } @Article{Birkhoff:1946:FVG, author = "Garrett Birkhoff", title = "Formulacion de una conjetura de {G. D. Birkhoff} mediante una ecuacion integral", journal = "Bolet{\'\i}n de la Sociedad Matem{\'a}tica Mexicana", volume = "3", pages = "57--60", year = "1946", MRclass = "53.0X", MRnumber = "22379", MRreviewer = "Gustav A. Hedlund", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0063.00404", acknowledgement = ack-nhfb, ajournal = "Bol. Soc. Mat. Mexicana", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bolet{\'\i}n de la Sociedad Matem{\'a}tica Mexicana", GB-number = "55", xxtitle = "{Formulierung einer Vermutung von G. D. Birkhoff mit Hilfe einer Integralgleichung}. ({German}) [{Formulation} of a conjecture of {George D. Birkhoff} by means of an integral equation]", ZBmath = "3103214", } @Article{Birkhoff:1946:GAG, author = "Garrett Birkhoff", title = "Sobre los grupos de automorfismos", journal = "Revista de la Uni{\'o}n Matem{\'a}tica Argentina", volume = "11", pages = "155--157", year = "1946", ISSN = "0041-6932 (print), 1669-9637 (electronic)", ISSN-L = "0041-6932", MRclass = "20.0X", MRnumber = "15387", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0063.00403", acknowledgement = ack-nhfb, ajournal = "Rev. Un. Mat. Argentina", ajournal-2 = "Rev. Uni{\'o}n Mat. Argent.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Revista de la Uni{\'o}n Matem{\'a}tica Argentina", GB-number = "52", language = "Spanish", xxlanguage = "German", xxtitle = "{{\"U}ber Gruppen von Automorphismen}. ({German}) [On groups of automorphisms]", ZBmath = "3103213", } @Article{Birkhoff:1946:RTD, author = "Garrett Birkhoff", title = "Reversibility and two-dimensional airfoil theory", journal = j-AM-J-MATH, volume = "68", pages = "247--256", year = "1946", CODEN = "AJMAAN", DOI = "https://doi.org/10.2307/2371836", ISSN = "0002-9327 (print), 1080-6377 (electronic)", ISSN-L = "0002-9327", MRclass = "76.1X", MRnumber = "17084", MRreviewer = "L. M. Milne-Thomson", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0061.44801", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "American Journal of Mathematics", GB-number = "50", journal-URL = "https://www.jstor.org/journal/amerjmath", ZBmath = "3102587", } @Article{Birkhoff:1946:TOA, author = "Garrett Birkhoff", title = "Tres observaciones sobre el algebra lineal. ({Spanish}) [{Three} observations on linear algebra]", journal = "Univ. Nac. Tucum{\'a}n. Revista A.", volume = "5", pages = "147--151", year = "1946", MRclass = "09.1X", MRnumber = "20547", MRreviewer = "J. L. Dorroh", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "See also \cite{Alvis:2001:BTP}.", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Universidad Nacional de Tucum{\'a}n. Facultad de Ciencias Exactas y Tecnolog{\'\i}a. Revista. Serie A. Matem{\'a}tica y F{\'\i}sica Te{\'o}rica", fjournal-2 = "Univ. Nac. Tucum{\'a}n. Revista A.", GB-number = "53", xxpages = "145--151", xxtitle = "Tres notas sobre el algebra lineal", } @InProceedings{Birkhoff:1946:UA, author = "Garrett Birkhoff", booktitle = "{Proceedings of the First Canadian Mathematics Congress, Montreal, 1945}", title = "Universal algebra", publisher = pub-U-TORONTO, address = pub-U-TORONTO:adr, pages = "310--326", year = "1946", MRclass = "09.1X", MRnumber = "19586", MRreviewer = "N. H. McCoy", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0060.06802", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "49", ZBmath = "3095825", } @Article{Birkhoff:1946:WL, author = "Garrett Birkhoff", title = "What is a lattice?", journal = "Gazeta de Matem{\'a}tica (Lisboa)", volume = "7", number = "27", pages = "1--3", year = "1946", ISSN = "0373-2681", MRclass = "09.1X", MRnumber = "15039", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0060.05807", acknowledgement = ack-nhfb, ajournal = "Gaz. Mat. (Lisbon)", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Gazeta de Matem{\'a}tica (Lisboa)", xxlanguage = "German", xxtitle = "{Was ist ein Verband}? ({German}) [{What} is a lattice?]", ZBmath = "3095751", } @Article{Birkhoff:1947:TOD, author = "Garrett Birkhoff and S. A. Kiss", title = "A ternary operation in distributive lattices", journal = j-BULL-AMS, volume = "53", pages = "749--752", year = "1947", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1947-08864-9", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", MRclass = "09.1X", MRnumber = "21540", MRreviewer = "J. Kuntzmann", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0031.25002", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "54", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "3048697", } @Article{Birkhoff:1948:ELC, author = "Garrett Birkhoff and Duncan P. MacDougall and Emerson Pugh and {Sir} Geoffrey Taylor", title = "Explosives with Lined Cavities", journal = j-J-APPL-PHYS, volume = "19", number = "6", pages = "563--582", month = jun, year = "1948", CODEN = "JAPIAU", DOI = "https://doi.org/10.1063/1.1698173", ISSN = "0021-8979 (print), 1089-7550 (electronic), 1520-8850", ISSN-L = "0021-8979", bibdate = "Wed Nov 01 06:26:57 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://pubs.aip.org/aip/jap/article-pdf/19/6/563/7916271/563_1_online.pdf", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Applied Physics", GB-number = "56", journal-URL = "http://aip.scitation.org/toc/jap/current", received = "16 January 1948", remark = "From the first paragraph: ``For over a century mining engineers have known that some of the force of an explosive charge could be concentrated on a small area by hollowing out the charge opposite to the area (``hollow charge principle''). The earliest known reference to this is 1792; a popular account appeared in von Nostrand's Magazine in 1884. The effect became known as the Munroe effect in England and the United States, and as the Neumann effect in Germany, in honor of later workers (1885, 1911).''", xxnote = "Check author order", } @InProceedings{Birkhoff:1948:HP, author = "Garrett Birkhoff", editor = "Evert Willem Beth and Hendrik Josephus Pos and J. H. A. Hollak", booktitle = "Library of the Tenth International Congress on Philosophy ({Amsterdam, 11--18 August, 1948})", title = "Hydrodynamical Paradoxes", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "349--350", year = "1948", LCCN = "B20 .I6 1948x", bibdate = "Wed Nov 01 06:33:08 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Two volumes.", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "62", } @Book{Birkhoff:1948:LT, author = "Garrett Birkhoff", title = "Lattice Theory", volume = "25", publisher = pub-AMS, address = pub-AMS:adr, edition = "Revised", pages = "xiii + 283", year = "1948", ISSN = "0065-9258", MRclass = "06-02 09.1X", MRnumber = "29876", MRreviewer = "O. Frink", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "American Mathematical Society Colloquium Publications", ZMnumber = "0033.10103", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fseries = "Colloquium Publications. American Mathematical Society", ZBmath = "3050845", } @Article{Birkhoff:1948:MEI, author = "Garrett Birkhoff", title = "Mathematics for Engineers -- {III}: Dimensional Analysis of Partial Differential Equations", journal = j-ELECTR-ENG, volume = "67", number = "12", pages = "1185--1188", month = dec, year = "1948", CODEN = "ELENAC", DOI = "https://doi.org/10.1109/EE.1948.6444503", ISSN = "0095-9197 (print), 2376-7804 (electronic)", ISSN-L = "0095-9197", bibdate = "Wed Nov 01 06:30:08 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Electrical Engineering (American Institute of Electrical Engineers)", GB-number = "59", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714", xxtitle = "Dimensional Analysis of Partial Differential Equations", } @InProceedings{Birkhoff:1948:RDF, author = "Garrett Birkhoff", booktitle = "{Proceedings of the Seventh International Congress on Applied Mechanics, London}", title = "Recent developments in free boundary theory", volume = "2", publisher = "????", address = "????", pages = "7--16", year = "1948", MRclass = "76.1X", MRnumber = "34156", MRreviewer = "E. Pinney", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "64", } @Article{Birkhoff:1948:RLS, author = "Garrett Birkhoff and Orrin {Frink, Jr.}", title = "Representations of lattices by sets", journal = j-TRANS-AM-MATH-SOC, volume = "64", number = "2", pages = "299--316", month = sep, year = "1948", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/1990504", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "06-XX 09.1X", MRnumber = "27263", MRreviewer = "O. Bor\ocirc{u}vka", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0032.00504", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Transactions of the American Mathematical Society", GB-number = "58", journal-URL = "http://www.ams.org/journals/tran/", ZBmath = "3049232", } @Article{Birkhoff:1948:RSD, author = "Garrett Birkhoff", title = "Remarks on streamlines of discontinuity", journal = "Revista de Ciencias, Lima", volume = "50", pages = "105--116", year = "1948", ISSN = "0034-7760", MRclass = "76.1X", MRnumber = "29614", MRreviewer = "L. M. Milne-Thomson", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0031.32703", acknowledgement = ack-nhfb, ajournal = "Rev. Ci. (Lima)", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Revista de Ciencias, Lima", GB-number = "57", xxpages = "105--130", ZBmath = "3048933", } @Article{Birkhoff:1949:FFP, author = "Garrett Birkhoff and Thomas E. Caywood", title = "Fluid Flow Patterns", journal = j-J-APPL-PHYS, volume = "20", number = "7", pages = "646--659", month = jul, year = "1949", CODEN = "JAPIAU", DOI = "https://doi.org/10.1063/1.1698450", ISSN = "0021-8979 (print), 1089-7550 (electronic), 1520-8850", ISSN-L = "0021-8979", bibdate = "Wed Nov 01 06:35:30 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://pubs.aip.org/aip/jap/article-pdf/20/7/646/7916862/646_1_online.pdf", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Applied Physics", GB-number = "63", journal-URL = "http://aip.scitation.org/toc/jap/current", } @Article{Birkhoff:1949:GR, author = "Garrett Birkhoff", title = "Groupes R{\'e}ticul{\'e}s", journal = j-ANN-INST-HENRI-POINCARE, volume = "11", pages = "241--250", year = "1949", CODEN = "AIHPA2", ISSN = "0365-320x (print), 2400-4855 (electronic)", MRclass = "06-XX 20.0X 09.1X", MRnumber = "34770", MRreviewer = "P. M. Whitman", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "http://www.numdam.org/item?id=AIHP_1949__11_5_241_0", ZMnumber = "0034.01902", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Annales de l'Institut Henri Poincar{\'e}", GB-number = "65", language = "French", ZBmath = "3051984", } @Article{Birkhoff:1949:NNF, author = "Garrett Birkhoff and Lindley Burton", title = "Note on {Newtonian} force-fields", journal = j-CAN-J-MATH, volume = "1", number = "??", pages = "199--208", month = "????", year = "1949", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/cjm-1949-019-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "31.0X 31-XX", MRnumber = "0029018 (10,534e)", MRreviewer = "M. Brelot", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "http://cms.math.ca/cjm/v1/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/canjmath.bib; https://www.math.utah.edu/pub/tex/bib/canjmath1940.bib; MathSciNet database", URL = "www.smc.math.ca/cjm/v1/p199", ZMnumber = "0031.40404", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", GB-number = "61", journal-URL = "http://cms.math.ca/cjm/", ZBmath = "3049146", } @InProceedings{Birkhoff:1949:RDF, author = "Garrett Birkhoff", booktitle = "Nonlinear Problems in Mechanics of Continua {(Proceedings of the Symposia on Applied Mathematics, Brown University 2--4 August 1947, Vol. I)}", title = "Recent developments in free boundary theory", publisher = pub-AMS, address = pub-AMS:adr, pages = "47--47", year = "1949", MRclass = "76.1X", MRnumber = "34157", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0033.13901", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3050966", } @Article{Birkhoff:1949:RJL, author = "Garrett Birkhoff and Philip M. Whitman", title = "Representation of {Jordan} and {Lie} algebras", journal = j-TRANS-AM-MATH-SOC, volume = "65", number = "1", pages = "116--136", month = jan, year = "1949", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/1990517", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "09.1X", MRnumber = "29366", MRreviewer = "C. Chevalley", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0032.25102", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Transactions of the American Mathematical Society", GB-number = "60", journal-URL = "http://www.ams.org/journals/tran/", xxauthor = "Garrett Birkhoff and Phillip M. Whitman", ZBmath = "3049965", } @Article{Birkhoff:1949:TAT, author = "Garrett Birkhoff", title = "Th{\'e}orie et applications des treillis", journal = j-ANN-INST-HENRI-POINCARE, volume = "11", pages = "227--240", year = "1949", CODEN = "AIHPA2", ISSN = "0365-320x (print), 2400-4855 (electronic)", MRclass = "06-XX 20.0X 09.1X", MRnumber = "34751", MRreviewer = "P. M. Whitman", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "http://www.numdam.org/item?id=AIHP_1949__11_5_227_0", ZMnumber = "0034.01901", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Annales de l'Institut Henri Poincar{\'e}", GB-number = "65", language = "French", ZBmath = "3051983", } @Article{Birkhoff:1950:ELG, author = "Garrett Birkhoff", title = "Extensions of {Lie} groups", journal = j-MATH-Z, volume = "53", pages = "226--235", year = "1950", CODEN = "MAZEAX", DOI = "https://doi.org/10.1007/BF01175658", ISSN = "0025-5874 (print), 1432-1823 (electronic)", ISSN-L = "0025-5874", MRclass = "20.0X", MRnumber = "49200", MRreviewer = "S. Chern", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0039.02003", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Mathematische Zeitschrift", GB-number = "67", journal-URL = "http://link.springer.com/journal/209", ZBmath = "3058902", } @Book{Birkhoff:1950:HSL, author = "Garrett Birkhoff", title = "Hydrodynamics. {A} Study in Logic, Fact, and Similitude", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "xiii + 186", year = "1950", MRclass = "76.1X", MRnumber = "38180", MRreviewer = "J. Kravtchenko and R. Gerber", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0041.53903", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3063774", } @InCollection{Birkhoff:1950:MFB, author = "Garrett Birkhoff", booktitle = "Alg{\`e}bre et Th{\'e}orie des Nombres. ({French}) [{Algebra} and number theory]", title = "Moyennes des fonctions born{\'e}es. ({French}) [{Means} of bounded functions]", number = "24", publisher = "CNRS", address = "Paris, France", pages = "143--153", year = "1950", MRclass = "46.3X", MRnumber = "44044", MRreviewer = "I. Halperin", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Colloq. Internat. CNRS", ZMnumber = "0041.44306; 0045.38103", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "68", language = "French", ZBmath = "3070705; 3063334", } @Article{Birkhoff:1950:NQA, author = "Garrett Birkhoff and David M. Young", title = "Numerical Quadrature of Analytic and Harmonic Functions", journal = j-J-MATH-PHYS-MIT, volume = "29", number = "1--4", pages = "217--221", month = apr, year = "1950", CODEN = "JMPHA9", DOI = "https://doi.org/10.1002/sapm1950291217", ISSN = "0097-1421", ISSN-L = "0097-1421", MRclass = "65D32 30E20 41A55 31A05 65.0X", MRnumber = "38728", MRreviewer = "J. Kuntzmann", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib", URL = "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1950291217", ZMnumber = "0039.34202", acknowledgement = ack-nhfb, ajournal = "J. Math. Phys. (MIT)", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematics and Physics (MIT)", GB-number = "69", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590", onlinedate = "April 1950", ZBmath = "3059869", } @Article{Birkhoff:1950:WEC, author = "Garrett Birkhoff and Milton Plesset and N. Simmons", title = "Wall effects in cavity flow. {I}", journal = j-QUART-APPL-MATH, volume = "8", number = "2", pages = "151--168", month = jul, year = "1950", CODEN = "QAMAAY", DOI = "https://doi.org/10.1090/qam/37671", ISSN = "0033-569X (print), 1552-4485 (electronic)", ISSN-L = "0033-569X", MRclass = "76.1X", MRnumber = "37671", MRreviewer = "D. Gilbarg", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0038.12205", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Quarterly of Applied Mathematics", GB-number = "66", journal-URL = "http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam", ZBmath = "3057765", } @Article{Birkhoff:1951:ECT, author = "G. Birkhoff and D. M. Young and E. H. Zarantonello", title = "Effective conformal transformation of smooth, simply connected domains", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "37", number = "7", pages = "411--414", day = "1", month = jul, year = "1951", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.37.7.411", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", MRclass = "65.0X", MRnumber = "43582", MRreviewer = "Charles Saltzer", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib", URL = "www.ncbi.nlm.nih.gov/pmc/articles/PMC1063389", ZMnumber = "0043.12502", acknowledgement = ack-nhfb, author-dates = "David M. Young, Jr. (October 20, 1923--December 21, 2008); Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the National Academy of Sciences of the United States of America", GB-number = "70", journal-URL = "http://www.pnas.org/content/by/year", ZBmath = "3066192", } @InCollection{Birkhoff:1952:FAW, author = "Garrett Birkhoff and Jack Kotik", editor = "G. Keulegan", booktitle = "Gravity Waves", title = "{Fourier} analysis of wave trains", volume = "Circular 521", publisher = pub-USGPO, address = pub-USGPO:adr, pages = "221--234", year = "1952", MRclass = "76.1X", MRnumber = "55864", MRreviewer = "J. Kamp{\'e} de F{\'e}riet", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "National Bureau of Standards", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "77", } @Article{Birkhoff:1952:IMF, author = "Garrett Birkhoff", title = "Induced mass with free boundaries", journal = j-QUART-APPL-MATH, volume = "10", number = "1", pages = "81--86", month = apr, year = "1952", CODEN = "QAMAAY", DOI = "https://doi.org/10.1090/qam/47441", ISSN = "0033-569X (print), 1552-4485 (electronic)", ISSN-L = "0033-569X", MRclass = "76.1X", MRnumber = "47441", MRreviewer = "D. Gilbarg", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://www.ams.org/journals/qam/1952-10-01/S0033-569X-1952-47441-0/S0033-569X-1952-47441-0.pdf", ZMnumber = "0047.18307", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Quarterly of Applied Mathematics", GB-number = "73", journal-URL = "http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam", received = "16 July 1951", remark = "TO DO: Wall effects I is \cite{Birkhoff:1950:WEC}. Where is II from??", xx-GB-number = "72", xxauthor = "Garrett Birkhoff and Milton Plesset and N. Simmons", xxnote = "Check: differs from volume/number/pages in GB bibliography.", xxtitle = "Wall effects in cavity flow. {II}", ZBmath = "3073718", } @Article{Birkhoff:1952:NTV, author = "Garrett Birkhoff", title = "A new theory of vortex streets", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "38", number = "5", pages = "409--410", day = "1", month = may, year = "1952", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.38.5.409", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", MRclass = "76.1X", MRnumber = "48986", MRreviewer = "M. J. Lighthill", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0046.18510", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the National Academy of Sciences of the United States of America", GB-number = "75", journal-URL = "http://www.pnas.org/content/by/year", ZBmath = "3071698", } @InProceedings{Birkhoff:1952:SPL, author = "Garrett Birkhoff", booktitle = "Proceedings of the {International Congress of Mathematicians, Cambridge, Mass., 30 August--6 September 1950, vol. 2}", title = "Some problems of lattice theory", publisher = pub-AMS, address = pub-AMS:adr, pages = "4--7", year = "1952", MRclass = "09.1X", MRnumber = "46339", MRreviewer = "O. Frink", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0049.01602", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "74", ZBmath = "3076666", } @Article{Birkhoff:1952:WEC, author = "Garrett Birkhoff and Milton Plesset and N. Simmons", title = "Wall effects in cavity flow. {II}", journal = j-QUART-APPL-MATH, volume = "9", number = "4", pages = "413--421", month = jan, year = "1952", CODEN = "QAMAAY", DOI = "https://doi.org/10.1090/qam/44278", ISSN = "0033-569X (print), 1552-4485 (electronic)", ISSN-L = "0033-569X", MRclass = "76.1X", MRnumber = "44278", MRreviewer = "D. Gilbarg", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0046.18503", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Quarterly of Applied Mathematics", journal-URL = "http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam", ZBmath = "3071691", } @Article{Birkhoff:1953:FVS, author = "Garrett Birkhoff", title = "Formation of vortex streets", journal = j-J-APPL-PHYS, volume = "24", pages = "98--103", year = "1953", CODEN = "JAPIAU", DOI = "https://doi.org/10.1063/1.1721143", ISSN = "0021-8979 (print), 1089-7550 (electronic), 1520-8850", ISSN-L = "0021-8979", MRclass = "76.1X", MRnumber = "54423", MRreviewer = "M. J. Lighthill", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0050.19401", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Applied Physics", GB-number = "76", journal-URL = "http://aip.scitation.org/toc/jap/current", ZBmath = "3079224", } @Article{Birkhoff:1953:IMV, author = "Garrett Birkhoff", title = "Induced mass with variable density", journal = j-QUART-APPL-MATH, volume = "11", number = "1", pages = "109--110", month = apr, year = "1953", CODEN = "QAMAAY", DOI = "https://doi.org/10.1090/qam/55092", ISSN = "0033-569X (print), 1552-4485 (electronic)", ISSN-L = "0033-569X", MRclass = "76.1X", MRnumber = "55092", MRreviewer = "D. Gilbarg", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0051.16904", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Quarterly of Applied Mathematics", GB-number = "78", journal-URL = "http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam", ZBmath = "3081231", } @InProceedings{Birkhoff:1953:NMC, author = "G. Birkhoff and D. M. Young and E. H. Zarantonello", booktitle = "Proceedings of {Symposia in Applied Mathematics, Vol. IV, Fluid dynamics}", title = "Numerical methods in conformal mapping", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "117--140", year = "1953", MRclass = "65.0X", MRnumber = "57637", MRreviewer = "Charles Saltzer", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib", ZMnumber = "0053.26402", acknowledgement = ack-nhfb, author-dates = "David M. Young, Jr. (October 20, 1923--December 21, 2008); Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "71", ZBmath = "3085413", } @Book{Birkhoff:1953:SMA, author = "Garrett Birkhoff and Saunders {Mac Lane}", title = "A Survey of Modern Algebra", publisher = pub-MACMILLAN, address = pub-MACMILLAN:adr, edition = "Revised [second??]", pages = "xi + 472", year = "1953", MRclass = "09.0X", MRnumber = "54551", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Rev. ed", ZMnumber = "0052.25402", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", xxpages = "vii + 472", ZBmath = "3083503", } @InCollection{Birkhoff:1954:CAS, author = "Garrett Birkhoff and John M. Walsh", booktitle = "Publ. Sci. Tech. Minist{\`e}re de {l'Air}", title = "Conical, axially symmetric flows", publisher = "????", address = "????", pages = "1--12", year = "1954", MRclass = "76.1X", MRnumber = "63215", MRreviewer = "A. Robinson", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "M{\''}emoires sur la m{\''}ecanique des fluides offerts {\`a} M. Dimitri P. Riabouchinsky", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "80", } @Article{Birkhoff:1954:CPC, author = "Garrett Birkhoff and Herman H. Goldstine and E. H. Zarantonello", title = "Calculation of plane cavity flows past curved obstacles", journal = "Univ. e Politec. Torino Rend. Sem. Mat.", volume = "13", pages = "205--224", year = "1954", ISSN = "0373-1243", MRclass = "76.0X", MRnumber = "72601", MRreviewer = "D. Gilbarg", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0056.43004", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Universit\`a e Politecnico di Torino. Rendiconti del Seminario Matematico", GB-number = "88", xxtitle = "Calculations of plane cavity flows past curved obstacles", ZBmath = "3090812", } @Article{Birkhoff:1954:CPD, author = "Garrett Birkhoff", title = "Classification of Partial Differential Equations", journal = j-J-SIAM, volume = "2", number = "1", pages = "57--67", month = mar, year = "1954", CODEN = "JSIMAV", DOI = "https://doi.org/10.1137/0102005", ISSN = "0368-4245 (print), 1095-712X (electronic)", ISSN-L = "0368-4245", MRclass = "35.0X", MRnumber = "62907", MRreviewer = "H. G. Garnir", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siam.bib; JSTOR database", URL = "semanticscholar.org/paper/1c342287001b694d7ee47717e024dce9d30befea", ZMnumber = "0059.08702", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of the Society for Industrial and Applied Mathematics", GB-number = "83", journal-URL = "http://epubs.siam.org/loi/smjmap.1", ZBmath = "3094503", } @Article{Birkhoff:1954:FSH, author = "Garrett Birkhoff", title = "{Fourier} synthesis of homogeneous turbulence", journal = j-COMM-PURE-APPL-MATH, volume = "7", pages = "19--44", year = "1954", CODEN = "CPAMAT, CPMAMV", DOI = "https://doi.org/10.1002/cpa.3160070104", ISSN = "0010-3640 (print), 1097-0312 (electronic)", ISSN-L = "0010-3640", MRclass = "76.1X", MRnumber = "63868", MRreviewer = "J. Bass", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0055.12504", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Communications on Pure and Applied Mathematics", GB-number = "82", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312", ZBmath = "3087280", } @InCollection{Birkhoff:1954:IP, author = "Garrett Birkhoff", booktitle = "Studies in mathematics and mechanics presented to {Richard von Mises}", title = "Induced potentials", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "88--96", year = "1954", MRclass = "31.0X", MRnumber = "65719", MRreviewer = "M. Pinl", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0059.09402", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "87", ZBmath = "3094521", } @Article{Birkhoff:1954:MTH, author = "Garrett Birkhoff and Joseph {Kamp{\'e} de F{\'e}riet}", title = "Sur un mod{\`e}le de turbulence homog{\`e}ne isotrope", journal = j-C-R-ACAD-SCI-PARIS, volume = "239", pages = "16--18", year = "1954", ISSN = "0001-4036 (print), 2419-6304 (electronic)", MRclass = "76.1X", MRnumber = "62575", MRreviewer = "J. Bass", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0055.36905", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Comptes Rendus Hebdomadaires des S{\'e}ances de l'Acad{\'e}mie des Sciences, Paris", GB-number = "84", journal-URL = "http://gallica.bnf.fr/ark:/12148/cb343481087/date", language = "French", ZBmath = "3088541", } @Article{Birkhoff:1954:NHE, author = "Garrett Birkhoff and Jack Kotik", title = "Note on the heat equation", journal = j-PROC-AM-MATH-SOC, volume = "5", pages = "162--167", year = "1954", CODEN = "PAMYAR", DOI = "https://doi.org/10.2307/2032123", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "36.0X", MRnumber = "60120", MRreviewer = "J. L. B. Cooper", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0055.08603", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the American Mathematical Society", GB-number = "81", journal-URL = "http://www.ams.org/journals/proc", ZBmath = "3087115", } @Article{Birkhoff:1954:NMS, author = "Garrett Birkhoff and John M. Walsh", title = "Note on maximum shock deflection", journal = j-QUART-APPL-MATH, volume = "12", number = "1", pages = "83--86", month = apr, year = "1954", CODEN = "QAMAAY", DOI = "https://doi.org/10.1090/qam/60374", ISSN = "0033-569X (print), 1552-4485 (electronic)", ISSN-L = "0033-569X", MRclass = "76.1X", MRnumber = "60374", MRreviewer = "D. C. Pack", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0057.42004", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Quarterly of Applied Mathematics", GB-number = "79", journal-URL = "http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam", ZBmath = "3092403", } @Article{Birkhoff:1954:NTI, author = "Garrett Birkhoff", title = "Note on {Taylor} instability", journal = j-QUART-APPL-MATH, volume = "12", number = "3", pages = "306--309", year = "1954", CODEN = "QAMAAY", DOI = "https://doi.org/10.1090/qam/65316", ISSN = "0033-569X (print), 1552-4485 (electronic)", ISSN-L = "0033-569X", MRclass = "76.1X", MRnumber = "65316", MRreviewer = "James B. Serrin", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0057.41502", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Quarterly of Applied Mathematics", GB-number = "85", journal-URL = "http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam", ZBmath = "3092379", } @Article{Birkhoff:1954:STM, author = "Garrett Birkhoff and Jack Kotik", title = "Some transformations of {Michell}'s integral", journal = "Publications from the National Technical University of Athens", volume = "1954", number = "10", pages = "26--26", year = "1954", MRclass = "76.0X", MRnumber = "78119", MRreviewer = "F. Ursell", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, ajournal = "Publ. Nat. Tech. Univ. Athens", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Publications from the National Technical University of Athens", GB-number = "89", } @TechReport{Birkhoff:1954:TIL, author = "Garrett Birkhoff", title = "{Taylor} Instability and Laminar Mixing", type = "Report", number = "LA-1862", institution = "Los Alamos National Laboratory", address = "Los Alamos, NM, USA", pages = "i + 76", day = "1", month = dec, year = "1954", DOI = "https://doi.org/10.2172/4372366", bibdate = "Wed Nov 01 07:13:47 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "See also Appendices A--H published separately in Report LA-1927 (1956) \cite{Birkhoff:1956:TIA}.", URL = "https://www.osti.gov/biblio/4372366", abstract = "Taylor instability involves five successive stages of mixing: infinitesimal amplitude, finite amplitude, Taylor's ``asymptotic'' inter penetration by spikes and round-ended columns, breakup of these spikes, and turbulent mixing. The existing theory of Taylor instability is critically reviewed and extended. This theory covers the first three stages in the growth of periodic disturbances of the interface separating two non-viscous, incompressible fluids. (Using Fourier analysis, the first stage can be treated without assuming periodicity.)\par The analysis is based on classical hydrodynamics, supplemented by modern numerical methods. It is indicated bow the fourth stage can be treated similarly. However, the fifth stage must be treated by statistical methods, which also throw light on the first four stages. The application of statistical methods to Taylor instability will be treated in a later report.\par A supplement to the present report, consisting of appendices which give expanded mathematical discussions of special topics, will also appear later", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "115", } @Article{Birkhoff:1954:TWR, author = "Garrett Birkhoff and Jack Kotik", title = "Theory of the wave of resistance of ships. {II}. {The} calculation of {Michell}'s integral", journal = "Transactions of the Society of Naval Architects and Marine Engineers", volume = "62", pages = "372--385", year = "1954", ISSN = "0081-1661", MRclass = "76.0X", MRnumber = "78118", MRreviewer = "F. Ursell", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, ajournal = "Trans. Soc. Naval Arch. Marine Engrs.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Transactions. Society of Naval Architects and Marine Engineers", journal-URL = "https://navalmarinearchive.com/collections/sname.html; https://www.biodiversitylibrary.org/bibliography/38774", remark = "Not found at journal Web sites. Is this the same as \cite{Birkhoff:1954:WRS}??", } @Article{Birkhoff:1954:WRS, author = "Garrett Birkhoff and Jack Kotik and B. Korvin-Kroukovsky", title = "Wave Resistance of Ships", journal = "Transactions of the Society of Naval Architects and Marine Engineers", volume = "??", number = "??", pages = "359--396", month = "????", year = "1954", bibdate = "Wed Nov 01 06:49:12 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, ajournal = "Trans. Soc. Nav. Arch. Marine Eng.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Transactions. Society of Naval Architects and Marine Engineers", GB-number = "86", journal-URL = "https://navalmarinearchive.com/collections/sname.html; https://www.biodiversitylibrary.org/bibliography/38774", remark = "Is this the same as \cite{Birkhoff:1954:TWR}??", xxnote = "Check author order??", } @Book{Birkhoff:1955:H, author = "G. Birkhoff", title = "Hydrodynamique", publisher = pub-DUNOD, address = pub-DUNOD:adr, pages = "xii + 228", year = "1955", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Traduit de l'am{\'e}ricain par M. Jorand.", ZMnumber = "0068.18801", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", language = "French", ZBmath = "3115654", } @Book{Birkhoff:1955:HSL, author = "Garrett Birkhoff", title = "Hydrodynamics. {A} Study in Logic, Fact, and Similitude", publisher = pub-DOVER, address = pub-DOVER:adr, pages = "xiii + 186", year = "1955", MRclass = "76.1X", MRnumber = "70349", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0066.42204", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3113345", } @Article{Birkhoff:1956:LOR, author = "Garrett Birkhoff and R. S. Pierce", title = "Lattice-ordered rings", journal = "Anais da Academia Brasileira de Ci{\^e}ncias", volume = "28", pages = "41--69", year = "1956", ISSN = "0001-3765 (print), 1678-2690 (electronic)", ISSN-L = "0001-3765", MRclass = "20.0X", MRnumber = "80099", MRreviewer = "P. F. Conrad", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0070.26602", acknowledgement = ack-nhfb, ajournal = "An. Acad. Brasil. Ci.", ajournal-2 = "Anais Acad. Brasil. Ci.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Anais da Academia Brasileira de Ci{\^e}ncias", GB-number = "91", ZBmath = "3117624", } @Article{Birkhoff:1956:NLN, author = "Garrett Birkhoff and J. B. Diaz", title = "Non-linear network problems", journal = j-QUART-APPL-MATH, volume = "13", number = "4", pages = "431--443", year = "1956", CODEN = "QAMAAY", DOI = "https://doi.org/10.1090/qam/77398", ISSN = "0033-569X (print), 1552-4485 (electronic)", ISSN-L = "0033-569X", MRclass = "78.0X", MRnumber = "77398", MRreviewer = "R. J. Duffin", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0074.32802", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Quarterly of Applied Mathematics", GB-number = "90", journal-URL = "http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam", xxtitle = "Non-linear network theory", ZBmath = "3124260", } @Article{Birkhoff:1956:SSB, author = "Garrett Birkhoff", title = "Stability of spherical bubbles", journal = j-QUART-APPL-MATH, volume = "13", number = "4", pages = "451--453", year = "1956", CODEN = "QAMAAY", DOI = "https://doi.org/10.1090/qam/79932", ISSN = "0033-569X (print), 1552-4485 (electronic)", ISSN-L = "0033-569X", MRclass = "76.0X", MRnumber = "79932", MRreviewer = "James B. Serrin", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0070.19603", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Quarterly of Applied Mathematics", GB-number = "92", journal-URL = "http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam", ZBmath = "3117302", } @TechReport{Birkhoff:1956:TIA, author = "Garrett Birkhoff", title = "{Taylor} Instability: Appendixes to {Report LA-1862}", type = "Report", number = "LA-1927", institution = "Los Alamos National Laboratory", address = "Los Alamos, NM, USA", pages = "iv + 91", day = "2", month = may, year = "1956", DOI = "https://doi.org/10.2172/4364508", bibdate = "Wed Nov 01 09:54:43 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Report written September 1955. Report distributed May 1956. Report reprinted December 1976. See also \cite{Birkhoff:1954:TIL}.", URL = "https://sgp.fas.org/othergov/doe/lanl/lib-www/la-pubs/00353563.pdf", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "115", remark = "From the introductionn ``The material below consists of a more elaborate analysis of various topics discussed in Report LA-1862, ``Taylor Instability and Laminar Mixing'' \cite{Birkhoff:1954:TIL}.", } @Article{Birkhoff:1957:EJT, author = "Garrett Birkhoff", title = "Extensions of {Jentzsch}'s theorem", journal = j-TRANS-AM-MATH-SOC, volume = "85", number = "1", pages = "219--227", month = may, year = "1957", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/1992971", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "46.2X", MRnumber = "87058", MRreviewer = "E. H. Rothe", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0079.13502", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Transactions of the American Mathematical Society", GB-number = "93", journal-URL = "http://www.ams.org/journals/tran/", ZBmath = "3129763", } @TechReport{Birkhoff:1957:IAD, author = "Garrett Birkhoff and Richard S. Varga", title = "Implicit Alternating Direction Methods", type = "Technical Report", number = "WAPD-T-650; NSA-12-003044", institution = "Westinghouse Electric Corporation Bettis Plant", address = "Pittsburgh, PA, USA", pages = "??", day = "1", month = oct, year = "1957", bibdate = "Sat Nov 04 07:38:59 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib", URL = "https://www.osti.gov/biblio/4317092", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Richard S. Varga (8 October 1928--25 February 2022)", remark = "Published in \cite{Birkhoff:1959:IAD}.", } @Book{Birkhoff:1957:JWC, author = "Garrett Birkhoff and E. H. Zarantonello", title = "Jets, Wakes, and Cavities", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "xii + 353", year = "1957", MRclass = "76.0X", MRnumber = "88230", MRreviewer = "D. Gilbarg", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0077.18703", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3126283", } @TechReport{Birkhoff:1957:RCN, author = "Garrett Birkhoff and Richard S. Varga", title = "Reactor Criticality and Non-Negative Matrices", type = "Technical Report", number = "WAPD-166; NSA-11-013507", institution = "Westinghouse Electric Corporation Bettis Plant", address = "Pittsburgh, PA, USA", pages = "??", day = "1", month = aug, year = "1957", bibdate = "Sat Nov 04 07:43:00 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib", URL = "https://www.osti.gov/biblio/4334992", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Richard S. Varga (8 October 1928--25 February 2022)", } @Article{Birkhoff:1957:RPB, author = "Garrett Birkhoff and David Carter", title = "Rising plane bubbles", journal = j-J-MATH-MECH, volume = "6", number = "4", pages = "769--779", year = "1957", CODEN = "JOMMAN", DOI = "https://doi.org/10.1512/iumj.1957.6.56042", ISSN = "0095-9057 (print), 1943-5274 (electronic)", ISSN-L = "0095-9057", MRclass = "76.0X", MRnumber = "91691", MRreviewer = "P. R. Garabedian", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0080.18403", acknowledgement = ack-nhfb, ajournal = "J. Math. Mech.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematics and Mechanics", GB-number = "94", journal-URL = "http://www.iumj.indiana.edu/", ZBmath = "3131687", } @InProceedings{Birkhoff:1958:JWC, author = "Garrett Birkhoff", editor = "????", booktitle = "Hydrodynamic noise, cavity flow: [proceedings of the] second Symposium on Naval Hydrodynamics, August 25--29, 1958, Washington, {D.C}.", title = "Jets, Wakes and Cavities", publisher = "Office of Naval Research", address = "Washington, DC, USA", bookpages = "vi + 583", pages = "261--276", year = "1958", bibdate = "Wed Nov 01 07:04:23 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "ACR-38.", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "108", xxbooktitle = "Proceedings of the Second Symposium on Naval Hydrodynamics", } @Article{Birkhoff:1958:NLT, author = "Garrett Birkhoff", title = "{Von Neumann} and lattice theory", journal = j-BULL-AMS, volume = "64", number = "3 (part 2)", pages = "50--56", month = may, year = "1958", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1958-10192-5", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", MRclass = "01.00 (06.00)", MRnumber = "0095754 (20 \#2255)", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib", URL = "http://projecteuclid.org/euclid.bams/1183522370", ZMnumber = "0080.00412", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "96", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", remark = "Special issue in memory of John von Neumann (1903--1957).", ZBmath = "3131053", } @Article{Birkhoff:1958:RCN, author = "Garrett Birkhoff and Richard S. Varga", title = "Reactor Criticality and Nonnegative Matrices", journal = j-J-SIAM, volume = "6", number = "4", pages = "354--377", month = dec, year = "1958", CODEN = "JSIMAV", DOI = "https://doi.org/10.1137/0106025", ISSN = "0368-4245 (print), 1095-712X (electronic)", ISSN-L = "0368-4245", MRclass = "82.00 (60.00)", MRnumber = "100984", MRreviewer = "D. M. Young, Jr.", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib; https://www.math.utah.edu/pub/tex/bib/siam.bib; JSTOR database", note = "See errata \cite{Birkhoff:1959:ERC}.", URL = "hdl.handle.net/2027/mdp.39015095064807; http://www.math.kent.edu/~varga/pub/paper_8.pdf", ZMnumber = "0086.23301", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Richard S. Varga (8 October 1928--25 February 2022)", fjournal = "Journal of the Society for Industrial and Applied Mathematics", GB-number = "99", journal-URL = "http://epubs.siam.org/loi/smjmap.1", ZBmath = "3141279", } @Article{Birkhoff:1958:RPD, author = "Garrett Birkhoff and Thomas Mullikin", title = "Regular partial differential equations", journal = j-PROC-AM-MATH-SOC, volume = "9", number = "1", pages = "18--25", month = feb, year = "1958", CODEN = "PAMYAR", DOI = "https://doi.org/10.2307/2033391", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "35.00", MRnumber = "96030", MRreviewer = "K. Chandrasekharan", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0084.08802", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the American Mathematical Society", GB-number = "95", journal-URL = "http://www.ams.org/journals/proc", received = "26 June 1956 (revised 17 May 1957)", xxtitle = "WRONG!: Regularity of Partial Differential Equations", ZBmath = "3137614", } @Article{Birkhoff:1958:SBG, author = "Garrett Birkhoff and R. S. Margulies and W. A. Horning", title = "Spherical bubble growth", journal = j-PHYS-FLUIDS, volume = "1", pages = "201--204", year = "1958", CODEN = "PHFLE6", DOI = "https://doi.org/10.1063/1.1724342", ISSN = "0031-9171", ISSN-L = "1070-6631", MRclass = "80.00 (76.00)", MRnumber = "114549", MRreviewer = "P. R. Garabedian", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "The Physics of Fluids", GB-number = "97", journal-URL = "http://scitation.aip.org/content/aip/journal/pof1", } @Article{Birkoff:1958:KHT, author = "Garrett Birkhoff and Joseph {Kamp{\'e} de F{\'e}riet}", title = "Kinematics of homogeneous turbulence", journal = j-J-MATH-MECH, volume = "7", number = "5", pages = "663--703", year = "1958", CODEN = "JOMMAN", DOI = "https://doi.org/10.1512/iumj.1958.7.57038", ISSN = "0095-9057 (print), 1943-5274 (electronic)", ISSN-L = "0095-9057", MRclass = "76.00 (28.00)", MRnumber = "98539", MRreviewer = "J. Bass", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0081.41103", acknowledgement = ack-nhfb, ajournal = "J. Math. Mech.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematics and Mechanics", GB-number = "98", journal-URL = "http://www.iumj.indiana.edu/", ZBmath = "3134055", } @Article{Birkhoff:1959:DVS, author = "Garrett Birkhoff and Joseph Fisher", title = "Do vortex sheets roll up?", journal = "Rendiconti del Circolo Matem{\`a}tico di Palermo. Serie II", volume = "8", pages = "77--90", year = "1959", DOI = "https://doi.org/10.1007/BF02843773", ISSN = "0009-725x (print), 1973-4409 (electronic)", MRclass = "76.00", MRnumber = "114424", MRreviewer = "P. R. Garabedian", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0091.17602", acknowledgement = ack-nhfb, ajournal = "Rend. Circ. Mat. Palermo (2)", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Rendiconti del Circolo Matem{\`a}tico di Palermo. Serie II", GB-number = "102", journal-URL = "https://link.springer.com/journal/12215", ZBmath = "3148941", } @Article{Birkhoff:1959:ERC, author = "Garrett Birkhoff and Richard S. Varga", title = "Errata: {``Reactor Criticality and Nonnegative Matrices'' [J. SIAM {\bf 6} (1958), no. 4, 354--377]}", journal = j-J-SIAM, volume = "7", number = "3", pages = "343--343", month = sep, year = "1959", CODEN = "JSIMAV", ISSN = "0368-4245 (print), 1095-712X (electronic)", ISSN-L = "0368-4245", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib; https://www.math.utah.edu/pub/tex/bib/siam.bib; JSTOR database", note = "See \cite{Birkhoff:1958:RCN}.", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Richard S. Varga (8 October 1928--25 February 2022)", fjournal = "Journal of the Society for Industrial and Applied Mathematics", journal-URL = "http://epubs.siam.org/loi/smjmap.1", } @Article{Birkhoff:1959:IAD, author = "Garrett Birkhoff and Richard S. Varga", title = "Implicit alternating direction methods", journal = j-TRANS-AM-MATH-SOC, volume = "92", number = "1", pages = "13--24", month = jul # "\slash " # sep, year = "1959", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/1993164", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "65.00 (35.00)", MRnumber = "105814", MRreviewer = "J. Douglas, Jr.", bibdate = "Wed Apr 20 14:10:28 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib", URL = "http://www.math.kent.edu/~varga/pub/paper_10.pdf; https://www.ams.org/journals/tran/1959-092-01/S0002-9947-1959-0105814-4/S0002-9947-1959-0105814-4.pdf; https://www.jstor.org/stable/1993164", ZMnumber = "0093.31201", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Richard S. Varga (8 October 1928--25 February 2022)", fjournal = "Transactions of the American Mathematical Society", GB-number = "101", journal-URL = "http://www.ams.org/journals/tran/", ZBmath = "3152585", } @Article{Birkhoff:1959:RCT, author = "Garrett Birkhoff", title = "Reactor criticality in transport theory", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "45", number = "4", pages = "567--569", day = "1", month = apr, year = "1959", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.45.4.567", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", MRclass = "82.00 (60.00) 82D75", MRnumber = "104376", MRreviewer = "R. Bellman", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0087.23502", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the National Academy of Sciences of the United States of America", GB-number = "100", journal-URL = "http://www.pnas.org/content/by/year", ZBmath = "3142845", } @InCollection{Birkhoff:1960:AFE, author = "Garrett Birkhoff", booktitle = "Boundary problems in differential equations {(Proceedings of the Symposium, Madison, April 20--22, 1959}", title = "Albedo functions for elliptic equations", publisher = "University of Wisconsin Press", address = "Madison, WI, USA", pages = "163--178", year = "1960", MRclass = "35.06 (35.45)", MRnumber = "145193", MRreviewer = "R. S. Varga", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0136.09304", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "103", ZBmath = "3220648", } @Article{Birkhoff:1960:CSL, author = "Garrett Birkhoff and Gian-Carlo Rota", title = "On the completeness of {Sturm--Liouville} expansions", journal = j-AMER-MATH-MONTHLY, volume = "67", number = "9", pages = "835--841", month = nov, year = "1960", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2309440", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "34.30", MRnumber = "125274", MRreviewer = "E. C. Titchmarsh", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0132.05502", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "American Mathematical Monthly", GB-number = "105", journal-URL = "http://www.jstor.org/journals/00029890.html", ZBmath = "3213847", } @Book{Birkhoff:1960:HSL, author = "Garrett Birkhoff", title = "Hydrodynamics: a Study in Logic, Fact and Similitude", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, edition = "Revised", pages = "xi + 184 + 1", year = "1960", MRclass = "76.00", MRnumber = "122193", MRreviewer = "K. Stewartson", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Reprinted in \cite{Birkhoff:2016:H}.", ZMnumber = "0095.20303", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3155418", } @InCollection{Birkhoff:1960:SMP, author = "Garrett Birkhoff", editor = "R. E. Langer", booktitle = "Frontiers of Numerical Mathematics (Symposium in {Madison, WI}, 1959)", title = "Some mathematical problems of nuclear reactor theory", publisher = "University of Wisconsin Press", address = "Madison, WI, USA", pages = "23--44", year = "1960", MRclass = "82.00", MRnumber = "144738", MRreviewer = "R. S. Varga", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0105.23201; 0151.45802", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "104", ZBmath = "3243720; 3171906", } @Article{Birkhoff:1960:SSI, author = "Garrett Birkhoff and Henry L. Garabedian", title = "Smooth Surface Interpolation", journal = j-J-MATH-PHYS-MIT, volume = "39", number = "1--4", pages = "258--268", month = apr, year = "1960", CODEN = "JMPHA9", DOI = "https://doi.org/10.1002/sapm1960391258", ISSN = "0097-1421", ISSN-L = "0097-1421", MRclass = "65.00", MRnumber = "119387", MRreviewer = "A. S. Householder", bibdate = "Sat Aug 19 13:36:05 MDT 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib", URL = "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1960391258", ZMnumber = "0161.12903", acknowledgement = ack-nhfb, ajournal = "J. Math. Phys. (MIT)", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematics and Physics (MIT)", GB-number = "109", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590", onlinedate = "April 1960", ZBmath = "3257801", } @Article{Birkhoff:1961:CPF, author = "Garrett Birkhoff", title = "Calculation of Potential Flows with Free Streamlines", journal = j-J-HYDRAULICS-DIV, volume = "87", number = "6", pages = "17--22", month = nov, year = "1961", CODEN = "JYCEAJ", DOI = "https://doi.org/10.1061/JYCEAJ.0000657", ISSN = "0044-796X", ISSN-L = "0044-796X", bibdate = "Wed Nov 01 07:06:47 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://ascelibrary.org/doi/10.1061/JYCEAJ.0000657", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of the Hydraulics Division", GB-number = "110", journal-URL = "https://ascelibrary.org/journal/jhend8", xxjournal = "Proc. Am. Soc. Civ. Eng.", xxtitle = "Calculation of Potential Flows with Free Boundaries", } @InProceedings{Birkhoff:1961:LAM, author = "Garrett Birkhoff", booktitle = "{Proceedings of the Symposia on Pure Mathematics, Vol. II}", title = "Lattices in applied mathematics", publisher = pub-AMS, address = pub-AMS:adr, pages = "155--184", year = "1961", MRclass = "06.99", MRnumber = "177919", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0101.27201", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "107", ZBmath = "3165614", } @Book{Birkhoff:1961:LT, author = "Garrett Birkhoff", title = "Lattice Theory", volume = "25", publisher = pub-AMS, address = pub-AMS:adr, pages = "xiii + 283", year = "1961", MRclass = "06.30 06-02", MRnumber = "123490", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Revised ed", series = "American Mathematical Society Colloquium Publications", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3204690", } @InProceedings{Birkhoff:1961:PC, author = "Garrett Birkhoff", booktitle = "{Proceedings of the Symposia Applied Pure Mathematics, Vol. XI}", title = "Positivity and criticality", publisher = pub-AMS, address = pub-AMS:adr, pages = "116--126", year = "1961", MRclass = "82.00", MRnumber = "120814", MRreviewer = "A. Peres", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "106", } @InCollection{Birkhoff:1962:ADI, author = "Garrett Birkhoff and Richard S. Varga and David Young", editor = "Franz L. Alt and M. Rubinoff", booktitle = "Advances in Computers", title = "Alternating direction implicit methods", volume = "3", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, bookpages = "361", pages = "189--273", year = "1962", DOI = "https://doi.org/10.1016/S0065-2458(08)60620-8", ISSN = "0065-2458", ISSN-L = "0065-2458", MRclass = "65.65", MRnumber = "168131", MRreviewer = "J. Douglas, Jr.", bibdate = "Wed Apr 20 14:10:28 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib", URL = "http://www.math.kent.edu/~varga/pub/paper_20.pdf", ZMnumber = "0111.31402", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Richard S. Varga (8 October 1928--25 February 2022)", GB-number = "117", ZBmath = "3180492", } @Article{Birkhoff:1962:CCS, author = "Garrett Birkhoff and Robert Morris", title = "Confocal Conics in Space--Time", journal = j-AMER-MATH-MONTHLY, volume = "69", number = "1", pages = "1--4", month = jan, year = "1962", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2312724", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "50.48", MRnumber = "133039", MRreviewer = "F. {\c{S}}emin", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0103.44401", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "American Mathematical Monthly", GB-number = "113", journal-URL = "http://www.jstor.org/journals/00029890.html", ZBmath = "3169372", } @InProceedings{Birkhoff:1962:HTI, author = "Garrett Birkhoff", booktitle = "{Proceedings of the Symposia on Applied Mathematics, Vol. XIII}", title = "{Helmholtz} and {Taylor} instability", publisher = pub-AMS, address = pub-AMS:adr, pages = "55--76", year = "1962", MRclass = "76.99", MRnumber = "137423", MRreviewer = "J. W. Miles", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0107.42702", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "115", ZBmath = "3175931", } @Article{Birkhoff:1962:KHT, author = "Garrett Birkhoff and Joseph {Kamp{\'e} de F{\'e}riet}", title = "Kinematics of homogeneous turbulence. {D}. {Metric} transitivity", journal = j-J-MATH-MECH, volume = "11", number = "3", pages = "319--340", year = "1962", CODEN = "JOMMAN", DOI = "https://doi.org/10.1512/iumj.1962.11.11021", ISSN = "0095-9057 (print), 1943-5274 (electronic)", ISSN-L = "0095-9057", MRclass = "76.60 76F05", MRnumber = "149778", MRreviewer = "J. Bass", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0106.18705", acknowledgement = ack-nhfb, ajournal = "J. Math. Mech.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematics and Mechanics", GB-number = "114", journal-URL = "http://www.iumj.indiana.edu/", ZBmath = "3173425", } @TechReport{Birkhoff:1962:LHC, author = "Garrett Birkhoff and Robert E. Lynch", title = "{Lagrangian} Hydrodynamic Computations and Molecular Models of Matter", type = "Report", number = "LA-2618", institution = "Los Alamos National Laboratory", address = "Los Alamos, NM, USA", pages = "iii + 58", year = "1962", DOI = "https://doi.org/10.2172/4821933", bibdate = "Wed Nov 01 07:09:38 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://www.osti.gov/servlets/purl/4821933", abstract = "An analysis is made of the analogy between schemes for integrating the equations of motion of a compressible fluid, in Lagrangian coordinates, and molecular models of matter. Computation schemes involving one and two independent variables are considered, for flows with and without shocks", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "111", remark = "Summarized in Ann. Harvard Comp. Lab. 31 (1962), 23--31", } @Article{Birkhoff:1962:NIT, author = "Garrett Birkhoff", title = "A new interval topology for dually directed sets: [homenaje a {A. Terracini} y {F. Cernuschi}]", journal = "Univ. Nac. Tucum{\'a}n Rev. Ser. A", volume = "14", pages = "325--331", year = "1962", ISSN = "0080-2360", MRclass = "54F05 06B30 06.20", MRnumber = "166120", MRreviewer = "O. Frink", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0135.22702", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Universidad Nacional de Tucum{\'a}n. Facultad de Ciencias Exactas y Tecnolog{\'\i}a. Revista. Serie A. Matem{\'a}tica y F{\'\i}sica Te{\'o}rica", GB-number = "118", ZBmath = "3219507", } @Book{Birkhoff:1962:ODE, author = "Garrett Birkhoff and Gian-Carlo Rota", title = "Ordinary Differential Equations", publisher = "Ginn and Company", address = "Boston, Mass.-New York-Toronto", pages = "vii + 318", year = "1962", MRclass = "34.00", MRnumber = "138810", MRreviewer = "N. D. Kazarinoff", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Introductions to Higher Mathematics", ZMnumber = "0102.29901", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3167285", } @Article{Birkhoff:1962:SMH, author = "G. Birkhoff and R. E. Lynch", title = "Synthetic materials for hydrodynamical computations", journal = "Annals of Harvard University", volume = "31", pages = "23--31", year = "1962", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0151.40504", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3243536", } @Article{Birkhoff:1962:USP, author = "Garrett Birkhoff", title = "Uniformly semi-primitive multiplicative processes", journal = j-TRANS-AM-MATH-SOC, volume = "104", number = "1", pages = "37--51", month = jul, year = "1962", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/1993931", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "06.80", MRnumber = "146100", MRreviewer = "A. C. Choudhury", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0101.33304", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Transactions of the American Mathematical Society", GB-number = "116", journal-URL = "http://www.ams.org/journals/tran/", ZBmath = "3165794", } @Article{Birkhoff:1963:BCM, author = "Garrett Birkhoff and Jerome Eckerman", title = "Binary collision modeling", journal = j-J-MATH-MECH, volume = "12", number = "4", pages = "543--556", year = "1963", CODEN = "JOMMAN", DOI = "https://doi.org/10.1512/iumj.1963.12.12034", ISSN = "0095-9057 (print), 1943-5274 (electronic)", ISSN-L = "0095-9057", MRclass = "76.99", MRnumber = "152234", MRreviewer = "K. Stewartson", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, ajournal = "J. Math. Mech.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematics and Mechanics", GB-number = "120", journal-URL = "http://www.iumj.indiana.edu/", } @Article{Birkhoff:1963:FBP, author = "Garrett Birkhoff and Donald F. Hays", title = "Free Boundaries in Partial Lubrication", journal = j-J-MATH-PHYS-MIT, volume = "42", number = "1--4", pages = "126--138", month = apr, year = "1963", CODEN = "JMPHA9", DOI = "https://doi.org/10.1002/sapm1963421126", ISSN = "0097-1421", ISSN-L = "0097-1421", MRclass = "76.99", MRnumber = "153199", MRreviewer = "K. Stewartson", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib", URL = "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1963421126", ZMnumber = "0124.43405", acknowledgement = ack-nhfb, ajournal = "J. Math. Phys. (MIT)", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematics and Physics (MIT)", GB-number = "121", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590", onlinedate = "April 1963", ZBmath = "3202358", } @Book{Birkhoff:1963:HSL, author = "G. Birkhoff", title = "Hydrodynamics. {A} study in logic, fact and similitude", publisher = "{Verlag f{\"u}r ausl{\"a}ndische Literatur}", address = "Moskau, USSR", pages = "244", year = "1963", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0114.17804", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", language = "Russian", ZBmath = "3185647", } @InCollection{Birkhoff:1963:LOD, author = "G. Birkhoff", booktitle = "Alg{\`e}bre Th{\'e}orie Nombres, Sem. P. Dubreil, M.-L. Dubreil-Jacotin et C. Pisot 14 (1960/61)", title = "Lattice-ordered demigroups", publisher = "????", address = "????", pages = "26", year = "1963", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0122.02101", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "112", ZBmath = "3197146", } @Article{Birkhoff:1963:RCN, author = "Garrett Birkhoff", title = "Reactor criticality in neutron transport theory", journal = "Rendiconti di Matematica e delle sue Applicazioni. Serie V", volume = "22", pages = "102--126", year = "1963", ISSN = "1120-7175", MRclass = "82.47", MRnumber = "169648", MRreviewer = "R. S. Varga", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0178.50305", acknowledgement = ack-nhfb, ajournal = "Rend. Mat. e Appl. (5)", ajournal-2 = "Rend. Mat. Appl., V. Ser.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Rendiconti di Matematica e delle sue Applicazioni. Serie V", GB-number = "119", xxISSN = "0034-4427", ZBmath = "3285743", } @Article{Birkhoff:1963:VPN, author = "Garrett Birkhoff", title = "A variational principle for nonlinear networks", journal = j-QUART-APPL-MATH, volume = "21", number = "2", pages = "160--162", month = jul, year = "1963", CODEN = "QAMAAY", DOI = "https://doi.org/10.1090/qam/156706", ISSN = "0033-569X (print), 1552-4485 (electronic)", ISSN-L = "0033-569X", MRclass = "94.30", MRnumber = "156706", MRreviewer = "T. L. Saaty", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Quarterly of Applied Mathematics", GB-number = "122", journal-URL = "http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam", xxpages = "159--162", } @Book{Birkgof:1964:CSS, author = "G. Birkgof and {\`E}. Sarantonello", title = "{{\cyr Strui, sledy i kaverny}}. ({Russian}) [Jets, wakes and cavities]", publisher = "Izdat. ``Mir''", address = "Moscow, USSR", pages = "466", year = "1964", MRclass = "76.49", MRnumber = "177579", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0124.18803", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", language = "Russian", xxauthor = "G. Birkhoff and E. H. Zarantonello", ZBmath = "3201379", } @Article{Birkhoff:1964:ACL, author = "Garrett Birkhoff", title = "Averaged conservation laws in pipes", journal = j-J-MATH-ANAL-APPL, volume = "8", number = "1", pages = "66--77", month = feb, year = "1964", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(64)90084-8", ISSN = "0022-247x (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "76.35", MRnumber = "158609", MRreviewer = "S. I. Pai", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0126.41801", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematical Analysis and Applications", GB-number = "123", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ZBmath = "3206031", } @Article{Birkhoff:1964:BRD, author = "Garrett Birkhoff", title = "Book Review: {{\booktitle{Differential--difference equations}}. By Richard Bellman. Academic Press, New York, London, 1963. xvi + 462 pp.}", journal = j-QUART-APPL-MATH, volume = "22", number = "2", pages = "164--165", month = jul, year = "1964", CODEN = "QAMAAY", ISSN = "0033-569x (print), 1552-4485 (electronic)", ISSN-L = "0033-569X", MRclass = "94C05 49J40", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0222.94028", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Quarterly of Applied Mathematics", journal-URL = "http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam", xxtitle = "A variational principle for nonlinear networks", ZBmath = "3353156", } @Article{Birkhoff:1964:EBS, author = "Garrett Birkhoff and Carl de Boor", title = "Error bounds for spline interpolation", journal = j-J-MATH-MECH, volume = "13", number = "5", pages = "827--835", year = "1964", CODEN = "JOMMAN", DOI = "https://doi.org/10.1512/iumj.1964.13.13048", ISSN = "0095-9057 (print), 1943-5274 (electronic)", ISSN-L = "0095-9057", MRclass = "41.15", MRnumber = "165294", MRreviewer = "I. J. Schoenberg", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0143.28503", acknowledgement = ack-nhfb, ajournal = "J. Math. Mech.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematics and Mechanics", GB-number = "126", journal-URL = "http://www.iumj.indiana.edu/", ZBmath = "3231189", } @InProceedings{Birkhoff:1964:FBP, author = "Garrett Birkhoff", editor = "R. M. Davies", booktitle = "{Cavitation in Real Liquids (Proceedings of a Symposium, General Motors Research Laboratory, Warren, Mich., 1962)}", title = "Free boundary problems for viscous flows in channels", publisher = pub-ELSEVIER, address = pub-ELSEVIER:adr, pages = "102--121", year = "1964", MRclass = "76.35", MRnumber = "183204", MRreviewer = "W. Langlois", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "125", } @Book{Birkhoff:1964:HIT, author = "Garrett Birkhoff and Richard Bellman and C. C. Lin", title = "Hydrodynamic instability", publisher = "{Verlag 'Mir'}", address = "Moskau, USSR", pages = "372", year = "1964", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Translation from the English by A. S. Monin.", ZMnumber = "0119.20502", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", language = "Russian", ZBmath = "3194377", } @Article{Birkhoff:1964:WSC, author = "Garrett Birkhoff", title = "Well-set {Cauchy} problems and {$ C_0 $}-semigroups", journal = j-J-MATH-ANAL-APPL, volume = "8", number = "2", pages = "303--324", month = apr, year = "1964", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(64)90071-X", ISSN = "0022-247x (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "35.31", MRnumber = "159125", MRreviewer = "R. Carroll", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0168.35303", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematical Analysis and Applications", GB-number = "124", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ZBmath = "3270174", } @Book{Birkhoff:1965:BSM, author = "Garrett Birkhoff and Saunders {Mac Lane}", title = "A Brief Survey of Modern Algebra", publisher = pub-MACMILLAN, address = pub-MACMILLAN:adr, edition = "Second", pages = "vii + 279", year = "1965", LCCN = "QA251 .B5 1965", MRclass = "00.00 (20.00)", MRnumber = "180595", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", } @Article{Birkhoff:1965:DEW, author = "Garrett Birkhoff and Richard S. Varga", title = "Discretization Errors for Well-Set {Cauchy} Problems. {I}", journal = j-J-MATH-PHYS-MIT, volume = "44", number = "1--4", pages = "1--23", month = apr, year = "1965", CODEN = "JMPHA9", DOI = "https://doi.org/10.1002/sapm19654411", ISSN = "0097-1421", ISSN-L = "0097-1421", MRclass = "65.65", MRnumber = "179952", MRreviewer = "M. Lees", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib; https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib", URL = "http://www.math.kent.edu/~varga/pub/paper_28.pdf; https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm19654411", ZMnumber = "0134.13406", acknowledgement = ack-nhfb, ajournal = "J. Math. Phys. (MIT)", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Richard S. Varga (8 October 1928--25 February 2022)", fjournal = "Journal of Mathematics and Physics (MIT)", GB-number = "128", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590", onlinedate = "April 1965", ZBmath = "3217412", } @Article{Birkhoff:1965:EPS, author = "Garrett Birkhoff and Leon Kotin", title = "Essentially positive systems of linear differential equations", journal = j-BULL-AMS, volume = "71", number = "4", pages = "771--772", month = jul, year = "1965", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0002-9904-1965-11386-6", ISSN = "0002-9904 (print), 1936-881x (electronic)", ISSN-L = "0002-9904", MRclass = "34.20", MRnumber = "179414", MRreviewer = "G. R. Sell", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0132.31203", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "132", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", ZBmath = "3214778", } @Article{Birkhoff:1965:NPL, author = "Garrett Birkhoff", title = "Note on positive linear operators", journal = j-PROC-AM-MATH-SOC, volume = "16", pages = "14--16", year = "1965", CODEN = "PAMYAR", DOI = "https://doi.org/10.2307/2033991", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "47.20", MRnumber = "172097", MRreviewer = "R. Cristescu", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0136.11702", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the American Mathematical Society", GB-number = "127", journal-URL = "http://www.ams.org/journals/proc", ZBmath = "3220722", } @InProceedings{Birkhoff:1965:PDM, author = "Garrett Birkhoff", booktitle = "{Proceedings of the IBM Scientific Computing Symposium on Large-Scale Problems in Physics (Yorktown Heights, NY, 1963)}", title = "Partial difference methods", publisher = "IBM", address = "White Plains, NY, USA", pages = "17--36", year = "1965", MRclass = "65.66", MRnumber = "251926", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "133", } @InProceedings{Birkhoff:1965:PPI, author = "Garrett Birkhoff and Carl R. de Boor", title = "Piecewise polynomial interpolation and approximation", crossref = "Garabedian:1965:AFP", pages = "164--190", year = "1965", MRclass = "65.20", MRnumber = "189219", MRreviewer = "R. A. Valentin", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0136.04703", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "130", xxtitle = "Piecewise Polynomial Surface Fitting", ZBmath = "3220498", } @Book{Birkhoff:1965:SMA, author = "Garrett Birkhoff and Saunders {Mac Lane}", title = "A Survey of Modern Algebra", publisher = pub-MACMILLAN, address = pub-MACMILLAN:adr, edition = "Third", pages = "x + 437", year = "1965", MRclass = "00.00 (12.00)", MRnumber = "177992", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", } @Article{Birkhoff:1965:USP, author = "Garrett Birkhoff", title = "Uniformly semi-primitive multiplicative processes. {II}", journal = j-J-MATH-MECH, volume = "14", number = "3", pages = "507--512", year = "1965", CODEN = "JOMMAN", DOI = "https://doi.org/10.1512/iumj.1965.14.14034", ISSN = "0095-9057 (print), 1943-5274 (electronic)", ISSN-L = "0095-9057", MRclass = "06.80 46-XX", MRnumber = "180509", MRreviewer = "A. C. Choudhury", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0131.33401", acknowledgement = ack-nhfb, ajournal = "J. Math. Mech.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematics and Mechanics", GB-number = "131", journal-URL = "http://www.iumj.indiana.edu/", ZBmath = "3213151", } @Article{Birkhoff:1965:WLP, author = "G. Birkhoff", title = "The {William Lowell Putnam Mathematical Competition}: Early History", journal = j-AMER-MATH-MONTHLY, volume = "72", number = "5", pages = "469--473", month = may, year = "1965", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:53 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "http://www.jstor.org/stable/2314116", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "American Mathematical Monthly", GB-number = "129", journal-URL = "http://www.jstor.org/journals/00029890.html", } @Article{Birkhoff:1966:ABS, author = "Garrett Birkhoff and Leon Kotin", title = "Asymptotic behavior of solutions of first-order linear differential-delay equations", journal = j-J-MATH-ANAL-APPL, volume = "13", number = "1", pages = "8--18", month = jan, year = "1966", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(66)90072-2", ISSN = "0022-247x (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "34.75 (34.50)", MRnumber = "190488", MRreviewer = "Kenneth R. Meyer", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0134.30202", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematical Analysis and Applications", GB-number = "135", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ZBmath = "3218065", } @Article{Birkhoff:1966:IDD, author = "Garrett Birkhoff and Leon Kotin", title = "Integro-differential delay equations of positive type", journal = j-J-DIFFER-EQU, volume = "2", pages = "320--327", year = "1966", CODEN = "JDEQAK", DOI = "https://doi.org/10.1016/0022-0396(66)90072-6", ISSN = "0022-0396 (print), 1090-2732 (electronic)", ISSN-L = "0022-0396", MRclass = "45.40", MRnumber = "198169", MRreviewer = "W. T. Reid", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0152.11802", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Differential Equations", GB-number = "138", journal-URL = "https://www.sciencedirect.com/journal/journal-of-differential-equations/issues", ZBmath = "3244166", } @InProceedings{Birkhoff:1966:NSR, author = "Garrett Birkhoff", editor = "Donald Greenspan", booktitle = "Numerical Solutions of Nonlinear Differential Equations: Proceedings of an advanced symposium conducted by the {Mathematics Research Center, United States Army, at the University of Wisconsin, Madison, May 9--11, 1966}", title = "Numerical Solution of the Reactor Kinetics Equations", publisher = pub-WILEY, address = pub-WILEY:adr, bookpages = "x + 347", pages = "3--20", year = "1966", LCCN = "QA3 .U45 no. 17", MRclass = "82.00 (65.00)", MRnumber = "213131", MRreviewer = "R. R. Coveyou", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0202.45402", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "139", remark = "See book review \cite{G:1968:BRD}", ZBmath = "3321663", } @InProceedings{Birkhoff:1966:NST, author = "Garrett Birkhoff and Robert E. Lynch", booktitle = "Numerical Solution of Partial Differential Equations {(Proceedings of a Symposium University of Maryland, 1965)}", title = "Numerical solution of the telegraph and related equations", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "289--315", year = "1966", MRclass = "65.67", MRnumber = "203953", MRreviewer = "W. F. Ames", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0202.45703", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "136", } @Article{Birkhoff:1966:RRA, author = "Garrett Birkhoff and C. de Boor and B. Swartz and B. Wendroff", title = "{Rayleigh--Ritz} Approximation by Piecewise Cubic Polynomials", journal = j-SIAM-J-NUMER-ANAL, volume = "3", number = "2", pages = "188--203", month = jun, year = "1966", CODEN = "SJNAAM", DOI = "https://doi.org/10.1137/0703015", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65.40", MRnumber = "203926", MRreviewer = "C. W. Clenshaw", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", ZMnumber = "0143.38002", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "SIAM Journal on Numerical Analysis", GB-number = "137", journal-URL = "http://epubs.siam.org/sinum", ZBmath = "3231517", } @InProceedings{Birkhoff:1966:SEE, author = "Garrett Birkhoff and Bruce Kellogg", booktitle = "{Proceedings of the Symposium on Generalized Networks (New York, 1966)}", title = "Solution of equilibrium equations in thermal networks", volume = "XVI", publisher = "Brooklyn Polytechnic", address = "Brooklyn, NY, USA", pages = "443--452", year = "1966", MRclass = "65-XX 80A20 94.30", MRnumber = "282739", MRreviewer = "M. Ma\v{n}as", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Microwave Research Institute Symposia Series", ZMnumber = "0183.44803", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "140", xxtitle = "Equilibrium Equations in Thermal Networks", ZBmath = "3292380", } @Article{Birkhoff:1966:TTH, author = "Garrett Birkhoff and J. Eckerman and W. McKay", title = "Transition and Turbulence in Hypersonic Wakes", journal = j-PHYS-FLUIDS, volume = "9", number = "3", pages = "446--452", month = mar, year = "1966", CODEN = "PHFLE6", DOI = "https://doi.org/10.1063/1.1761696", ISSN = "1070-6631", ISSN-L = "1070-6631", bibdate = "Wed Nov 01 07:31:16 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://pubs.aip.org/aip/pfl/article-pdf/12481629/446_1_online.pdf", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "The Physics of Fluids", GB-number = "134", journal-URL = "http://scitation.aip.org/content/aip/journal/pof1", } @Article{Birkhoff:1967:HIE, author = "Garrett Birkhoff and Arthur S. Priver", title = "{Hermite} Interpolation Errors for Derivatives", journal = j-J-MATH-PHYS-MIT, volume = "46", number = "1--4", pages = "440--447", month = apr, year = "1967", CODEN = "JMPHA9", DOI = "https://doi.org/10.1002/sapm1967461440", ISSN = "0097-1421", ISSN-L = "0097-1421", MRclass = "41.10", MRnumber = "218799", MRreviewer = "R. A. Askey", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib", URL = "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1967461440", ZMnumber = "0176.14202", acknowledgement = ack-nhfb, ajournal = "J. Math. Phys. (MIT)", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematics and Physics (MIT)", GB-number = "145", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590", onlinedate = "April 1967", ZBmath = "3281249", } @Article{Birkhoff:1967:LFA, author = "Garrett Birkhoff", title = "A limitation of {Fourier} analysis", journal = j-J-MATH-MECH, volume = "17", number = "5", pages = "443--447", year = "1967", CODEN = "JOMMAN", DOI = "https://doi.org/10.1512/iumj.1968.17.17025", ISSN = "0095-9057 (print), 1943-5274 (electronic)", ISSN-L = "0095-9057", MRclass = "60.20 (82.00)", MRnumber = "217834", MRreviewer = "J.-P. Kahane", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0201.44202", acknowledgement = ack-nhfb, ajournal = "J. Math. Mech.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematics and Mechanics", GB-number = "144", journal-URL = "http://www.iumj.indiana.edu/", ZBmath = "3319811", } @Article{Birkhoff:1967:LSA, author = "Garrett Birkhoff", title = "Local spline approximation by moments", journal = j-J-MATH-MECH, volume = "16", number = "9", pages = "987--990", year = "1967", CODEN = "JOMMAN", DOI = "https://doi.org/10.1512/iumj.1967.16.16064", ISSN = "0095-9057 (print), 1943-5274 (electronic)", ISSN-L = "0095-9057", MRclass = "41.17", MRnumber = "208241", MRreviewer = "J. R. Rice", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0148.29204", acknowledgement = ack-nhfb, ajournal = "J. Math. Mech.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematics and Mechanics", GB-number = "142", journal-URL = "http://www.iumj.indiana.edu/", ZBmath = "3239696", } @Article{Birkhoff:1967:LSOa, author = "Garrett Birkhoff and Leon Kotin", title = "Linear second-order differential equations of positive type", journal = j-J-ANAL-MATH, volume = "18", pages = "43--52", year = "1967", CODEN = "JOAMAV", DOI = "https://doi.org/10.1007/BF02798033", ISSN = "0021-7670 (print), 1565-8538 (electronic)", ISSN-L = "0021-7670", MRclass = "34.20", MRnumber = "212247", MRreviewer = "C. Olech", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0148.05904", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal d'Analyse Math{\'e}matique", GB-number = "141", journal-URL = "http://link.springer.com/journal/11854", ZBmath = "3238810", } @Book{Birkhoff:1967:LT, author = "Garrett Birkhoff", title = "Lattice Theory", volume = "25", publisher = pub-AMS, address = pub-AMS:adr, edition = "Third", pages = "vi + 418", year = "1967", ISSN = "0065-9258", MRclass = "06-02 06.30", MRnumber = "227053", MRreviewer = "P. A. Fillmore", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "American Mathematical Society Colloquium Publications", ZMnumber = "0153.02501", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fseries = "Colloquium Publications. American Mathematical Society", tableofcontents = "Types of lattices \\ Postulates for lattices \\ Structure and representation theory \\ Geometric lattices \\ Complete lattices \\ Universal algebra \\ Applications to algebra \\ Transfinite induction \\ Applications to general topology \\ Metric and topological lattices \\ Borel algebras and von Neumann lattices \\ Applications to logic and probability \\ Lattice-ordered groups \\ Lattice-ordered monoids \\ Vector lattices \\ Positive linear operators \\ Lattice-ordered rings", ZBmath = "3245483", } @Article{Birkhoff:1967:LTI, author = "Garrett Birkhoff", title = "Linear transformations with invariant cones", journal = j-AMER-MATH-MONTHLY, volume = "74", number = "3", pages = "274--276", month = mar, year = "1967", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2316020", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "15.25", MRnumber = "214605", MRreviewer = "A. Jaeger", bibdate = "Mon Jun 28 12:38:34 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0192.26703", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "American Mathematical Monthly", GB-number = "143", journal-URL = "http://www.jstor.org/journals/00029890.html", xxtitle = "Mathematical Notes: Linear Transformations with Invariant Cones", ZBmath = "3305613", } @Article{Birkhoff:1967:RRA, author = "Garrett Birkhoff and George Fix", title = "{Rayleigh--Ritz} approximation by trigonometric polynomials", journal = j-INDIAN-J-MATH, volume = "9", pages = "269--277", year = "1967", CODEN = "IJOMAL", ISSN = "0019-5324", MRclass = "65.62", MRnumber = "261794", MRreviewer = "L. Hageman", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0187.11202", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Indian Journal of Mathematics", GB-number = "152", journal-URL = "http://www.amsallahabad.org/ijm.html", ZBmath = "3298266", } @Book{MacLane:1967:A, author = "Saunders {Mac Lane} and Garrett Birkhoff", title = "Algebra", publisher = pub-MACMILLAN, address = pub-MACMILLAN:adr, pages = "xix + 598", year = "1967", MRclass = "00.00", MRnumber = "214415", MRreviewer = "C. W. Curtis", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0153.32401", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", ZBmath = "3246263", } @Article{Birkhoff:1968:DRE, author = "Garrett Birkhoff and William J. Gordon", title = "The Draftsman's and related equations", journal = j-J-APPROX-THEORY, volume = "1", pages = "199--208", year = "1968", CODEN = "JAXTAZ", DOI = "https://doi.org/10.1016/0021-9045(68)90024-5", ISSN = "0021-9045 (print), 1096-0430 (electronic)", ISSN-L = "0021-9045", MRclass = "65.67", MRnumber = "235752", MRreviewer = "J. W. Schmidt", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0189.40902", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Approximation Theory", GB-number = "147", journal-URL = "http://www.sciencedirect.com/science/journal/00219045", ZBmath = "3302624", } @Article{Birkhoff:1968:PHI, author = "G. Birkhoff and M. H. Schultz and R. S. Varga", title = "Piecewise {Hermite} interpolation in one and two variables with applications to partial differential equations", journal = j-NUM-MATH, volume = "11", number = "3", pages = "232--256", month = mar, year = "1968", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/BF02161845", ISSN = "0029-599x (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65.20 (41.00)", MRnumber = "226817", MRreviewer = "F. Perrin", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", URL = "http://www.math.kent.edu/~varga/pub/paper_37.pdf", ZMnumber = "0159.20904", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Richard S. Varga (8 October 1928--25 February 2022)", fjournal = "Numerische Mathematik", GB-number = "146", journal-URL = "http://link.springer.com/journal/211", ZBmath = "3256231", } @Article{Birkhoff:1969:BRT, author = "Garrett Birkhoff", title = "Book Review: {{\booktitle{The Theory of Splines and Their Applications}} (J. H. Ahlberg, E. N. Nilson and J. L. Walsh)}", journal = j-SIAM-REVIEW, volume = "11", number = "1", pages = "91--92", month = "????", year = "1969", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1011018", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Thu Mar 27 09:06:04 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/11/1; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "January 1969", } @Article{Birkhoff:1969:HST, author = "Garrett Birkhoff and Ibrahim Abu-Shumays", title = "Harmonic solutions of transport equations", journal = j-J-MATH-ANAL-APPL, volume = "28", number = "1", pages = "211--221", month = oct, year = "1969", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(69)90123-1", ISSN = "0022-247x (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "82.45 (45.00)", MRnumber = "246609", MRreviewer = "E. Bareiss", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://pdf.sciencedirectassets.com/272578/1-s2.0-S0022247X00X04994/1-s2.0-0022247X69901231/main.pdf?", ZMnumber = "0202.38902", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematical Analysis and Applications", GB-number = "150", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ZBmath = "3321482", } @Article{Birkhoff:1969:MP, author = "Garrett Birkhoff", title = "Mathematics and Psychology", journal = j-SIAM-REVIEW, volume = "11", number = "4", pages = "429--469", month = "????", year = "1969", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1011085", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "00.50 (92.00)", MRnumber = "262038", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "http://epubs.siam.org/toc/siread/11/4; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", ZMnumber = "0202.19104", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "SIAM Review", GB-number = "153", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "October 1969", ZBmath = "3320902", } @InCollection{Birkhoff:1969:NSE, author = "G. Birkhoff", booktitle = "Lectures on Differential Equations ({USA} 1966--1967)", title = "Numerical solution of elliptic equations", volume = "2", publisher = "????", address = "????", pages = "197--232", year = "1969", MRclass = "65N06 65N22 65N12 35J99 65D07", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0208.19202", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3331257", } @Book{Birkhoff:1969:ODE, author = "Garrett Birkhoff and Gian-Carlo Rota", title = "Ordinary Differential Equations", publisher = pub-BLAISDELL, address = pub-BLAISDELL:adr, edition = "Second", pages = "xiv + 366", year = "1969", MRclass = "34.00", MRnumber = "236441", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0183.35601", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3292104", } @InProceedings{Birkhoff:1969:PBI, author = "Garrett Birkhoff", editor = "I. J. Schoenberg", booktitle = "Approximations with Special Emphasis on Spline Functions {(Proceedings of the Symposium, University of Wisconsin, Madison, Wisconsin, 1969)}", title = "Piecewise bicubic interpolation and approximation in polygons", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "185--221", year = "1969", MRclass = "41A05 41A15 65D05 41.30 (65.00)", MRnumber = "271586", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0279.41003", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "151", ZBmath = "3439382", } @InCollection{Birkhoff:1969:STEa, author = "G. Birkhoff", booktitle = "Probl. Gidrodinam. Mekh. sploshn. Sredy", title = "Similarity and the transport equation", publisher = "????", address = "????", pages = "49--54", year = "1969", MRclass = "76A99 76R50 82C70", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0208.53803", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3332295", } @InCollection{Birkhoff:1969:STEb, author = "Garrett Birkhoff", booktitle = "Sedov Anniversary Volume", title = "Similarity and the Transport Equation", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "55--62", year = "1969", bibdate = "Wed Nov 01 07:38:58 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "149", } @Article{Birkhoff:1969:TOP, author = "Garrett Birkhoff and Leon Kotin", title = "Third order positive cyclic systems of linear differential equations", journal = j-J-DIFFER-EQU, volume = "5", pages = "182--196", year = "1969", CODEN = "JDEQAK", DOI = "https://doi.org/10.1016/0022-0396(69)90111-9", ISSN = "0022-0396 (print), 1090-2732 (electronic)", ISSN-L = "0022-0396", MRclass = "34.42", MRnumber = "234054", MRreviewer = "G. Sansone", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0169.11303", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Differential Equations", GB-number = "148", journal-URL = "https://www.sciencedirect.com/journal/journal-of-differential-equations/issues", ZBmath = "3270898", } @InProceedings{Birkhoff:1970:AEC, author = "Garrett Birkhoff and George Fix", editor = "Garrett Birkhoff and Richard S. Varga", booktitle = "Numerical Solution of Field Problems in Continuum Physics {(Proceedings of the Symposium on Applied Mathematics, Durham, N.C., 1968), SIAM-AMS Proceedings, Vol. II}", title = "Accurate eigenvalue computations for elliptic problems", volume = "II", publisher = pub-AMS, address = pub-AMS:adr, pages = "111--151", year = "1970", MRclass = "65N25 65N30 65.66", MRnumber = "260199", MRreviewer = "P. Laasonen", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "SIAM-AMS Proc.", ZMnumber = "0231.65087", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", editor-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Richard S. Varga (8 October 1928--25 February 2022)", GB-number = "157", ZBmath = "3366493", } @Article{Birkhoff:1970:EAS, author = "Garrett Birkhoff and Ibrahim K. Abu-Shumays", title = "Exact analytic solutions of transport equations", journal = j-J-MATH-ANAL-APPL, volume = "32", number = "3", pages = "468--481", month = dec, year = "1970", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(70)90271-4", ISSN = "0022-247x (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "35K57 82.35", MRnumber = "275818", MRreviewer = "K. Schram", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0217.41102", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematical Analysis and Applications", GB-number = "158", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ZBmath = "3345716", } @Article{Birkhoff:1970:HA, author = "Garrett Birkhoff and John D. Lipson", title = "Heterogeneous algebras", journal = j-J-COMB-THEORY, volume = "8", pages = "115--133", year = "1970", CODEN = "JCTHAR", DOI = "https://doi.org/10.1016/S0021-9800(70)80014-X", ISSN = "0021-9800 (print), 1878-1756 (electronic)", ISSN-L = "0021-9800", MRclass = "02.88 (08.00) 68Q70", MRnumber = "250887", MRreviewer = "J. A. Schatz", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0211.02003", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Combinatorial Theory", GB-number = "154", journal-URL = "http://www.sciencedirect.com/science/journal/00219800", xxISSN = "0097-3165 (print), 1096-0899 (electronic)", ZBmath = "3334171", } @Book{Birkhoff:1970:MAAa, author = "Garrett Birkhoff and Thomas Creson Bartee", title = "Modern Applied Algebra", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "xi + 431", year = "1970", ISBN = "0-07-005381-2, 0-7005-3812-0", ISBN-13 = "978-0-07-005381-6, 978-0-7005-3812-6", LCCN = "QA251 .B49", MRclass = "00A05 00-01 68-01 94-01", bibdate = "Sat Oct 28 07:47:58 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0215.31302", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", tableofcontents = "1: Sets and Functions / 1 \\ 2: Binary Relations and Graphs / 31 \\ 3: Finite State Machines / 63 \\ 4: Programming Languages / 99 \\ 5: Boolean Algebras / 129 \\ 6: Optimization and Computer Design / 161 \\ 7: Monoids and Groups / 197 \\ 8: Binary Group Codes / 231 \\ 9: Lattices / 257 \\ 10: Rings and Ideals / 281 \\ 11: Polynomial Rings and Polynomial Codes / 315 \\ 12: Finite Fields / 339 \\ 13: Recurrent Sequences / 367 \\ 14: Computability / 397 \\ Index / 425", ZBmath = "3341950", } @Book{Birkhoff:1970:MAAb, author = "Garrett Birkhoff and Thomas Creson Bartee", title = "Modern Applied Algebra", publisher = "Kogakucha", address = "Tokyo, Japan", pages = "xi + 431", year = "1970", LCCN = "QD154 B619m 1970", bibdate = "Sat Oct 28 08:12:33 MDT 2023", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "1911--1996", subject = "Algebra; Alg{\`e}bre; algebra.; Algebra.", } @Article{Birkhoff:1970:PCS, author = "Garrett Birkhoff and Leon Kotin", title = "Positive cyclic systems of linear differential equations", journal = j-J-DIFFER-EQU, volume = "7", pages = "407--416", year = "1970", CODEN = "JDEQAK", DOI = "https://doi.org/10.1016/0022-0396(70)90089-6", ISSN = "0022-0396 (print), 1090-2732 (electronic)", ISSN-L = "0022-0396", MRclass = "34.42", MRnumber = "261083", MRreviewer = "G. Sansone", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0202.08501", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Differential Equations", GB-number = "156", journal-URL = "https://www.sciencedirect.com/journal/journal-of-differential-equations/issues", ZBmath = "3320578", } @Book{Birkhoff:1970:TLT, author = "Garrett Birkhoff and Samuel S. {Holland, Jr.} and Henry Crapo and Gian-Carlo Rota and George Gr{\"a}tzer", title = "Trends in Lattice Theory", volume = "31", publisher = pub-VAN-NOSTRAND-REINHOLD, address = pub-VAN-NOSTRAND-REINHOLD:adr, pages = "ix + 215", year = "1970", MRclass = "06-02", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Van Nostrand Reinhold Mathematical Studies", ZMnumber = "0198.33603", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3316070", } @InProceedings{Birkhoff:1970:WCL, author = "Garrett Birkhoff", title = "What can Lattices Do for You?", crossref = "Abbott:1970:TLT", pages = "1--40", year = "1970", bibdate = "Wed Nov 01 07:41:38 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "155", } @Book{MacLane:1970:ATS, author = "Saunders {Mac Lane} and Garrett Birkhoff", title = "Alg{\`e}bre. {Tome I}: {Structures} fondamentales", volume = "XXXV", publisher = pub-GAUTHIER-VILLARS, address = pub-GAUTHIER-VILLARS:adr, pages = "xxiii + 408", year = "1970", MRclass = "00.00", MRnumber = "266716", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Traduit de l'anglais par J. Weil, Pr{\'e}face de J. Dieudonn{\'e}", series = "Cahiers Scientifiques [Scientific Reports]", ZMnumber = "0201.01801", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", ZBmath = "3318658", } @Article{Birkhof:1971:MPIa, author = "Garet Birkhof", title = "Mathematics and psychology. {I}", journal = "Fiz.-Mat. Spis. B\bud lgar. Akad. Nauk.", volume = "14", number = "47", pages = "212--231", year = "1971", ISSN = "0015-3265", MRclass = "00A25 (92A25)", MRnumber = "396145", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "B\bud lgarska Akademiya na Naukite. Fizicheski Institut. Matematicheski Institut. Fiziko-Matematichesko Spisanie", } @Article{Birkhof:1971:MPIb, author = "Garet Birkhof", title = "Mathematics and psychology. {II}", journal = "Fiz.-Mat. Spis. B\bud lgar. Akad. Nauk.", volume = "14", number = "47", pages = "297--322", year = "1971", ISSN = "0015-3265", MRclass = "00A25 (92A25)", MRnumber = "396145", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "B\bud lgarska Akademiya na Naukite. Fizicheski Institut. Matematicheski Institut. Fiziko-Matematichesko Spisanie", } @TechReport{Birkhoff:1971:ASE, author = "Garrett Birkhoff", title = "Angular Singularities of Elliptic Problems", type = "Technical Report", number = "HUX-3971-5; NSA-25-018228", institution = "Harvard University", address = "Cambridge, MA, USA", pages = "??", day = "31", month = oct, year = "1971", bibdate = "Sat Nov 04 07:31:29 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://www.osti.gov/biblio/4035800", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", remark = "Published in \cite{Birkhoff:1972:ASE}.", } @Article{Birkhoff:1971:FEM, author = "Garrett Birkhoff and George J. Fix", title = "Finite Element Methods in Reactor Design Calculations", journal = j-TRANS-AM-NUCL-SOC, volume = "14", number = "1", pages = "199--??", month = jun, year = "1971", CODEN = "TANSAO", ISSN = "0003-018X", bibdate = "Sat Nov 04 07:35:20 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://www.osti.gov/biblio/4021529", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Transactions of the American Nuclear Society", journal-URL = "https://www.ans.org/pubs/transactions/", } @Book{Birkhoff:1971:NSE, author = "Garrett Birkhoff", title = "The Numerical Solution of Elliptic Equations", volume = "1", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xi + 82", year = "1971", MRclass = "65Mxx 65-01 65Nxx 65M99 65N99 35J99", MRnumber = "311125", MRreviewer = "J. Burlak", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics", ZMnumber = "0232.65068", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fseries = "CBMS-NSF Regional Conference Series in Applied Mathematics", ZBmath = "3368114", } @Article{Birkhoff:1971:OSG, author = "Garrett Birkhoff and Arthur S. Priver", title = "Optimal smoothing of {Gaussian} periodic data", journal = j-INDIANA-UNIV-MATH-J, volume = "21", number = "2", pages = "103--113", year = "1971", CODEN = "IUMJAB", DOI = "https://doi.org/10.1512/iumj.1971.21.21009", ISSN = "0022-2518", ISSN-L = "0022-2518", MRclass = "62.85 65D10", MRnumber = "282484", MRreviewer = "E. J. Hannan", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0251.65004", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Indiana University Mathematics Journal", GB-number = "161", journal-URL = "http://www.iumj.indiana.edu/", received = "8 March 1971", remark = "Web site says 1972 in citation output, but journal pages say 1971.", ZBmath = "3396976", } @InProceedings{Birkhoff:1971:PCS, author = "Garrett Birkhoff and Leon Kotin", booktitle = "Transactions of the Sixteenth Conference Army Mathematics", title = "Positive cyclic systems of linear differential equations", volume = "71-1", publisher = "U.S. Army Research Office", address = "Durham, NC, USA", pages = "102--111", year = "1971", MRclass = "34A30", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0265.34015", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3417866", } @InProceedings{Birkhoff:1971:RMA, author = "Garrett Birkhoff", editor = "Garrett Birkhoff and Marshall Hall", booktitle = "Computers in algebra and number theory {(Proceedings of the SIAM-AMS Symposium on Applied Mathematics, New York, 1970)}", title = "The role of modern algebra in computing", volume = "IV", publisher = pub-AMS, address = pub-AMS:adr, pages = "1--47", year = "1971", MRclass = "68-01 68W99 68Q25 94B99 94C11 93C05 68Q45 68-02", MRnumber = "378453", MRreviewer = "Bostwick F. Wyman", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "SIAM-AMS Proc.", ZMnumber = "0241.68003", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "169", ZBmath = "3381831", } @Article{Birkhoff:1971:TPI, author = "Garrett Birkhoff", title = "Tricubic polynomial interpolation", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "68", number = "6", pages = "1162--1164", day = "1", month = jun, year = "1971", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.68.6.1162", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", MRclass = "41A10 41A05 41A15", MRnumber = "299982", MRreviewer = "H. Brunner", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0242.41007", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the National Academy of Sciences of the United States of America", GB-number = "159", journal-URL = "http://www.pnas.org/content/by/year", ZBmath = "3382966", } @Book{MacLane:1971:ATI, author = "Saunders {Mac Lane} and Garrett Birkhoff", title = "Alg{\`e}bre, {Tome II}: {Les} grands th{\'e}or{\`e}mes", volume = "XXXVI", publisher = pub-GAUTHIER-VILLARS, address = pub-GAUTHIER-VILLARS:adr, pages = "xiv + 343 (+ loose errata)", year = "1971", MRclass = "00.00 08-01", MRnumber = "277320", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Traduit de l'anglais par J. Weil", series = "Cahiers Scientifiques [Scientific Reports]", ZMnumber = "0213.28901", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", ZBmath = "3338480", } @Article{Birkhoff:1972:ASE, author = "Garrett Birkhoff", title = "Angular singularities of elliptic problems", journal = j-J-APPROX-THEORY, volume = "6", pages = "215--230", year = "1972", CODEN = "JAXTAZ", DOI = "https://doi.org/10.1016/0021-9045(72)90075-5", ISSN = "0021-9045 (print), 1096-0430 (electronic)", ISSN-L = "0021-9045", MRclass = "35J15 35A35 65N30 35J25 (65P05)", MRnumber = "361423", MRreviewer = "Hans Kaper", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0252.35003", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Approximation Theory", GB-number = "162", journal-URL = "http://www.sciencedirect.com/science/journal/00219045", ZBmath = "3397996", } @Article{Birkhoff:1972:CTA, author = "Garrett Birkhoff", title = "Current trends in algebra", journal = "Matematikai Lapok. Bolyai J{\'a}nos Matematikai T{\'a}rsulat", volume = "23", pages = "237--255", year = "1972", ISSN = "0025-519X", MRclass = "01A65 (65-XX)", MRnumber = "360123", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, ajournal = "Mat. Lapok", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Matematikai Lapok. Bolyai J{\'a}nos Matematikai T{\'a}rsulat", } @Article{Birkhoff:1972:MEI, author = "Garrett Birkhoff", title = "Mathematical Education: The Impact of Computers on Undergraduate Mathematical Education in 1984", journal = j-AMER-MATH-MONTHLY, volume = "79", number = "6", pages = "648--657", month = jun # "\slash " # jul, year = "1972", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2317098", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:36:47 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "American Mathematical Monthly", GB-number = "163", journal-URL = "http://www.jstor.org/journals/00029890.html", } @InProceedings{Birkhoff:1972:PAI, author = "Garrett Birkhoff", editor = "A. K. Aziz", booktitle = "The mathematical foundations of the finite element method with applications to partial differential equations (Proceedings of the Symposium, University of Maryland, Baltimore, Md., 1972)", title = "Piecewise analytic interpolation and approximation in triangulated polygons", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "363--385", year = "1972", MRclass = "65D05 (65N30)", MRnumber = "411117", MRreviewer = "M. Zl{\'a}mal", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0305.65069", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "164", ZBmath = "3478346", } @Book{MacLane:1972:ASD, author = "S. {Mac Lane} and G. Birkhoff", title = "Alg{\`e}bre", publisher = pub-GAUTHIER-VILLARS, address = pub-GAUTHIER-VILLARS:adr, pages = "xii + 220", year = "1972", MRclass = "00A05 03-01 12-01 16-01", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Solutions d{\'e}velopp{\'e}es des exercises par J. Weil et J. Hocquemiller. 1re partie: Ensembles. Groupes. Anneaux. Corps.", ZMnumber = "0246.00001", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", language = "French", ZBmath = "3388951", } @Article{Barnhill:1973:SIT, author = "R. E. Barnhill and G. Birkhoff and W. J. Gordon", title = "Smooth interpolation in triangles", journal = j-J-APPROX-THEORY, volume = "8", pages = "114--128", year = "1973", CODEN = "JAXTAZ", DOI = "https://doi.org/10.1016/0021-9045(73)90020-8", ISSN = "0021-9045 (print), 1096-0430 (electronic)", ISSN-L = "0021-9045", MRclass = "41A05 65D05", MRnumber = "368382", MRreviewer = "T. J. Rivlin", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0271.41002", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Approximation Theory", GB-number = "170", journal-URL = "http://www.sciencedirect.com/science/journal/00219045", ZBmath = "3426165", } @Book{Birkhoff:1973:AAD, author = "Garrett Birkhoff and Thomas C. Bartee", title = "{Angewandte Algebra}. ({German}) [{Applied} Algebra]", publisher = pub-OLDENBOURG, address = pub-OLDENBOURG:adr, pages = "431 + 98 + 13", year = "1973", MRclass = "00A05", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Deutsche {\"U}bersetzung von Rudolf Herschel und Albert Lutz.", ZMnumber = "0272.00004", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", language = "German", ZBmath = "3427235", } @Article{Birkhoff:1973:CTA, author = "Garrett Birkhoff", title = "Current trends in algebra", journal = j-AMER-MATH-MONTHLY, volume = "80", number = "7", pages = "760--782", month = aug # "\slash " # sep, year = "1973", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2318163", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "01A65 (65-XX) 12-03 00A05", MRnumber = "321665", MRreviewer = "Peter M. Neumann", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0286.01013", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "American Mathematical Monthly", GB-number = "160", journal-URL = "http://www.jstor.org/journals/00029890.html", ZBmath = "3448513", } @InProceedings{Birkhoff:1973:END, author = "Garrett Birkhoff and Alan George", booktitle = "Complexity of sequential and parallel numerical algorithms ({Proceedings of the Symposium, Carnegie-Mellon Univ., Pittsburgh, Pa., 1973})", title = "Elimination by nested dissection", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "221--269", year = "1973", MRclass = "65F05 (68A20) 68Q25", MRnumber = "366010", MRreviewer = "Stephen A. Gourley", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0293.65017", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "167", ZBmath = "3459757", } @InProceedings{Birkhoff:1973:GLI, author = "Garrett Birkhoff and Leon Kotin", booktitle = "Transactions of the {Eighteenth Conference of Army Mathematicians (Feltman Research Laboratory, Picatinny Arsenal, Dover, New Jersey, 1972)}", title = "A generalization of {Liapunov}'s inequality", volume = "73-1", publisher = "U.S. Army Research Office (Durham)", address = "Durham, NC, USA", pages = "203--211", year = "1973", MRclass = "34B10 49K30 70J99 70K99", MRnumber = "382771", MRreviewer = "Pan-Tai Liu", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "U.S. Army Research Office (Durham), Report", ZMnumber = "0352.49006", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3548010", } @Article{Birkhoff:1973:IBD, author = "Garrett Birkhoff", title = "Interpolation to boundary data in triangles", journal = j-J-MATH-ANAL-APPL, volume = "42", number = "2", pages = "474--484", month = may, year = "1973", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(73)90154-6", ISSN = "0022-247x (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "65D05 (41A05) 41A10 41A63 65D05", MRnumber = "339445", MRreviewer = "R. E. Barnhill", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Collection of articles dedicated to Salomon Bochner", ZMnumber = "0262.41003", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematical Analysis and Applications", GB-number = "166", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ZBmath = "3413182", } @InProceedings{Birkhoff:1973:MAC, author = "Garrett Birkhoff", editor = "L. I. Sedov and G. Yu. Stepanov", booktitle = "{Neustan. Tecenija Vody bol's. Skorost., Trudy mezdunarod. Simpoz. Leningrad 1971}", title = "Mathematical analysis of cavitation", publisher = "Nauka", address = "Moscow, USSR", pages = "19--38", year = "1973", MRclass = "76B10 65Z05", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0286.76011", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "168", xxbooktitle = "Proceedings of the IUTAM Symposium on Non-Steady Flow of Water at High Speeds", ZBmath = "3449895", } @Article{Birkhoff:1973:NTF, author = "Garrett Birkhoff", title = "Numerical techniques of fluid flow", journal = j-TRANS-AM-NUCL-SOC, volume = "17", number = "??", pages = "242--??", month = nov, year = "1973", CODEN = "TANSAO", DOI = "TANSAO", ISSN = "0003-018X", ISSN-L = "0003-018X", bibdate = "Sat Nov 04 06:50:55 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://www.osti.gov/biblio/4391942", acknowledgement = ack-nhfb, ajournal = "Trans. Am. Nucl. Soc.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Transactions of the American Nuclear Society", journal-URL = "https://www.ans.org/pubs/transactions/", remark = "Joint meeting of the American Nuclear Society and the Atomic Industrial Forum and Nuclear Energy Exhibition, San Francisco, California, USA, 11 Nov 1973.", } @Book{Birkhoff:1973:SBC, editor = "Garrett Birkhoff", title = "A Source Book in Classical Analysis", publisher = pub-HARVARD, address = pub-HARVARD:adr, pages = "xii + 470", year = "1973", ISBN = "0-674-82245-5 (hardcover)", ISBN-13 = "978-0-674-82245-0 (hardcover)", LCCN = "QA300 .B54 1973", MRclass = "01A55 00A05 26-03 01A60 30-03 40-03 41-03 33-03 34-03 35-03 49-03 45-03", bibdate = "Sat Oct 28 08:27:05 MDT 2023", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Source books in the history of the sciences", ZMnumber = "0275.01009", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", shorttableofcontents = "1. Foundations of real analysis \\ A. Cauchy's partial rigorization \\ B. Continuity and integrability \\ \\ 2. Foundations of complex analysis \\ A. Early developments \\ B. Riemann's influence \\ \\ 3. Convergent expansions \\ A. The convergence of power series \\ B. The influence of Weierstrass \\ \\ 4. Asymptotic expansions \\ A. Analytic number theory \\ B. Asymptotic series \\ \\ 5. Fourier series and integrals \\ A. Fourier series \\ B. The Fourier integral \\ \\ 6. Elliptic and abelian integrals \\ \\ 7. Elliptic and automorphic functions \\ A. Elliptic and hyperelliptic functions \\ B. Automorphic functions \\ \\ 8. Ordinary differential equations I \\ A. Existence and uniqueness theorems \\ B. Sturm--Liouville theory \\ \\ 9. Ordinary differential equations II \\ A. Regular singular points \\ B. Other fundamental contributions \\ \\ 10. Partial differential equations \\ A. The Cauchy--Kowalewski theorem \\ B. Beginnings of potential theory \\ C. Potential theory develops \\ \\ 11. Calculus of variations \\ A. Variational principles of dynamics \\ B. Intuitive uses of variational principles \\ C. Rigorous existence theorems \\ \\ 12. Wave equations and characteristics \\ \\ 13. Integral equations", subject = "Mathematical analysis; History; Sources; Analyse math{\'e}matique; Histoire; Mathematical analysis.", tableofcontents = "1: Foundations of Real Analysis / 1 \\ A. Cauchy's Partial Rigorization / 1 \\ 1a. Cauchy on Limits and Continuity / 2 \\ 1b. Cauchy on convergence / 3 \\ 1c. Cauchy on the Radius of Convergence / 4 \\ 2. Cauchy on the Derivative as a Limit / 4 \\ 3. Cauchy on Maclaurin's Theorem / 6 \\ 4. Cauchy--Moigno on the Fundamental Theorem of the Calculus / 8 \\ B. Continuity and Integrability / 11 \\ 5. Bolzano on Continuity and Limits / 15 \\ 6. Riemann on Fourier Series and the Riemann Integral / 16 \\ 7a. Heine Discusses Fourier Series / 23 \\ 7b. Heine on the Foundations of Function Theory / 25 \\ 8. Stieltjes on the Stieltjes Integral / 26 \\ \\ 2: Foundations of Complex Analysis / 31 \\ A. Early Developments / 31 \\ 9. Cauchy's Integral Theorem / 33 \\ 10. Cauchy's Integral Formula / 37 \\ 11. Cauchy's Calculus of Residues / 40 \\ 12a. Cauchy on Liouville's Theorem / 44 \\ 12b. Jordan on Liouville's Theorem / 45 \\ B. Riemann's Influence / 46 \\ 13. Riemann on the Cauchy--Riemann Equations / 48 \\ 14. Riemann on Riemann Surfaces / 50 \\ 15. Schwarz on Conformal Mapping / 56 \\ \\ 3: Convergent Expansions / 60 \\ A. The Convergence of Power Series / 60 \\ 16. Gauss on the Hypergeometric Series / 62 \\ 17. Abel on the Binomial Series / 68 \\ B. The Influence of Weierstrass / 71 \\ 18. Weierstrass on Analytic Functions of several Variables / 74 \\ 19. Picard on Picard's Theorem / 79 \\ 20a. Weierstrass on Infinite Products / 80 \\ 20b. Mittag-Leffler's Theorem / 88 \\ \\ 4: Asymptotic Expansions / 93 \\ A. Analytic Number Theory / 93 \\ 21. Riemann on the Riemann Zeta Function / 95 \\ 22. Hadamard on the Distribution of Primes / 98 \\ B. Asymptotic Series / 104 \\ 23. Stirling's Formula / 105 \\ 24. Laplace on Generating Functions / 108 \\ 25. Abel on the Laplace Transform / 115 \\ 26. Poincar{\'e} on Asymptotic Series / 117 \\ 27. Lerch on Lerch's Theorem / 125 \\ \\ 5: Fourier Series and Integrals / 130 \\ A. Fourier Series / 130 \\ 28. Fourier on Heat Flow in a Slab / 132 \\ 29a. Fourier on Expansions in Sine Series / 138 \\ 29b. Fourier on Heat Flow in a Ring / 141 \\ 30. Dirichlet on the Convergence of Fourier Series / 145 \\ 31. Wilbraham on the Gibbs Phenomenon / 147 \\ 32. Fej{\'e}r on the Convergence of Fourier Series / 150 \\ B. The Fourier Integral / 156 \\ 33a--b. Cauchy on the Fourier Integral / 157 \\ 34. Fourier on the Fourier Integral / 164 \\ 35. Cauchy on Linear Partial Differential Equations with Constant Coefficients / 170 \\ \\ 6: Elliptic and Abelian Integrals / 175 \\ 36. Legendre on Elliptic Integrals / 177 \\ 37. Abel's Addition Theorem / 188 \\ 38. Abel on Hyperelliptic Integrals / 190 \\ 39a. Riemann on Abelian Integrals / 196 \\ 39b. Roch on the Riemann--Roch Theorem / 201 \\ \\ 7: Elliptic and Automorphic Functions / 204 \\ A. Elliptic and Hyperelliptic Functions / 204 \\ 40. Abel on Elliptic Functions / 206 \\ 41. Jacobi on Elliptic Functions / 207 \\ 42. Jacobi on Some Identities / 212 \\ 43. Jacobi on the Jacobi Theta Functions / 218 \\ 44. Weierstrass's Al Functions / 224 \\ B. Automorphic Functions / 229 \\ 45. Poincar{\'e} on Automorphic Functions / 230 \\ 46. Klein on Fundamental Regions of Discontinuous Groups / 000 \\ \\ 8: Ordinary Differential Equations. I. / 242 \\ A. Existence and Uniqueness Theorems / 242 \\ 47. Cauchy on the Cauchy Polygon Method / 243 \\ 48. Lipschitz on the Lipschitz Condition / 247 \\ 49. Picard on the Picard Method / 250 \\ 50. Osgood's Existence Theorem / 251 \\ B. Sturm--Liouville Theory / 258 \\ 51. Sturm on Sturm's Theorems / 259 \\ 52. Liouville on Sturm--Liouville Expansions. I. / 268 \\ 53. Liouville on Sturm--Liouville Expansions. II. / 276 \\ \\ 9: Ordinary Differential Equations. II. / 282 \\ A. Regular Singular Points / 282 \\ 54. Fuchs on Isolated Singular Points / 283 \\ 55. Frobenius on Regular Singular Points / 293 \\ B. Other Fundamental Contributions / 299 \\ 56. Lie on Groups of Transformations / 300 \\ 57. Poincar{\'e} on the Qualitative Theory of Differential Equations / 305 \\ 58. Peano on the Peano Series / 311 \\ \\ 10: Partial Differential Equations / 318 \\ A. The Cauchy--Kowalewski Theorem / 318 \\ 59. Cauchy on the Cauchy--Kowalewski Theorem / 319 \\ 60. Kowalewski on the Cauchy--Kowalewski Theorem / 327 \\ B. Beginnings of Potential Theory / 335 \\ 61. Laplace on the Laplacian Operator / 336 \\ 62. Legendre on Legendre Polynomials / 338 \\ 63. Poisson on the Poisson Equation / 342 \\ C. Potential Theory Develops / 346 \\ 64. Green on Green's Identities / 347 \\ 65. Gauss on Potential Theory / 358 \\ 66. Kelvin on Inversion / 362 \\ \\ 11: Calculus of Variations / 365 \\ A. Variational Principles of Dynamics / 365 \\ 67. Lagrange on Properties Related to Least Action / 367 \\ 68. Hamilton on Hamilton's Principle / 370 \\ 69. Jacobi on the Hamilton--Jacobi Equations / 374 \\ B. Intuitive Uses of Variational Principles / 379 \\ 70a. Kelvin on the Dirichlet Principle / 380 \\ 70b. Kelvin on a Variational Principle of Hydrodynamics / 383 \\ 71a. Dirichlet on the Dirichlet Principle / 385 \\ 71b. Rayleigh on the Rayleigh--Ritz Method / 386 \\ C. Rigorous Existence Theorems / 396 \\ 72. Du Bois--Reymond on the Fundamental Theorem of the Calculus of Variations / 392 \\ 73. Poincar{\'e} on His M{\'e}thode de Balayage / 395 \\ 74. Hilbert on Dirichlet's Principle / 399 \\ \\ 12: Wave Equations and Characteristics / 403 \\ 75. Riemann on Plane Waves of Finite Amplitude / 406 \\ 76. Helmholtz on the Helmholtz Equation / 414 \\ 77. Kirchhoff's Identities for the Wave Equation / 417 \\ 78. Volterra on Characteristics / 421 \\ \\ 13: Integral Equations / 435 \\ 79. Abel's Integral Equation / 437 \\ 80. Volterra on Inverting Integral Equations / 442 \\ 81. Fredholm on the Theory of Integral Equations / 449 \\ \\ Short Bibliography / 466 \\ \\ Index / 468", ZBmath = "3432186", } @InCollection{Birkhoff:1973:SWS, author = "Garr Birkhoff and J. Bona and Joseph {Kamp{\'e} de F{\'e}riet}", booktitle = "Probabilistic methods in applied mathematics, {Vol}. 3", title = "Statistically well-set {Cauchy} problems", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "1--120", year = "1973", MRclass = "35R99 (60H99)", MRnumber = "610264", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "165", } @Book{MacLane:1973:ASD, author = "S. {Mac Lane} and G. Birkhoff", title = "Alg{\`e}bre. {Solutions} d{\'e}velopp{\'e}es des exercices par {D. Allouch, A. Mezard, J.-C. Vaillant, J. Weil}. 2i{\`e}me partie: {Alg{\`e}bre} lin{\'e}aire", publisher = pub-GAUTHIER-VILLARS, address = pub-GAUTHIER-VILLARS:adr, pages = "x + 233", year = "1973", MRclass = "00A05 15-01", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0275.00002", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", language = "French", ZBmath = "3432168", } @Article{Birkhof:1974:CTA, author = "Garet Birkhof", title = "Current trends in algebra", journal = "Fiz.-Mat. Spis. B\bud lgar. Akad. Nauk.", volume = "17(50)", pages = "190--210", year = "1974", ISSN = "0015-3265", MRclass = "00A05", MRnumber = "396133", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "B\bud lgarska Akademiya na Naukite. Fizicheski Institut. Matematicheski Institut. Fiziko-Matematichesko Spisanie", } @Article{Birkhoff:1974:BRO, author = "Garrett Birkhoff", title = "Book Review: {{\booktitle{Origins of modern algebra}}: By Lubos Novy. Prague (Academia), 1973. 260 p}", journal = j-HIST-MATH, volume = "1", number = "3", pages = "333--337", month = aug, year = "1974", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:16:24 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086074900780", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", } @Article{Birkhoff:1974:CCT, author = "Garrett Birkhoff", title = "Corrections to: {``Current trends in algebra'' (Amer. Math. Monthly {\bf 80} (1973), 760--782)}", journal = j-AMER-MATH-MONTHLY, volume = "81", number = "7", pages = "746", month = aug # "\slash " # sep, year = "1974", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2319563", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "01A65 (65-XX) 00A05 12-03", MRnumber = "345777", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0292.01020", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", ZBmath = "3456869", } @Article{Birkhoff:1974:CTFa, author = "Garrett Birkhoff and Lois Mansfield", title = "Compatible triangular finite elements", journal = j-J-MATH-ANAL-APPL, volume = "47", number = "3", pages = "531--553", month = sep, year = "1974", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(74)90006-7", ISSN = "0022-247x (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "35J30 35A99 35A35 65N12 65N30 (41A05)", MRnumber = "359353", MRreviewer = "R. E. Barnhill", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0284.35021", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematical Analysis and Applications", GB-number = "171", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ZBmath = "3445723", } @Article{Birkhoff:1974:CTFb, author = "Garrett Birkhoff", title = "Current trends in algebra", journal = "Matematikai Lapok. Bolyai J{\'a}nos Matematikai T{\'a}rsulat", volume = "23", pages = "237--255", year = "1974", ISSN = "0025-519X", MRclass = "01A65 13-03 12-03", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0302.01002", acknowledgement = ack-nhfb, ajournal = "Mat. Lapok", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Matematikai Lapok", language = "Hungarian", ZBmath = "3472012", } @Article{Birkhoff:1974:MAL, author = "Garrett Birkhoff and James C. Cavendish and William J. Gordon", title = "Multivariate approximation by locally blended univariate interpolants", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "71", number = "9", pages = "3423--3425", day = "1", month = sep, year = "1974", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.71.9.3423", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", MRclass = "65N35 (41A05) 41A63 65D05 41A15 41A25 65N30", MRnumber = "356543", MRreviewer = "C. W. Clenshaw", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0292.41002", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the National Academy of Sciences of the United States of America", GB-number = "172", journal-URL = "http://www.pnas.org/content/by/year", ZBmath = "3457466", } @Article{Birkhoff:1974:OFP, author = "Garrett Birkhoff and Surender Gulati", title = "Optimal few-point discretizations of linear source problems", journal = j-SIAM-J-NUMER-ANAL, volume = "11", pages = "700--728", year = "1974", CODEN = "SJNAAM", DOI = "https://doi.org/10.1137/0711057", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65N05 65N06 65N12", MRnumber = "362933", MRreviewer = "Clarence M. Ablow", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0293.65079", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "SIAM Journal on Numerical Analysis", GB-number = "173", journal-URL = "http://epubs.siam.org/sinum", ZBmath = "3459819", } @InProceedings{Birkhoff:1974:UAA, author = "Garrett Birkhoff and John D. Lipson", booktitle = "Proceedings of the {Tarski Symposium (Proceedings of the Symposium on Pure Mathematics in Honor of Alfred Tarski, Vol. XXV, University of California, Berkeley, Calif., 1971)}", title = "Universal algebra and automata", volume = "XXV", publisher = pub-AMS, address = pub-AMS:adr, pages = "41--51", year = "1974", MRclass = "68Q45 08Axx 68A25 (08A25)", MRnumber = "359400", MRreviewer = "F. G{\'e}cseg", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Proceedings of the Symposium Pure Math.", ZMnumber = "0312.94025", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "174", remark = "Published for the Association for Symbolic Logic by the AMS.", ZBmath = "3489035", } @Article{Anonymous:1975:ORC, author = "Anonymous", title = "Opening remarks for the conference by {Garrett Birkhoff} and {I. B. Cohen}", journal = j-HIST-MATH, volume = "2", number = "4", pages = "433--436", month = nov, year = "1975", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:16:33 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086075900993", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Birkhoff:1975:B, author = "Garrett Birkhoff and Sue Ann Garwood", title = "Bibliographies", journal = j-HIST-MATH, volume = "2", number = "4", pages = "605--615", month = nov, year = "1975", CODEN = "HIMADS", DOI = "https://doi.org/10.1016/0315-0860(75)90130-5", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", MRclass = "01-01 (00A15)", MRnumber = "472305", bibdate = "Wed Jun 26 06:16:33 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086075901305", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860", } @TechReport{Birkhoff:1975:FRS, author = "Garrett Birkhoff", title = "Final report [on solving the multigroup diffusion equations]", institution = "Office of Scientific and Technical Information ({OSTI})", address = "Washington, DC, USA", pages = "5", month = jan, year = "1975", DOI = "https://doi.org/10.2172/4110081", bibdate = "Sat Nov 04 07:17:44 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://www.osti.gov/servlets/purl/4110081", abstract = "Progress achieved in the development of variational methods for solving the multigroup neutron diffusion equations is described. An appraisal is made of the extent to which improved variational methods could advantageously replace difference methods currently used.", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @InProceedings{Birkhoff:1975:GTO, author = "Garrett Birkhoff and Leon Kotin", booktitle = "Transactions of the {20th Conference on Army Mathematics, Natick, Mass. 1974}", title = "The geometry of third-order positive cyclic systems of linear differential equations", publisher = "????", address = "????", pages = "97--112", year = "1975", MRclass = "34C10 34A30", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0348.34021", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3542806", } @Article{Birkhoff:1975:Ia, author = "Garrett Birkhoff", title = "Introduction", journal = j-HIST-MATH, volume = "2", number = "4", pages = "437--438", month = nov, year = "1975", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:16:33 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086075901007", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", } @Article{Birkhoff:1975:Ib, author = "Garrett Birkhoff", title = "Introduction", journal = j-HIST-MATH, volume = "2", number = "4", pages = "473--474", month = nov, year = "1975", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:16:33 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086075901081", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", } @Article{Birkhoff:1975:Ic, author = "Garrett Birkhoff", title = "Introduction", journal = j-HIST-MATH, volume = "2", number = "4", pages = "503--505", month = nov, year = "1975", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:16:33 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086075901123", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", } @Article{Birkhoff:1975:Id, author = "Garrett Birkhoff", title = "Introduction", journal = j-HIST-MATH, volume = "2", number = "4", pages = "535--536", month = nov, year = "1975", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:16:33 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086075901172", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", } @Article{Birkhoff:1975:Ie, author = "Garrett Birkhoff", title = "Introduction", journal = j-HIST-MATH, volume = "2", number = "4", pages = "573--574", month = nov, year = "1975", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:16:33 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086075901238", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", } @Article{Birkhoff:1975:MCS, author = "Garrett Birkhoff", title = "Mathematics and Computer Science: Skillful combinations of mathematics and computer science hold great promise for the future", journal = j-AM-SCI, volume = "63", number = "1", pages = "83--91", month = jan # "\slash " # feb, year = "1975", CODEN = "AMSCAC", ISSN = "0003-0996 (print), 1545-2786 (electronic)", ISSN-L = "0003-0996", bibdate = "Wed Nov 01 07:54:48 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://www.jstor.org/stable/27845273", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "American Scientist", journal-URL = "http://www.americanscientist.org/issues/past.aspx; https://www.jstor.org/journal/amerscie", remark = "Journal Web site has no coverage before 1998.", } @InProceedings{Birkhoff:1975:NSHa, author = "Garrett Birkhoff and Vassilios A. Dougalis", editor = "R. Vichnevetsky", booktitle = "Advances in computer methods for partial differential equations: proceedings of the {AICA International Symposium on Computer Methods for Partial Differential Equations, held at Lehigh University, Bethlehem, Pennsylvania, U.S.A., June 17--19, 1975}", title = "Numerical Solution of Hydrodynamic Problems", publisher = "AICA", address = "New Brunswick, NJ, USA", bookpages = "vii + 402", pages = "7--13", year = "1975", LCCN = "QA377 .A2 1975", bibdate = "Wed Nov 01 08:00:39 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "177", xxbooktitle = "Proceedings of the {AICA} International Symposium on Computer Methods", } @Article{Birkhoff:1975:NSHb, author = "Garrett Birkhoff and Vassilios A. Dougalis", title = "Numerical solution of hydrodynamic problems", journal = "AICA", volume = "17", pages = "88--94", year = "1975", CODEN = "AAICAE", ISSN = "0020-594X", ISSN-L = "0020-594X", MRclass = "76Q05 76B15 65N06 65N12", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0316.76048", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "AICA. Annales de l'Association Internationale pour le Calcul Analogique et de Simulation Hybrides", ZBmath = "3495788", } @Article{Birkhoff:1975:P, author = "Garrett Birkhoff and Sue Ann Garwood", title = "Preface", journal = j-HIST-MATH, volume = "2", number = "4", pages = "429--430", month = nov, year = "1975", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:16:33 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/031508607590097X", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", } @Article{Birkhoff:1975:THN, author = "Garrett Birkhoff", title = "Two {Hadamard} numbers for matrices", journal = j-CACM, volume = "18", number = "1", pages = "25--29", month = jan, year = "1975", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/360569.360655", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", MRclass = "65F15 65F35 15A12", MRnumber = "373264", MRreviewer = "John Todd", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib", note = "Collection of articles honoring Alston S. Householder", ZMnumber = "0304.65026", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Communications of the Association for Computing Machinery", GB-number = "175", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", ZBmath = "3476475", } @Book{Hooker:1975:LAA, editor = "C. A. Hooker", title = "The logico-algebraic approach to quantum mechanics. {Vol}. {I}: {Historical} evolution", volume = "5", publisher = "D. Reidel Publishing Company, Dordrecht", year = "1975", ISSN = "1566-659X", MRclass = "03G12 03-06 03-03 81Pxx 81-06 81-03 81-02 01A60 01A75 03-02", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Univ. West. Ont. Ser. Philos. Sci.", ZMnumber = "0429.03045", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fseries = "The University of Western Ontario Series in Philosophy of Science", ZBmath = "3668602", } @Article{Birkhoff:1976:AFD, author = "Garrett Birkhoff and Leon Kotin", title = "Autonomous families of differential systems", journal = j-J-MATH-ANAL-APPL, volume = "55", number = "2", pages = "466--475", month = aug, year = "1976", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(76)90176-1", ISSN = "0022-247x (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "37-XX 34C10 (93C15)", MRnumber = "499435", MRreviewer = "E. O. Roxin", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0342.34031", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematical Analysis and Applications", GB-number = "180", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ZBmath = "3533333", } @InProceedings{Birkhoff:1976:CNM, author = "Garrett Birkhoff and Vassilios A. Dougalis", editor = "Joanna W. Schot and Nils Salvesen", booktitle = "Proceedings of the {First International Conference on Numerical Ship Hydrodynamics, 20--22 October, 1975}", title = "Comparison of Numerical Methods for Solving Wave Equations", publisher = "David W. Taylor Naval Ship Research and Development Center", address = "Bethesda, MD, USA", bookpages = "x + 733", pages = "231--252", year = "1976", LCCN = "VM156 .I568 1975", bibdate = "Wed Nov 01 08:02:49 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "181", xxbooktitle = "First International Conference on Numerical Ship Hydrodynamics, {David Taylor Model Basin}", xxnote = "Check author order??", } @Article{Birkhoff:1976:CTAa, author = "Garrett Birkhoff", title = "Current trends in algebra", journal = j-POKROKY-MAT-FYS-ASTRON, volume = "21", number = "4", pages = "199--211", year = "1976", CODEN = "PMFAA4", ISSN = "0032-2423", ISSN-L = "0032-2423", MRclass = "01A65 12-03 20-03 17-03 03-03", MRnumber = "504993", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0338.01011; 0328.01013", acknowledgement = ack-nhfb, ajournal = "Pokroky Mat. Fyz. Astronom.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Vyd{\'a}v{\'a} Jednota {\v{C}}esk{\'y}ch Matematik\ocirc{u} a Fyzik\ocirc{u} a Jednota Slovensk{\'y}ch Matematikov a Fyzikov. Pokroky Matematiky Fyziky \& Astronomie", language = "Slovak", ZBmath = "3528186; 3513729", } @Article{Birkhoff:1976:CTAb, author = "Garrett Birkhoff", title = "Current trends in algebra", journal = j-POKROKY-MAT-FYS-ASTRON, volume = "21", number = "??", pages = "249--259", year = "1976", CODEN = "PMFAA4", ISSN = "0032-2423", ISSN-L = "0032-2423", MRclass = "01A65 12-03", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0338.01011", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Pokroky Matematiky, Fyziky \& Astronomie", language = "Slovak", ZBmath = "3528186", } @Article{Birkhoff:1976:HMA, author = "Garrett Birkhoff", title = "House monotone apportionment schemes", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "73", number = "3", pages = "684--686", day = "1", month = mar, year = "1976", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.73.3.684", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", MRclass = "90C90 90C10 92D25 92A20", MRnumber = "403731", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0322.90075", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Proceedings of the National Academy of Sciences of the United States of America", GB-number = "178", journal-URL = "http://www.pnas.org/content/by/year", ZBmath = "3504711", } @Article{Birkhoff:1976:MP, author = "Garrett Birkhoff", title = "Mathematics and psychology", journal = j-POKROKY-MAT-FYS-ASTRON, volume = "21", pages = "1--16", year = "1976", CODEN = "PMFAA4", ISSN = "0032-2423", ISSN-L = "0032-2423", MRclass = "91E99", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0315.92018", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Pokroky Matematiky, Fyziky \& Astronomie", language = "Czech", ZBmath = "3494220", } @Article{Birkhoff:1976:NUT, author = "Garrett Birkhoff", title = "Note on universal topological algebra", journal = j-ALGEBRA-UNIVERS, volume = "6", number = "1", pages = "21--23", year = "1976", DOI = "https://doi.org/10.1007/BF02485812", ISSN = "0002-5240 (print), 1420-8911 (electronic)", ISSN-L = "0002-5240", MRclass = "06B23 06-00 08A05 08A25", MRnumber = "398949", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0375.06006", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Algebra Universalis", GB-number = "179", journal-URL = "https://www.springer.com/journal/12", ZBmath = "3583874", } @Article{Birkhoff:1976:OSU, author = "Garrett Birkhoff and Leon Kotin", title = "The orbit structure of uniformly positive cyclic systems", journal = j-J-MATH-ANAL-APPL, volume = "55", number = "2", pages = "476--489", month = aug, year = "1976", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(76)90177-3", ISSN = "0022-247x (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "37-XX 34A30 34C05 34C10 93A99 (34C25 58F15)", MRnumber = "490112", MRreviewer = "Milan Medve\v{d}", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0342.34032", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", ZBmath = "3533334", } @Article{Birkhoff:1976:PM, author = "Garret Birkhoff", title = "Psychology of mathematics", journal = j-POKROKY-MAT-FYS-ASTRON, volume = "21", number = "1", pages = "1--16", year = "1976", CODEN = "PMFAA4", ISSN = "0032-2423", ISSN-L = "0032-2423", MRclass = "00A25 (92A25)", MRnumber = "484896", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Translated from the English (SIAM Rev. {\bf 11} (1969), 429--469).", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Vyd{\'a}v{\'a} Jednota {\v{C}}esk{\'y}ch Matematik\ocirc{u} a Fyzik\ocirc{u} a Jednota Slovensk{\'y}ch Matematikov a Fyzikov. Pokroky Matematiky Fyziky \& Astronomie", } @InCollection{Birkhoff:1976:RMAa, author = "Garrett Birkhoff", editor = "Dalton Tarwater", booktitle = "Men and Institutions in {America}", title = "The Rise of Modern Algebra to 1936", volume = "13", publisher = "Texas Technological University", address = "Lubbock, TX, USA", pages = "41--63", year = "1976", bibdate = "Wed Nov 01 08:05:05 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Texas Tech. Graduate Studies", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "182a", } @InCollection{Birkhoff:1976:RMAb, author = "Garrett Birkhoff", editor = "Dalton Tarwater", booktitle = "Men and Institutions in {America}", title = "The Rise of Modern Algebra, 1936--1950", volume = "13", publisher = "Texas Technological University", address = "Lubbock, TX, USA", pages = "65--85", year = "1976", bibdate = "Wed Nov 01 08:05:05 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Texas Tech. Graduate Studies", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "182b", } @Book{MacLane:1976:ASD, author = "S. {Mac Lane} and G. Birkhoff", title = "Alg{\`e}bre", publisher = pub-GAUTHIER-VILLARS, address = pub-GAUTHIER-VILLARS:adr, pages = "184", year = "1976", MRclass = "20-01 12-01 15-01 11R32 20F99 20K99 20H99", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Solutions d{\'e}velopp{\'e}es des exercices par Charles DeLorme, Alain Mezard, Christine Lavit, Jean-Claude Raoult. 3e partie: Les grands th{\'e}oremes.", ZMnumber = "0346.20001", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", language = "French", ZBmath = "3539418", } @Book{Birkgoff:1977:CMP, author = "Garret Birkgoff", title = "{{\cyr Matematika i psikhologiya}}", publisher = "Izdat. ``Sovetskoe Radio''", address = "Moscow, USSR", pages = "96", year = "1977", MRclass = "92A25", MRnumber = "469346", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Translated from the English by G. N. Povarov", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @InCollection{Birkhoff:1977:AMF, author = "Garrett Birkhoff", editor = "Edward Teller and Robb W. Thomson", booktitle = "Science and Technology in {America}: an Assessment", title = "Applied Mathematics and its Future", volume = "465", publisher = pub-NBS, address = pub-NBS:adr, bookpages = "vi + 162", pages = "82--104", year = "1977", CODEN = "XNBSAV", bibdate = "Wed Nov 01 08:06:28 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/t/teller-edward.bib", note = "The Distinguished Lecture Series published on the occasion of the 75th Anniversary of the National Bureau of Standards.", series = "National Bureau of Standards Special Publication", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "183", } @Article{Birkhoff:1977:BRA, author = "Garrett Birkhoff", title = "Book Review: {{\booktitle{Adventures of a mathematician}}: By S. M. Ulam. New York (Scribners). 1976. 317 pp. \$17.50}", journal = j-HIST-MATH, volume = "4", number = "2", pages = "233--236", month = may, year = "1977", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:16:45 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086077901318", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", } @InProceedings{Birkhoff:1977:SLA, author = "Garrett Birkhoff", title = "Some Leaders in {American} Mathematics", crossref = "Tarwater:1977:BTA", pages = "25--78", year = "1977", bibdate = "Wed Nov 01 08:20:15 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "185", remark = "John von Neuman has several mentions, particularly on pages 65--67.", subject-dates = "Neumann J{\'a}nos (1903-1957)", } @Book{Birkhoff:1977:SMA, author = "Garrett Birkhoff and Saunders {Mac Lane}", title = "A Survey of Modern Algebra", publisher = pub-MACMILLAN, address = pub-MACMILLAN:adr, edition = "Fourth", pages = "xi + 500", year = "1977", ISBN = "0-02-310070-2", ISBN-13 = "978-0-02-310070-3", LCCN = "QA162 .B57 1977", MRclass = "00A05 13-01 12-01 03-01 15-01 16-01", bibdate = "Sun Oct 29 06:02:57 MDT 2023", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0365.00006", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", shorttableofcontents = "1: The integers \\ 2: Rational numbers and fields \\ 3: Polynomials \\ 4: Real numbers \\ 5: Complex numbers \\ 6: Groups \\ 7: Vectors and vector spaces \\ 8: The algebra of matrices \\ 9: Linear group \\ 10: Determinants and canonical forms \\ 11: Boolean algebras and lattices \\ 12: Transfinite arithmetic \\ 13: Rings and ideals \\ 14: Algebraic number fields \\ 15: Galois theory \\ Bibliography \\ List of Special Symbols \\ Index", tableofcontents = "Preface to the Fourth Edition / v \\ \\ 1: The Integers / 1 \\ 1.1 Commutative Rings; Integral Domains / 1 \\ 1.2 Elementary Properties of Commutative Rings / 3 \\ 1.3 Ordered Domains / 8 \\ 1.4 Well-Ordering Principle / 11 \\ 1.5 Finite Induction; Laws of Exponents / 12 \\ 1.6 Divisibility / 16 \\ 1.7 The Euclidean Algorithm / 18 \\ 1.8 Fundamental Theorem of Arithmetic / 23 \\ 1.9 Congruences / 25 \\ 1.10 The Rings $Z_n$ / 29 \\ 1.11 Sets, Functions, and Relations / 32 \\ 1.12 Isomorphisms and Automorphisms / 35 \\ \\ 2: Rational Numbers and Fields / 38 \\ 2.1 Definition of a Field / 38 \\ 2.2 Construction of the Rationals / 42 \\ 2.3 Simultaneous Linear Equations / 47 \\ 2.4 Ordered Fields / 52 \\ 2.5 Postulates for the Positive Integers / 54 \\ 2.6 Peano Postulates / 57 \\ \\ 3: Polynomials / 61 \\ 3.1 Polynomial Forms / 61 \\ 3.2 Polynomial Functions / 65 \\ 3.3 Homomorphisms of Commutative Rings / 69 \\ 3.4 Polynomials in Several Variables / 72 \\ 3.5 The Division Algorithm / 74 \\ 3.6 Units and Associates / 76 \\ 3.7 Irreducibie Polynomials / 78 \\ 3.8 Unique Factorization Theorem / 80 \\ 3.9 Other Domains with Unique Factorization / 84 \\ 3.10 Eisenstein s Irreducibility Criterion / 88 \\ 3.11 Partial Fractions / 90 \\ \\ 4: Real Numbers / 94 \\ 4.1 Dilemma of Pythagoras / 94 \\ 4.2 Upper and Lower Bounds / 96 \\ 4.3 Postulates for Real Numbers / 98 \\ 4.4 Roots of Polynomial Equations / 101 \\ 4.5 Dedekind Cuts / 104 \\ \\ 5: Complex Numbers / 107 \\ 5.1 Definition / 107 \\ 5.2 The Complex Plane / 110 \\ 5.3 Fundamental Theorem of Algebra / 113 \\ 5.4 Conjugate Numbers and Real Polynomials / 117 \\ 5.6 Quadratic and Cubic Equations / 118 \\ 5.6 Solution of Quartic by Radicals / 121 \\ 5.7 Equations of Stable Type / 122 \\ \\ 6: Groups / 124 \\ 6.1 Symmetries of the Square / 124 \\ 6.2 Groups of Transformations / 126 \\ 6.3 Further Examples / 131 \\ 6.4 Abstract Groups / 133 \\ 6.5 Isomorphism / 137 \\ 6.6 Cyclic Groups / 140 \\ 6.7 Subgroups / 143 \\ 6.8 Lagrange s Theorem / 146 \\ 6.9 Permutation Groups / 150 \\ 6.10 Even and Odd Permutations / 153 \\ 6.11 Homomorphisms / 1556 \\ 6.12 Automorphisms; Conjugate Elements / 157 \\ 6.13 Quotient Groups / 161 \\ 6.14 Equivalence and Congruence Relations / 164 \\ \\ 7: Vectors and Vector Spaces / 168 \\ 7.1 Vectors in a Plane / 168 \\ 7.2 Generalizations / 169 \\ 7.3 Vector Spaces and Subspaces / 171 \\ 7.4 Linear Independence and Dimension / 176 \\ 7.5 Matrices and Row-equivalence / 180 \\ 7.6 Tests for Linear Dependence / 183 \\ 1.7 Vector Equations; Homogeneous Equations / 188 \\ 7.8 Bases and Coordinate Systems / 193 \\ 7.9 Inner Products / 198 \\ 7.10 Euclidean Vector Spaces / 200 \\ 7.11 Normal Orthogonal Bases / 203 \\ 7.12 Quotient-spaces / 206 \\ 7.13 Linear Functions and Dual Spaces / 208 \\ \\ 8: The Algebra of Matrices / 214 \\ 8.1 Linear Transformations and Matrices / 214 \\ 8.2 Matrix Addition / 220 \\ 8.3 Matrix Multiplication / 222 \\ 8.4 Diagonal, Permutation, and Triangular Matrices / 228 \\ 8.5 Rectangular Matrices / 230 \\ 8.6 Inverses / 235 \\ 8.7 Rank and Nullity / 241 \\ 8.8 Elementary Matrices / 243 \\ 8.9 Equivalence and Canonical Form / 248 \\ 8.10 Bilinear Functions and Tensor Products / 251 \\ 8.11 Quaternions / 255 \\ \\ 9: Linear Groups / 260 \\ 9.1 Change of Basis / 260 \\ 9.2 Similar Matrices and Eigenvectors / 263 \\ 9.3 The Full Linear and Affine Groups / 268 \\ 9.4 The Orthogonal and Euclidean Groups / 272 \\ 9.5 Invariants and Canonical Forms / 277 \\ 9.6 Linear and Bilinear Forms / 280 \\ 9.7 Quadratic Forms / 283 \\ 9.8 Quadratic Forms Under the Full Linear Group / 286 \\ 9.9 Real Quadratic Forms Under the Full Linear Group / 288 \\ 9.10 Quadratic Forms Under the Orthogonal Group / 292 \\ 9.11 Quadrics Under the Affine and Euclidean Groups / 296 \\ 9.12 Unitary and Hermitian Matrices / 300 \\ 9.13 Affine Geometry / 305 \\ 9.14 Projective Geometry / 312 \\ \\ 10: Determinants and Canonical Forms / 318 \\ 10.1 Definition and Elementary Properties of Determinants / 318 \\ 10.2 Products of Determinants / 323 \\ 10.3 Determinants as Volumes / 327 \\ 10.4 The Characteristic Polynomial / 331 \\ 10.5 The Minimal Polynomial / 336 \\ 10.6 Cayley -Hamilton Theorem / 340 \\ 10.7 Invariant Subspaces and Reducibility / 342 \\ 10.8 First Decomposition Theorem / 346 \\ 10.9 Second Decomposition Theorem / 349 \\ 10.10 Rational and Jordan Canonical Forms / 352 \\ \\ 11: Boolean Algebras and Lattices / 357 \\ 11.1 Basic Definition / 357 \\ 11.2 Laws: Analogy with Arithmetic / 359 \\ 11.3 Boolean Algebra / 361 \\ 11.4 Deduction of Other Basic Laws / 364 \\ 11.6 Canonical Forms of Boolean Polynomials / 368 \\ 11.6 Partial Orderings / 371 \\ 11.7 Lattices / 374 \\ 11.8 Representation by Sets / 377 \\ \\ 12: Transfinite Arithmetic / 381 \\ 12.1 Numbers and Sets / 381 \\ 12.2 Countable Sets / 383 \\ 12.3 Other Cardinal Numbers / 386 \\ 12.4 Addition and Multiplication of Cardinals / 390 \\ 12.5 Exponentiation / 392 \\ \\ 13: Rings and Ideals / 395 \\ 13.1 Rings / 395 \\ 13.2 Homomorphisms / 399 \\ 13.3 Quotient-rings / 403 \\ 13.4 Algebra of Ideals / 407 \\ 13.5 Polynomial Ideals / 410 \\ 13.6 Ideals in Linear Algebras / 413 \\ 13.7 The Characteristic of a Ring / 415 \\ 13.8 Characteristics of Fields / 418 \\ \\ 14: Algebraic Number Fields / 420 \\ 14.1 Algebraic and Transcendental Extensions / 420 \\ 14.2 Elements Algebraic over a Field / 423 \\ 14.3 Adjunction of Roots / 425 \\ 14.4 Degrees and Finite Extensions / 429 \\ 14.5 Iterated Algebraic Extensions / 431 \\ 14.6 Algebraic Numbers / 435 \\ 14.7 Gaussian Integers / 439 \\ 14.8 Algebraic Integers / 443 \\ 14.9 Sums and Products of Integers / 445 \\ 14.10 Factorization of Quadratic integers / 448 \\ \\ 15: Galois Theory / 452 \\ 15.1 Root Fields for Equations / 452 \\ 15.2 Uniqueness Theorem / 454 \\ 15.3 Finite Fields / 456 \\ 15.4 The Galois Group / 459 \\ 15.5 Separable and Inseparable Polynomials / 464 \\ 15.6 Properties of the Galois Group / 467 \\ 15.7 Subgroups and Subfields / 471 \\ 15.8 Irreducible Cubic Equations / 474 \\ 15.9 Insolvability of Quintic Equations / 478 \\ \\ Bibliography / 483 \\ \\ List of Special Symbols / 486 \\ \\ Index / 489", ZBmath = "3568615", } @Article{Birkhoff:1978:BRH, author = "Garrett Birkhoff", title = "Book Review: {{\booktitle{A History of Numerical Analysis from the 16th Through the 19th Century}}, by Herman H. Goldstine}", journal = j-HIST-MATH, volume = "5", number = "4", pages = "479--482", month = nov, year = "1978", CODEN = "HIMADS", DOI = "https://doi.org/10.1016/0315-0860(78)90226-4", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:17:00 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086078902264", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", GB-number = "184", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", } @Book{Birkhoff:1978:ODE, author = "Garrett Birkhoff and Gian-Carlo Rota", title = "Ordinary Differential Equations", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Third", pages = "xi + 342", year = "1978", ISBN = "0-471-07411-X", ISBN-13 = "978-0-471-07411-3", MRclass = "34-01 34A30 34A12 34A45 65J99 34L99", MRnumber = "507190", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0377.34001", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", shorttableofcontents = "1: First-Order Differential Equations \\ 2: Second-Order Linear Equations \\ 3: Linear Equations with Constant Coefficients \\ 4: Power Series Solutions \\ 5: Plane Autonomous Systems \\ 6: Existence and Uniqueness Theorems \\ 7: Approximate Solutions \\ 8: Efficient Numerical Integration \\ 9: Regular Singular Points \\ 10: Sturm--Liouville Systems \\ 11: Expansions in Eigenfunctions \\ Appendix A: Linear Systems \\ Appendix B: Numerical Integration in BASIC \\ Bibliography \\ Index", tableofcontents = "1: First-Order Differential Equations 1 \\ Introduction / 1 \\ 2 Fundamental theorem of the calculus / 3 \\ 3 First-order linear equations / 7 \\ 4 Level curves and quasilinear DE's / 8 \\ 5 Separable variables / 11 \\ 6 Exact differentials; integrating factors / 12 \\ 7 The linear fractional equation / 16 \\ 8 Graphical integration / 17 \\ *9 Regular and normal curve families / 20 \\ 10 Initial value problems / 21 \\ 11 Uniqueness and continuity / 23 \\ 12 The comparison theorem / 26 \\ \\ 2 Second-Order Linear Equations \\ 1 Initial value problem / 29 \\ 2 Constant coefficient case / 32 \\ 3 Uniqueness theorem; Wronskian / 33 \\ 4 Separation and comparison theorems / 38 \\ *5 Poincar{\'e} phase plane / 40 \\ 6 Adjoint operators / 42 \\ 7 Lagrange identity / 44 \\ 8 Green's functions / 46 \\ 9 Variation of parameters / 48 \\ *10 Two-endpoint problems / 51 \\ *11 Green's functions / 52 \\ \\ 3 Linear Equations with Constant Coefficients \\ 1 The characteristic polynomial / 58 \\ 2 Real and complex solutions / 60 \\ 3 Linearly independent solutions / 62 \\ 4 Solution bases / 63 \\ 5 Stability / 66 \\ 6 Inhomogeneous equations / 68 \\ 7 The transfer function / 70 \\ *8 The Nyquist diagram / 73 \\ 9 The Green's function / 75 \\ \\ 4 Power Series Solutions \\ 1 Introduction / 81 \\ 2 Method of undetermined coefficients / 82 \\ *3 Sine and cosine functions / 85 \\ *4 Bessel functions / 88 \\ 5 Analytic functions / 92 \\ 6 Method of majorants / 94 \\ 7 First-order nonlinear differential equations / 96 \\ 8 Undetermined coefficients / 98 \\ *9 Radius of convergence / 100 \\ *10 Method of majorants, IT / 101 \\ *11 Complex solutions / 103 \\ \\ 5 Plane Autonomous Systems \\ 1 Autonomous systems / 106 \\ 2 Plane autonomous systems / 108 \\ 3 Poincar{\'e} phase plane / 111 \\ 4 Linear autonomous systems / 114 \\ 9 Equivalent systems / 116 \\ 6 Linear equivalence / 117 \\ 7 Stability / 121 \\ 8 Focal, nodal, and saddle points / 124 \\ 9 Method of Liapunov / 127 \\ 10 Undamped nonlinear oscillations / 129 \\ 11 Soft and hard springs / 130 \\ 12 Damped nonlinear oscillations / 133 \\ *13 Limit cycles / 134 \\ \\ 6 Existence and Uniqueness Theorems \\ 1 Introduction / 139 \\ 2 Lipschitz condition / 140 \\ 3 Well-set problems / 142 \\ 4 Continuity / 145 \\ *5 Normal systems / 147 \\ 6 Equivalent integral equation / 151 \\ 7 Successive approximation / 152 \\ 8 Linear systems / 155 \\ 9 Local existence theorem / 157 \\ *10 Analytic equations / 158 \\ 11 Continuation of solutions / 161 \\ *12 The perturbation equation / 163 \\ 13 Plane autonomous systems / 165 \\ *14 The Peano existence theorem / 166 \\ \\ 7 Approximate Solutions \\ Introduction / 170 \\ 2 Cauchy polygons / 171 \\ 3 Error bound / 174 \\ 4 Sharper results / 176 \\ 5 Midpoint quadrature / 177 \\ 6 Trapezoidal quadrature / 181 \\ 7 Trapezoidal integration / 183 \\ 8 Order of accuracy / 185 \\ 9 The improved Euler method / 187 \\ 10 The modified Euler method / 189 \\ *11 The cumulative error / 190 \\ \\ 8 Efficient Numerical Integration \\ 1 Introduction / 194 \\ 2 Difference operators / 195 \\ 3 Characteristic equation; stability / 196 \\ 4 Polynomial interpolation / 198 \\ 5 The interpolation error / 200 \\ 6 Numerical differentiation / 202 \\ 7 Roundoff errors / 204 \\ 8 Milne's method / 206 \\ 9 Higher-order quadrature / 208 \\ *10 Gaussian quadrature / 211 \\ 11 Multistep Methods / 213 \\ 12 Richardson Extrapolation / 214 \\ 13 Local power series / 217 \\ 14 The Runge--Kutta method / 217 \\ \\ 9 Regular Singular Points \\ The Continuation principle / 222 \\ *2 Movable singular points / 224 \\ 3 First-order equations / 225 \\ 4 Circuit matrix / 228 \\ 5 Canonical bases / 230 \\ 6 Regular singular points / 233 \\ 7 Bessel equation / 235 \\ 8 The fundamental theorem / 240 \\ *9 Alternative proof of the fundamental theorem / 243 \\ *10 Hypergeometric functions / 245 \\ *11 The Jacobi polynomials / 246 \\ *12 Singular points at infinity / 249 \\ *13 Fuchsian equations / 251 \\ \\ 10 Sturm--Liouville Systems \\ 1 Sturm--Liouville systems / 256 \\ 2 Sturm--Liouville series / 257 \\ *3 Physical interpretations / 260 \\ 4 Singular systems / 263 \\ 3 Pr{\"u}fer substitution / 266 \\ 6 The Sturm comparison theorem / 267 \\ 7 The oscillation theorem / 269 \\ 8 The sequence of eigenfunctions / 272 \\ 9 The Liouville normal form / 274 \\ 100 Modified Pr{\"u}fer substitution / 276 \\ *11 The asymptotic behavior of Bessel functions / 279 \\ 12 Distribution of eigenvalues / 280 \\ 13 Normalized eigenfunctions / 282 \\ 14 Inhomogeneous equations / 285 \\ 15 Green's functions / 286 \\ *16 The Schroedinger equation / 287 \\ *17 The square-well potential / 289 \\ *18 Mixed spectrum / 290 \\ \\ 11 Expansions in Eigenfunctions \\ 1 Fourier series / 295 \\ 2 Orthogonal expansions / 297 \\ 3 Mean-square approximation / 298 \\ 4 Completeness / 300 \\ 3 Orthogonal polynomials / 302 \\ *6 Properties of orthogonal polynomials / 304 \\ *7 Chebyshev polynomials / 308 \\ 8 Euclidean vector spaces / 310 \\ 9 Completeness of eigenfunctions / 312 \\ *10 Hilbert space / 313 \\ *11 Proof of completeness / 316 \\ \\ Appendix A: Linear Systems \\ 1 Matrix norm / 320 \\ 2 Constant-coefficient systems / 321 \\ 3 The matrizant / 323 \\ 4 Floquet theorem; canonical bases / 325 \\ \\ Appendix B: Numerical Integration in BASIC \\ 1 Rudiments of BASIC / 327 \\ 2 Cauchy polygon method / 328 \\ 3 Quadrature programs / 330 \\ 4 Improved and modified Euler methods / 331 \\ 5 Fourth-order Runge--Kutta / 333 \\ \\ Bibliography / 336 \\ \\ Index / 339", ZBmath = "3587373", } @InProceedings{Birkhoff:1978:STP, author = "Garrett Birkhoff", editor = "N. H. Ibragimov and L. V. Ovsjannikov", booktitle = "Group theoretical methods in mechanics, {Proceedings of the joint IUTAM\slash IMU Symposium, Novosibirsk 1978}", title = "Similarity in two-phase fluid flows", publisher = "????", address = "????", pages = "58--78", year = "1978", MRclass = "76T99 76-04 22E70", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0441.76083", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "186", xxpages = "58--79", ZBmath = "3689057", } @InProceedings{Birkhoff:1979:AMI, author = "Garrett Birkhoff", editor = "C. V. Coffman and G. J. Fix", booktitle = "Constructive approaches to mathematical models {(Proceedings of a Conference in honor of R. J. Duffin, Pittsburgh, Pa., 1978)}", title = "The algebra of multivariate interpolation", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "345--363", year = "1979", ISBN = "0-12-178150-X", ISBN-13 = "978-0-12-178150-7", MRclass = "41A05 (65D05) 41A15 17A99", MRnumber = "559505", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0463.41001", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "188", ZBmath = "3724993", } @Article{Birkhoff:1979:IDT, author = "Garrett Birkhoff and Surender Gulati", title = "Isotropic distributions of test matrices", journal = j-Z-ANGE-MATH-PHYS, volume = "30", number = "2", pages = "148--158", year = "1979", CODEN = "ZAMPDB", DOI = "https://doi.org/10.1007/BF01601929", ISSN = "0044-2275 (print), 1420-9039 (electronic)", ISSN-L = "0044-2275", MRclass = "65F99 (65G05) 65F35 60B11", MRnumber = "535975", MRreviewer = "James E. Gentle", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0397.65029", acknowledgement = ack-nhfb, ajournal = "ZAMP. Zeitschrift f{\"u}r angewandte Mathematik und Physik", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Zeitschrift f{\"u}r Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Math{\'e}matiques et de Physique Appliqu{\'e}es", GB-number = "187", journal-URL = "http://link.springer.com/journal/33", ZBmath = "3617447", } @Book{Birkhoff:1979:LT, author = "Garrett Birkhoff", title = "Lattice Theory", volume = "25", publisher = pub-AMS, address = pub-AMS:adr, edition = "Third", pages = "vi + 418", year = "1979", ISBN = "0-8218-1025-1", ISBN-13 = "978-0-8218-1025-5", MRclass = "06-01 (46A40 47B55 54H12)", MRnumber = "598630", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "American Mathematical Society Colloquium Publications", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", tableofcontents = "Types of lattices \\ Postulates for lattices \\ Structure and representation theory \\ Geometric lattices \\ Complete lattices \\ Universal algebra \\ Applications to algebra \\ Transfinite induction \\ Applications to general topology \\ Metric and topological lattices \\ Borel algebras and von Neumann lattices \\ Applications to logic and probability \\ Lattice-ordered groups \\ Lattice-ordered monoids \\ Vector lattices \\ Positive linear operators \\ Lattice-ordered rings", } @Book{Birkhoff:1979:LTC, author = "Garrett Birkhoff", title = "Lattice Theory", volume = "25", publisher = pub-AMS, address = pub-AMS:adr, edition = "Third (corrected reprint)", year = "1979", ISSN = "0065-9258", MRclass = "06-02", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Colloq. Publ., Am. Math. Soc.", ZMnumber = "0505.06001", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fseries = "Colloquium Publications. American Mathematical Society", ZBmath = "3796014", } @Article{Birkhoff:1979:RGG, author = "Garrett Birkhoff", title = "Review of {G. Gr{\"a}tzer, \booktitle{General Lattice Theory}}", journal = j-BULL-AMS, volume = "1", number = "??", pages = "789--92", month = "????", year = "1979", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881X (electronic)", ISSN-L = "0002-9904", bibdate = "Wed Nov 01 08:25:04 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "191a", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", } @Article{Birkhoff:1979:RJD, author = "Garrett Birkhoff", title = "Review of {J. Dieudonn{\'e}, \booktitle{Abr{\'e}g{\'e} d'Histoire des Math{\'e}matiques: 1700--1900}}", journal = j-ADV-MATH, volume = "34", number = "??", pages = "185--194", month = "????", year = "1979", CODEN = "ADMTA4", DOI = "", ISSN = "0001-8708 (print), 1090-2082 (electronic)", ISSN-L = "0001-8708", bibdate = "Wed Nov 01 08:23:07 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Advances in Mathematics", GB-number = "190", journal-URL = "http://www.sciencedirect.com/science/journal/00018708", } @Article{Birkhoff:1979:RRT, author = "Garrett Birkhoff", title = "Review of {Roberto Torretti, \booktitle{Philosophy of Geometry from Riemann to Poincar{\'e}}, Reidel, 1978}", journal = j-ADV-MATH, volume = "34", number = "??", pages = "399--400", month = "????", year = "1979", CODEN = "ADMTA4", DOI = "", ISSN = "0001-8708 (print), 1090-2082 (electronic)", ISSN-L = "0001-8708", bibdate = "Wed Nov 01 08:28:42 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Advances in Mathematics", GB-number = "191c", journal-URL = "http://www.sciencedirect.com/science/journal/00018708", } @Book{MacLane:1979:A, author = "Saunders {Mac Lane} and Garrett Birkhoff", title = "Algebra", publisher = pub-MACMILLAN, address = pub-MACMILLAN:adr, edition = "Second", pages = "xv + 586", year = "1979", ISBN = "0-02-374310-7", ISBN-13 = "978-0-02-374310-8", MRclass = "00A05", MRnumber = "524398", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0428.00002", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", ZBmath = "3666702", } @Article{Birkhoff:1980:AMC, author = "Garrett Birkhoff and Robert E. Lynch", title = "Added mass of cylinders", journal = j-MATH-COMP-SIM, volume = "22", number = "4", pages = "291--297", year = "1980", CODEN = "MCSIDR", DOI = "https://doi.org/10.1016/0378-4754(80)90066-X", ISSN = "0378-4754 (print), 1872-7166 (electronic)", ISSN-L = "0378-4754", MRclass = "76B40 (65N30) 76B99 76M99", MRnumber = "595985", MRreviewer = "Mutsuto Kawahara", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0513.76018", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Mathematics and Computers in Simulation", GB-number = "189", journal-URL = "http://www.sciencedirect.com/science/journal/03784754", ZBmath = "3811143", } @Article{Birkhoff:1980:BRC, author = "Garrett Birkhoff", title = "Book Review: {{\booktitle{Computational analysis with the HP 25 pocket calculator}}, by Peter Henrici, John Wiley, New York, 1977, 280 pp.; \booktitle{Compact numerical methods for computers: linear algebra and function minimization}, by J. C. Nash, John Wiley \& Sons, New York, 1979, x + 227 pp.; \booktitle{LINPACK: User's guide}, by J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, Society for Industrial and Applied Mathematics, Philadelphia, 1979 368 pp.}", journal = j-BULL-AMS, volume = "2", number = "3", pages = "503--505", month = may, year = "1980", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0273-0979-1980-14785-0", ISSN = "0002-9904 (print), 1936-881X (electronic)", ISSN-L = "0002-9904", bibdate = "Wed Nov 01 08:26:39 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib; https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", URL = "https://www.ams.org/journals/bull/1980-02-03/S0273-0979-1980-14785-0/S0273-0979-1980-14785-0.pdf", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "191b", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", subject-dates = "Peter Karl Henrici (13 September 1923--13 March 1987)", } @Article{Birkhoff:1980:BRE, author = "Garrett Birkhoff", title = "Book Review: {{\booktitle{Die entstehung der verbandsteorie}}: By Herbert Mehrtens. Hildesheim (Gerstenberg Verlag). 1979. ix + 363 pp. 42 DM}", journal = j-HIST-MATH, volume = "7", number = "4", pages = "454--457", month = nov, year = "1980", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:17:21 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086080900154", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", } @InProceedings{Birkhoff:1980:CDS, author = "Garrett Birkhoff", title = "Computer developments 1935--1955, as seen from {Cambridge, U.S.A.}", crossref = "Metropolis:1980:HCT", pages = "21--30", year = "1980", bibdate = "Wed Nov 01 08:31:21 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "192", } @Article{Birkhoff:1980:RBC, author = "Garrett Birkhoff", title = "Review of books on computers by {Peter Henrici} and others", journal = j-BULL-AMS, volume = "2", number = "??", pages = "503--535", month = "????", year = "1980", CODEN = "BAMOAD", DOI = "", ISSN = "0002-9904 (print), 1936-881X (electronic)", ISSN-L = "0002-9904", bibdate = "Wed Nov 01 08:26:39 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib", URL = "", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Bulletin of the American Mathematical Society", GB-number = "191b", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", } @Article{Birkhoff:1980:RHM, author = "Garrett Birkhoff", title = "Review of {H. Mehrtens, \booktitle{Die Entstelung der Verbandstheorie}}", journal = j-HIST-MATH, volume = "??", number = "??", pages = "??--??", month = "????", year = "1980", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Nov 01 08:29:55 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", GB-number = "191d", journal-URL = "http://www.sciencedirect.com/science/journal/03150860", } @InProceedings{Birkhoff:1981:SEP, author = "Garrett Birkhoff", title = "Solving Elliptic Problems: 1930--1980", crossref = "Schultz:1981:EPS", pages = "17--38", year = "1981", MRclass = "65-02 (65Nxx) 65Nxx 65-03 35Jxx 01A65 35-03 65Fxx", MRnumber = "652526", MRreviewer = "Max D. Gunzburger", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0473.65063", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "193", ZBmath = "3742545", } @Book{Birkhoff:1981:TRR, author = "Garrett Birkhoff", title = "{{\cyr Teoriya reshetok}}. ({Russian}) [{Lattice} theory]", publisher = "``{Nauka}''", address = "Moscow, USSR", pages = "568", year = "1981", MRclass = "06-02", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Translated from the English by V. N. Salij. Edited by L. A. Skornyakov.", series = "Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury", ZMnumber = "0537.06001", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", language = "Russian", ZBmath = "3853149", } @InCollection{Birkhoff:1982:GDB, author = "Garrett Birkhoff", booktitle = "Selected studies: physics-astrophysics, mathematics, history of science", title = "{George D. Birkhoff}'s theory of gravitation", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "57--77", year = "1982", ISBN = "0-444-86161-0", ISBN-13 = "978-0-444-86161-0", MRclass = "01A60 (83-03) 70F15 83A05 83D05 70-03", MRnumber = "662852", MRreviewer = "H. Treder", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/einstein.bib", note = "See \cite{}.", ZMnumber = "0491.70014", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "195", remark = "Volume dedicated to Albert Einstein.", ZBmath = "3773023", } @InProceedings{Birkhoff:1982:OSG, author = "Garrett Birkhoff", booktitle = "Ordered sets {(Proceedings of the NATO Advanced Study Institute, Banff, Alta., 1981)}", title = "Ordered sets in geometry", volume = "83", publisher = pub-REIDEL, address = pub-REIDEL:adr, pages = "407--443", year = "1982", ISBN = "90-277-1396-0", ISBN-13 = "978-90-277-1396-4", MRclass = "51D25 (06A15 51-02) 06C20 51G05 51Exx 51M10", MRnumber = "661302", MRreviewer = "Ulrich Faigle", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Appendix by M. K. Bennett on pages 436--443.", series = "NATO Adv. Study Inst. Ser. C: Math. Phys. Sci.", ZMnumber = "0492.51010", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "196", ZBmath = "3774417", } @InProceedings{Birkhoff:1982:SAU, author = "Garrett Birkhoff", booktitle = "Universal algebra {(Proceedings of the Colloquium of the Mathematical Society Janos Bolya, Esztergom, Hungary, 1977)}", title = "Some applications of universal algebra", volume = "29", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "107--128", year = "1982", ISBN = "0-444-85405-3", ISBN-13 = "978-0-444-85405-6", MRclass = "03G10 94C10 06D25 08A40 (03G20 08B20 68B99 68C99)", MRnumber = "660852", MRreviewer = "H.-J. Hoehnke", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Colloq. Math. Soc. J{\'a}nos Bolyai", ZMnumber = "0519.03049", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "194", ZBmath = "3821729", } @Article{Birkhoff:1983:BRB, author = "Garrett Birkhoff", title = "Book Review: {{\booktitle{John von Neumann and Norbert Wiener}}: By Steve Heims. Cambridge, Mass., and London (M.I.T. Press). 1981}", journal = j-HIST-MATH, volume = "10", number = "2", pages = "243--248", month = may, year = "1983", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:17:39 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086083900745", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", GB-number = "198", journal-URL = "http://www.sciencedirect.com/science/journal/03150860", } @Article{Birkhoff:1983:BRJ, author = "Garrett Birkhoff", title = "Book Review: {{\booktitle{John von Neumann and Norbert Wiener}}: By Steve Heims. Cambridge, Mass., and London (M.I.T. Press). 1981}", journal = j-HIST-MATH, volume = "10", number = "2", pages = "243--248", month = may, year = "1983", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:17:39 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086083900745", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", } @Article{Birkhoff:1983:NFD, author = "Garrett Birkhoff", title = "Numerical fluid dynamics", journal = j-SIAM-REVIEW, volume = "25", number = "1", pages = "1--34", month = jan, year = "1983", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1025001", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "76-02 76M99 76-03 01-02 65M99 65N99 76-08 (01A60)", MRnumber = "693712", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://www.jstor.org/stable/2030018", ZMnumber = "0508.76001", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "SIAM Review", GB-number = "197", journal-URL = "http://epubs.siam.org/sirev", ZBmath = "3802971", } @InCollection{Birkhoff:1983:NPI, author = "Garrett Birkhoff", editor = "Themistocles M. Rassias", booktitle = "Global analysis --- analysis on manifolds", title = "Nonlinear product integration", volume = "57", publisher = pub-TEUBNER, address = pub-TEUBNER:adr, pages = "43--50", year = "1983", MRclass = "34G10 34C40 34A12 37J35 37K10 22E05", MRnumber = "730601", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Dedicated to M. Morse.", series = "Teubner-Texte Math.", ZMnumber = "0536.34039", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "199", ZBmath = "3851548", } @Article{Birkhoff:1983:RMY, author = "Garrett Birkhoff", title = "{Richard von Mises}' years at {Harvard}", journal = j-Z-ANGE-MATH-MECH, volume = "63", number = "7", pages = "283--284", year = "1983", CODEN = "ZAMMAX", DOI = "https://doi.org/10.1002/zamm.19830630705", ISSN = "0044-2267 (print), 1521-4001 (electronic)", ISSN-L = "0044-2267", MRclass = "01A70", MRnumber = "718662", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0527.01012", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik. Ingenieurwissenschaftliche Forschungsarbeiten", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001", language = "German", ZBmath = "3835980", } @Article{Birkhoff:1983:SEP, author = "Garrett Birkhoff", title = "Solving elliptic problems: 1930--1980", journal = "Appl. Math. Math. Comput.", volume = "6", pages = "1--10", year = "1983", MRclass = "65-02 (65Nxx)", MRnumber = "749095", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Translated from the English by Jia Chang Sun", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Applied Mathematics \& Mathematics of Computation. Yingyong Shuxue yu Jisuan Shuxue", } @InCollection{Bennett:1984:PAC, author = "M. K. Bennett and Garrett Birkhoff", booktitle = "{Calcutta Mathematical Society. Diamond-cum-platinum jubilee commemoration volume (1908--1983), Part I}", title = "A {Peano} axiom for convexity lattices", publisher = "Calcutta Mathematical Society", address = "Calcutta, Bengal, India", pages = "33--43", year = "1984", MRclass = "06B05 (52A01) 06C10", MRnumber = "845037", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0594.06003", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "203", ZBmath = "3954982", } @Book{Birkgof:1984:CTR, author = "G. Birkgof", title = "{{\cyr Teoriya reshetok}}. ({Russian}) [{Lattice} theory]", publisher = "``Nauka''", address = "Moscow, USSR", pages = "566", year = "1984", MRclass = "06-02 (06Bxx)", MRnumber = "751233", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Edited by L. A. Skornyakov. Translated from the English and with an appendix by V. N. Sali{\u{\i}}.", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", language = "Russian", } @InProceedings{Birkhoff:1984:CAM, author = "G. Birkhoff and John F. Brophy and R. E. Lynch", title = "Computing added mass coefficients", crossref = "Birkhoff:1984:EPS", pages = "427--437", year = "1984", MRclass = "65Z05 76B99 65N22 35J05 76-08", MRnumber = "764247", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0598.65088", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "200", ZBmath = "3965390", } @Article{Birkhoff:1984:EFA, author = "Garrett Birkhoff and Erwin Kreyszig", title = "The establishment of functional analysis", journal = j-HIST-MATH, volume = "11", number = "3", pages = "258--321", month = aug, year = "1984", CODEN = "HIMADS", DOI = "https://doi.org/10.1016/0315-0860(84)90036-3", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", MRclass = "01A60 (01A55 46-03 47-03) 01A05", MRnumber = "765342", MRreviewer = "Jesper L{\"u}tzen", bibdate = "Wed Jun 26 06:17:47 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086084900363", ZMnumber = "0549.01001", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", GB-number = "202", journal-URL = "http://www.sciencedirect.com/science/journal/03150860", ZBmath = "3875196", } @Article{Birkhoff:1984:NFDa, author = "Garrett Birkhoff", title = "Numerical fluid dynamics", journal = "Fiz.-Mat. Spis. B\bud lgar. Akad. Nauk.", volume = "26(59)", number = "2", pages = "150--167", year = "1984", ISSN = "0015-3265", MRclass = "76-02 76M99 76-03 01-02 65M99 76-08", MRnumber = "769952", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Translated from the English by R. Lazov", ZMnumber = "0657.76005", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "B\bud lgarska Akademiya na Naukite. Fizicheski Institut. Matematicheski Institut. Fiziko-Matematichesko Spisanie", ZBmath = "4074650", } @Article{Birkhoff:1984:NFDb, author = "Garet Birkhoff", title = "Numerical fluid dynamics. {II}", journal = "Fiz.-Mat. Spis. B\bud lgar. Akad. Nauk.", volume = "26(59)", number = "3", pages = "271--294", year = "1984", ISSN = "0015-3265", MRclass = "76-08", MRnumber = "776881", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Translated from the English by Pet\cprime o P. Petkov", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "B\bud lgarska Akademiya na Naukite. Fizicheski Institut. Matematicheski Institut. Fiziko-Matematichesko Spisanie", } @Book{Birkhoff:1984:NSE, author = "Garrett Birkhoff and Robert E. Lynch", title = "Numerical Solution of Elliptic Problems", volume = "6", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xi + 319", year = "1984", DOI = "https://doi.org/10.1137/1.9781611970869", ISBN = "0-89871-197-5", ISBN-13 = "978-0-89871-197-4", MRclass = "65Nxx 65-02 65E05 35Jxx 35P15 65F05 65F10 35-04 65-01 (65Nxx)", MRnumber = "769468", MRreviewer = "R. S. Anderssen", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "SIAM Studies in Applied Mathematics", ZMnumber = "0556.65078", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fseries = "SIAM Studies in Applied Mathematics", tableofcontents = "Preface / ix \\ 1: Typical Elliptic Problems / 1 \\ 2: Classical Analysis / 21 \\ 3: Difference Approximations / 45 \\ 4: Direct and Iterative Methods / 97 \\ 5: Accelerating Convergence / 149 \\ 6: Direct Variational Methods / 183 \\ 7: Finite Element Approximations / 221 \\ 8: Integral Equation Methods / 251 \\ 9: ELLPACK / 283 \\ Bibliography / 303 \\ Index / 315", ZBmath = "3887036", } @Article{Bennett:1985:CL, author = "M. K. Bennett and Garrett Birkhoff", title = "Convexity lattices", journal = j-ALGEBRA-UNIVERS, volume = "20", number = "1", pages = "1--26", year = "1985", DOI = "https://doi.org/10.1007/BF01236802", ISSN = "0002-5240 (print), 1420-8911 (electronic)", ISSN-L = "0002-5240", MRclass = "06B05 (52A01) 51G05 52A35 06B20 51D05", MRnumber = "790901", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0566.06005", acknowledgement = ack-nhfb, ajournal = "Algebra Univers.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Algebra Universalis", GB-number = "201", journal-URL = "https://www.springer.com/journal/12", ZBmath = "3902717", } @Article{Birkhoff:1985:CLP, author = "Garrett Birkhoff and M. K. Bennett", title = "The convexity lattice of a poset", journal = j-ORDER-DORDRECHT, volume = "2", number = "3", pages = "223--242", year = "1985", CODEN = "ORDRE5", DOI = "https://doi.org/10.1007/BF00333128", ISSN = "0167-8094 (print), 1572-9273 (electronic)", ISSN-L = "0167-8094", MRclass = "06B05 06A06 06B15 06A10 (06A15)", MRnumber = "824696", MRreviewer = "D. Duffus", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0591.06009", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Order", journal-URL = "http://link.springer.com/journal/11083", ZBmath = "3948344", } @Article{Birkhoff:1985:SMP, author = "Garrett Birkhoff", title = "Some mathematical problems of numerical ocean acoustics", journal = j-COMPUT-MATH-APPL, volume = "11", number = "7--8", pages = "643--654", year = "1985", CODEN = "CMAPDK", DOI = "https://doi.org/10.1016/0898-1221(85)90161-0", ISSN = "0898-1221 (print), 1873-7668 (electronic)", ISSN-L = "0898-1221", MRclass = "76Q05 (35J05 35L05 65M99 65N99 76-08 86-08) 76B15 86A05 35Q99 35J05", MRnumber = "809598", MRreviewer = "R. F. Millar", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Reprinted in \cite{Birkhoff:1986:SMP}.", ZMnumber = "0611.76088", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Computers \& Mathematics with Applications. An International Journal", GB-number = "204", journal-URL = "http://www.sciencedirect.com/science/journal/08981221", ZBmath = "3988983", } @InCollection{Birkhoff:1986:SMP, author = "Garrett Birkhoff", editor = "Ding Lee and M. H. Schultz", booktitle = "Numerical Ocean Acoustics", title = "Some mathematical problems of numerical ocean acoustics", publisher = pub-PERGAMON, address = pub-PERGAMON:adr, pages = "??--??", year = "1986", DOI = "", ISBN = "", ISBN-13 = "", LCCN = "", bibdate = "Wed Nov 01 08:44:48 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Computational ocean acoustics (New Haven, Conn., 1984)", URL = "", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", GB-number = "204", } @Article{Birkhoff:1987:HGG, author = "Garrett Birkhoff and Mary Katherine Bennett", title = "{Hilbert}'s ``{{\booktitle{{Grundlagen} der Geometrie}}}''", journal = "Rendiconti del Circolo Matem{\`a}tico di Palermo. Serie II", volume = "36", number = "3", pages = "343--389", year = "1987", DOI = "https://doi.org/10.1007/BF02844894", ISSN = "0009-725x (print), 1973-4409 (electronic)", MRclass = "51-02 51-03 01A55 01A60 01A72 51M05 51M10 01A55 (01A60 51-03)", MRnumber = "981143", MRreviewer = "Cyril W. L. Garner", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0664.51001", acknowledgement = ack-nhfb, ajournal = "Rend. Circ. Mat. Palermo (2)", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Rendiconti del Circolo Matem{\`a}tico di Palermo. Serie II", journal-URL = "https://link.springer.com/journal/12215", ZBmath = "4086410", } @Article{Birkhoff:1987:SWF, author = "Garrett Birkhoff", title = "Sound waves in fluids", journal = j-APPL-NUM-MATH, volume = "3", number = "1-2", pages = "3--24", year = "1987", CODEN = "ANMAEL", DOI = "https://doi.org/10.1016/0168-9274(87)90003-1", ISSN = "0168-9274 (print), 1873-5460 (electronic)", ISSN-L = "0168-9274", MRclass = "76Q05 (76-08) 70H20 78A05 74J10 76M99", MRnumber = "896323", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0619.76102", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Applied Numerical Mathematics. An IMACS Journal", journal-URL = "http://www.sciencedirect.com/science/journal/01689274", ZBmath = "4005900", } @InProceedings{Birkhoff:1988:FKH, author = "Garrett Birkhoff and M. K. Bennett", booktitle = "History and philosophy of modern mathematics. Proceedings of the conference, {University of Minnesota, Minneapolis, MN, USA, May 17--19, 1985}", title = "{Felix Klein} and his ``{Erlanger Programm}''", volume = "XI", publisher = pub-U-MINNESOTA, address = pub-U-MINNESOTA:adr, pages = "145--176", year = "1988", ISBN = "0-8166-1566-7; 0-8166-1567-5", ISBN-13 = "978-0-8166-1566-7; 978-0-8166-1567-4", MRclass = "01A55 01A60 01A70 51-03", MRnumber = "945470", MRreviewer = "J. Dieudonn{\'e}", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Minnesota Stud. Philos. Sci.", ZMnumber = "1366.01009", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "6745038", } @InCollection{Birkhoff:1988:ROC, author = "Garrett Birkhoff", booktitle = "Reliability in computing", title = "The role of order in computing", volume = "19", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "357--378", year = "1988", ISBN = "0-12-505630-3", ISBN-13 = "978-0-12-505630-4", MRclass = "65G10 (06A99 65C10 68M99) 65J05 65-02 65G30", MRnumber = "988469", MRreviewer = "Florica Luban", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Perspectives in Computing", ZMnumber = "0659.65059", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "4078658", } @InProceedings{Birkhoff:1988:SWF, author = "Garrett Birkhoff", booktitle = "Applied mathematics, fluid mechanics, astrophysics {(Cambridge, MA, 1987)}", title = "Sound waves in fluids: mathematical models and physical reality", publisher = pub-WORLD-SCI, address = pub-WORLD-SCI:adr, pages = "35--45", year = "1988", ISBN = "9971-5-0245-3", ISBN-13 = "978-9971-5-0245-4", MRclass = "76Q05", MRnumber = "973914", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Book{MacLane:1988:A, author = "Saunders {Mac Lane} and Garrett Birkhoff", title = "Algebra", publisher = "Chelsea Publishing Company", address = "New York, NY, USA", edition = "Third", pages = "xx + 626", year = "1988", ISBN = "0-8284-0330-9", ISBN-13 = "978-0-8284-0330-6", MRclass = "12-01 12Fxx 13-01 00A05 51-01", MRnumber = "941522", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0641.12001", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", tableofcontents = "List of Symbols \\ \\ I: Sets, Functions, and Integers / 1 \\ 1. Sets / 1 \\ 2. Functions / 4 \\ 3. Relations and Binary Operations / 10 \\ 4. The Natural Numbers / 15 \\ 5. Addition and Multiplication / 18 \\ 6. Inequalities / 20 \\ 7. The Integers / 23 \\ 8. The Integers Modulo $n$ / 28 \\ 9. Equivalence Relations and Quotient Sets \\ 10. Morphisms / 37 \\ 11. Semigroups and Monoids / 39 \\ \\ II: Groups / 43 \\ 1. Groups and Symmetry / 43 \\ 2. Rules of Calculation / 47 \\ 3. Cyclic Groups / 51 \\ 4. Subgroups / 56 \\ 5. Defining Relations / 59 \\ 6. Symmetric and Alternating Groups / 63 \\ 7. Transformation Groups / 68 \\ 8. Cosets / 72 \\ 9. Kernel and Image / 75 \\ 10. Quotient Groups / 79 \\ \\ III: Rings / 85 \\ 1. Axioms for Rings / 85 \\ 2. Constructions for Rings / 90 \\ 3. Quotient Rings / 95 \\ 4. Integral Domains and Fields / 99 \\ 5. The Field of Quotients / 101 \\ 6. Polynomials / 104 \\ 7. Polynomials as Functions / 109 \\ 8. The Division Algorithm / 111 \\ 9. Principal Ideal Domains / 115 \\ 10. Unique Factorization / 116 \\ 11. Prime Fields / 120 \\ 12. The Euclidean Algorithm / 122 \\ 13. Commutative Quotient Rings / 124 \\ \\ IV: Universal Constructions / 129 \\ 1. Examples of Universals / 129 \\ 2. Functors / 131 \\ 3. Universal Elements / 134 \\ 4. Polynomials in Several Variables / 137 \\ 5. Categories / 141 \\ 6. Posets and Lattices / 143 \\ 7. Contravariance and Duality / 146 \\ 8. The Category of Sets / 153 \\ 9. The Category of Finite Sets / 156 \\ \\ V: Modules / 160 \\ 1. Sample Modules / 160 \\ 2. Linear Transformations / 163 \\ 3. Submodules / 167 \\ 4. Quotient Modules / 171 \\ 5. Free Modules / 173 \\ 6. Biproducts / 178 \\ 7. Dual Modules / 185 \\ \\ VI: Vector Spaces / 193 \\ 1. Bases and Coordinates / 194 \\ 2. Dimension / 199 \\ 3. Constructions for Bases / 202 \\ 4. Dually Paired Vector Spaces / 207 \\ 5. Elementary Operations / 212 \\ 6. Systems of Linear Equations / 219 \\ \\ VII: Matrices / 223 \\ 1. Matrices and Free Modules / 224 \\ 2. Matrices and Biproducts / 232 \\ 3. The Matrix of a Map / 236 \\ 4. The Matrix of a Composite / 240 \\ 5. Ranks of Matrices / 244 \\ 6. Invertible Matrices / 246 \\ 7. Change of Bases / 251 \\ 8. Eigenvectors and Eigenvalues / 257 \\ \\ VIII: Special Fields / 261 \\ 1. Ordered Domains / 261 \\ 2. The Ordered Field $Q$ / 265 \\ 3. Polynomial Equations / 267 \\ 4. Convergence in Ordered Fields / 269 \\ 5. The Real Field $R$ / 271 \\ 6. Polynomials over $R$ / 274 \\ 7. The Complex Plane / 276 \\ 8. The Quaternions / 281 \\ 9. Extended Formal Power Series / 284 \\ 10. Valuations and $p$-adic Numbers / 286 \\ \\ IX: Determinants and Tensor Products / 293 \\ 1. Multilinear and Alternating Functions / 293 \\ 2. Determinants of Matrices / 296 \\ 3. Cofactors and Cramer's Rule / 301 \\ 4. Determinants of Maps / 305 \\ 5. The Characteristic Polynomial / 309 \\ 6. The Minimal Polynomial / 312 \\ 7. Universal Bilinear Functions / 318 \\ 8. Tensor Products / 319 \\ 9. Exact Sequences / 326 \\ 10. Identities on Tensor Products / 329 \\ 11. Change of Rings / 331 \\ 12. Algebras / 334 \\ \\ X: Bilinear and Quadratic Forms / 338 \\ 1. Bilinear Forms / 338 \\ 2. Symmetric Matrices / 341 \\ 3. Quadratic Forms / 343 \\ 4. Real Quadratic Forms / 347 \\ 5. Inner Products / 351 \\ 6. Orthonormal Bases / 355 \\ 7. Orthogonal Matrices / 360 \\ 8. The Principal Axis Theorem / 364 \\ 9. Unitary Spaces / 369 \\ 10. Normal Matrices / 374 \\ \\ XI: Similar Matrices and Finite Abelian Groups / 378 \\ 1. Noetherian Modules / 378 \\ 2. Cyclic Modules / 381 \\ 3. Torsion Modules / 383 \\ 4. The Rational Canonical Form for Matrices / 388 \\ 5. Primary Modules / 392 \\ 6. Free Modules / 397 \\ 7. Equivalence of Matrices / 400 \\ 8. The Calculation of Invariant Factors / 404 \\ \\ XII: Structure of Groups / 409 \\ 1. Isomorphism Theorems / 409 \\ 2. Group Extensions / 413 \\ 3. Characteristic Subgroups / 417 \\ 4. Conjugate Classes / 419 \\ 5. The Sylow Theorems / 422 \\ 6. Nilpotent Groups / 426 \\ 7. Solvable Groups / 428 \\ 8. The Jordan-Holder Theorem / 430 \\ 9. Simplicity of An / 433 \\ \\ XIII: Galois Theory / 436 \\ 1. Quadratic and Cubic Equations / 436 \\ 2. Algebraic and Transcendental Elements / 439 \\ 3. Degrees / 442 \\ 4. Ruler and Compass / 445 \\ 5. Splitting Fields / 446 \\ 6. Galois Groups of Polynomials / 450 \\ 7. Separable Polynomials / 453 \\ 8. Finite Fields / 456 \\ 9. Normal Extensions / 458 \\ 10. The Fundamental Theorem / 462 \\ 11. The Solution of Equations by Radicals / 465 \\ \\ XIV: Lattices / 470 \\ 1. Posets: Duality Principle / 470 \\ 2. Lattice Identities / 473 \\ 3. Sublattices and Products of Lattices / 476 \\ 4. Modular Lattices / 478 \\ 5. Jordan-Holder-Dedekind Theorem / 480 \\ 6. Distributive Lattices / 483 \\ 7. Rings of Sets / 485 \\ 8. Boolean Algebras / 487 \\ 9. Free Boolean Algebras / 491 \\ \\ XV: Categories and Adjoint Functors / 495 \\ 1. Categories / 495 \\ 2. Functors / 501 \\ 3. Contravariant Functors / 504 \\ 4. Natural Transformations / 506 \\ 5. Representable Functors and Universal Elements / 511 \\ 6. Adjoint Functors / 517 \\ \\ XVI: Multilinear Algebra / 522 \\ 1. Iterated Tensor Products / 522 \\ 2. Spaces of Tensors / 524 \\ 3. Graded Modules / 530 \\ 4. Graded Algebras / 533 \\ 5. The Graded Tensor Algebra / 539 \\ 6. The Exterior Algebra of a Module / 543 \\ 7. Determinants by Exterior Algebra / 547 \\ 8. Subspaces by Exterior Algebra / 552 \\ 9. Duality n Exterior Algebra / 555 \\ 10. Alternating Forms and Skew-Symmetric Tensors / 558 \\ \\ Appendix: Affine and Projective Spaces / 561 \\ 1. The Affine Line / 417 \\ 2. Affine Spaces / 420 \\ 3. The Affine Group / 570 \\ 4. Affine Subspaces / 576 \\ 5. Biaffine and Quadratic Functionals / 578 \\ 6. Euclidean Spaces / 586 \\ 7. Euclidean Quadrics / 590 \\ 8. Projective Spaces / 592 \\ 9. Projective Quadrics / 596 \\ 10. Affine and Projective Spaces / 598 \\ \\ Bibliography / 595 \\ \\ Index / 604", ZBmath = "193022", } @InCollection{Birkhoff:1989:MH, author = "Garrett Birkhoff", booktitle = "A century of mathematics in {America}, {Part II}", title = "Mathematics at {Harvard}, 1836--1944", volume = "2", publisher = pub-AMS, address = pub-AMS:adr, pages = "3--58", year = "1989", ISBN = "0-8218-0130-9", ISBN-13 = "978-0-8218-0130-7", MRclass = "01A73 (01A55 01A60)", MRnumber = "1003118", MRreviewer = "Renate Tobies", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Hist. Math.", ZMnumber = "0665.01010", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "4087617", } @Book{Birkhoff:1989:ODE, author = "Garrett Birkhoff and Gian-Carlo Rota", title = "Ordinary Differential Equations", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Fourth", pages = "xii + 399", year = "1989", ISBN = "0-471-86003-4", ISBN-13 = "978-0-471-86003-7", MRclass = "34-01", MRnumber = "972977", MRreviewer = "Michal {\v{C}}ver\v{c}ko", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", shorttableofcontents = "1: First-Order Of Differential Equations / 1 \\ 2: Second-Order Linear Equations / 34 \\ 3: Linear Equations with Constant Coefficients / 71 \\ 7: Approximate Solutions / 204 \\ 8: Efficient Numerical Integration / 230 \\ 9: Regular Singular Points / 261 \\ 10: Sturm-Liouville Systems / 300 \\ 11: Expansions in Eigenfunctions / 344 \\ Appendix: A: Linear Systems / 371 \\ Appendix: B: Bifurcation Theory / 380 \\ Bibliography: / 392 \\ Index: / 395", tableofcontents = "\\ 1: First-Order Of Differential Equations / 1 \\ 1. Introduction / 1 \\ 2. Fundamental Theorem of the Calculus / 2 \\ 3. First-order Linear Equations / 7 \\ 4. Separable Equations / 9 \\ 5. Quasilinear Equations; Implicit Solutions / 11 \\ 6. Exact Differentials; Integrating Factors / 15 \\ 7. Linear Fractional Equations / 17 \\ 8. Graphical and Numerical Integration / 20 \\ 9. The Initial Value Problem / 24 \\ *10. Uniqueness and Continuity / 26 \\ *11. A Comparison Theorem / 29 \\ *12. Regular and Normal Curve Families / 31 \\ \\ 2: Second-Order Linear Equations / 34 \\ 1. Bases of Solutions / 34 \\ 2. Initial Value Problems / 37 \\ 3. Qualitative Behavior; Stability / 39 \\ 4. Uniqueness Theorem / 40 \\ 5. The Wronskian / 43 \\ 6. Separation and Comparison Theorems / 47 \\ 7. The Phase Plane / 49 \\ 8. Adjoint Operators; Lagrange Identity / 54 \\ 9. Green's Functions / 58 \\ *10. Two-endpoint Problems / 63 \\ *11. Green's Functions, II / 65 \\ \\ 3: Linear Equations with Constant Coefficients / 71 \\ 1. The Characteristic Polynomial / 71 \\ 2. Complex Exponential Functions / 72 \\ 3. The Operational Calculus / 76 \\ 4. Solution Bases / 78 \\ 5. Inhomogeneous Equations / 83 \\ 6. Stability / 85 \\ 7. The Transfer Function / 86 \\ *8. The Nyquist Diagram / 90 \\ *9, The Green's Function / 93 \\ \\ 4: Power Series Solutions / 99 \\ 1. Introduction / 99 \\ 2. Method of Undetermined Coefficients / 101 \\ 3. More Examples / 105 \\ 4. Three First-order DEs / 107 \\ 5. Analytic Functions / 110 \\ 6. Method of Majorants / 113 \\ *7. Sine and Cosine Functions / 116 \\ *8. Bessel Functions / 117 \\ 9. First-order Nonlinear DEs / 121 \\ 10. Radius of Convergence / 124 \\ *11. Method of Majorants, IT / 126 \\ *12. Complex Solutions / 128 \\ \\ 5: Plane Autonomous Systems / 131 \\ 1. Autonomous Systems / 131 \\ 2. Plane Autonomous Systems / 134 \\ 3. The Phase Plane, II / 136 \\ 4. Linear Autonomous Systems / 141 \\ 5. Linear Equivalence / 144 \\ 6. Equivalence Under Diffeomorphisms / 151 \\ 7. Stability / 153 \\ 8. Method of Liapunov / 157 \\ 9. Undamped Nonlinear Oscillations / 158 \\ 10. Soft and Hard Springs / 159 \\ 11. Damped Nonlinear Oscillations / 163 \\ *12. Limit Cycles / 164 \\ \\ 6: Existence and Uniqueness Theorems / 170 \\ 1. Introduction / 170 \\ 2. Lipschitz conditions / 172 \\ 3. Well-posed Problems / 174 \\ 4. Continuity / 177 \\ *5. Normal Systems / 180 \\ 6. Equivalent Integral Equation / 183 \\ 7. Successive Approximation / 185 \\ 8. Linear Systems / 188 \\ 9. Local Existence Theorem / 190 \\ *10. The Peano Existence Theorem / 191 \\ *11. Analytic Equations / 193 \\ *12. Continuation of Solutions / 197 \\ *13. The Perturbation Equation / 198 \\ \\ 7: Approximate Solutions / 204 \\ 1. Introduction / 204 \\ 2. Error Bounds / 205 \\ *3. Deviation and Error / 207 \\ 4. Mesh-halving; Richardson Extrapolation / 210 \\ 5. Midpoint Quadrature / 212 \\ 6. Trapezoidal Quadrature / 215 \\ *7. Trapezoidal Integration / 218 \\ 8. The Improved Euler Method / 222 \\ *9. The Modified Euler Method / 224 \\ *10. Cumulative Error Bound / 226 \\ \\ 8: Efficient Numerical Integration / 230 \\ 1. Difference Operators / 230 \\ 2. Polynomial Interpolation / 232 \\ *3. Interpolation Errors / 235 \\ 4. Stability / 237 \\ *5. Numerical Differentiation; Roundoff / 240 \\ *6. Higher Order Quadrature / 244 \\ *7. Gaussian Quadrature / 248 \\ 8. Fourth-order Runge-Kutta / 250 \\ *9. Milne's Method / 256 \\ *10. Multistep Methods / 258 \\ \\ 9: Regular Singular Points / 261 \\ 1. Introduction / 261 \\ *2. Movable Singular Points / 263 \\ 3. First-order Linear Equations / 264 \\ 4. Continuation Principle; Circuit Matrix / 268 \\ 5. Canonical Bases / 270 \\ 6. Regular Singular Points / 274 \\ 7. Bessel Equation / 276 \\ 8. The Fundamental Theorem / 281 \\ *9. Alternative Proof of the Fundamental Theorem / 285 \\ *10. Hypergeometric Functions / 287 \\ *11. The Jacobi Polynomials / 289 \\ *12. Singular Points at Infinity / 292 \\ *13. Fuchsian Equations / 294 \\ \\ 10: Sturm-Liouville Systems / 300 \\ 1. Sturm-Liouville Systems / 300 \\ 2. Sturm-Liouville Series / 302 \\ *3. Physical Interpretations / 305 \\ 4. Singular Systems / 308 \\ 5. Pr{\"u}fer Substitution / 312 \\ 6. Sturm Comparison Theorem / 313 \\ 7. Sturm Oscillation Theorem / 314 \\ 8. The Sequence of Eigenfunctions / 318 \\ 9. The Liouville Normal Form / 320 \\ 10. Modified Pr{\"u}fer Substitution / 323 \\ *11. The Asymptotic Behavior of Bessel Functions / 326 \\ 12. Distribution of Eigenvalues / 328 \\ 13. Normalized Eigenfunctions / 329 \\ 14. Inhomogeneous Equations / 333 \\ 15. Green's Functions / 334 \\ *16. The Schroedinger Equation / 336 \\ *17. The Square-well Potential / 338 \\ *18. Mixed Spectrum / 339 \\ \\ 11: Expansions in Eigenfunctions / 344 \\ 1. Fourier Series / 344 \\ 2. Orthogonal Expansions / 346 \\ 3. Mean-square Approximation / 347 \\ 4. Completeness / 350 \\ 5. Orthogonal Polynomials / 352 \\ *6. Properties of Orthogonal Polynomials / 354 \\ *7. Chebyshev Polynomials / 358 \\ 8. Euclidean Vector Spaces / 360 \\ 9. Completeness of Eigenfunctions / 363 \\ *10. Hilbert Space / 365 \\ *11. Proof of Completeness / 367 \\ \\ Appendix A: Linear Systems / 371 \\ 1. Matrix Norm / 371 \\ 2. Constant-coefficient Systems / 372 \\ 3. The Matrizant / 375 \\ 4. Floquet Theorem; Canonical Bases / 377 \\ \\ Appendix B: Bifurcation Theory / 380 \\ 1. What Is Bifurcation? / 380 \\ *2. Poincare Index Theorem / 381 \\ 3. Hamiltonian Systems / 383 \\ 4. Hamiltonian Bifurcations / 386 \\ 5. Poincar{\'e} Maps / 387 \\ 6. Periodically Forced Systems / 389 \\ \\ Bibliography / 392 \\ \\ Index / 395", } @Article{Birkhoff:1990:DMS, author = "G. Birkhoff and E. C. {Gartland, Jr.} and R. E. Lynch", title = "Difference methods for solving convection-diffusion equations", journal = j-COMPUT-MATH-APPL, volume = "19", number = "11", pages = "147--160", year = "1990", CODEN = "CMAPDK", DOI = "https://doi.org/10.1016/0898-1221(90)90158-G", ISSN = "0898-1221 (print), 1873-7668 (electronic)", ISSN-L = "0898-1221", MRclass = "65L10 65L12 65N06 65N15 35J25 34B05 34E15 65L70 65M06", MRnumber = "1051746", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0718.65060", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Computers \& Mathematics with Applications. An International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/08981221", ZBmath = "4184959", } @InProceedings{Birkhoff:1990:EIR, author = "Garrett Birkhoff and Robert E. Lynch", booktitle = "Iterative methods for large linear systems {(Austin, TX, 1988)}", title = "{ELLPACK} and {ITPACK} as research tools for solving elliptic problems", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "41--63", year = "1990", DOI = "https://doi.org/10.1016/B978-0-12-407475-0.50009-7", ISBN = "0-12-407475-8", ISBN-13 = "978-0-12-407475-0", MRclass = "65F10", MRnumber = "1038087", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @InProceedings{Birkhoff:1990:FDR, author = "Garrett Birkhoff", title = "Fluid dynamics, reactor computations, and surface representation", crossref = "Nash:1990:HSC", pages = "63--87", year = "1990", MRclass = "01A60", MRnumber = "1203102", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Birkhoff:1990:SCQ, author = "Garrett Birkhoff and Robert E. Lynch", title = "Some current questions on solving linear elliptic problems", journal = j-NUM-MATH, volume = "57", number = "6-7", pages = "527--545", year = "1990", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/BF01386426", ISSN = "0029-599x (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65N12 65N15 65N06 35J05 65N22", MRnumber = "1062364", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0708.65092", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", ZBmath = "4164080", } @InCollection{Birkhoff:1991:CH, author = "Garrett Birkhoff", booktitle = "{Constantin Carath{\'e}odory}: an international tribute, {Vol. I, II}", title = "{Carath{\'e}odory} and {Harvard}", publisher = pub-WORLD-SCI, address = pub-WORLD-SCI:adr, pages = "65--75", year = "1991", ISBN = "981-02-0544-9", ISBN-13 = "978-981-02-0544-7", MRclass = "01A60 28-03", MRnumber = "1130830", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0734.01011", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", subject-dates = "Constantin Carath{\'e}odory (13 September 1873--2 February 1950)", ZBmath = "4213936", } @Article{Birkhoff:1992:SMA, author = "Garrett Birkhoff and Saunders {Mac Lane}", title = "{{\booktitle{A survey of modern algebra}}}: the fiftieth anniversary of its publication", journal = j-MATH-INTEL, volume = "14", number = "1", pages = "26--31", year = "1992", CODEN = "MAINDC", DOI = "https://doi.org/10.1007/BF03024138", ISSN = "0343-6993 (print), 1866-7414 (electronic)", ISSN-L = "0343-6993", MRclass = "01A60 (01A70)", MRnumber = "1147344", MRreviewer = "Gerald J. Janusz", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0753.01012", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", fjournal = "The Mathematical Intelligencer", journal-URL = "http://link.springer.com/journal/283", ZBmath = "58233", } @Article{Bennett:1994:TFN, author = "M. K. Bennett and G. Birkhoff", title = "Two families of {Newman} lattices", journal = j-ALGEBRA-UNIVERS, volume = "32", number = "1", pages = "115--144", year = "1994", DOI = "https://doi.org/10.1007/BF01190819", ISSN = "0002-5240 (print), 1420-8911 (electronic)", ISSN-L = "0002-5240", MRclass = "06B05 (06A07) 06C15 06D05 05C99", MRnumber = "1287019", MRreviewer = "Ralph Freese", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0810.06006", acknowledgement = ack-nhfb, ajournal = "Algebra Univers.", author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Algebra Universalis", journal-URL = "https://www.springer.com/journal/12", ZBmath = "679612", } @InProceedings{Birkhoff:1995:LTA, author = "Garrett Birkhoff", booktitle = "Lattice theory and its applications {(In celebration of Garrett Birkhoff's 80th birthday. Darmstadt, 1991)}", title = "Lattices and their applications", volume = "23", publisher = "Heldermann Verlag", address = "Lemgo, Germany", pages = "7--25", year = "1995", ISBN = "3-88538-223-7", ISBN-13 = "978-3-88538-223-2", MRclass = "06-03 (01A60 06-02) 01A65", MRnumber = "1366862", MRreviewer = "Ralph Freese", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Res. Exp. Math.", ZMnumber = "0843.06001", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "802710", } @Book{MacLane:1996:A, author = "Saunders {Mac Lane} and Garrett Birkhoff", title = "Alg{\`e}bre", publisher = "{\'E}ditions Jacques Gabay", address = "Paris, France", pages = "737", year = "1996", ISBN = "2-87647-138-8", ISBN-13 = "978-2-87647-138-2", MRclass = "01A75 (00A05)", MRnumber = "1452598", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Et solutions d{\'e}velopp{\'e}es des exercices. [With detailed solutions of the exercises], Structures fondamentales. Les grands th{\'e}or{\`e}mes. Th{\'e}orie de Galois. [Fundamental structures. The major theorems. Galois theory], With a preface by J. Dieudonn{\'e}", series = "Les Grands Classiques Gauthier-Villars. [Gauthier-Villars Great Classics]", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", language = "French", } @Article{Birkhoff:1997:BRJ, author = "Garrett Birkhoff", title = "Book Review: {{\booktitle{John von Neumann}}. By Norman Macrae. New York (Random House). 1992}", journal = j-HIST-MATH, volume = "24", number = "1", pages = "98--100", month = feb, year = "1997", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:19:13 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0315086097921376", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", } @Book{Birkhoff:1997:SMA, author = "Garrett Birkhoff and Saunders Mac Lane", title = "A Survey of Modern Algebra", publisher = pub-A-K-PETERS, address = pub-A-K-PETERS:adr, edition = "Fifth", year = "1997", ISBN = "1-56881-068-7", ISBN-13 = "978-1-56881-068-3", MRclass = "00A05 01A75 12-01 13-01 06-01 20-01", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0863.00001", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", shorttableofcontents = "1: The integers \\ 2: Rational numbers and fields \\ 3: Polynomials \\ 4: Real numbers \\ 5: Complex numbers \\ 6: Groups \\ 7: Vectors and vector spaces \\ 8: The algebra of matrices \\ 9: Linear group \\ 10: Determinants and canonical forms \\ 11: Boolean algebras and lattices \\ 12: Transfinite arithmetic \\ 13: Rings and ideals \\ 14: Algebraic number fields \\ 15: Galois theory \\ Bibliography \\ List of Special Symbols \\ Index", ZBmath = "993346", } @TechReport{Birkhoff:1974:HOF, author = "Garrett Birkhoff and George Fix", title = "Higher-Order Finite Element Methods", type = "Report", institution = "Oak Ridge National Laboratory", address = "Oak Ridge, TN, USA", pages = "34", day = "1", month = mar, year = "1974", bibdate = "Sat Nov 04 07:21:36 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://www.semanticscholar.org/paper/Higher-Order-Linear-Finite-Element-Methods.-Birkhoff-Fix/59d0368b4202d42832af1d0a7a88a26b2f9e912a", abstract = "During the past decade, a great variety of 'finite element' methods have been developed for reducing boundary value problems, especially those of continuum mechanics, to systems of algebraic equations in a large (100--100,000) but finite number of unknowns. Moreover one can often greatly reduce the number of unknowns needed to achieve a given accuracy by using higher-order (e.g., bicubic spline) approximations. This raises several questions: (1) When are such finite element methods more effective than the difference methods developed in the 1950's, and why. (2) How should one solve the resulting systems of algebraic equations. (3) Which higher-order finite element methods are most efficient, and under what circumstances should they be used. The present report gives some partial answers to these questions for some typical classes of linear problems", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", remark = "Imprecisely cited in \cite[ref. 6]{Birkhoff:1975:FRS}. URL and date located by Web search.", } @Article{Birkhoff:2003:SSP, author = "Garrett Birkhoff and Marco Martens and Charles Tresser", title = "On the scaling structure for period doubling", journal = "Ast{\'e}risque", volume = "286", pages = "xix, 167--186", year = "2003", ISBN = "2-85629-138-4", ISBN-13 = "978-2-85629-138-2", ISSN = "0303-1179", ISSN-L = "0303-1179", MRclass = "37E05 (37G99)", MRnumber = "2052301", MRreviewer = "Fernando Fl{\'a}vio Ferreira", bibdate = "Sun Oct 22 09:59:52 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Geometric methods in dynamics (I). Volume in honor of Jacob Palis. In part papers presented at the international conference on dynamical systems held at {IMPA}, Rio de Janeiro, Brazil, July 2000, to celebrate Jacob Palis' 60th birthday.", ZMnumber = "1156.37310", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Ast{\'e}risque", ZBmath = "2070171", } @Book{Birkhoff:2016:H, author = "Garrett Birkhoff", title = "Hydrodynamics", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "xi + 184 + 1", day = "19", month = apr, year = "2016", DOI = "https://doi.org/10.1515/9781400877775", ISBN = "1-4008-7777-6", ISBN-13 = "978-1-4008-7777-5", LCCN = "QA911 .B48 1960", bibdate = "Wed Nov 1 12:35:50 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Princeton Legacy Library reprint of \cite{Birkhoff:1960:HSL}.", URL = "https://press.princeton.edu/books/hardcover/9780691652269/hydrodynamics", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", }

%%% ==================================================================== %%% Part 2: Publications about Garrett Birkhoff and his works %%% %%% Bibliography entries, sorted by year, and then by citation label:

@Article{Richardson:1911:IAA, author = "Lewis Fry Richardson", title = "{IX}. {The} approximate arithmetical solution by finite differences of physical problems involving differential equations with an application to the stresses in a masonry dam", journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A, volume = "A210", number = "459--470", pages = "307--357", day = "1", month = jan, year = "1911", CODEN = "PTRMAD, PTMSFB", DOI = "https://doi.org/10.1098/rsta.1911.0009", ISSN = "1364-503X (print), 1471-2962 (electronic)", ISSN-L = "1364-503X", bibdate = "Sun Oct 29 07:04:54 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib", URL = "https://royalsocietypublishing.org/doi/10.1098/rsta.1911.0009", acknowledgement = ack-nhfb, fjournal = "Philosophical Transactions of the Royal Society A: Mathematical, Physical, and Engineering Sciences", journal-URL = "http://rsta.royalsocietypublishing.org/", } @Article{Liebmann:1918:AEH, author = "H. Liebmann", title = "{Die Angenaharte Ermittleung Harmonischer Functionen und Konformer Abbildungen}. ({German}) [{The} hard determination of harmonic functions and conformal mappings]", journal = "{Sitzungsber., Akad. Wiss. Math. Phys. Kl.}", volume = "47", number = "??", pages = "385--416", month = "????", year = "1918", bibdate = "Sun Oct 29 06:58:45 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, } @Article{Anning:1933:PSA, author = "Norman Anning", title = "Problems and Solutions: Advanced Problems: Problems for Solution: 3631", journal = j-AMER-MATH-MONTHLY, volume = "40", number = "8", pages = "495--496", month = oct, year = "1933", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:08 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "See also \cite{Anning:1934:PSA,Court:1934:PSAb,Dunkel:1935:PSAa,Ore:1937:PSA,Rosenbaum:1934:PSSb}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", xxnote = "Check pages??", } @Article{Anning:1934:PSA, author = "Norman Anning and B. D. Roberts", title = "Problems and Solutions: Advanced Problems: 3631", journal = j-AMER-MATH-MONTHLY, volume = "41", number = "8", pages = "525--527", month = oct, year = "1934", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:31 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "See also \cite{Anning:1933:PSA}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", } @Article{Court:1934:PSAb, author = "N. A. Court and A. D. Bradley", title = "Problems and Solutions: Advanced Problems: 3633", journal = j-AMER-MATH-MONTHLY, volume = "41", number = "8", pages = "527--527", month = oct, year = "1934", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:31 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "See also \cite{Anning:1933:PSA}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", } @Article{Escott:1934:PSA, author = "E. B. Escott", title = "Problems and Solutions: Advanced Problems: Problems for Solution: 3673", journal = j-AMER-MATH-MONTHLY, volume = "41", number = "4", pages = "269--270", month = apr, year = "1934", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:22 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "See also \cite{Birkhoff:1935:PSA,Dunkel:1935:PSAb,Escott:1935:PSA,Gaines:1935:PSS,Grossman:1935:PSAc,Jones:1935:PSAb}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", xxnote = "Check pages??", } @Article{Rosenbaum:1934:PSSb, author = "J. Rosenbaum and L. M. Kelly", title = "Problems and Solutions: Solutions: 3634", journal = j-AMER-MATH-MONTHLY, volume = "41", number = "8", pages = "527--528", month = oct, year = "1934", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:31 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "See also \cite{Anning:1933:PSA}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", } @Article{Dunkel:1935:PSAa, author = "Otto Dunkel", title = "Problems and Solutions: Advanced Problems: 3637", journal = j-AMER-MATH-MONTHLY, volume = "42", number = "3", pages = "178--180", month = mar, year = "1935", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:42 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "See also \cite{Anning:1933:PSA}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", } @Article{Dunkel:1935:PSAb, author = "Otto Dunkel and E. P. Starke", title = "Problems and Solutions: Advanced Problems: Solutions: 3677", journal = j-AMER-MATH-MONTHLY, volume = "42", number = "9", pages = "572--577", month = nov, year = "1935", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Fri Jul 9 08:04:38 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Part 1. See also \cite{Escott:1934:PSA}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", } @Article{Escott:1935:PSA, author = "E. B. Escott and F. D. Rigby and Hansraj Gupta and E. E. Strock and Morgan Ward", title = "Problems and Solutions: Advanced Problems: 3673", journal = j-AMER-MATH-MONTHLY, volume = "42", number = "8", pages = "516--518", month = oct, year = "1935", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:55 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "See also \cite{Escott:1934:PSA}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", } @Article{Gaines:1935:PSS, author = "R. E. Gaines and C. L. Weaver", title = "Problems and Solutions: Solutions: 3676", journal = j-AMER-MATH-MONTHLY, volume = "42", number = "8", pages = "522--525", month = oct, year = "1935", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:55 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "See also \cite{Escott:1934:PSA}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", } @Article{Grossman:1935:PSAc, author = "H. Grossman and Harry Langman", title = "Problems and Solutions: Advanced Problems: 3675", journal = j-AMER-MATH-MONTHLY, volume = "42", number = "8", pages = "521--522", month = oct, year = "1935", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:55 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "See also \cite{Escott:1934:PSA}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", } @Article{Jones:1935:PSAb, author = "B. W. Jones and E. E. Strock", title = "Problems and Solutions: Advanced Problems: Solutions: 3678", journal = j-AMER-MATH-MONTHLY, volume = "42", number = "9", pages = "577--579", month = nov, year = "1935", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Fri Jul 9 08:04:38 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Part 1. See also \cite{Escott:1934:PSA}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", } @Article{Ore:1937:PSA, author = "{\O}ystein {\O}re and M. F. Becker", title = "Problems and Solutions: Advanced Problems: 3638", journal = j-AMER-MATH-MONTHLY, volume = "44", number = "6", pages = "395--397", month = jun # "\slash " # jul, year = "1937", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:38:35 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "See also \cite{Anning:1933:PSA}.", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", } @Article{Sarton:1937:EG, author = "George Sarton", title = "{{\'E}variste Galois}", journal = j-OSIRIS, volume = "3", number = "??", pages = "241--259", month = "????", year = "1937", CODEN = "OSIRAX", DOI = "https://doi.org/10.2307/301589", ISSN = "0369-7827 (print), 1933-8287 (electronic)", ISSN-L = "0369-7827", bibdate = "Mon Mar 30 15:08:56 MDT 2015", bibsource = "http://www.jstor.org/action/showPublication?journalCode=osiris; http://www.jstor.org/stable/i213314; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/i/infeld-leopold.bib; https://www.math.utah.edu/pub/tex/bib/osiris.bib", URL = "http://www.jstor.org/stable/301589", ZMnumber = "0018.19701", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fjournal = "Osiris", journal-URL = "http://www.jstor.org/page/journal/osiris/about.html", remark = "From the preface: ``The text is the same as in the first edition except for minor corrections, but there has been added to it: (1) A study on Galois and group theory by Garrett Birkhoff (Harvard University). (2) A short bibliography by myself. (3) Galois's portrait and an autograph, both derived from Paul Dupuy's fundamental memoir of 1896.", ZBmath = "3029101", } @Book{Southwell:1946:RMT, author = "R. V. (Richard Vynne) {Southwell, F.R.S.}", title = "Relaxation Methods in Theoretical Physics: a Continuation of the Treatise, Relaxation Methods in Engineering Science", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "vi + 1 + 248", year = "1946", LCCN = "QA431 .S6", bibdate = "Sun Oct 29 07:18:33 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Two volumes.", acknowledgement = ack-nhfb, author-dates = "Sir Richard Vynne Southwell (2 July 1888--9 December 1970)", } @Article{Frankel:1950:CRI, author = "Stanley P. Frankel", title = "Convergence Rates of Iterative Treatments of Partial Differential Equations", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "4", number = "30", pages = "65--75", month = apr, year = "1950", CODEN = "MTTCAS", ISSN = "0891-6837 (print), 2326-4853 (electronic)", ISSN-L = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", journal-URL = "http://www.ams.org/mcom/", } @PhdThesis{Young:1950:IMS, author = "David M. Young", title = "Iterative methods for solving partial differential equations of elliptic type", type = "{Ph.D.} dissertation", school = "Harvard University", address = "Cambridge, MA, USA", year = "1950", bibdate = "Tue Feb 15 09:45:13 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib", acknowledgement = ack-nhfb, advisor = "Garrett Birkhoff", } @Article{Shortley:1953:UTP, author = "George Shortley", title = "Use of {Tschebyscheff} polynomial operators in the numerical solution of boundary value problems", journal = j-J-APPL-PHYS, volume = "24", number = "4", pages = "392--397", month = apr, year = "1953", CODEN = "JAPIAU", DOI = "https://doi.org/10.1063/1.1721292", ISSN = "0021-8979 (print), 1089-7550 (electronic), 1520-8850", ISSN-L = "0021-8979", bibdate = "Sun Oct 29 07:14:26 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://pubs.aip.org/aip/jap/article/24/4/392/346540/Use-of-Tschebyscheff-Polynomial-Operators-in-the", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Physics", journal-URL = "http://aip.scitation.org/toc/jap/current", } @Article{Young:1953:RMS, author = "David Young", title = "On {Richardson}'s Method for Solving Linear Systems with Positive Definite Matrices", journal = j-J-MATH-PHYS-MIT, volume = "32", number = "1--4", pages = "243--255", month = apr, year = "1953", CODEN = "JMPHA9", DOI = "https://doi.org/10.1002/sapm1953321243", ISSN = "0097-1421", ISSN-L = "0097-1421", bibdate = "Sat Aug 19 13:35:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib; https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib", URL = "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1953321243", acknowledgement = ack-nhfb, ajournal = "J. Math. Phys. (MIT)", fjournal = "Journal of Mathematics and Physics (MIT)", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590", onlinedate = "April 1953", } @Article{Young:1954:IMS, author = "David Young", title = "Iterative methods for solving partial difference equations of elliptic type", journal = j-TRANS-AM-MATH-SOC, volume = "76", number = "1", pages = "92--111", month = jan, year = "1954", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/1990745", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "65.0X", MRnumber = "59635", MRreviewer = "M. Hyman", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib", fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", } @Article{Peaceman:1955:NSP, author = "D. W. Peaceman and H. H. {Rachford, Jr.}", title = "The Numerical Solution of Parabolic and Elliptic Differential Equations", journal = j-J-SIAM, volume = "3", number = "1", pages = "28--41", month = mar, year = "1955", CODEN = "JSIMAV", ISSN = "0368-4245 (print), 1095-712X (electronic)", ISSN-L = "0368-4245", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siam.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Journal of the Society for Industrial and Applied Mathematics", journal-URL = "http://epubs.siam.org/loi/smjmap.1", } @Article{Douglas:1956:NSH, author = "J. {Douglas, Jr.} and H. H. {Rachford, Jr.}", title = "On the numerical solution of heat conduction problems in two or three space variables", journal = j-TRANS-AM-MATH-SOC, volume = "82", number = "2", pages = "421--439", month = jul, year = "1956", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/1993056", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "65.3X", MRnumber = "MR0084194", MRreviewer = "Charles Saltzer", bibdate = "Sun Oct 29 06:45:51 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", received = "21 December 1955 (presented 27 December 1955)", } @Article{Brainerd:1960:BPM, author = "Barron Brainerd", title = "On {Birkhoff}'s problem 73 for monoids", journal = j-CAN-MATH-BULL, volume = "3", number = "??", pages = "217--220", month = "????", year = "1960", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1960-026-3", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", MRclass = "20.93", MRnumber = "0124428 (23 \#A1740)", MRreviewer = "G. B. Preston", bibdate = "Thu Sep 8 10:02:58 MDT 2011", bibsource = "http://cms.math.ca/cmb/v3/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib; MathSciNet database", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Johnson:1960:AGB, author = "Diane M. Johnson and A. L. Dulmage and N. S. Mendelsohn", title = "On an algorithm of {G. Birkhoff} concerning doubly stochastic matrices", journal = j-CAN-MATH-BULL, volume = "3", number = "??", pages = "237--242", month = "????", year = "1960", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1960-029-5", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", MRclass = "15.65", MRnumber = "0130267 (24 \#A133)", MRreviewer = "M. Marcus", bibdate = "Thu Sep 8 10:02:58 MDT 2011", bibsource = "http://cms.math.ca/cmb/v3/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib; MathSciNet database", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Howlett:1962:BRB, author = "J. Howlett", title = "Book Review: {{\booktitle{Proceedings of Symposia in Applied Mathematics, vol. XI, Nuclear Reactor Theory}}, by G. Birkhoff and E. P. Wigner}", journal = j-MATH-GAZ, volume = "46", number = "357", pages = "248--250", month = oct, year = "1962", CODEN = "MAGAAS", ISSN = "0025-5572 (print), 2056-6328 (electronic)", bibdate = "Sat Jul 28 18:44:10 MDT 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib", URL = "http://www.jstor.org/stable/3614048", acknowledgement = ack-nhfb, fjournal = "Mathematical Gazette", journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Secrest:1962:BRB, author = "E. Leigh Secrest", title = "Book Review: {{\booktitle{Proceedings of the Eleventh Symposium in Applied Mathematics of the American Mathematical Society}}, edited by Birkhoff and Wigner}", journal = j-MATH-MAG, volume = "35", number = "5", pages = "307--308", month = nov, year = "1962", CODEN = "MAMGA8", ISSN = "0025-570X", bibdate = "Sat Jul 28 18:44:10 MDT 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib", URL = "http://www.jstor.org/stable/2688212", acknowledgement = ack-nhfb, fjournal = "Mathematics Magazine", journal-URL = "http://www.maa.org/pubs/mathmag.html", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Book{Varga:1962:MIA, author = "Richard S. Varga", title = "Matrix Iterative Analysis", publisher = pub-PH, address = pub-PH:adr, pages = "xiii + 322", year = "1962", LCCN = "QA263 .V3 1962", MRclass = "65.35 (65.65)", MRnumber = "0158502", MRreviewer = "A. O. Garder", bibdate = "Wed Apr 20 14:10:28 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/t/taussky-todd-olga.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/bibnet/subjects/domain-decomp.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib", acknowledgement = ack-nhfb, author-dates = "Richard S. Varga (8 October 1928--25 February 2022)", tableofcontents = "Matrix properties and concepts \\ Non-negative matrices \\ Basic iterative methods and comparison theorems \\ Successive overrelaxation iterative methods \\ Semi-iterative methods \\ Derivation and solution of elliptic difference equations \\ Alternating-direction implicit iterative methods \\ Matrix methods for parabolic partial differential equations \\ Estimation of acceleration parameters", } @Article{Antosiewicz:1963:BRO, author = "H. A. Antosiewicz", title = "Book Review: {{\booktitle{Ordinary Differential Equations}} (G. Birkhoff and G. C. Rota)}", journal = j-SIAM-REVIEW, volume = "5", number = "2", pages = "160--161", month = "????", year = "1963", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1005043", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Thu Mar 27 09:05:02 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/5/2; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "April 1963", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Cuthill:1963:BRB, author = "Elizabeth Cuthill", title = "Book Review: {{\booktitle{Proceedings of Symposia in Applied Mathematics, vol. XI, Nuclear Reactor Theory}}, by G. Birkhoff and E. P. Wigner}", journal = j-MATH-COMPUT, volume = "17", number = "84", pages = "475--476", month = oct, year = "1963", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Sat Jul 28 18:44:10 MDT 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib", URL = "http://www.jstor.org/stable/2004032", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Langenhop:1963:RPP, author = "C. E. Langenhop", title = "Recent Publications and Presentations: {{\em Ordinary Differential Equations}}, by {G. Birkhoff and G.-C. Rota}", journal = j-AMER-MATH-MONTHLY, volume = "70", number = "7", pages = "777--778", month = aug # "\slash " # sep, year = "1963", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2312290", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:11 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Stiefel:1965:PRT, author = "Eduard Stiefel and J{\"o}rg Waldvogel", title = "Probl{\`e}me restreint des trois corps. {G}{\'e}n{\'e}ralisation de la r{\'e}gularisation de {Birkhoff} pour le mouvement du mobile dans l'espace {\`a} trois dimensions. ({French}) [{Restricted} problem of three bodies. {Generalization} of the {Birkhoff} regularization for the motion of the mobile in three-dimensional space]", journal = j-C-R-ACAD-SCI-PARIS, volume = "260", pages = "805", year = "1965", ISSN = "0001-4036 (print), 2419-6304 (electronic)", ISSN-L = "0001-4036", MRclass = "85.34 (70.34)", MRnumber = "174367", MRreviewer = "E. Leimanis", bibdate = "Wed Sep 2 16:23:13 2020", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib", acknowledgement = ack-nhfb, author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)", fjournal = "Comptes Rendus Hebdomadaires des S\'{e}ances de l'Acad\'{e}mie des Sciences", journal-URL = "http://gallica.bnf.fr/ark:/12148/cb343481087/date", language = "French", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Gumbel:1966:BRS, author = "E. J. Gumbel", title = "Book Review: {{\booktitle{Selected Papers of Richard von Mises. edited by Ph. Frank, S. Goldstein, M. Kac, W. Prager, G. Szeg{\H{o}}, and G. Birkhoff. Volume I Geometry, Mechanics, Analysis. Volume II --- Probability and Statistics}}. American Mathematical Society. Providence, Rhode Island}", journal = j-ECONOMETRICA, volume = "34", number = "1", pages = "251--253", month = jan, year = "1966", CODEN = "ECMTA7", DOI = "https://doi.org/10.2307/1909881", ISSN = "0012-9682", bibdate = "Mon Oct 30 15:09:16 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "http://www.jstor.org/stable/1909881", acknowledgement = ack-nhfb, fjournal = "Econometrica", journal-URL = "http://www.jstor.org/journal/econometrica", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Austin:1967:NBE, author = "D. G. Austin", title = "A Note on the {Birkhoff} Ergodic Theorem", journal = j-ANN-MATH-STAT, volume = "38", number = "3", pages = "922--923", month = jun, year = "1967", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177698887", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", MRclass = "28.70", MRnumber = "0222248 (36 \#5300)", MRreviewer = "W. Parry", bibdate = "Sat May 31 09:11:10 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/annmathstat.bib", URL = "http://projecteuclid.org/euclid.aoms/1177698887", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Barrar:1967:PFP, author = "Richard B. Barrar", title = "Proof of the fixed point theorems of {Poincar{\'e}} and {Birkhoff}", journal = j-CAN-J-MATH, volume = "19", number = "??", pages = "333--343", month = "????", year = "1967", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1967-024-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:38:36 MDT 2011", bibsource = "http://cms.math.ca/cjm/v19/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/canjmath1960.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Mewborn:1967:RAS, author = "A. C. Mewborn", title = "Reviews: {{\em Algebra}}, by {Saunders Mac Lane and Garrett Birkhoff}", journal = j-AMER-MATH-MONTHLY, volume = "74", number = "10", pages = "1279--1279", month = dec, year = "1967", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2315715", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:38:50 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{G:1968:BRD, author = "W. G.", title = "Book Review: {Donald Greenspan, editor, \booktitle{Numerical Solutions of Nonlinear Differential Equations}, John Wiley \& Sons, Inc., New York, 1966, x + 347 pp.}", journal = j-MATH-COMPUT, volume = "22", number = "104", pages = "896--898", month = oct, year = "1968", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2004598", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Wed Nov 1 10:55:04 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib", URL = "https://doi.org/10.2307/2004598", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Sharma:1968:AHB, author = "A. Sharma and J. Prasad", title = "On {Abel--Hermite--Birkhoff} Interpolation", journal = j-SIAM-J-NUMER-ANAL, volume = "5", number = "4", pages = "864--881", month = dec, year = "1968", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Atkinson:1969:PCP, author = "K. Atkinson and A. Sharma", title = "A Partial Characterization of Poised {Hermite--Birkhoff} Interpolation Problems", journal = j-SIAM-J-NUMER-ANAL, volume = "6", number = "2", pages = "230--235", month = jun, year = "1969", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Gladwell:1969:SEP, author = "Ian Gladwell", title = "Some Extensions of a Paper by {Birkhoff} and {Priver}", journal = j-SIAM-J-NUMER-ANAL, volume = "6", number = "2", pages = "294--298", month = jun, year = "1969", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Schechter:1969:HBI, author = "Murray Schechter", title = "{Hermite--Birkhoff} Interpolation Problems with Complex Nodes", journal = j-AMER-MATH-MONTHLY, volume = "76", number = "10", pages = "1119--1122", month = dec, year = "1969", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2317184", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:39:36 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Boyling:1970:BGF, author = "J. B. Boyling", title = "{Birkhoff} Gravitational Field of {Milne}'s Universe", journal = j-J-MATH-PHYS, volume = "11", number = "3", pages = "867--870", month = mar, year = "1970", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.1665225", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Fri Oct 28 16:39:23 MDT 2011", bibsource = "http://jmp.aip.org/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v11/i3/p867_s1", acknowledgement = ack-nhfb, classification = "A0330 (Special relativity); A9880 (Cosmology)", corpsource = "Univ. Leeds, UK", fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", keywords = "astronomical spectra; cosmology; gravitation", onlinedate = "28 October 2003", pagecount = "4", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Bewley:1971:EBN, author = "Truman Bewley", title = "Extension of the {Birkhoff} and {von Neumann} ergodic theorems to semigroup actions", journal = j-ANN-INST-HENRI-POINCARE-N-S-B-CALC-PROBAB-STAT, volume = "7", number = "4", pages = "283--291", month = oct # "--" # dec, year = "1971", CODEN = "AHPBAR", ISSN = "0020-2347", ISSN-L = "0020-2347", MRnumber = "306444", bibdate = "Mon Jun 9 05:30:47 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/annihpb.bib", URL = "http://www.numdam.org/item?id=AIHPB_1971__7_4_283_0", ZMnumber = "0226.28009", acknowledgement = ack-nhfb, fjournal = "Annales de l'Institut Henri Poincar{\'e}. Nouvelle s{\'e}rie. Section B. Calcul des Probabilit{\'e}s et Statistique", journal-URL = "http://www.numdam.org/numdam-bin/feuilleter?j=AIHPB", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Bogart:1971:RAS, author = "K. P. Bogart", title = "Reviews: {{\em Algebra}}, by {Saunders Mac Lane and Garret Birkhoff}", journal = j-AMER-MATH-MONTHLY, volume = "78", number = "1", pages = "92--93", month = jan, year = "1971", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2317507", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:36:11 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Lorentz:1971:BI, author = "G. G. Lorentz and K. L. Zeller", title = "{Birkhoff} Interpolation", journal = j-SIAM-J-NUMER-ANAL, volume = "8", number = "1", pages = "43--48", month = mar, year = "1971", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Klotz:1972:RMA, author = "E. Klotz", title = "Reviews: {{\em Modern Applied Algebra}}, by {Garrett Birkhoff and Thomas C. Bartee}", journal = j-AMER-MATH-MONTHLY, volume = "79", number = "5", pages = "529--530", month = may, year = "1972", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2317587", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:36:45 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Chalmers:1974:RRH, author = "B. L. Chalmers and D. J. Johnson and F. T. Metcalf and G. D. Taylor", title = "Remarks on the Rank of {Hermite--Birkhoff} Interpolation", journal = j-SIAM-J-NUMER-ANAL, volume = "11", number = "2", pages = "254--259", month = apr, year = "1974", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Ferguson:1974:SCM, author = "David R. Ferguson", title = "Sign Changes and Minimal Support Properties of {Hermite--Birkhoff} Splines with Compact Support", journal = j-SIAM-J-NUMER-ANAL, volume = "11", number = "4", pages = "769--779", month = sep, year = "1974", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Makela:1974:EFM, author = "Matti M{\"a}kel{\"a} and Olavi Nevanlinna and Aarne H. Sipil{\"a}", title = "Exponentially Fitted Multistep Methods by Generalized {Hermite--Birkhoff} Interpolation", journal = j-BIT, volume = "14", number = "4", pages = "437--451", month = dec, year = "1974", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/BF01932540", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", bibdate = "Wed Jan 4 18:52:13 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=14&issue=4; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/bit.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=14&issue=4&spage=437", acknowledgement = ack-nhfb, fjournal = "BIT (Nordisk tidskrift for informationsbehandling)", journal-URL = "http://link.springer.com/journal/10543", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Grattan-Guinness:1975:BRMa, author = "I. Grattan-Guinness", title = "Book Review: {Mathematics: A Source Book in Classical Analysis. Ed. by G. Birkhoff, with the assistance of U. Merzbach. Cambridge, Mass: Harvard University Press, 1973. Pp. xii + 470. \pounds 12.50}", journal = j-BRITISH-J-HIST-SCI, volume = "8", number = "2", pages = "176--177", month = jul, year = "1975", CODEN = "BJHSAT", DOI = "https://doi.org/10.1017/S0007087400014035", ISSN = "0007-0874 (print), 1474-001X (electronic)", ISSN-L = "0007-0874", bibdate = "Thu Sep 23 07:34:43 MDT 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/bjhs.bib", URL = "http://www.jstor.org/stable/4025644", acknowledgement = ack-nhfb, fjournal = "British Journal for the History of Science", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BJH", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Koppelman:1975:BRB, author = "Elaine Koppelman", title = "Book Review: {{\booktitle{A Source Book in Classical Analysis}} by Garrett Birkhoff; Uta Merzbach}", journal = j-ISIS, volume = "66", number = "2", pages = "284--285", month = jun, year = "1975", CODEN = "ISISA4", ISSN = "0021-1753 (print), 1545-6994 (electronic)", ISSN-L = "0021-1753", bibdate = "Tue Jul 30 21:29:18 MDT 2013", bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302313; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/isis1970.bib", URL = "http://www.jstor.org/stable/229444", acknowledgement = ack-nhfb, fjournal = "Isis", journal-URL = "http://www.jstor.org/journal/isis", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Lether:1976:BYQ, author = "Frank Lether", title = "On {Birkhoff--Young} quadrature of analytical functions", journal = j-J-COMPUT-APPL-MATH, volume = "2", number = "2", pages = "81--84", month = jun, year = "1976", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 11:59:14 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib", URL = "http://www.sciencedirect.com/science/article/pii/0771050X76900127", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Anonymous:1977:BRSd, author = "Anonymous", title = "Book Review: {{\booktitle{A source book in classical analysis}}: Edited by Garrett Birkhoff with the assistance of Uta Merzbach. Cambridge, Mass. (Harvard University Press). 1973}", journal = j-HIST-MATH, volume = "4", number = "3", pages = "364--365", month = aug, year = "1977", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Wed Jun 26 06:16:47 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/0315086077900726", acknowledgement = ack-nhfb, fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Horndeski:1978:BTM, author = "Gregory Walter Horndeski", title = "{Birkhoff}'s theorem and magnetic monopole solutions for a system of generalized {Einstein--Maxwell} field equations", journal = j-J-MATH-PHYS, volume = "19", number = "3", pages = "668--674", month = mar, year = "1978", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.523710", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Sat Oct 29 11:28:18 MDT 2011", bibsource = "http://jmp.aip.org/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1975.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v19/i3/p668_s1", acknowledgement = ack-nhfb, classification = "A0420J (Solutions to equations in general relativity); A0440 (Continuous media; electromagnetic and other mixed gravitational systems)", corpsource = "Dept. of Appl. Math., Univ. of Waterloo, Waterloo, Ont., Canada", fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", keywords = "Birkhoff's theorem; electromagnetic field theory; general relativity; generalised Einstein Maxwell equations; magnetic monopole solutions; magnetic monopoles", onlinedate = "11 August 2008", pagecount = "7", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", treatment = "T Theoretical or Mathematical", } @Article{Lutz:1979:BIM, author = "Donald A. Lutz", title = "{Birkhoff} invariants and meromorphic differential equations", journal = j-LECT-NOTES-MATH, volume = "712", pages = "66--76", year = "1979", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/BFb0062816", ISBN = "3-540-09250-1 (print), 3-540-35314-3 (e-book)", ISBN-13 = "978-3-540-09250-6 (print), 978-3-540-35314-0 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", MRclass = "34A20 (14D05)", MRnumber = "548144 (80i:34007)", MRreviewer = "Andrew J. Sommese", bibdate = "Fri May 9 19:07:38 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/lnm1975.bib", URL = "http://link.springer.com/chapter/10.1007/BFb0062816/", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/BFb0062810", book-URL = "http://www.springerlink.com/content/978-3-540-35314-0", fjournal = "Lecture Notes in Mathematics", journal-URL = "http://link.springer.com/bookseries/304", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Nishi:1979:EPJ, author = "Akihiro Nishi", title = "An elementary proof of {Johnson--Dulmage--Mendelsohn}'s refinement of {Birkhoff}'s theorem on doubly stochastic matrices", journal = j-CAN-MATH-BULL, volume = "22", number = "1", pages = "81--86", month = mar, year = "1979", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1979-011-4", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", bibdate = "Thu Sep 8 10:04:53 MDT 2011", bibsource = "http://cms.math.ca/cmb/v22/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Cavaretta:1980:HBI, author = "A. S. {Cavaretta, Jr.} and A. Sharma and R. S. Varga", title = "{Hermite--Birkhoff} interpolation in the $n$-th roots of unity", journal = j-TRANS-AM-MATH-SOC, volume = "259", number = "2", pages = "621--628", month = jun, year = "1980", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/1998252", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "30E05", MRnumber = "567101 (81c:30064)", MRreviewer = "Jean Tzimbalario", bibdate = "Wed Apr 20 14:10:28 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib", URL = "http://www.math.kent.edu/~varga/pub/paper_118.pdf", ZMnumber = "431.41001", acknowledgement = ack-nhfb, author-dates = "Richard S. Varga (8 October 1928--25 February 2022)", fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Clapp:1980:BTD, author = "M. H. Clapp and R. C. Shiflett", title = "A {Birkhoff} Theorem for Doubly Stochastic Matrices with Vector Entries", journal = j-STUD-APPL-MATH, volume = "62", number = "3", pages = "273--279", month = jun, year = "1980", CODEN = "SAPMB6", DOI = "https://doi.org/10.1002/sapm1980623273", ISSN = "0022-2526 (print), 1467-9590 (electronic)", ISSN-L = "0022-2526", bibdate = "Sun Aug 20 10:41:59 MDT 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/studapplmath.bib", URL = "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1980623273", acknowledgement = ack-nhfb, ajournal = "Stud. Appl. Math.", fjournal = "Studies in Applied Mathematics", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590", onlinedate = "June 1980", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Book{Hageman:1981:AIM, author = "Louis A. Hageman and David M. Young", title = "Applied Iterative Methods", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "xvii + 386", year = "1981", ISBN = "0-12-313340-8", ISBN-13 = "978-0-12-313340-3", LCCN = "QA297.8 .H34 1981", MRclass = "65F10 (65-01 65-02)", MRnumber = "83c:65064", MRreviewer = "Themistocles M. Rassias", bibdate = "Tue Dec 14 22:54:41 1993", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib; https://www.math.utah.edu/pub/tex/bib/master.bib", series = "Computer Science and Applied Mathematics, Editor: Werner Rheinboldt", acknowledgement = ack-nhfb, tableofcontents = "Background on linear algebra and related topics \\ Background on basic iterative methods \\ Polynomial acceleration \\ Chebyshev acceleration \\ An adaptive Chebyshev procedure using special norms \\ Adaptive Chebyshev acceleration \\ Conjugate gradient acceleration \\ Special methods for red/black partitionings \\ Adaptive procedures for the successive overrelaxation method \\ The use of iterative methods in the solution of partial differential equations \\ Case studies \\ The nonsymmetrizable case \\ Chebyshev acceleration subroutine \\ CCSI subroutine \\ SOR subroutine", } @Article{Muhlbach:1981:AAH, author = "G. M{\"u}hlbach", title = "An algorithmic approach to {Hermite--Birkhoff} interpolation", journal = j-NUM-MATH, volume = "37", number = "3", pages = "339--347", month = jul, year = "1981", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65D05", MRnumber = "83a:65011", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", acknowledgement = ack-nhfb, classification = "C4130 (Interpolation and function approximation)", corpsource = "Inst. f{\"u}r Prakt. Math., Univ. Hannover, Hannover, West Germany", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "algebraic polynomials; algorithmic approach; HB-interpolation; Hermite--Birkhoff-interpolation; interpolation", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", treatment = "T Theoretical or Mathematical", } @Article{Riemenschneider:1981:BIR, author = "S. D. Riemenschneider and A. Sharma", title = "{Birkhoff} interpolation at the $n$ th roots of unity: convergence", journal = j-CAN-J-MATH, volume = "33", number = "??", pages = "362--371", month = "????", year = "1981", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1981-030-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:38:54 MDT 2011", bibsource = "http://cms.math.ca/cjm/v33/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/canjmath1980.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Benson:1982:DSM, author = "R. V. Benson and R. C. Shiflett", title = "Doubly stochastic matrices over arbitrary vector spaces and the {Birkhoff} theorem", journal = j-LINEAR-ALGEBRA-APPL, volume = "42", number = "??", pages = "145--158", month = feb, year = "1982", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(82)90145-8", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A51", MRnumber = "84e:15022", MRreviewer = "Thomas H. Foregger", bibdate = "Wed Nov 30 13:48:55 MST 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", URL = "http://www.sciencedirect.com/science/article/pii/0024379582901458", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Brualdi:1982:NBA, author = "Richard A. Brualdi", title = "Notes on the {Birkhoff} algorithm for doubly stochastic matrices", journal = j-CAN-MATH-BULL, volume = "25", number = "2", pages = "191--199", month = jun, year = "1982", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1982-026-3", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", bibdate = "Thu Sep 8 10:05:09 MDT 2011", bibsource = "http://cms.math.ca/cmb/v25/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib", note = "See comments \cite{Bongiovanni:1988:CPR}.", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Dyn:1982:CBI, author = "N. Dyn and G. G. Lorentz and S. D. Riemenschneider", title = "Continuity of the {Birkhoff} Interpolation", journal = j-SIAM-J-NUMER-ANAL, volume = "19", number = "3", pages = "507--509", month = jun, year = "1982", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "41A05", MRnumber = "83k:41001", MRreviewer = "A. Sharma", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Jetter:1982:NCG, author = "Kurt Jetter", title = "A new class of {Gaussian} quadrature formulas based on {Birkhoff} type data", journal = j-SIAM-J-NUMER-ANAL, volume = "19", number = "5", pages = "1081--1089", month = oct, year = "1982", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "41A55 (65D07)", MRnumber = "84d:41054", MRreviewer = "I. P. Mysovskikh", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Kincaid:1982:AIF, author = "David R. Kincaid and John R. Respess and David M. Young and Roger G. Grimes", title = "{Algorithm 586}: {ITPACK 2C}: {A FORTRAN} Package for Solving Large Sparse Linear Systems by Adaptive Accelerated Iterative Methods", journal = j-TOMS, volume = "8", number = "3", pages = "302--322", month = sep, year = "1982", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/356004.356009", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Mon Aug 29 23:49:22 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "http://dl.acm.org/pub.cfm?id=J782", keywords = "algorithms; documentation; iterative methods; numerical software; sparse matrix", } @Article{Lorentz:1982:ACB, author = "G. G. Lorentz", title = "The analytic character of the {Birkhoff} interpolation polynomials", journal = j-CAN-J-MATH, volume = "34", number = "??", pages = "765--768", month = "????", year = "1982", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1982-053-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:38:56 MDT 2011", bibsource = "http://cms.math.ca/cjm/v34/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/canjmath1980.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Alexanderson:1983:CGB, author = "G. L. Alexanderson and Carroll Wilde", title = "A Conversation with {Garrett Birkhoff}", journal = j-TWO-YEAR-COLL-MATH-J, volume = "14", number = "2", pages = "126--145", month = mar, year = "1983", CODEN = "????", DOI = "https://doi.org/10.1080/00494925.1983.11972669", ISSN = "0049-4925 (print), 2325-9116 (electronic)", ISSN-L = "0049-4925", bibdate = "Thu Feb 14 09:49:41 MST 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/collegemathj.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/00494925.1983.11972669", acknowledgement = ack-nhfb, fjournal = "Two-Year College Mathematics Journal", journal-URL = "https://maa.tandfonline.com/loi/ucmj20; http://www.jstor.org/journals/00494925.html", onlinedate = "30 Jan 2018", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Saxena:1983:HBI, author = "R. B. Saxena and A. Sharma and Z. Ziegler", title = "{Hermite--Birkhoff} interpolation on roots of unity and {Walsh} equiconvergence", journal = j-LINEAR-ALGEBRA-APPL, volume = "52/53", number = "??", pages = "603--615", year = "1983", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "30E05 (41A05)", MRnumber = "85g:30065", bibdate = "Thu Jan 23 11:18:08 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Dyn:1984:CHB, author = "Nira Dyn", title = "Composite {Hermite--Birkhoff} quadrature formulas of {Gaussian} type", journal = j-MATH-COMPUT, volume = "43", number = "168", pages = "535--541", month = oct, year = "1984", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "41A55 (41A50)", MRnumber = "85k:41043", MRreviewer = "Yury Girshovich", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Majima:1984:SPR, author = "Hideyuki Majima", title = "{Stokes} phenomena and {Riemann--Hilbert--Birkhoff} problem", journal = j-LECT-NOTES-MATH, volume = "1075", pages = "111--133", year = "1984", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/BFb0071554", ISBN = "3-540-13375-5 (print), 3-540-38931-8 (e-book)", ISBN-13 = "978-3-540-13375-9 (print), 978-3-540-38931-6 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", bibdate = "Fri May 9 19:07:11 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/lnm1980.bib", URL = "http://link.springer.com/chapter/10.1007/BFb0071554/", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/BFb0071550", book-URL = "http://www.springerlink.com/content/978-3-540-38931-6", fjournal = "Lecture Notes in Mathematics", journal-URL = "http://link.springer.com/bookseries/304", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Servizi:1984:CPB, author = "G. Servizi and G. Turchetti", title = "A computer program for the {Birkhoff} series of area preserving maps", journal = j-COMP-PHYS-COMM, volume = "32", number = "2", pages = "201--207", month = may, year = "1984", CODEN = "CPHCBZ", DOI = "https://doi.org/10.1016/0010-4655(84)90071-7", ISSN = "0010-4655 (print), 1879-2944 (electronic)", ISSN-L = "0010-4655", bibdate = "Mon Feb 13 10:28:07 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib", URL = "http://www.sciencedirect.com/science/article/pii/0010465584900717", acknowledgement = ack-nhfb, fjournal = "Computer Physics Communications", journal-URL = "http://www.sciencedirect.com/science/journal/00104655", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Bogart:1985:RBA, author = "Kenneth Bogart", title = "Reviews: {{\em Basic Algebra}}, by {Nathan Jacobson, W. H. Freeman, Saunders Mac Lane, and Garrett Birkhoff}", journal = j-AMER-MATH-MONTHLY, volume = "92", number = "10", pages = "743--745", month = dec, year = "1985", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2323244", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:38:09 MDT 1999", bibsource = "http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Saunders Mac Lane (1909--2005)", } @Article{Fabrykowski:1985:SBI, author = "J. Fabrykowski and A. Sharma and H. Zassenhaus", title = "Some {Birkhoff} interpolation problems on the roots of unity", journal = j-LINEAR-ALGEBRA-APPL, volume = "65", number = "??", pages = "1--23", month = feb, year = "1985", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(85)90084-9", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "41A05 (30E05)", MRnumber = "86b:41003", MRreviewer = "Jean Tzimbalario", bibdate = "Wed Nov 30 13:49:40 MST 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", URL = "http://www.sciencedirect.com/science/article/pii/0024379585900849", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Saez:1985:STT, author = "D. S{\'a}ez and J. V. Arnau", title = "On the scalar-tetradic theory {A} --- the {Birkhoff} theorem: horizons and singularities", journal = j-J-MATH-PHYS, volume = "26", number = "11", pages = "2902--2908", month = nov, year = "1985", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.526715", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", MRclass = "83D05", MRnumber = "87e:83051", MRreviewer = "Carl Brans", bibdate = "Mon Oct 31 11:57:31 MDT 2011", bibsource = "http://jmp.aip.org/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v26/i11/p2902_s1", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", pagecount = "7", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Ali:1986:SBG, author = "M. K. Ali and W. Robert Wood and J. S. Devitt", title = "On the summation of the {Birkhoff--Gustavson} normal form of an anharmonic oscillator", journal = j-J-MATH-PHYS, volume = "27", number = "7", pages = "1806--1812", month = jul, year = "1986", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.527048", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", MRclass = "81C15 (34E15)", MRnumber = "87h:81046", MRreviewer = "Y. Kato", bibdate = "Mon Oct 31 11:57:45 MDT 2011", bibsource = "http://jmp.aip.org/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v27/i7/p1806_s1", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", pagecount = "7", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Lewandowski:1986:APG, author = "J. L. Lewandowski and C. L. Liu and J. W. S. Liu", title = "An algorithmic proof of a generalization of the {Birkhoff--von Neumann} theorem", journal = j-J-ALG, volume = "7", number = "3", pages = "323--330", month = sep, year = "1986", CODEN = "JOALDV", DOI = "https://doi.org/10.1016/0196-6774(86)90024-6", ISSN = "0196-6774 (print), 1090-2678 (electronic)", ISSN-L = "0196-6774", bibdate = "Tue Dec 11 09:14:30 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jalg.bib", URL = "http://www.sciencedirect.com/science/article/pii/0196677486900246", acknowledgement = ack-nhfb, fjournal = "Journal of Algorithms", journal-URL = "http://www.sciencedirect.com/science/journal/01966774", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Reutenauer:1986:TPB, author = "Christophe Reutenauer", title = "Theorem of {Poincar{\`e}--Birkhoff--Witt}, logarithm and symmetric group representations of degrees equal to {Stirling} numbers", journal = j-LECT-NOTES-MATH, volume = "1234", pages = "267--284", year = "1986", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/BFb0072520", ISBN = "3-540-17207-6 (print), 3-540-47402-1 (e-book)", ISBN-13 = "978-3-540-17207-9 (print), 978-3-540-47402-9 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", MRclass = "05A15 (05A05 17B10 20C30)", MRnumber = "927769 (89i:05029)", MRreviewer = "Luis Verde-Star", bibdate = "Fri May 9 19:07:52 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/lnm1985.bib", URL = "http://link.springer.com/chapter/10.1007/BFb0072520/", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/BFb0072503", book-URL = "http://www.springerlink.com/content/978-3-540-47402-9", fjournal = "Lecture Notes in Mathematics", journal-URL = "http://link.springer.com/bookseries/304", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Singh:1986:BTT, author = "Tarkeshwar Singh", title = "{Birkhoff}-type theorem in self-creation cosmology", journal = j-J-MATH-PHYS, volume = "27", number = "4", pages = "1074--1075", month = apr, year = "1986", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.527150", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", MRclass = "83D05", MRnumber = "87g:83103", MRreviewer = "Kenneth Dunn", bibdate = "Mon Oct 31 11:57:39 MDT 2011", bibsource = "http://jmp.aip.org/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v27/i4/p1074_s1", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", pagecount = "2", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Tinhofer:1986:GIT, author = "G. Tinhofer", title = "Graph isomorphism and theorems of {Birkhoff} type", journal = j-COMPUTING, volume = "36", number = "4", pages = "285--300", month = dec, year = "1986", CODEN = "CMPTA2", ISSN = "0010-485X (print), 1436-5057 (electronic)", ISSN-L = "0010-485X", MRclass = "05C50 (15A51 52A25)", MRnumber = "87h:05148", MRreviewer = "R. A. Brualdi", bibdate = "Tue Oct 12 16:33:42 MDT 1999", bibsource = "Compendex database; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/computing.bib; MathSciNet database", acknowledgement = ack-nhfb, classification = "921", fjournal = "Computing", journal-URL = "http://link.springer.com/journal/607", journalabr = "Computing (Vienna/New York)", keywords = "convex polytopes; cycles; doubly stochastic matrices; graph isomorphism; Graph Theory; mathematical techniques; trees", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Jetter:1987:UGB, author = "Kurt Jetter", title = "Uniqueness of {Gauss--Birkhoff} Quadrature Formulas", journal = j-SIAM-J-NUMER-ANAL, volume = "24", number = "1", pages = "147--154", month = feb, year = "1987", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65D32 (41A55)", MRnumber = "88e:65026", MRreviewer = "G. A. Evans", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Weiser:1987:BRE, author = "Alan Weiser", title = "Book Review: {{\booktitle{Elliptic Problem Solvers II}} (Garrett Birkhoff and Arthur Schoenstadt, eds.)}", journal = j-SIAM-REVIEW, volume = "29", number = "3", pages = "502--503", month = "????", year = "1987", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1029103", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Sat Mar 29 09:54:17 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/29/3; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "September 1987", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Benci:1988:BLT, author = "Vieri Benci and Donato Fortunato", title = "A {``Birkhoff--Lewis''} type result for non autonomous differential equations", journal = j-LECT-NOTES-MATH, volume = "1324", pages = "85--96", year = "1988", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/BFb0100784", ISBN = "3-540-50111-8 (print), 3-540-45928-6 (e-book)", ISBN-13 = "978-3-540-50111-4 (print), 978-3-540-45928-6 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", MRclass = "58F22 (34C25 58E05)", MRnumber = "965527 (90e:58132)", MRreviewer = "Mario Girardi", bibdate = "Thu May 15 18:46:23 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/lnm1985.bib", URL = "http://link.springer.com/chapter/10.1007/BFb0100784/", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/BFb0100778", book-URL = "http://www.springerlink.com/content/978-3-540-45928-6", fjournal = "Lecture Notes in Mathematics", journal-URL = "http://link.springer.com/bookseries/304", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Bona:1988:NPG, author = "C. Bona", title = "A new proof of the generalized {Birkhoff} theorem", journal = j-J-MATH-PHYS, volume = "29", number = "6", pages = "1440--1441", month = jun, year = "1988", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.527936", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", MRclass = "83C40", MRnumber = "89f:83051", MRreviewer = "P. Achuthan", bibdate = "Mon Oct 31 11:58:21 MDT 2011", bibsource = "http://jmp.aip.org/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v29/i6/p1440_s1", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", pagecount = "2", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Bongiovanni:1988:CPR, author = "G. Bongiovanni and D. P. Bovet and A. Cerioli", title = "Comments on a paper of {R. A. Brualdi}: {``Notes on the Birkhoff algorithm for doubly stochastic matrices''}", journal = j-CAN-MATH-BULL, volume = "31", number = "4", pages = "394--398", month = dec, year = "1988", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1988-056-5", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", bibdate = "Thu Sep 8 10:05:43 MDT 2011", bibsource = "http://cms.math.ca/cmb/v31/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib", note = "See \cite{Brualdi:1982:NBA}.", acknowledgement = ack-nhfb, fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Kuang:1988:BTT, author = "Zhi Quan Kuang and Can Bin Liang", title = "{Birkhoff} and {Taub} theorems generalized to metrics with conformal symmetries", journal = j-J-MATH-PHYS, volume = "29", number = "11", pages = "2475--2478", month = nov, year = "1988", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.528085", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", MRclass = "83C15 (83C40)", MRnumber = "90a:83014", MRreviewer = "Colin B. G. McIntosh", bibdate = "Mon Oct 31 11:58:28 MDT 2011", bibsource = "http://jmp.aip.org/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v29/i11/p2475_s1", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", pagecount = "4", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Ali:1989:BGN, author = "M. K. Ali and W. Robert Wood", title = "The {Birkhoff--Gustavson} normal form of one-dimensional double-well {Hamiltonians}", journal = j-J-MATH-PHYS, volume = "30", number = "6", pages = "1238--1244", month = jun, year = "1989", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.528350", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", MRclass = "81C05", MRnumber = "90d:81027", MRreviewer = "Tuan W. Chen", bibdate = "Mon Oct 31 11:58:38 MDT 2011", bibsource = "http://jmp.aip.org/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v30/i6/p1238_s1", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", pagecount = "7", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Borgers:1989:NSR, author = "Christoph B{\"o}rgers", title = "On the numerical solution of the regularized {Birkhoff} equations", journal = j-MATH-COMPUT, volume = "53", number = "187", pages = "141--156", month = jul, year = "1989", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "76C05 (76-08 76D25)", MRnumber = "90g:76037", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib; JSTOR database", acknowledgement = ack-nhfb, classcodes = "A4730 (Rotational flow, vortices, buoyancy and other flows involving body forces); A0260 (Numerical approximation and analysis)", corpsource = "Dept. of Math., Michigan Univ., Ann Arbor, MI, USA", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "approximations; convergence; convergence of numerical methods; evolution; fixed regularization; Krasny; numerical; numerical solution; numerical test; problem; regularized Birkhoff equations; two-dimensional inviscid jet; vortex sheets; vortices", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", treatment = "T Theoretical or Mathematical", } @Article{Bojanov:1990:CBT, author = "Borislav Bojanov and Geno Nikolov", title = "Comparison of {Birkhoff} Type Quadrature Formulae", journal = j-MATH-COMPUT, volume = "54", number = "190", pages = "627--648", month = apr, year = "1990", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65D30 (41A55)", MRnumber = "91e:65034", MRreviewer = "Helmut Brass", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib; JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290M (Numerical integration and differentiation); B0290H (Linear algebra); B0290B (Error analysis in numerical methods); C4160 (Numerical integration and differentiation); C4140 (Linear algebra); C4110 (Error analysis in numerical methods)", corpsource = "Dept. of Math., Sofia Univ., Bulgaria", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "algebraic degree of; Birkhoff type quadrature formulae; error; error analysis; integration; matrix algebra; precision", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", treatment = "T Theoretical or Mathematical", } @Article{Gasca:1990:SBH, author = "M. Gasca and J. J. Mart{\'\i}nez", title = "On the solvability of bivariate {Hermite--Birkhoff} interpolation problems", journal = j-J-COMPUT-APPL-MATH, volume = "32", number = "1--2", pages = "77--82", day = "26", month = nov, year = "1990", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 12:20:46 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib", URL = "http://www.sciencedirect.com/science/article/pii/037704279090418Y", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Liang:1990:CBT, author = "Can Bin Liang", title = "Conformal {Birkhoff} and {Taub} theorems in higher dimensions", journal = j-J-MATH-PHYS, volume = "31", number = "6", pages = "1464--1466", month = jun, year = "1990", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.528738", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", MRclass = "83E15 (83C15)", MRnumber = "91e:83084", MRreviewer = "A. H. Taub", bibdate = "Tue Nov 1 08:57:13 MDT 2011", bibsource = "http://jmp.aip.org/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v31/i6/p1464_s1", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", pagecount = "3", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Higham:1991:RKD, author = "Desmond J. Higham", title = "{Runge--Kutta} Defect Control Using {Hermite--Birkhoff} Interpolation", journal = j-SIAM-J-SCI-STAT-COMP, volume = "12", number = "5", pages = "991--999", month = sep, year = "1991", CODEN = "SIJCD4", DOI = "https://doi.org/10.1137/0912053", ISSN = "0196-5204", ISSN-L = "0196-5204", MRclass = "65L06 (65L07)", MRnumber = "92g:65081", MRreviewer = "Masaharu Nakashima", bibdate = "Mon Mar 31 10:00:47 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific and Statistical Computing", journal-URL = "http://epubs.siam.org/loi/sijcd4", onlinedate = "September 1991", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Sun:1991:ELB, author = "Yong Sun", title = "Equational Logics ({Birkhoff}'s Method Revisited) (*)", journal = j-LECT-NOTES-COMP-SCI, volume = "516", pages = "401--406", year = "1991", CODEN = "LNCSD9", DOI = "https://doi.org/10.1007/3-540-54317-1_108", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Mon May 13 08:51:55 MDT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/lncs1991.bib", acknowledgement = ack-nhfb, fjournal = "Lecture Notes in Computer Science", journal-URL = "http://link.springer.com/bookseries/558", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Gasca:1992:BHB, author = "Mariano Gasca and Jos{\'e} J. Mart{\'i}nez", title = "Bivariate {Hermite--Birkhoff} interpolation and {Vandermonde} determinants", journal = j-NUMER-ALGORITHMS, volume = "3", number = "1--4", pages = "193--199", month = dec, year = "1992", CODEN = "NUALEG", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", MRclass = "65D05 (41A05 41A63 65F99)", MRnumber = "93h:65013", bibdate = "Fri Nov 6 18:06:29 MST 1998", bibsource = "http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib", note = "Extrapolation and rational approximation (Puerto de la Cruz, 1992).", acknowledgement = ack-nhfb, fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Lorentz:1992:BPB, author = "Rudolph A. Lorentz", title = "Basic properties of {Birkhoff} interpolation", journal = j-LECT-NOTES-MATH, volume = "1516", pages = "9--22", year = "1992", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/BFb0088791", ISBN = "3-540-55870-5 (print), 3-540-47300-9 (e-book)", ISBN-13 = "978-3-540-55870-5 (print), 978-3-540-47300-8 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", bibdate = "Fri May 9 19:07:00 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/lnm1990.bib", URL = "http://link.springer.com/chapter/10.1007/BFb0088791/", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/BFb0088788", book-URL = "http://www.springerlink.com/content/978-3-540-47300-8", fjournal = "Lecture Notes in Mathematics", journal-URL = "http://link.springer.com/bookseries/304", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Lorentz:1992:KIB, author = "Rudolph A. Lorentz", title = "{Kergin} interpolation via {Birkhoff} interpolation", journal = j-LECT-NOTES-MATH, volume = "1516", pages = "162--170", year = "1992", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/BFb0088801", ISBN = "3-540-55870-5 (print), 3-540-47300-9 (e-book)", ISBN-13 = "978-3-540-55870-5 (print), 978-3-540-47300-8 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", bibdate = "Fri May 9 19:07:00 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/lnm1990.bib", URL = "http://link.springer.com/chapter/10.1007/BFb0088801/", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/BFb0088788", book-URL = "http://www.springerlink.com/content/978-3-540-47300-8", fjournal = "Lecture Notes in Mathematics", journal-URL = "http://link.springer.com/bookseries/304", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Book{Lorentz:1992:MBI, author = "Rudolph A. Lorentz", title = "Multivariate {Birkhoff} Interpolation", volume = "1516", publisher = pub-SV, address = pub-SV:adr, pages = "x + 192", year = "1992", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/BFb0088788", ISBN = "3-540-55870-5 (print), 3-540-47300-9 (e-book)", ISBN-13 = "978-3-540-55870-5 (print), 978-3-540-47300-8 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", LCCN = "QA3 .L28 no. 1516", MRclass = "41A05 (41-02 41A63 65D05 65N30)", MRnumber = "1222648 (94h:41001)", MRreviewer = "Petru P. Blaga", bibdate = "Tue May 6 14:55:12 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/lnm1990.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib", series = ser-LECT-NOTES-MATH, URL = "http://link.springer.com/book/10.1007/BFb0088788; http://www.springerlink.com/content/978-3-540-47300-8", acknowledgement = ack-nhfb, series-URL = "http://link.springer.com/bookseries/304", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", tableofcontents = "Front Matter / i--ix \\ 1: Introduction / 1--3 \\ 2: Univariate interpolation / 4--8 \\ 3: Basic properties of Birkhoff interpolation / 9--22 \\ 4: Singular interpolation schemes / 23--49 \\ 5: Shifts and coalescences / 50--61 \\ 6: Decomposition theorems / 62--71 \\ 7: Reduction / 72--74 \\ 8: Examples / 75--89 \\ 9: Uniform Hermite interpolation of tensor--product type / 90--102 \\ 10: Uniform Hermite interpolation of type total degree / 103--138 \\ 11: Vandermonde determinants / 139--155 \\ 12: A theorem of Severi / 156--161 \\ 13: Kergin interpolation via Birkhoff interpolation / 162--170 \\ A: Appendix --- A Bibliography on Multivariate Interpolation / 171--182 \\ References / 183--189 \\ Glossary of notation / 190--192", } @Article{Manca:1992:SCB, author = "V. Manca and A. Salibra", title = "Soundness and completeness of the {Birkhoff} equational calculus for many-sorted algebras with possibly empty carrier sets", journal = j-THEOR-COMP-SCI, volume = "94", number = "1", pages = "101--124", day = "02", month = mar, year = "1992", CODEN = "TCSCDI", ISSN = "0304-3975 (print), 1879-2294 (electronic)", ISSN-L = "0304-3975", bibdate = "Sat Nov 22 13:24:22 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/tcs1990.bib", acknowledgement = ack-nhfb, classification = "C4210 (Formal logic)", corpsource = "Dipartimento di Inf., Pisa Univ., Italy", fjournal = "Theoretical Computer Science", journal-URL = "http://www.sciencedirect.com/science/journal/03043975/", keywords = "algebras; Birkhoff equational calculus; completeness; computability; many-sorted algebras; many-valued logics; possibly empty carrier sets; soundness; strong satisfiability; strongly sensible signatures; sufficient and necessary conditions; weak satisfiability", pubcountry = "Netherlands", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", treatment = "T Theoretical or Mathematical", } @Article{Marshall:1992:PBC, author = "Murray Marshall", title = "The {Pierce--Birkhoff} conjecture for curves", journal = j-CAN-J-MATH, volume = "44", number = "??", pages = "1262--1271", month = "????", year = "1992", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1992-075-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:03 MDT 2011", bibsource = "http://cms.math.ca/cjm/v44/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/canjmath1990.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Bojanov:1993:IPS, author = "Borislav Bojanov", title = "Interpolation by periodic splines with {Birkhoff} knots", journal = j-NUM-MATH, volume = "65", number = "1", pages = "63--75", month = may, year = "1993", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "41A15 (65D05 65D07 65D15)", MRnumber = "94e:41022", MRreviewer = "Mircea Ivan", bibdate = "Thu Jan 23 07:49:52 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Brodbeck:1993:GBT, author = "Othmar Brodbeck and Norbert Straumann", title = "A generalized {Birkhoff} theorem for the {Einstein--Yang--Mills} system", journal = j-J-MATH-PHYS, volume = "34", number = "6", pages = "2412--2423", month = jun, year = "1993", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.530126", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", MRclass = "53C07 (81T13 83C20)", MRnumber = "94a:53059", MRreviewer = "Alan D. Rendall", bibdate = "Tue Nov 1 08:57:58 MDT 2011", bibsource = "http://jmp.aip.org/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v34/i6/p2412_s1", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", pagecount = "12", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Kaluza:1993:PBG, author = "Matjaz Kaluza", title = "Program for {Birkhoff--Gustavson} normal form for {$N$} degrees of freedom --- {BIRKHOFF 1.2}", journal = j-COMP-PHYS-COMM, volume = "74", number = "3", pages = "441--449", month = mar, year = "1993", CODEN = "CPHCBZ", DOI = "https://doi.org/10.1016/0010-4655(93)90025-8", ISSN = "0010-4655 (print), 1879-2944 (electronic)", ISSN-L = "0010-4655", bibdate = "Mon Feb 13 21:29:36 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib", URL = "http://www.sciencedirect.com/science/article/pii/0010465593900258", acknowledgement = ack-nhfb, fjournal = "Computer Physics Communications", journal-URL = "http://www.sciencedirect.com/science/journal/00104655", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Landau:1993:BTD, author = "L. J. Landau and R. F. Streater", title = "On {Birkhoff}'s Theorem for Doubly Stochastic Completely Positive Maps of Matrix Algebras", journal = j-LINEAR-ALGEBRA-APPL, volume = "193", pages = "107--127", day = "1", month = nov, year = "1993", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "47B49 (15A51 46L99)", MRnumber = "95c:47041", MRreviewer = "Jaroslav Zem{\'a}nek", bibdate = "Wed Jan 22 17:57:24 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala1990.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{McEwan:1993:CFG, author = "J. McEwan", title = "A complex formulation of generalized {Hamiltonian} ({Birkhoffian}) theory", journal = j-FOUND-PHYS, volume = "23", number = "2", pages = "313--327", month = feb, year = "1993", CODEN = "FNDPA4", DOI = "https://doi.org/10.1007/BF01883632", ISSN = "0015-9018 (print), 1572-9516 (electronic)", ISSN-L = "0015-9018", bibdate = "Tue Jun 11 20:35:47 MDT 2013", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0015-9018&volume=23&issue=2; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/foundphys.bib", URL = "http://link.springer.com/article/10.1007/BF01883632", acknowledgement = ack-nhfb, ajournal = "Found. Phys.", fjournal = "Foundations of Physics", journal-URL = "http://link.springer.com/journal/10701", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Amrhein:1994:BHT, author = "B. Amrhein", title = "{Birkhoff}'s {HSP-Theorem} for Cumulative Logic Programs", journal = j-LECT-NOTES-COMP-SCI, volume = "798", pages = "24--36", year = "1994", CODEN = "LNCSD9", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Wed Sep 15 10:01:31 MDT 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/lncs1994.bib", acknowledgement = ack-nhfb, fjournal = "Lecture Notes in Computer Science", journal-URL = "http://link.springer.com/bookseries/558", keywords = "ELP; logic programming", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Bazzani:1995:PCB, author = "A. Bazzani and M. Giovannozzi and E. Todesco", title = "A program to compute {Birkhoff} normal forms of symplectic maps in {$ R^4 $}", journal = j-COMP-PHYS-COMM, volume = "86", number = "1--2", pages = "199--207", month = apr, year = "1995", CODEN = "CPHCBZ", DOI = "https://doi.org/10.1016/0010-4655(94)00140-W", ISSN = "0010-4655 (print), 1879-2944 (electronic)", ISSN-L = "0010-4655", bibdate = "Mon Feb 13 21:29:52 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib", URL = "http://www.sciencedirect.com/science/article/pii/001046559400140W", acknowledgement = ack-nhfb, fjournal = "Computer Physics Communications", journal-URL = "http://www.sciencedirect.com/science/journal/00104655", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Jiang:1995:NKB, author = "Tianzi Jiang", title = "On a new kind of {Birkhoff} type trigonometric interpolation", journal = j-BIT-NUM-MATH, volume = "35", number = "4", pages = "540--547", month = dec, year = "1995", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/BF01739825", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", MRclass = "42A15 (41A10)", MRnumber = "97i:42005", bibdate = "Wed Jan 4 18:52:24 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=35&issue=4; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/bit.bib", URL = "http://www.mai.liu.se/BIT/contents/bit35.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=35&issue=4&spage=540", acknowledgement = ack-nhfb, fjournal = "BIT Numerical Mathematics", journal-URL = "http://link.springer.com/journal/10543", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Book{Corry:1996:MAR, author = "Leo Corry", title = "Modern Algebra and the Rise of Mathematical Structures", volume = "0017", publisher = pub-BIRKHAUSER, address = pub-BIRKHAUSER:adr, pages = "xviii + 452", year = "1996", ISBN = "0-7167-1376-4, 0-8176-5311-2 (Boston), 3-7643-5311-2 (Basel)", ISBN-13 = "978-0-7167-1376-0, 978-0-8176-5311-8 (Boston), 978-3-7643-5311-7 (Basel)", LCCN = "QA151 .C67 1996", bibdate = "Sat Nov 4 10:17:52 MDT 2023", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Science networks", acknowledgement = ack-nhfb, author-dates = "1956--", remark = "Contains several references to Garrett Birkhoff and Lattice Theory.", subject = "Algebra; History; Categories (Mathematics); Alg{\`e}bre; Histoire; Cat{\'e}gories (Math{\'e}matiques); 31.20 algebra: general; Algebra; Categories (Mathematics); Geschichte; Struktur; Mathematik; Algebra; History; Categories (Mathematics); Mathematics; Histoire; Cat{\'e}gories (Math{\'e}matiques)", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", tableofcontents = "Introduction: Structures in Mathematics / 1 \\ Part One: Structures in the Images of Mathematics / 15 \\ 1: Structures in Algebra: Changing Images / 21 \\ 2: Richard Dedekind: Numbers and Ideals / 66 \\ 3: David Hilbert: Algebra and Axiomatics / 137 \\ 4: Concrete and Abstract: Numbers, Polynomials, Rings / 184 \\ 5: Emmy Noether: Ideals and Structures / 221 \\ Part Two: Structures in the Body of Mathematics / 255 \\ 6: Oystein Ore: Algebraic Structures / 263 \\ 7: Nicolas Bourbaki: Theory of Structures / 293 \\ 8: Category Theory: Early Stages / 343 \\ 9: Categories and Images of Mathematics / 384 \\ Bibliography / 405 \\ Author Index / 443 \\ Subject Index / 451", } @Article{Gonzalez-Vega:1996:AQE, author = "Laureano Gonzalez-Vega", title = "Applying Quantifier Elimination to the {Birkhoff} Interpolation Problem", journal = j-J-SYMBOLIC-COMP, volume = "22", number = "1", pages = "83--103", month = jul, year = "1996", CODEN = "JSYCEH", DOI = "https://doi.org/10.1006/jsco.1996.0042", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", MRclass = "41A05 (03C10 68Q40)", MRnumber = "1 421 260", bibdate = "Sat May 10 15:54:09 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib", acknowledgement = ack-nhfb, classcodes = "B0290H (Linear algebra); B0290F (Interpolation and function approximation); C4140 (Linear algebra); C7310 (Mathematics computing); C4130 (Interpolation and function approximation)", corpsource = "Dept. de Matematicas, Estadistica y Comput., Cantabria Univ., Santander, Spain", fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", keywords = "Algebra; Birkhoff interpolation; Computer; formal manipulation; interpolation; matrix algebra; multivariate polynomials; polynomial entries; quantifier elimination; Sign Determination; Sturm-Habicht sequences; symbol manipulation; univariate polynomial inequalities", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", treatment = "T Theoretical or Mathematical", } @Article{Nikolaev:1996:DQB, author = "A. S. Nikolaev", title = "On the diagonalization of quantum {Birkhoff--Gustavson} normal form", journal = j-J-MATH-PHYS, volume = "37", number = "6", pages = "2643--2661", month = jun, year = "1996", CODEN = "JMAPAQ", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", MRclass = "81Q15 (34C29 70H15 81Q20)", MRnumber = "97c:81041", MRreviewer = "Raghu R. Gompa", bibdate = "Fri Jan 2 07:23:17 MST 1998", bibsource = "http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1995.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Saxon:1996:GBM, author = "Wolfgang Saxon", title = "{Garrett Birkhoff}, 85, Mathematics Theorist, Dies", journal = j-NY-TIMES, volume = "??", number = "??", pages = "D-22--D-22", day = "28", month = nov, year = "1996", CODEN = "NYTIAO", ISSN = "0362-4331 (print), 1542-667X, 1553-8095", ISSN-L = "0362-4331", bibdate = "Sat Nov 04 10:31:36 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", URL = "https://www.nytimes.com/1996/11/28/us/garrett-birkhoff-85-mathematics-theorist-dies.html", acknowledgement = ack-nhfb, fjournal = "New York Times", journal-URL = "http://www.nytimes.com/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Young:1997:GBA, author = "David M. Young", title = "{Garrett Birkhoff} and applied mathematics", journal = j-NAMS, volume = "44", number = "11", pages = "1446--1450", month = dec, year = "1997", CODEN = "AMNOAN", ISSN = "0002-9920 (print), 1088-9477 (electronic)", ISSN-L = "0002-9920", MRclass = "01A70", MRnumber = "1488573", bibdate = "Tue Feb 15 08:56:10 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib; https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib", URL = "https://www.ams.org/journals/notices/199712/199712FullIssue.pdf", acknowledgement = ack-nhfb, fjournal = "Notices of the American Mathematical Society", journal-URL = "http://www.ams.org/notices/", remark-1 = "From the second paragraph: ``The author gratefully acknowledges the contributions of Richard Varga and Carl de Boor. Varga contributed the section entitled `Reactor Calculations and Nuclear Power', and de Boor contributed the section entitled `Spline Approximations'.''", remark-2 = "From page 1447, column 2: ``David Kincaid and David Young, who directed the development at The University of Texas of the ITPACK software package for solving large sparse linear systems by iterative methods, regard Birkhoff as the `godfather' of the project.''", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Richard S. Varga (8 October 1928--25 February 2022)", } @Article{Zhu:1997:BIP, author = "Ping Zhu", title = "On {Birkhoff} interpolation by polynomials in several variables", journal = j-J-COMPUT-APPL-MATH, volume = "85", number = "2", pages = "263--270", day = "12", month = nov, year = "1997", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 12:36:04 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377042797001222", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Bautista:1998:PBW, author = "C{\'e}sar Bautista", title = "A {Poincar{\'e}--Birkhoff--Witt} theorem for generalized {Lie} color algebras", journal = j-J-MATH-PHYS, volume = "39", number = "7", pages = "3828--3843", month = jul, year = "1998", CODEN = "JMAPAQ", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Fri Oct 20 08:18:04 MDT 2000", bibsource = "http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1995.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{MacLane:1998:GBJ, author = "Saunders {Mac Lane}", title = "{Garrett Birkhoff (10 January 1911--22 November 1996)}", journal = j-PROC-AMER-PHIL-SOC, volume = "142", number = "4", pages = "646--649", month = dec, year = "1998", CODEN = "PAPCAA", ISSN = "0003-049X (print), 2326-9243 (electronic)", ISSN-L = "0003-049X", bibdate = "Sat Aug 24 19:38:23 MDT 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/procamerphilsoc1950.bib", URL = "https://www.jstor.org/stable/3152287", acknowledgement = ack-nhfb, ajournal = "Proc. Amer. Philos. Soc.", author-dates = "Saunders Mac Lane (1909--2005)", fjournal = "Proceedings of the American Philosophical Society", journal-URL = "http://www.jstor.org/journal/procamerphilsoci", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Rutz:1998:TBT, author = "Solange F. Rutz", title = "Theorems of {Birkhoff} type in {Finsler} spaces", journal = j-COMP-PHYS-COMM, volume = "115", number = "2--3", pages = "300--315", day = "2", month = dec, year = "1998", CODEN = "CPHCBZ", DOI = "https://doi.org/10.1016/S0010-4655(98)00120-9", ISSN = "0010-4655 (print), 1879-2944 (electronic)", ISSN-L = "0010-4655", bibdate = "Mon Feb 13 21:30:33 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0010465598001209", acknowledgement = ack-nhfb, fjournal = "Computer Physics Communications", journal-URL = "http://www.sciencedirect.com/science/journal/00104655", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Varga:1998:MGB, author = "Richard S. Varga", title = "In memoriam: {Garrett Birkhoff: January 10, 1911--November 11, 1996}", journal = j-J-APPROX-THEORY, volume = "95", number = "1", pages = "iv, 1--4", year = "1998", CODEN = "JAXTAZ", DOI = "https://doi.org/10.1006/jath.1998.3288", ISSN = "0021-9045 (print), 1096-0430 (electronic)", ISSN-L = "0021-9045", MRclass = "01A70", MRnumber = "1645974", bibdate = "Wed Apr 20 14:10:28 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib", acknowledgement = ack-nhfb, author-dates = "Richard S. Varga (8 October 1928--25 February 2022)", fjournal = "Journal of Approximation Theory", journal-URL = "http://www.sciencedirect.com/science/journal/00219045", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Bueso:1999:WFG, author = "J. L. Bueso and J. G{\'o}mez Torrecillas and F. J. Lobillo", title = "When is a finitely generated algebra of {Poincar{\'e}--Birkhoff--Witt} type?", journal = j-SIGSAM, volume = "33", number = "3", pages = "14--15", month = sep, year = "1999", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Fri Feb 8 18:27:06 MST 2002", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, ajournal = "SIGSAM Bull.", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Ton-That:1999:PPC, author = "Tuong Ton-That and Thai-Duong Tran", title = "{Poincar{\'e}}'s proof of the so-called {Birkhoff--Witt} theorem", journal = j-REV-HIST-MATH, volume = "5", number = "2", pages = "249--284 (2000)", year = "1999", CODEN = "????", ISSN = "1262-022X (print), 1777-568X (electronic)", ISSN-L = "1262-022X", MRclass = "01A60 (01A55 17-03 17B35)", MRnumber = "1793103", bibdate = "Wed Mar 28 09:42:44 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/revhistmath.bib", URL = "http://smf4.emath.fr/Publications/RevueHistoireMath/5/html/smf_rhm_5_249-284.html", acknowledgement = ack-nhfb, ajournal = "Rev. Histoire Math.", fjournal = "Revue d'Histoire des Math{\'e}matiques. Journal for the History of Mathematics", journal-URL = "http://smf4.emath.fr/Publications/RevueHistoireMath/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Anonymous:19xx:BRA, author = "Anonymous", title = "Book Review: {{\booktitle{Advances in Computers, Volume 3}}. Franz L. Alt and Morris Rubinoff, eds. Academic Press, New York, 1962. 361 pp.}", journal = j-TRANS-AM-NUCL-SOC, volume = "??", number = "??", pages = "465--465", month = "????", year = "19xx", CODEN = "TANSAO", DOI = "", ISSN = "0003-018X", bibdate = "Sat Nov 04 07:01:54 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib; https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib", URL = "https://www.ans.org/pubs/journals/download/article-26563/", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Nuclear Society", journal-URL = "https://www.ans.org/pubs/transactions/", remark = "The page images carry no volume, issue, month, year data, and I cannot find an archive of the issues of this journal.", remark = "From the review: ``The book consists of six articles: The Computation of Satellite Orbit Trajectories, by Samuel D. Conte, pp. 2--76. Multiprogramming, by E. F. Codd, pp. 78--153. Recent Developments in Nonlinear Programming, by Philip Wolfe, pp. 156--187. Alternating Direction Implicit Methods, by Garrett Birkhoff, Richard S. Varga, and David Young, pp. 190--273. Combined Analog--Digital Techniques in Simulation, by Harold K. Skramstad, pp. 275--298. Information Technology and the Law, by Reed C. Lawlor, pp. 299--346.''", subject-dates = "David M. Young, Jr. (October 20, 1923--December 21, 2008); Garrett Birkhoff (19 January 1911--22 November 1996); Richard S. Varga (8 October 1928--25 February 2022)", } @Article{Bokhari:2000:BIS, author = "M. A. Bokhari and H. P. Dikshit and A. Sharma", title = "{Birkhoff} interpolation on some perturbed roots of unity: revisited", journal = j-NUMER-ALGORITHMS, volume = "25", number = "1--4", pages = "47--62", month = sep, year = "2000", CODEN = "NUALEG", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", MRclass = "41A05 (65D15)", MRnumber = "1 827 145", bibdate = "Mon Sep 29 08:37:05 MDT 2003", bibsource = "http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib; MathSciNet database", note = "Mathematical journey through analysis, matrix theory and scientific computation (Kent, OH, 1999).", URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/3/25/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/3/25/fulltext.pdf", acknowledgement = ack-nhfb, fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Carnicer:2000:BHB, author = "J. M. Carnicer and M. Gasca", title = "Bivariate {Hermite--Birkhoff} polynomial interpolation with asymptotic conditions", journal = j-J-COMPUT-APPL-MATH, volume = "119", number = "1--2", pages = "69--79", day = "1", month = jul, year = "2000", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 12:43:35 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib", URL = "http://www.sciencedirect.com/science/article/pii/S037704270000371X", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Chekanov:2000:GSC, author = "N. A. Chekanov and V. A. Rostovtsev and Y. Uwano and S. I. Vinitsky", title = "{GITA} $^{-1}$: a symbolic computing program for an inverse problem of the {Birkhoff--Gustavson} normal form expansion", journal = j-COMP-PHYS-COMM, volume = "126", number = "1--2", pages = "47--50", month = apr, year = "2000", CODEN = "CPHCBZ", DOI = "https://doi.org/10.1016/S0010-4655(99)00491-9", ISSN = "0010-4655 (print), 1879-2944 (electronic)", ISSN-L = "0010-4655", bibdate = "Mon Feb 13 23:40:37 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0010465599004919", acknowledgement = ack-nhfb, fjournal = "Computer Physics Communications", journal-URL = "http://www.sciencedirect.com/science/journal/00104655", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{deBruin:2000:BIN, author = "Marcel G. {de Bruin} and A. Sharma", title = "{Birkhoff} interpolation on non-uniformly distributed roots of unity", journal = j-NUMER-ALGORITHMS, volume = "25", number = "1--4", pages = "123--138", month = sep, year = "2000", CODEN = "NUALEG", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", MRclass = "41A05 (65D15)", MRnumber = "1 827 150", bibdate = "Mon Sep 29 08:37:05 MDT 2003", bibsource = "http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib; MathSciNet database", note = "Mathematical journey through analysis, matrix theory and scientific computation (Kent, OH, 1999).", URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/3/4/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/3/4/fulltext.pdf", acknowledgement = ack-nhfb, fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{deBruin:2000:BIU, author = "M. G. {de Bruin} and H. P. Dikshit and A. Sharma", title = "{Birkhoff} interpolation on unity and on {M{\"o}bius} transform of the roots of unity", journal = j-NUMER-ALGORITHMS, volume = "23", number = "1", pages = "115--125", month = mar, year = "2000", CODEN = "NUALEG", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", MRclass = "41A05 (65D05)", MRnumber = "2001e:41002", MRreviewer = "Knut Petras", bibdate = "Mon Sep 29 08:37:01 MDT 2003", bibsource = "http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib; MathSciNet database", URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/24/6/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/24/6/fulltext.pdf", acknowledgement = ack-nhfb, fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Alvis:2001:BTP, author = "Dean Alvis and Michael Kinyon", title = "{Birkhoff}'s Theorem for Panstochastic Matrices", journal = j-AMER-MATH-MONTHLY, volume = "108", number = "1", pages = "28--37", month = jan, year = "2001", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2695673", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jan 30 12:00:12 MST 2012", bibsource = "http://www.jstor.org/journals/00029890.html; http://www.jstor.org/stable/i346001; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib", note = "Refers to \cite{Birkhoff:1946:TOA}.", URL = "http://www.jstor.org/stable/2695673", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Chang:2001:LBB, author = "Cheng-Shang Chang and Duan-Shin Lee and Ching-Ming Lien", title = "Load balanced {Birkhoff--von Neumann} switches with resequencing", journal = j-SIGMETRICS, volume = "29", number = "3", pages = "23--24", month = dec, year = "2001", CODEN = "????", DOI = "https://doi.org/10.1145/507553.507563", ISSN = "0163-5999 (print), 1557-9484 (electronic)", ISSN-L = "0163-5999", bibdate = "Thu Jun 26 11:37:25 MDT 2008", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib", abstract = "In [2], we proposed the load balanced Birkhoff--von Neumann switch with one-stage buffering (see Figure 1). Such a switch consists of two stages of crossbar switching fabrics and one stage of buffering. The buffer at the input port of the second stage uses the Virtual Output Queueing (VOQ) technique to solve the problem of head-of-line blocking. In such a switch, packets are of the same size. Also, time is slotted and synchronized so that exactly one packet can be transmitted within a time slot. In a time slot, both crossbar switches set up connection patterns corresponding to permutation matrices that are periodically generated from a one-cycle permutation matrix.\par The reasoning behind such a switch architecture is as follows: since the connection patterns are periodic, packets from the same input port of the first stage are distributed in a round-robin fashion to the second stage according to their arrival times. Thus, the first stage performs load balancing for the incoming traffic. As the traffic coming into the second stage is load balanced, it suffices to use simple periodic connection patterns to perform switching at the second stage. This is shown in [2] as a special case of the original Birkhoff-von Neumann decomposition used in [1]. There are several advantages of using such an architecture, including scalability, low hardware complexity, 100\% throughput, low average delay in heavy load and bursty traffic, and efficient buffer usage. However, the main drawback of the load balanced Birkhoff-von Neumann switch with one-stage buffering is that packets might be out of sequence.\par The main objective of this paper is to solve the out-of-sequence problem that occurs in the load balanced Birkhoff-von Neumann switch with one-stage buffering. One quick fix is to add a resequencing-and-output buffer after the second stage. However, as packets are distributed according to their {\em arrival times\/} at the first stage, there is no guarantee on the size of the resequencing-and-output buffer to prevent packet losses. For this, one needs to distributed packets according to their {\em flows}, as indicated in the paper by Iyer and McKeown [5]. This is done by adding a flow splitter and a load-balancing buffer in front of the first stage (see Figure 2). For an $ N \times N $ switch, the load-balancing buffer at each input port of the first stage consists of $N$ virtual output queues (VOQ) destined for the $N$ output ports of that stage. Packets form the same {\em flow\/} are split in the round-robin fashion to the $N$ virtual output queues and scheduled under the First Come First Served (FCFS) policy. By so doing, load balancing can be achieved for each flow as packets from the same flow are split almost evenly to the input ports of the second stage. More importantly, as pointed out in [5], the delay and the buffer size of the load-balancing buffer are bounded by constants that only depend on the size of the switch and the number of flows. The resequencing-and-output buffer after the second stage not only performs resequencing to keep packets in sequence, but also stores packets waiting for transmission from the output links.\par In this paper, we consider a traffic model with multicasting flows. This is a more general model than the point-to-point traffic model in [5]. A multicasting flow is stream of packets that has one common input and a set of common outputs. For the multicasting flows, fanout splitting (see e.g., [4]) is performed at the central buffers (the VOQ in front of the second stage). The central buffers are assumed to be infinite so that no packets are lost in the switch. We consider two types of scheduling policies in the central buffers: the FCFS policy and the Earliest Deadline First (EDF) policy. For the FCFS policy, a jitter control mechanism, is added in the VOQ in front of the second stage. Such a jitter control mechanism delays every packet to its maximum delay at the first stage so that the flows entering the second stage are simply time-shifted flows of the original ones. Our main result for the FCFS scheme with jitter controls is the following theorem. The proof of Theorem 1 is shown in the full report [3].\par Theorem 1: Suppose that all the buffers are empty at time 0. Then the followings hold for FCFS scheme with jitter control.\par (i) The end-to-end delay for a packet through our switch with multi-stage buffering is bounded above by the sum of the delay through the corresponding FCFS output-buffered switch and $ N L_{\rm max} + (N + 1) M_{\rm max}$, where $ L_{\rm max}$ (resp. $ M_{\rm max}$) is the maximum number of flows at an input (resp. output) port.\par (ii) The load-balancing buffer at an input port of the first stage is bounded above by $ N L_{\rm max}$.\par (iii) The delay through the load-balancing buffer at an input port of the first stage is bounded above by $ N L_{\rm max}$.\par (iv) The resequencing-and-output buffer at an output port of the second stage is bounded above $ (N + 1) M_{\rm max}$.\par In the EDF scheme (see Figure 3), every packet is assigned a deadline that is the departure time from the corresponding FCFS output-buffered switch. Packets are scheduled according to their deadlines in the central buffers. For the EDF scheme, there is no need to implement the jitter control mechanism in the FCFS scheme. As such, average packet delay can be greatly reduced. However, as there is no jitter control, one might need a larger resequencing buffer than that in the FCFS scheme with jitter control. Since the first stage is the same as that in the FCFS scheme, both the delay and the buffer size of the load-balancing buffer are still bounded by $ N L_{\rm max}$. Moreover, we show the following theorem for the EDF scheme. Its proof is given in the full report [3].\par Theorem 2: Suppose that all the buffers are empty at time 0. Then the followings hold for the EDF scheme.\par (i) The end-to-end delay for a packet through our switch with multi-stage buffering is bounded above by the sum of the delay through the corresponding FCFS output-buffered switch and $ N (L_{\rm max} + M_{\rm max})$.\par (ii) The resequencing-and-output buffer at an output port of the second stage is bounded above $ N (L_{\rm max} + M_{\rm max})$.\par Computing the departure times from the corresponding FCFS output-buffered switch needs global information of all the inputs. A simple way is to use the packet arrival times as deadlines. Then the EDF scheme based on arrival times yields the same departure order except those packets that arrives at same time. Since there are at most $ M_{\rm max}$ packets that can arrive at the same time to an output port of the corresponding output-buffered switch, the end-to-end delay for a packet through the multi-stage switch using arrival times as deadlines is bounded above by the sum of the delay through the corresponding FCFS output-buffered switch and $ N L_{\rm max} + (N + 1) M_{\rm max}$. Also, the resequencing-and-output buffer at an output port of the second stage in this case is bounded above $ N L_{\rm max} + (N + 1) M_{\rm max}$.", acknowledgement = ack-nhfb, ajournal = "Perform. Eval. Rev.", fjournal = "ACM SIGMETRICS Performance Evaluation Review", journal-URL = "https://dl.acm.org/loi/sigmetrics", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{deBruin:2001:BIN, author = "Marcel G. de Bruin and A. Sharma", title = "{Birkhoff} interpolation on nonuniformly distributed roots of unity {II}", journal = j-J-COMPUT-APPL-MATH, volume = "133", number = "1--2", pages = "295--303", day = "1", month = aug, year = "2001", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 12:45:19 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377042700006464", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Goldblatt:2001:WCA, author = "Robert Goldblatt", title = "What is the coalgebraic analogue of {Birkhoff}'s variety theorem?", journal = j-THEOR-COMP-SCI, volume = "266", number = "1--2", pages = "853--886", day = "6", month = sep, year = "2001", CODEN = "TCSCDI", ISSN = "0304-3975 (print), 1879-2294 (electronic)", ISSN-L = "0304-3975", bibdate = "Mon Nov 19 08:33:25 MST 2001", bibsource = "http://www.elsevier.com/locate/issn/03043975; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/tcs2000.bib", URL = "http://www.elsevier.nl/gej-ng/10/41/16/216/27/54/abstract.html; http://www.elsevier.nl/gej-ng/10/41/16/216/27/54/article.pdf", acknowledgement = ack-nhfb, fjournal = "Theoretical Computer Science", journal-URL = "http://www.sciencedirect.com/science/journal/03043975/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Rouillier:2001:SBI, author = "Fabrice Rouillier and Mohab Safey {El Din} and {\'E}ric Schost", title = "Solving the {Birkhoff} Interpolation Problem via the Critical Point Method: an Experimental Study", journal = j-LECT-NOTES-COMP-SCI, volume = "2061", pages = "26--40", year = "2001", CODEN = "LNCSD9", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Sat Feb 2 13:04:17 MST 2002", bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2061.htm; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/lncs2001b.bib", URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2061/20610026.htm; http://link.springer-ny.com/link/service/series/0558/papers/2061/20610026.pdf", acknowledgement = ack-nhfb, fjournal = "Lecture Notes in Computer Science", journal-URL = "http://link.springer.com/bookseries/558", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{McCarthy:2002:BTC, author = "Nicholas McCarthy and David Ogilvie and Ilya Spitkovsky and Nahum Zobin", title = "{Birkhoff}'s theorem and convex hulls of {Coxeter} groups", journal = j-LINEAR-ALGEBRA-APPL, volume = "347", number = "1--3", pages = "219--231", day = "15", month = may, year = "2002", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Mon May 13 06:49:44 MDT 2002", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", URL = "http://www.elsevier.com/gej-ng/10/30/19/194/27/40/abstract.html", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Venezia:2002:CSI, author = "Antonio Venezia", title = "Un Caso Storico Irrisolto: Le Critiche di {Popper} alla Logica Quantistica di {Birkhoff} e {von Neumann}. ({Italian}) [A Case of Unsolved History: The Criticism of {Popper} of the Quantum Logic of {Birkhoff} and {von Neumann}]", journal = j-HIST-MATH, volume = "29", number = "??", pages = "138--156", month = "????", year = "2002", CODEN = "HIMADS", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", bibdate = "Tue Jun 25 11:19:44 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", acknowledgement = ack-nhfb, fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860", language = "Italian", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Zund:2002:GDB, author = "Joseph D. Zund", title = "{George David Birkhoff} and {John von Neumann}: a question of priority and the ergodic theorems, 1931--1932", journal = j-HIST-MATH, volume = "29", number = "2", pages = "138--156", month = may, year = "2002", CODEN = "HIMADS", DOI = "https://doi.org/10.1006/hmat.2001.2338", ISSN = "0315-0860 (print), 1090-249X (electronic)", ISSN-L = "0315-0860", MRclass = "01A60 (01A70 82-03)", MRnumber = "1896971 (2002m:01024)", bibdate = "Wed Jun 26 06:20:06 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0315086001923389", acknowledgement = ack-nhfb, fjournal = "Historia Mathematica", journal-URL = "http://www.sciencedirect.com/science/journal/03150860/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Broer:2003:BN, author = "Henk Broer and Igor Hoveijn and Gerton Lunter and Gert Vegter", title = "4. {Birkhoff} normalization", journal = j-LECT-NOTES-MATH, volume = "1806", pages = "71--84", year = "2003", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/978-3-540-36398-9_4", ISBN = "3-540-00403-3 (print), 3-540-36398-X (e-book)", ISBN-13 = "978-3-540-00403-5 (print), 978-3-540-36398-9 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", bibdate = "Fri May 9 19:07:01 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/lnm2000.bib", URL = "http://link.springer.com/chapter/10.1007/978-3-540-36398-9_4/", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/b10414", book-URL = "http://www.springerlink.com/content/978-3-540-36398-9", fjournal = "Lecture Notes in Mathematics", journal-URL = "http://link.springer.com/bookseries/304", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Cavazos-Cadena:2003:ADB, author = "Rolando Cavazos-Cadena", title = "An alternative derivation of {Birkhoff}'s formula for the contraction coefficient of a positive matrix", journal = j-LINEAR-ALGEBRA-APPL, volume = "375", number = "1", pages = "291--297", day = "1", month = dec, year = "2003", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Fri Jan 2 14:12:20 MST 2004", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Choirat:2003:FVB, author = "Christine Choirat and Christian Hess and Raffaello Seri", title = "A functional version of the {Birkhoff} ergodic theorem for a normal integrand: a variational approach", journal = j-ANN-PROBAB, volume = "31", number = "1", pages = "63--92", month = jan, year = "2003", CODEN = "APBYAE", ISSN = "0091-1798 (print), 2168-894X (electronic)", ISSN-L = "0091-1798", bibdate = "Sun Apr 20 10:44:17 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/annprobab2000.bib", URL = "http://projecteuclid.org/euclid.aop/1046294304", acknowledgement = ack-nhfb, fjournal = "Annals of Probability", journal-URL = "http://projecteuclid.org/all/euclid.aop", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{DeWit:2003:PBW, author = "David {De Wit}", title = "A {Poincar{\'e}--Birkhoff--Witt} commutator lemma for {$ {\rm U}_q[{\rm gl}(m | n)] $}", journal = j-J-MATH-PHYS, volume = "44", number = "1", pages = "315--327", month = jan, year = "2003", CODEN = "JMAPAQ", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Tue Dec 16 11:35:58 MST 2003", bibsource = "http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Barreira:2004:BAH, author = "Luis Barreira and Paulo Doutor", title = "{Birkhoff} Averages for Hyperbolic Flows: Variational Principles and Applications", journal = j-J-STAT-PHYS, volume = "115", number = "5--6", pages = "1567--1603", month = jun, year = "2004", CODEN = "JSTPSB", DOI = "https://doi.org/10.1023/B:JOSS.0000028069.64945.65", ISSN = "0022-4715 (print), 1572-9613 (electronic)", ISSN-L = "0022-4715", bibdate = "Sat Aug 30 12:53:09 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jstatphys2000.bib", URL = "http://link.springer.com/article/10.1023/B%3AJOSS.0000028069.64945.65", acknowledgement = ack-nhfb, fjournal = "Journal of Statistical Physics", journal-URL = "http://link.springer.com/journal/10955", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Carroll:2004:BCC, author = "Joseph E. Carroll", title = "{Birkhoff}'s contraction coefficient", journal = j-LINEAR-ALGEBRA-APPL, volume = "389", number = "1", pages = "227--234", day = "15", month = sep, year = "2004", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Tue Nov 9 07:02:36 MST 2004", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Girelli:2004:ABD, author = "Florian Girelli and Thomas Krajewski and Pierre Martinetti", title = "An algebraic {Birkhoff} decomposition for the continuous renormalization group", journal = j-J-MATH-PHYS, volume = "45", number = "12", pages = "4679--4697", month = dec, year = "2004", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.1794366", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Tue Oct 25 18:16:58 MDT 2011", bibsource = "http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v45/i12/p4679_s1", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", onlinedate = "15 November 2004", pagecount = "19", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Rouleux:2004:SCI, author = "Michel Rouleux", title = "Semi-classical Integrability,Hyperbolic Flows and the {Birkhoff} Normal Form", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "1034--1067", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2004-047-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Bambusi:2005:BLT, author = "Dario Bambusi and Massimiliano Berti", title = "A {Birkhoff--Lewis}-Type Theorem for Some {Hamiltonian PDEs}", journal = j-SIAM-J-MATH-ANA, volume = "37", number = "1", pages = "83--102", year = "2005", CODEN = "SJMAAH", DOI = "https://doi.org/10.1137/S0036141003436107", ISSN = "0036-1410 (print), 1095-7154 (electronic)", ISSN-L = "0036-1410", bibdate = "Thu Dec 29 09:30:22 MST 2005", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/37/1; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjmathana2000.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/43610", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Mathematical Analysis", journal-URL = "http://epubs.siam.org/sima", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{deBruin:2005:PTB, author = "M. G. de Bruin and H. P. Dikshit", title = "{P{\'a}l}-type {Birkhoff} interpolation on nonuniformly distributed points", journal = j-NUMER-ALGORITHMS, volume = "40", number = "1", pages = "1--16", month = sep, year = "2005", CODEN = "NUALEG", DOI = "https://doi.org/10.1007/s11075-005-1516-4", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", bibdate = "Sat Nov 26 18:05:19 MST 2005", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=40&issue=1; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=40&issue=1&spage=1", acknowledgement = ack-nhfb, fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Kamphorst:2005:FBC, author = "Sylvie Oliffson Kamphorst and S{\^o}nia Pinto-de-Carvalho", title = "The first {Birkhoff} coefficient and the stability of $2$-periodic orbits on billiards", journal = j-EXP-MATH, volume = "14", number = "3", pages = "299--306", month = "????", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1080/10586458.2005.10128923", ISSN = "1058-6458 (print), 1944-950X (electronic)", ISSN-L = "1058-6458", bibdate = "Mon Mar 5 15:33:58 MST 2012", bibsource = "http://projecteuclid.org/euclid.em; http://www.tandfonline.com/toc/uexm20/14/3; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/expmath.bib", URL = "http://projecteuclid.org/euclid.em/1128371755", acknowledgement = ack-nhfb, fjournal = "Experimental Mathematics", journal-URL = "http://www.tandfonline.com/loi/uexm20", onlinedate = "30 Jan 2011", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Zegers:2005:BTL, author = "Robin Zegers", title = "{Birkhoff}'s theorem in {Lovelock} gravity", journal = j-J-MATH-PHYS, volume = "46", number = "7", pages = "072502", month = jul, year = "2005", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.1960798", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Wed Oct 26 09:03:37 MDT 2011", bibsource = "http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2005.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v46/i7/p072502_s1", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", onlinedate = "15 July 2005", pagecount = "6", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Bernardi:2006:PBP, author = "Olga Bernardi and Franco Cardin", title = "{Poincar{\'e}--Birkhoff} periodic orbits for mechanical {Hamiltonian} systems on {$ T^* \mathbb {T}^n $}", journal = j-J-MATH-PHYS, volume = "47", number = "7", pages = "072701", month = jul, year = "2006", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.2211930", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Wed Oct 26 09:04:26 MDT 2011", bibsource = "http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2005.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v47/i7/p072701_s1", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", onlinedate = "11 July 2006", pagecount = "15", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Chang:2006:PGR, author = "Cheng-Shang Chang and Duan-Shin Lee and Chi-Yao Yue", title = "Providing guaranteed rate services in the load balanced {Birkhoff--von Neumann} switches", journal = j-IEEE-TRANS-NETWORKING, volume = "14", number = "3", pages = "644--656", year = "2006", CODEN = "IEANEP", ISSN = "1063-6692 (print), 1558-2566 (electronic)", ISSN-L = "1063-6692", bibdate = "Fri Jul 21 05:27:29 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/ieeetransnetworking.bib", acknowledgement = ack-nhfb, fjournal = "IEEE\slash ACM Transactions on Networking", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J771", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Kresic-Juric:2006:BFP, author = "Sasa Kresi{\'c}-Juri{\'c}", title = "On the {Birkhoff} factorization problem for the {Heisenberg} magnet and nonlinear {Schr{\"o}dinger} equations", journal = j-J-MATH-PHYS, volume = "47", number = "6", pages = "063501", month = jun, year = "2006", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.2203231", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Wed Oct 26 09:04:21 MDT 2011", bibsource = "http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2005.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v47/i6/p063501_s1", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", onlinedate = "31 May 2006", pagecount = "12", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{MarquesdeSa:2006:SSB, author = "Eduardo {Marques de S{\'a}}", title = "Some subpolytopes of the {Birkhoff} polytope", journal = j-ELECTRON-J-LINEAR-ALGEBRA, volume = "15", number = "1", pages = "1--7", year = "2006", CODEN = "????", ISSN = "1081-3810 (print), 1537-9582 (electronic)", ISSN-L = "1081-3810", MRclass = "52B11 (15A51)", MRnumber = "2201770 (2006k:52022)", MRreviewer = "Vakif Y. Dzhafarov", bibdate = "Tue Sep 16 07:27:40 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/ela.bib", URL = "http://repository.uwyo.edu/ela/vol15/iss1/1", acknowledgement = ack-nhfb, ajournal = "Electron. J. Linear Algebra", fjournal = "Electronic Journal of Linear Algebra", journal-URL = "http://repository.uwyo.edu/ela/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Bebiano:2007:EBT, author = "Nat{\'a}lia Bebiano and Jo{\~a}o da Provid{\^e}ncia and Alexander Kova{\v{c}}ec", title = "An extension of {Birkhoff}'s theorem with an application to determinants", journal = j-LINEAR-ALGEBRA-APPL, volume = "427", number = "1", pages = "130--137", day = "1", month = nov, year = "2007", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Mar 30 14:19:44 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Casas:2007:PBW, author = "Jos{\'e} Manuel Casas and Manuel A. Insua and Manuel Ladra", title = "{Poincar{\'e}--Birkhoff--Witt} theorem for {Leibniz} $n$", journal = j-J-SYMBOLIC-COMP, volume = "42", number = "11--12", pages = "1052--1065", month = nov # "\slash " # dec, year = "2007", CODEN = "JSYCEH", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", bibdate = "Wed Aug 25 20:13:18 MDT 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Lawson:2007:BCF, author = "Jimmie Lawson and Yongdo Lim", title = "A {Birkhoff} Contraction Formula with Applications to {Riccati} Equations", journal = j-SIAM-J-CONTROL-OPTIM, volume = "46", number = "3", pages = "930--951", month = "????", year = "2007", CODEN = "SJCODC", DOI = "https://doi.org/10.1137/050637637", ISSN = "0363-0129 (print), 1095-7138 (electronic)", ISSN-L = "0363-0129", bibdate = "Sun Mar 30 13:35:13 MDT 2014", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICON/46/3; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjcontroloptim.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Control and Optimization", journal-URL = "http://epubs.siam.org/sicon", journalabr = "SIAM J Control Optim", onlinedate = "January 2007", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Lim:2007:HPM, author = "Yongdo Lim", title = "{Hilbert}'s projective metric on {Lorenz} cones and {Birkhoff} formula for {Lorentzian} compressions", journal = j-LINEAR-ALGEBRA-APPL, volume = "423", number = "2--3", pages = "246--254", day = "1", month = jun, year = "2007", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Mar 30 14:19:26 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Costa:2008:DAB, author = "Liliana Costa and C. M. da Fonseca and Enide Andrade Martins", title = "The diameter of the acyclic {Birkhoff} polytope", journal = j-LINEAR-ALGEBRA-APPL, volume = "428", number = "7", pages = "1524--1537", day = "1", month = apr, year = "2008", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Mar 30 14:19:56 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Finden:2008:ETU, author = "W. F. Finden", title = "An error term and uniqueness for {Hermite--Birkhoff} interpolation involving only function values and\slash or first derivative values", journal = j-J-COMPUT-APPL-MATH, volume = "212", number = "1", pages = "1--15", day = "15", month = feb, year = "2008", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 13:13:21 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377042706007072", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Guo:2008:DAB, author = "Li Guo and Bin Zhang", title = "Differential algebraic {Birkhoff} decomposition and the renormalization of multiple zeta values", journal = j-J-NUMBER-THEORY, volume = "128", number = "8", pages = "2318--2339", month = aug, year = "2008", CODEN = "JNUTA9", DOI = "https://doi.org/10.1016/j.jnt.2007.10.005", ISSN = "0022-314X (print), 1096-1658 (electronic)", ISSN-L = "0022-314X", bibdate = "Wed Jul 15 08:48:31 MDT 2020", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jnumbertheory2000.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022314X07002144", acknowledgement = ack-nhfb, ajournal = "J. Number Theory", fjournal = "Journal of Number Theory", journal-URL = "http://www.sciencedirect.com/science/journal/0022314X", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Nguyen-Ba:2008:HBO, author = "Truong Nguyen-Ba and Philip W. Sharp and R{\'e}mi Vaillancourt", title = "{Hermite--Birkhoff--Obrechkoff} four-stage four-step {ODE} solver of order 14 with quantized step size", journal = j-J-COMPUT-APPL-MATH, volume = "222", number = "2", pages = "608--621", day = "15", month = dec, year = "2008", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 13:13:28 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377042707006358", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Shevchenko:2008:SCB, author = "I. I. Shevchenko", title = "Symbolic computation of the {Birkhoff} normal form in the problem of stability of the triangular libration points", journal = j-COMP-PHYS-COMM, volume = "178", number = "9", pages = "665--672", day = "1", month = may, year = "2008", CODEN = "CPHCBZ", DOI = "https://doi.org/10.1016/j.cpc.2007.12.001", ISSN = "0010-4655 (print), 1879-2944 (electronic)", ISSN-L = "0010-4655", bibdate = "Mon Feb 13 23:42:30 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0010465507004924", acknowledgement = ack-nhfb, fjournal = "Computer Physics Communications", journal-URL = "http://www.sciencedirect.com/science/journal/00104655", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Simson:2008:ASB, author = "Daniel Simson and Mariusz Wojew{\'o}dzki", title = "An Algorithmic Solution of a {Birkhoff} Type Problem", journal = j-FUND-INFO, volume = "83", number = "4", pages = "389--410", month = dec, year = "2008", CODEN = "FUMAAJ", ISSN = "0169-2968 (print), 1875-8681 (electronic)", ISSN-L = "0169-2968", bibdate = "Sat Mar 5 17:06:51 MST 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/fundinfo2000.bib", acknowledgement = ack-nhfb, fjournal = "Fundamenta Informaticae", journal-URL = "http://content.iospress.com/journals/fundamenta-informaticae", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Costa:2009:FCA, author = "Liliana Costa and C. M. da Fonseca and Enide Andrade Martins", title = "Face counting on an {Acyclic Birkhoff} polytope", journal = j-LINEAR-ALGEBRA-APPL, volume = "430", number = "4", pages = "1216--1235", day = "1", month = feb, year = "2009", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Mar 30 14:20:31 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Nguyen-Ba:2009:OSS, author = "Truong Nguyen-Ba and Han Hao and Hemza Yagoub and R{\'e}mi Vaillancourt", title = "One-step 5-stage {Hermite--Birkhoff--Taylor ODE} solver of order 12", journal = j-APPL-MATH-COMP, volume = "211", number = "2", pages = "313--328", day = "15", month = may, year = "2009", CODEN = "AMHCBQ", DOI = "https://doi.org/10.1016/j.amc.2009.01.043", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Fri Sep 3 10:53:24 MDT 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300309000770", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Wang:2009:NBM, author = "Xiaoying Wang and Shugong Zhang and Tian Dong", title = "{Newton} basis for multivariate {Birkhoff} interpolation", journal = j-J-COMPUT-APPL-MATH, volume = "228", number = "1", pages = "466--479", day = "1", month = jun, year = "2009", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 13:13:32 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377042708005128", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Bozic:2010:TSV, author = "Vladan Bozic and Truong Nguyen-Ba and R{\'e}mi Vaillancourt", title = "A three-stage, {VSVO}, {Hermite--Birkhoff--Taylor}, {ODE} solver", journal = j-APPL-MATH-COMP, volume = "216", number = "2", pages = "598--610", day = "15", month = mar, year = "2010", CODEN = "AMHCBQ", DOI = "https://doi.org/10.1016/j.amc.2010.01.082", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Fri Sep 3 10:53:26 MDT 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300310001062", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Costa:2010:FFT, author = "Liliana Costa and Enide Andrade Martins", title = "Faces of faces of the tridiagonal {Birkhoff} polytope", journal = j-LINEAR-ALGEBRA-APPL, volume = "432", number = "6", pages = "1384--1404", day = "1", month = mar, year = "2010", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Mar 30 23:04:04 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2010.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Faou:2010:BNFa, author = "Erwan Faou and Beno{\^\i}t Gr{\'e}bert and Eric Paturel", title = "{Birkhoff} normal form for splitting methods applied to semilinear {Hamiltonian PDEs}. {Part I}. {Finite}-dimensional discretization", journal = j-NUM-MATH, volume = "114", number = "3", pages = "429--458", month = jan, year = "2010", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Fri May 14 08:10:17 MDT 2010", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=114&issue=3; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/nummath2010.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=114&issue=3&spage=429", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Faou:2010:BNFb, author = "Erwan Faou and Beno{\^\i}t Gr{\'e}bert and Eric Paturel", title = "{Birkhoff} normal form for splitting methods applied to semilinear {Hamiltonian PDEs}. {Part II}. {Abstract} splitting", journal = j-NUM-MATH, volume = "114", number = "3", pages = "459--490", month = jan, year = "2010", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Fri May 14 08:10:17 MDT 2010", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=114&issue=3; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/nummath2010.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=114&issue=3&spage=459", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Ganikhodzhaev:2010:DSQ, author = "Rasul Ganikhodzhaev and Farruh Shahidi", title = "Doubly stochastic quadratic operators and {Birkhoff}'s problem", journal = j-LINEAR-ALGEBRA-APPL, volume = "432", number = "1", pages = "24--35", day = "1", month = jan, year = "2010", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Mar 30 23:04:01 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2010.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Nguyen-Ba:2010:OSS, author = "Truong Nguyen-Ba and Vladan Bozic and Emmanuel Kengne and R{\'e}mi Vaillancourt", title = "A one-step $7$-stage {Hermite--Birkhoff--Taylor ODE} solver of order $ 11$", journal = j-J-COMPUT-APPL-MATH, volume = "234", number = "1", pages = "192--208", day = "1", month = may, year = "2010", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 13:24:22 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377042709008231", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Schleich:2010:SPB, author = "Kristin Schleich and Donald M. Witt", title = "A simple proof of {Birkhoff}'s theorem for cosmological constant", journal = j-J-MATH-PHYS, volume = "51", number = "11", pages = "112502:1--112502:9", month = nov, year = "2010", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.3503447", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Thu Oct 27 09:16:49 MDT 2011", bibsource = "http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2010.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v51/i11/p112502_s1", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", onlinedate = "24 November 2010", pagecount = "9", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Butcher:2011:PAB, author = "John C. Butcher and Robert M. Corless and Laureano Gonzalez-Vega and Azar Shakoori", title = "Polynomial algebra for {Birkhoff} interpolants", journal = j-NUMER-ALGORITHMS, volume = "56", number = "3", pages = "319--347", month = mar, year = "2011", CODEN = "NUALEG", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", bibdate = "Wed Mar 16 09:58:49 MDT 2011", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=56&issue=3; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=56&issue=3&spage=319", acknowledgement = ack-nhfb, fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Chai:2011:PIS, author = "Junjie Chai and Na Lei and Ying Li and Peng Xia", title = "The proper interpolation space for multivariate {Birkhoff} interpolation", journal = j-J-COMPUT-APPL-MATH, volume = "235", number = "10", pages = "3207--3214", day = "15", month = mar, year = "2011", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 13:24:27 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377042711000070", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Chorianopoulos:2011:BJA, author = "Christos Chorianopoulos and Panayiotis Psarrakos", title = "{Birkhoff--James} approximate orthogonality sets and numerical ranges", journal = j-LINEAR-ALGEBRA-APPL, volume = "434", number = "9", pages = "2089--2108", day = "1", month = may, year = "2011", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Mar 30 23:04:16 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2010.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Lei:2011:FAM, author = "Na Lei and Junjie Chai and Peng Xia and Ying Li", title = "A fast algorithm for the multivariate {Birkhoff} interpolation problem", journal = j-J-COMPUT-APPL-MATH, volume = "236", number = "6", pages = "1656--1666", day = "15", month = oct, year = "2011", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 13:24:38 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377042711005073", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Milovanovic:2011:GBY, author = "Gradimir V. Milovanovi{\'c} and Aleksandar S. Cvetkovi{\'c} and Marija P. Stani{\'c}", title = "A generalized {Birkhoff--Young--Chebyshev} quadrature formula for analytic functions", journal = j-APPL-MATH-COMP, volume = "218", number = "3", pages = "944--948", day = "1", month = oct, year = "2011", CODEN = "AMHCBQ", DOI = "https://doi.org/10.1016/j.amc.2011.02.007", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Tue Oct 25 09:02:50 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib", note = "Special Issue in Honour of Hari M. Srivastava on his 70th birth anniversary.", URL = "http://www.sciencedirect.com/science/article/pii/S0096300311001652", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Nguyen-Ba:2011:SSP, author = "Truong Nguyen-Ba and Huong Nguyen-Thu and Thierry Giordano and R{\'e}mi Vaillancourt", title = "Strong-stability-preserving $3$-stage {Hermite--Birkhoff time}-discretization methods", journal = j-APPL-NUM-MATH, volume = "61", number = "4", pages = "487--500", month = apr, year = "2011", CODEN = "ANMAEL", ISSN = "0168-9274 (print), 1873-5460 (electronic)", ISSN-L = "0168-9274", bibdate = "Wed Mar 30 08:57:18 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applnummath.bib", acknowledgement = ack-nhfb, fjournal = "Applied Numerical Mathematics: Transactions of IMACS", journal-URL = "http://www.sciencedirect.com/science/journal/01689274/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Roque:2011:STP, author = "Tatiana Roque", title = "Stability of trajectories from {Poincar}{\'e} to {Birkhoff}: approaching a qualitative definition", journal = j-ARCH-HIST-EXACT-SCI, volume = "65", number = "3", pages = "295--342", month = may, year = "2011", CODEN = "AHESAN", ISSN = "0003-9519 (print), 1432-0657 (electronic)", ISSN-L = "0003-9519", bibdate = "Tue Jul 5 16:56:45 MDT 2011", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=????&volume=65&issue=3; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=????&volume=65&issue=3&spage=295", acknowledgement = ack-nhfb, fjournal = "Archive for History of Exact Sciences", journal-URL = "http://link.springer.com/journal/407", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Schlimm:2011:CRA, author = "Dirk Schlimm", title = "On the creative role of axiomatics. {The} discovery of lattices by {Schr{\"o}der}, {Dedekind}, {Birkhoff}, and others", journal = j-SYNTHESE, volume = "183", number = "1", pages = "47--68", month = nov, year = "2011", CODEN = "SYNTAE", DOI = "https://doi.org/10.1007/s11229-009-9667-9", ISSN = "0039-7857 (print), 1573-0964 (electronic)", ISSN-L = "0039-7857", bibdate = "Mon Sep 25 14:19:10 MDT 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/synthese2010.bib", URL = "http://link.springer.com/article/10.1007/s11229-009-9667-9; http://link.springer.com/content/pdf/10.1007/s11229-009-9667-9.pdf", acknowledgement = ack-nhfb, fjournal = "Synthese", journal-URL = "http://link.springer.com/journal/11229", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Yagoub:2011:VSV, author = "Hemza Yagoub and Truong Nguyen-Ba and R{\'e}mi Vaillancourt", title = "Variable-step variable-order $3$-stage {Hermite--Birkhoff--Obrechkoff DDE} solver of order $4$ to $ 14$", journal = j-APPL-MATH-COMP, volume = "217", number = "24", pages = "10247--10255", day = "15", month = aug, year = "2011", CODEN = "AMHCBQ", DOI = "https://doi.org/10.1016/j.amc.2011.05.023", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Tue Oct 25 12:05:45 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300311006783", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Adcock:2012:HOR, author = "Ben Adcock and Arieh Iserles and Syvert P. N{\o}rsett", title = "From high oscillation to rapid approximation {II}: expansions in {Birkhoff} series", journal = j-IMA-J-NUMER-ANAL, volume = "32", number = "1", pages = "105--140", month = jan, year = "2012", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/drq038", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", bibdate = "Fri Jan 20 06:55:39 MST 2012", bibsource = "http://imanum.oxfordjournals.org/content/32/1.toc; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib", URL = "http://imajna.oxfordjournals.org/content/32/1/105.full.pdf+html", acknowledgement = ack-nhfb, fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", onlinedate = "May 26, 2011", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Allasia:2012:MHB, author = "Giampietro Allasia and Cesare Bracco", title = "Multivariate {Hermite--Birkhoff} interpolation by a class of cardinal basis functions", journal = j-APPL-MATH-COMP, volume = "218", number = "18", pages = "9248--9260", day = "15", month = may, year = "2012", CODEN = "AMHCBQ", DOI = "https://doi.org/10.1016/j.amc.2012.03.002", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Wed Apr 18 14:52:18 MDT 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300312002330", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Arambasic:2012:BJO, author = "Ljiljana Arambasi{\'c} and Rajna Raji{\'c}", title = "The {Birkhoff--James} orthogonality in {Hilbert $ C^* $}-modules", journal = j-LINEAR-ALGEBRA-APPL, volume = "437", number = "7", pages = "1913--1929", day = "1", month = oct, year = "2012", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2012.05.011", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Fri Jul 13 12:53:39 MDT 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379512003631", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Nguyen-Ba:2012:SSP, author = "Truong Nguyen-Ba and Huong Nguyen-Thu and Thierry Giordano", title = "Strong-Stability-Preserving $7$-Stage {Hermite--Birkhoff} Time-Discretization Methods", journal = j-J-SCI-COMPUT, volume = "50", number = "1", pages = "63--90", month = jan, year = "2012", CODEN = "JSCOEB", DOI = "https://doi.org/10.1007/s10915-011-9473-7", ISSN = "0885-7474 (print), 1573-7691 (electronic)", ISSN-L = "0885-7474", bibdate = "Sat Dec 22 13:07:56 MST 2012", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0885-7474&volume=50&issue=1; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jscicomput.bib", URL = "http://link.springer.com/article/10.1007/s10915-011-9473-7; http://link.springer.com/content/pdf/10.1007/s10915-011-9473-7; http://www.springerlink.com/openurl.asp?genre=article&issn=0885-7474&volume=50&issue=1&spage=63-90", acknowledgement = ack-nhfb, fjournal = "Journal of Scientific Computing", journal-URL = "http://link.springer.com/journal/10915", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Sun:2012:GBR, author = "Hui Sun and David Uminsky and Andrea L. Bertozzi", title = "A Generalized {Birkhoff--Rott} Equation for Two-dimensional Active Scalar Problems", journal = j-SIAM-J-APPL-MATH, volume = "72", number = "1", pages = "382--404", month = "????", year = "2012", CODEN = "SMJMAP", DOI = "https://doi.org/10.1137/110819883", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", bibdate = "Tue Oct 30 15:07:40 MDT 2012", bibsource = "http://epubs.siam.org/toc/smjmap/72/1; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjapplmath2010.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", onlinedate = "January 2012", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Chorianopoulos:2013:CBJ, author = "Christos Chorianopoulos and Panayiotis J. Psarrakos", title = "On the continuity of {Birkhoff--James}-orthogonality sets", journal = j-LIN-MULT-ALGEBRA, volume = "61", number = "11", pages = "1447--1454", year = "2013", CODEN = "LNMLAZ", DOI = "https://doi.org/10.1080/03081087.2012.743024", ISSN = "0308-1087 (print), 1563-5139 (electronic)", ISSN-L = "0308-1087", bibdate = "Tue Sep 20 15:14:02 MDT 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linmultalgebra.bib", acknowledgement = ack-nhfb, fjournal = "Linear Multilinear Algebra", journal-URL = "http://www.tandfonline.com/loi/glma20", onlinedate = "11 Dec 2012", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Dehghan:2013:TNS, author = "Mehdi Dehghan and S. Aryanmehr and M. R. Eslahchi", title = "A technique for the numerical solution of initial-value problems based on a class of {Birkhoff}-type interpolation method", journal = j-J-COMPUT-APPL-MATH, volume = "244", number = "??", pages = "125--139", day = "15", month = may, year = "2013", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 13:26:16 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377042712005067", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Kong:2013:VIF, author = "Xinlei Kong and Huibin Wu and Fengxiang Mei", title = "Variational integrators for forced {Birkhoffian} systems", journal = j-APPL-MATH-COMP, volume = "225", number = "??", pages = "326--332", day = "1", month = dec, year = "2013", CODEN = "AMHCBQ", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Mon Dec 2 12:35:00 MST 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300313010242", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Liu:2013:LSP, author = "Junli Liu and Shilin Yang", title = "{Lusztig} symmetries and {Poincar{\'e}--Birkhoff--Witt} basis for {$ w U^d_{r, s}({\rm osp}(1 | 2 n)) $}", journal = j-J-MATH-PHYS, volume = "54", number = "12", pages = "121704", month = dec, year = "2013", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.4852355", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Wed Feb 12 11:30:09 MST 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2010.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Abreu:2014:SAB, author = "Nair Abreu and Liliana Costa and Geir Dahl and Enide Martins", title = "The skeleton of acyclic {Birkhoff} polytopes", journal = j-LINEAR-ALGEBRA-APPL, volume = "457", number = "??", pages = "29--48", day = "15", month = sep, year = "2014", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Mon Aug 11 10:41:15 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379514003127", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Cui:2014:BNT, author = "Lu-Bin Cui and Wen Li and Michael K. Ng", title = "{Birkhoff--von Neumann} Theorem for Multistochastic Tensors", journal = j-SIAM-J-MAT-ANA-APPL, volume = "35", number = "3", pages = "956--973", month = "????", year = "2014", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/120896499", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Sat Sep 13 12:06:59 MDT 2014", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/35/3; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2014", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Nguyen-Thu:2014:SSP, author = "Huong Nguyen-Thu and Truong Nguyen-Ba and R{\'e}mi Vaillancourt", title = "Strong-stability-preserving, {Hermite--Birkhoff} time-discretization based on $k$ step methods and 8-stage explicit {Runge--Kutta} methods of order 5 and 4", journal = j-J-COMPUT-APPL-MATH, volume = "263", number = "??", pages = "45--58", month = jun, year = "2014", CODEN = "JCAMDI", DOI = "https://doi.org/10.1016/j.cam.2013.11.013", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", MRclass = "65L06 (65L20 65M20)", MRnumber = "3162335", MRreviewer = "S. Hitotumatu", bibdate = "Sat Feb 25 13:34:43 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377042713006328", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", xxtitle = "Strong-stability-preserving, {Hermite--Birkhoff} time-discretization based on {[??IMAGE??]} step methods and $8$-stage explicit {Runge--Kutta} methods of order 5 and 4", } @Article{Arambasic:2015:OPS, author = "Ljiljana Arambasi{\'c} and Rajna Raji{\'c}", title = "Operators preserving the strong {Birkhoff--James} orthogonality on {$ B(H) $}", journal = j-LINEAR-ALGEBRA-APPL, volume = "471", number = "??", pages = "394--404", day = "15", month = apr, year = "2015", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Mon Feb 23 09:15:47 MST 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379515000403", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Cui:2015:SMB, author = "Kai Cui and Na Lei", title = "Stable monomial basis for multivariate {Birkhoff} interpolation problems", journal = j-J-COMPUT-APPL-MATH, volume = "277", number = "??", pages = "162--170", day = "15", month = mar, year = "2015", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 13:34:48 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377042714003914", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Fernandes:2015:CDV, author = "Ros{\'a}rio Fernandes", title = "Computing the degree of a vertex in the skeleton of acyclic {Birkhoff} polytopes", journal = j-LINEAR-ALGEBRA-APPL, volume = "475", number = "??", pages = "119--133", day = "15", month = jun, year = "2015", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Thu Apr 2 06:49:42 MDT 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379515000877", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Sain:2015:ONA, author = "Debmalya Sain and Kallol Paul and Sourav Hait", title = "Operator norm attainment and {Birkhoff--James} orthogonality", journal = j-LINEAR-ALGEBRA-APPL, volume = "476", number = "??", pages = "85--97", day = "1", month = jul, year = "2015", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Thu Apr 2 06:49:46 MDT 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379515001469", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Song:2015:NTB, author = "Chuan-Jing Song and Yi Zhang", title = "{Noether} theorem for {Birkhoffian} systems on time scales", journal = j-J-MATH-PHYS, volume = "56", number = "10", pages = "102701", month = oct, year = "2015", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.4932607", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Fri Nov 27 17:59:12 MST 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2015.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Su:2015:SPN, author = "Hongling Su and Shengtai Li", title = "Structure-Preserving Numerical Methods for Infinite-Dimensional {Birkhoffian} Systems", journal = j-J-SCI-COMPUT, volume = "65", number = "1", pages = "196--223", month = oct, year = "2015", CODEN = "JSCOEB", DOI = "https://doi.org/10.1007/s10915-014-9958-2", ISSN = "0885-7474 (print), 1573-7691 (electronic)", ISSN-L = "0885-7474", bibdate = "Tue Sep 29 09:59:29 MDT 2015", bibsource = "http://link.springer.com/journal/10915; http://link.springer.com/journal/10915/65/1; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jscicomput.bib", URL = "http://link.springer.com/article/10.1007/s10915-014-9958-2; http://link.springer.com/content/pdf/10.1007/s10915-014-9958-2.pdf", acknowledgement = ack-nhfb, fjournal = "Journal of Scientific Computing", journal-URL = "http://link.springer.com/journal/10915", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{DellAccio:2016:CHB, author = "F. Dell'Accio and F. {Di Tommaso}", title = "Complete {Hermite--Birkhoff} interpolation on scattered data by combined {Shepard} operators", journal = j-J-COMPUT-APPL-MATH, volume = "300", number = "??", pages = "192--206", month = jul, year = "2016", CODEN = "JCAMDI", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 13:35:49 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377042715006287", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{DeVos:2016:BTU, author = "Alexis {De Vos} and Stijn {De Baerdemacker}", title = "The {Birkhoff} theorem for unitary matrices of prime dimension", journal = j-LINEAR-ALGEBRA-APPL, volume = "493", number = "??", pages = "455--468", day = "15", month = mar, year = "2016", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Fri Feb 5 18:05:27 MST 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379515007156", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Dufosse:2016:NBN, author = "Fanny Dufoss{\'e} and Bora U{\c{c}}ar", title = "Notes on {Birkhoff--von Neumann} decomposition of doubly stochastic matrices", journal = j-LINEAR-ALGEBRA-APPL, volume = "497", number = "??", pages = "108--115", day = "15", month = may, year = "2016", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Mon Mar 7 09:44:14 MST 2016", bibsource = "????; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379516001257", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Jiao:2016:WCF, author = "Yujian Jiao and Li-Lian Wang and Can Huang", title = "Well-conditioned fractional collocation methods using fractional {Birkhoff} interpolation basis", journal = j-J-COMPUT-PHYS, volume = "305", number = "??", pages = "1--28", day = "15", month = jan, year = "2016", CODEN = "JCTPAH", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", bibdate = "Thu Dec 10 16:14:28 MST 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0021999115006932", acknowledgement = ack-nhfb, fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Joji:2016:SRA, author = "Du ko Joji", title = "Some remarks about acyclic and tridiagonal {Birkhoff} polytopes", journal = j-LINEAR-ALGEBRA-APPL, volume = "495", number = "??", pages = "108--121", day = "15", month = apr, year = "2016", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Thu Feb 25 06:03:18 MST 2016", bibsource = "????; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379516000501", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Nguyen-Ba:2016:VSH, author = "Truong Nguyen-Ba", title = "On variable step {Hermite--Birkhoff} solvers combining multistep and $4$-stage {DIRK} methods for stiff {ODEs}", journal = j-NUMER-ALGORITHMS, volume = "71", number = "4", pages = "855--888", month = apr, year = "2016", CODEN = "NUALEG", DOI = "https://doi.org/10.1007/s11075-015-0027-1", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", bibdate = "Thu Apr 7 12:13:13 MDT 2016", bibsource = "http://link.springer.com/journal/11075/71/4; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib", URL = "http://link.springer.com/article/10.1007/s11075-015-0027-1", acknowledgement = ack-nhfb, fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Paul:2016:BJO, author = "K. Paul and D. Sain and P. Ghosh", title = "{Birkhoff--James} orthogonality and smoothness of bounded linear operators", journal = j-LINEAR-ALGEBRA-APPL, volume = "506", number = "??", pages = "551--563", day = "1", month = oct, year = "2016", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Mon Aug 29 07:13:39 MDT 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379516302415", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Su:2016:EDP, author = "Hongling Su and Shengtai Li", title = "Energy\slash dissipation-preserving {Birkhoffian} multi-symplectic methods for {Maxwell}'s equations with dissipation terms", journal = j-J-COMPUT-PHYS, volume = "311", number = "??", pages = "213--240", day = "15", month = apr, year = "2016", CODEN = "JCTPAH", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", bibdate = "Tue Mar 8 07:54:45 MST 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0021999116000541", acknowledgement = ack-nhfb, fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Costabile:2017:CBL, author = "Francesco A. Costabile and Anna Napoli", title = "A class of {Birkhoff--Lagrange}-collocation methods for high order boundary value problems", journal = j-APPL-NUM-MATH, volume = "116", number = "??", pages = "129--140", month = jun, year = "2017", CODEN = "ANMAEL", ISSN = "0168-9274 (print), 1873-5460 (electronic)", ISSN-L = "0168-9274", bibdate = "Tue Mar 28 18:19:12 MDT 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applnummath.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0168927416302392", acknowledgement = ack-nhfb, fjournal = "Applied Numerical Mathematics: Transactions of IMACS", journal-URL = "http://www.sciencedirect.com/science/journal/01689274", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{DeBaerdemacker:2017:BTU, author = "Stijn {De Baerdemacker} and Alexis {De Vos} and Lin Chen and Li Yu", title = "The {Birkhoff} theorem for unitary matrices of arbitrary dimensions", journal = j-LINEAR-ALGEBRA-APPL, volume = "514", number = "??", pages = "151--164", day = "1", month = feb, year = "2017", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Tue Nov 22 15:28:01 MST 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379516305134", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Gaina:2017:BSC, author = "Daniel Gaina", title = "{Birkhoff} style calculi for hybrid logics", journal = j-FORM-ASP-COMPUT, volume = "29", number = "5", pages = "805--832", month = sep, year = "2017", CODEN = "FACME5", DOI = "https://doi.org/10.1007/s00165-016-0414-y", ISSN = "0934-5043 (print), 1433-299X (electronic)", ISSN-L = "0934-5043", bibdate = "Thu Nov 23 07:37:43 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/formaspcomput.bib", URL = "http://link.springer.com/article/10.1007/s00165-016-0414-y", acknowledgement = ack-nhfb, fjournal = "Formal Aspects of Computing", journal-URL = "http://link.springer.com/journal/165", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Milovanovic:2017:GWB, author = "Gradimir V. Milovanovi{\'c}", title = "Generalized weighted {Birkhoff--Young} quadratures with the maximal degree of exactness", journal = j-APPL-NUM-MATH, volume = "116", number = "??", pages = "238--255", month = jun, year = "2017", CODEN = "ANMAEL", ISSN = "0168-9274 (print), 1873-5460 (electronic)", ISSN-L = "0168-9274", bibdate = "Tue Mar 28 18:19:12 MDT 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applnummath.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0168927416301064", acknowledgement = ack-nhfb, fjournal = "Applied Numerical Mathematics: Transactions of IMACS", journal-URL = "http://www.sciencedirect.com/science/journal/01689274", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Moslehian:2017:COB, author = "Mohammad Sal Moslehian and Ali Zamani", title = "Characterizations of Operator {Birkhoff--James} Orthogonality", journal = j-CAN-MATH-BULL, volume = "60", number = "4", pages = "816--829", month = dec, year = "2017", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-2017-004-5", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", bibdate = "Sat Jan 13 15:26:56 MST 2018", bibsource = "http://cms.math.ca/cmb/v60/n4; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib", abstract = "In this paper, we obtain some characterizations of the (strong) Birkhoff--James orthogonality for elements of Hilbert $ C^*$-modules and certain elements of $ \mathbb {B}(\mathscr {H})$. Moreover, we obtain a kind of Pythagorean relation for bounded linear operators. In addition, for $ T \in \mathbb {B}(\mathscr {H})$ we prove that if the norm attaining set $ \mathbb {M}_T$ is a unit sphere of some finite dimensional subspace $ \mathscr {H}_0$ of $ \mathscr {H}$ and $ \| T \|_{{{\mathscr {H}}_0}^\perp } \lt \| T \| $, then for every $ S \in \mathbb {B}(\mathscr {H})$, $T$ is the strong Birkhoff--James orthogonal to $S$ if and only if there exists a unit vector $ \xi \in {\mathscr {H}}_0$ such that $ \| T \| \xi = |T| \xi $ and $ S^*T \xi = 0$. Finally, we introduce a new type of approximate orthogonality and investigate this notion in the setting of inner product $ C^*$-modules.", acknowledgement = ack-nhfb, fjournal = "Canadian mathematical bulletin = Bulletin canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Ye:2017:DCB, author = "Tong Ye and Jinghui Zhang and Tony T. Lee and Weisheng Hu", title = "Deflection-Compensated {Birkhoff--von Neumann} Switches", journal = j-IEEE-TRANS-NETWORKING, volume = "25", number = "2", pages = "879--895", month = apr, year = "2017", CODEN = "IEANEP", DOI = "https://doi.org/10.1109/TNET.2016.2606766", ISSN = "1063-6692 (print), 1558-2566 (electronic)", ISSN-L = "1063-6692", bibdate = "Mon Jun 5 18:46:21 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/ieeetransnetworking.bib", abstract = "Despite the high throughput and low complexity achieved by input scheduling based on Birkhoff-von-Neumann BvN decomposition, the performance of the BvN switch becomes less predictable when the input traffic is bursty. In this paper, we propose a deflection-compensated BvN D-BvN switch architecture to enhance the quasistatic scheduling based on BvN decomposition. D-BvN switches provide capacity guarantee for virtual circuits VCs and deflect bursty traffic when overflow occurs. The deflection scheme is devised to offset the excessive buffer requirement of each VC when input traffic is bursty. The design of our conditional deflection mechanism is based on the fact that it is unlikely that the traffic input to VCs is all bursty at the same time; most likely, some starving VCs have spare capacities when some other VCs are in the overflow state. The proposed algorithm makes full use of the spare capacities of those starving VCs to deflect the overflow traffic to other inputs and provide bandwidth for the deflected traffic to re-access the desired VC. Our analysis and simulation results show that this deflection-compensated mechanism can support BvN switches to achieve close to 100\% throughput of offered load even with bursty input traffic, and reduces the average end-to-end delay and delay jitter. Also, our result indicates that the packet out-of-sequence probability due to deflection of overflow traffic is negligible, and thus, only a small re-sequencing buffer is needed at each output port. We also compare D-BvN with the well-established online scheduling algorithm iSLIP, and the result demonstrates that D-BvN outperforms iSLIP in terms of the throughput of offered load when the traffic is non-uniform or the traffic load is not very high.", acknowledgement = ack-nhfb, fjournal = "IEEE\slash ACM Transactions on Networking", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J771", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Allasia:2018:HBI, author = "Giampietro Allasia and Roberto Cavoretto and Alessandra {De Rossi}", title = "{Hermite--Birkhoff} interpolation on scattered data on the sphere and other manifolds", journal = j-APPL-MATH-COMP, volume = "318", number = "??", pages = "35--50", day = "1", month = feb, year = "2018", CODEN = "AMHCBQ", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Tue Oct 24 16:17:36 MDT 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300317303065", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{DellAccio:2018:RFH, author = "Francesco Dell'Accio and Filomena {Di Tommaso} and Kai Hormann", title = "Reconstruction of a function from {Hermite--Birkhoff} data", journal = j-APPL-MATH-COMP, volume = "318", number = "??", pages = "51--69", day = "1", month = feb, year = "2018", CODEN = "AMHCBQ", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Tue Oct 24 16:17:36 MDT 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300317303727", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Dufosse:2018:FNB, author = "Fanny Dufoss{\'e} and Kamer Kaya and Ioannis Panagiotas and Bora U{\c{c}}ar", title = "Further notes on {Birkhoff--von Neumann} decomposition of doubly stochastic matrices", journal = j-LINEAR-ALGEBRA-APPL, volume = "554", number = "??", pages = "68--78", day = "1", month = oct, year = "2018", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2018.05.017", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Fri Aug 10 17:32:20 MDT 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379518302568", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Durkovic:2018:BNS, author = "Srdjan Durkovic and Zoran Cica", title = "{Birkhoff--von Neumann} Switch Based on Greedy Scheduling", journal = j-IEEE-COMPUT-ARCHIT-LETT, volume = "17", number = "1", pages = "13--16", month = jan # "\slash " # jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1109/LCA.2017.2707082", ISSN = "1556-6056 (print), 1556-6064 (electronic)", ISSN-L = "1556-6056", bibdate = "Tue Jun 25 07:41:05 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/ieeecomputarchitlett.bib", abstract = "It is important to develop high performance packet switches that are highly scalable. Among the popular solutions are input queued (IQ) switches and load balanced Birkhoff-von Neumann (LB-BvN) switches. However, both solutions have their drawbacks. Switch configuration pattern in IQ switches is random which can limit the supported port speed. On the other hand, LB-BvN switches require two switching stages which increase the overall cost. Also, some LB-BvN solutions suffer from the packet out of sequence problem. In this paper, we propose a novel packet switch architecture that combines the best properties of the IQ and LB-BvN switches and eliminates their drawbacks.", acknowledgement = ack-nhfb, affiliation = "Cica, Z (Reprint Author), Univ Belgrade, Sch Elect Engn, Belgrade 11120, Serbia. Durkovic, Srdjan; Cica, Zoran, Univ Belgrade, Sch Elect Engn, Belgrade 11120, Serbia.", author-email = "srdjad6@gmail.com zoran.cica@etf.rs", da = "2019-06-20", doc-delivery-number = "FZ6EO", eissn = "1556-6064", fjournal = "IEEE Computer Architecture Letters", journal-iso = "IEEE Comput. Archit. Lett.", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=10208", keywords = "Architecture; data communications; Delays; greedy scheduling; high performance packet; Internet; IP networks; IQ switches; LB-BvN solutions; LB-BvN switches; load balanced Birkhoff-von Neumann switches; packet switch architecture; packet switching; packet-switching networks; Ports (Computers); queueing theory; Random access memory; resource allocation; routers; Scheduling; switch configuration pattern; Switches; switching stages; telecommunication scheduling", keywords-plus = "2-STAGE SWITCHES; DESIGN; ALGORITHM", number-of-cited-references = "9", research-areas = "Computer Science", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", times-cited = "1", unique-id = "Durkovic:2018:BNS", web-of-science-categories = "Computer Science, Hardware \& Architecture", } @Article{Liu:2018:SAH, author = "Changying Liu and Arieh Iserles and Xinyuan Wu", title = "Symmetric and arbitrarily high-order {Birkhoff--Hermite} time integrators and their long-time behaviour for solving nonlinear {Klein--Gordon} equations", journal = j-J-COMPUT-PHYS, volume = "356", number = "??", pages = "1--30", day = "1", month = mar, year = "2018", CODEN = "JCTPAH", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", bibdate = "Sat Jan 13 12:33:11 MST 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0021999117308240", acknowledgement = ack-nhfb, fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{McCoid:2018:PSM, author = "Conor McCoid and Manfred R. Trummer", title = "Preconditioning of spectral methods via {Birkhoff} interpolation", journal = j-NUMER-ALGORITHMS, volume = "79", number = "2", pages = "555--573", month = oct, year = "2018", CODEN = "NUALEG", DOI = "https://doi.org/10.1007/s11075-017-0450-6", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", bibdate = "Fri Sep 28 20:26:22 MDT 2018", bibsource = "http://link.springer.com/journal/11075/79/2; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib", acknowledgement = ack-nhfb, fjournal = "Numerical Algorithms", journal-URL = "http://link.springer.com/journal/11075", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Paul:2018:ABJ, author = "Kallol Paul and Debmalya Sain and Arpita Mal", title = "Approximate {Birkhoff--James} orthogonality in the space of bounded linear operators", journal = j-LINEAR-ALGEBRA-APPL, volume = "537", number = "??", pages = "348--357", day = "15", month = jan, year = "2018", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Mon Oct 30 06:30:18 MDT 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379517305773", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Rajchel:2018:RHM, author = "Grzegorz Rajchel and Adam Gasiorowski and Karol Zyczkowski", title = "Robust {Hadamard} Matrices, Unistochastic Rays in {Birkhoff} Polytope and Equi-Entangled Bases in Composite Spaces", journal = j-MATH-COMPUT-SCI, volume = "12", number = "4", pages = "473--490", month = dec, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1007/s11786-018-0384-y", ISSN = "1661-8270 (print), 1661-8289 (electronic)", ISSN-L = "1661-8270", bibdate = "Mon Mar 4 06:59:44 MST 2019", bibsource = "http://link.springer.com/journal/11786/12/4; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/math-comput-sci.bib", URL = "http://link.springer.com/content/pdf/10.1007/s11786-018-0384-y.pdf", acknowledgement = ack-nhfb, fjournal = "Mathematics in Computer Science", journal-URL = "http://link.springer.com/journal/11786", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Chen:2019:BNT, author = "Haibin Chen and Liqun Qi and Louis Caccetta and Guanglu Zhou", title = "{Birkhoff--von Neumann} theorem and decomposition for doubly stochastic tensors", journal = j-LINEAR-ALGEBRA-APPL, volume = "583", number = "??", pages = "119--133", day = "15", month = dec, year = "2019", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Thu Oct 3 08:39:43 MDT 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S002437951930374X", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{DeVos:2019:BTU, author = "Alexis {De Vos} and Stijn {De Baerdemacker}", title = "The {Birkhoff} theorem for unitary matrices of prime-power dimension", journal = j-LINEAR-ALGEBRA-APPL, volume = "578", pages = "27--52", day = "1", month = oct, year = "2019", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2019.05.007", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Thu May 16 08:23:11 MDT 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", URL = "https://www.sciencedirect.com/science/article/pii/S0024379519302095", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Kane:2019:INB, author = "Daniel Kane and Shachar Lovett and Sankeerth Rao", title = "The Independence Number of the {Birkhoff} Polytope Graph, and Applications to Maximally Recoverable Codes", journal = j-SIAM-J-COMPUT, volume = "48", number = "4", pages = "1425--1435", month = "????", year = "2019", CODEN = "SMJCAT", DOI = "https://doi.org/10.1137/18M1205856", ISSN = "0097-5397 (print), 1095-7111 (electronic)", ISSN-L = "0097-5397", bibdate = "Wed Oct 9 17:51:04 MDT 2019", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/48/4; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjcomput.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Computing", journal-URL = "http://epubs.siam.org/sicomp", onlinedate = "January 2019", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Kim:2019:BJO, author = "Sun Kwang Kim and Han Ju Lee", title = "The {Birkhoff--James} orthogonality of operators on infinite dimensional {Banach} spaces", journal = j-LINEAR-ALGEBRA-APPL, volume = "582", number = "??", pages = "440--451", day = "1", month = dec, year = "2019", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Tue Sep 10 07:55:20 MDT 2019", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379519303520", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Paul:2019:SBJ, author = "Kallol Paul and Arpita Mal and Pawel W{\'o}jcik", title = "Symmetry of {Birkhoff--James} orthogonality of operators defined between infinite dimensional {Banach} spaces", journal = j-LINEAR-ALGEBRA-APPL, volume = "563", number = "??", pages = "142--153", day = "15", month = feb, year = "2019", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2018.10.022", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Thu Dec 27 15:29:01 MST 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2015.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379518305081", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{DeCarvalho:2020:BNG, author = "Marcelo H. {De Carvalho} and Nishad Kothari and Xiumei Wang and Yixun Lin", title = "{Birkhoff--von Neumann} Graphs that are {PM}-Compact", journal = j-SIAM-J-DISCR-MATH, volume = "34", number = "3", pages = "1769--1790", month = "????", year = "2020", CODEN = "SJDMEC", DOI = "https://doi.org/10.1137/18M1202347", ISSN = "0895-4801 (print), 1095-7146 (electronic)", ISSN-L = "0895-4801", bibdate = "Fri Mar 12 10:35:02 MST 2021", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIDMA/34/3; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/siamjdiscrmath.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Discrete Mathematics", journal-URL = "http://epubs.siam.org/sidma", onlinedate = "January 2020", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Maurya:2020:NHC, author = "Praveen K. Maurya and Manoj K. Rajpoot and Vivek S. Yadav and Ankit Singh", title = "New hybrid compact schemes for structured irregular meshes using {Birkhoff} polynomial basis", journal = j-J-COMPUT-PHYS, volume = "423", number = "??", pages = "Article 109808", day = "15", month = dec, year = "2020", CODEN = "JCTPAH", DOI = "https://doi.org/10.1016/j.jcp.2020.109808", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", bibdate = "Sat Mar 13 09:06:35 MST 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0021999120305829", acknowledgement = ack-nhfb, fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Arambasic:2021:OPM, author = "Ljiljana Aramba{\v{s}}i{\'c} and Alexander Guterman and Bojan Kuzma and Rajna Raji{\'c} and Svetlana Zhilina", title = "Operators preserving mutual strong {Birkhoff--James} orthogonality on {$ \mathcal {B}(H) $}", journal = j-LINEAR-ALGEBRA-APPL, volume = "624", number = "??", pages = "27--43", day = "1", month = sep, year = "2021", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2021.04.003", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Jan 26 07:45:26 MST 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379521001592", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Reyes:2021:MCS, author = "Armando Reyes and Camilo Rodr{\'\i}guez", title = "The {McCoy} Condition on Skew {Poincar{\'e}--Birkhoff--Witt} Extensions", journal = j-COMMUN-MATH-STAT, volume = "9", number = "1", pages = "1--21", month = mar, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1007/s40304-019-00184-5", ISSN = "2194-6701 (print), 2194-671X (electronic)", ISSN-L = "2194-6701", bibdate = "Wed Mar 31 15:34:20 MDT 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/communmathstat.bib", URL = "http://link.springer.com/article/10.1007/s40304-019-00184-5", acknowledgement = ack-nhfb, fjournal = "Communications in Mathematics and Statistics", journal-URL = "http://link.springer.com/journal/40304", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Valls:2021:BDR, author = "V{\'\i}ctor Valls and George Iosifidis and Leandros Tassiulas", title = "{Birkhoff}'s Decomposition Revisited: Sparse Scheduling for High-Speed Circuit Switches", journal = j-IEEE-TRANS-NETWORKING, volume = "29", number = "6", pages = "2399--2412", month = dec, year = "2021", CODEN = "IEANEP", DOI = "https://doi.org/10.1109/TNET.2021.3088327", ISSN = "1063-6692 (print), 1558-2566 (electronic)", ISSN-L = "1063-6692", bibdate = "Fri Apr 15 05:49:27 MDT 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/ieeetransnetworking.bib", URL = "https://dl.acm.org/doi/10.1109/TNET.2021.3088327", abstract = "Data centers are increasingly using high-speed circuit switches to cope with the growing demand and reduce operational costs. One of the fundamental tasks of circuit switches is to compute a sparse collection of switching configurations to support a \ldots{}", acknowledgement = ack-nhfb, fjournal = "IEEE\slash ACM Transactions on Networking", journal-URL = "https://dl.acm.org/loi/ton", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Wei:2021:CSP, author = "Chunqiu Wei and Lin He and Huibin Wu and Hairui Wen", title = "A class of structure-preserving discontinuous {Galerkin} variational time integrators for {Birkhoffian} systems", journal = j-APPL-MATH-COMP, volume = "393", number = "??", pages = "Article 125750", day = "15", month = mar, year = "2021", CODEN = "AMHCBQ", DOI = "https://doi.org/10.1016/j.amc.2020.125750", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Sat Mar 13 06:39:52 MST 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applmathcomput2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300320307037", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Arambasic:2022:RRS, author = "Ljiljana Arambasi{\'c} and Anda Valent", title = "On a relation related to strong {Birkhoff--James} orthogonality", journal = j-LIN-MULT-ALGEBRA, volume = "70", number = "11", pages = "2088--2096", year = "2022", CODEN = "LNMLAZ", DOI = "https://doi.org/10.1080/03081087.2020.1784082", ISSN = "0308-1087 (print), 1563-5139 (electronic)", ISSN-L = "0308-1087", bibdate = "Wed Jul 20 08:30:57 MDT 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linmultalgebra.bib", acknowledgement = ack-nhfb, fjournal = "Linear and Multilinear Algebra", journal-URL = "http://www.tandfonline.com/loi/glma20", onlinedate = "22 Jun 2020", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Benabdi:2022:BJO, author = "El Hassan Benabdi and Abderrahim Baghdad and Mohamed Chraibi Kaadoud", title = "{Birkhoff--James} orthogonality and algebraic maximal numerical range in {$ C^* $}-algebras", journal = j-LIN-MULT-ALGEBRA, volume = "70", number = "21", pages = "6523--6534", year = "2022", CODEN = "LNMLAZ", DOI = "https://doi.org/10.1080/03081087.2021.1959888", ISSN = "0308-1087 (print), 1563-5139 (electronic)", ISSN-L = "0308-1087", bibdate = "Tue Jun 6 06:29:24 MDT 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linmultalgebra.bib", acknowledgement = ack-nhfb, fjournal = "Linear and Multilinear Algebra", journal-URL = "http://www.tandfonline.com/loi/glma20", onlinedate = "30 Jul 2021", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Rajchel-Mieldzioc:2022:AGS, author = "Grzegorz Rajchel-Mieldzio{\'c} and Kamil Korzekwa and Zbigniew Pucha{\l}a and Karol Zyczkowski", title = "Algebraic and geometric structures inside the {Birkhoff} polytope", journal = j-J-MATH-PHYS, volume = "63", number = "1", pages = "012202", month = jan, year = "2022", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/5.0046581", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Tue Apr 5 13:42:17 MDT 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2020.bib", acknowledgement = ack-nhfb, ajournal = "J. Math. Phys.", fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Shitov:2022:EPF, author = "Yaroslav Shitov", title = "On the extreme points of a family of matrices related to a theorem of {Birkhoff}", journal = j-LINEAR-ALGEBRA-APPL, volume = "632", number = "??", pages = "233--240", day = "1", month = jan, year = "2022", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2021.09.016", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Jan 26 07:45:33 MST 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/linala2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379521003499", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Qiu:2023:SCD, author = "Zhiping Qiu and Yu Qiu", title = "Symplectic central difference scheme for quasi-linear autonomous {Birkhoffian} systems", journal = j-APPL-MATH-COMP, volume = "440", number = "??", pages = "??--??", day = "1", month = mar, year = "2023", CODEN = "AMHCBQ", DOI = "https://doi.org/10.1016/j.amc.2022.127661", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Sat Nov 26 07:09:34 MST 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applmathcomput2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300322007329", acknowledgement = ack-nhfb, articleno = "127661", fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Ross:2023:UBP, author = "I. M. Ross and R. J. Proulx and C. F. Borges", title = "A universal {Birkhoff} pseudospectral method for solving boundary value problems", journal = j-APPL-MATH-COMP, volume = "454", number = "??", pages = "??--??", day = "1", month = oct, year = "2023", CODEN = "AMHCBQ", DOI = "https://doi.org/10.1016/j.amc.2023.128101", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Thu Jun 1 10:43:57 MDT 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applmathcomput2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300323002709", acknowledgement = ack-nhfb, articleno = "128101", fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", } @Article{Xia:2023:LMU, author = "Peng Xia and Na Lei and Tian Dong", title = "On the linearization methods for univariate {Birkhoff} rational interpolation", journal = j-APPL-MATH-COMP, volume = "445", number = "??", pages = "??--??", day = "15", month = may, year = "2023", CODEN = "AMHCBQ", DOI = "https://doi.org/10.1016/j.amc.2022.127831", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Thu Feb 23 11:23:36 MST 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/tex/bib/applmathcomput2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300322008992", acknowledgement = ack-nhfb, articleno = "127831", fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003", subject-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", }

%%% ==================================================================== %%% Cross-referenced entries must come last. They are sorted by year %%% and then by citation label, with ``bibsort --byyear'':

@Book{Birkhoff:1959:PNS, editor = "Garrett Birkhoff and R. E. Langer", booktitle = "Proceedings of the {Ninth Symposium in Applied Mathematics of the American Mathematical Society. Held at New York University, April 4--6, 1957. Orbit theory}", title = "Proceedings of the {Ninth Symposium in Applied Mathematics of the American Mathematical Society. Held at New York University, April 4--6, 1957. Orbit theory}", volume = "9", publisher = pub-AMS, address = pub-AMS:adr, year = "1959", ISSN = "0160-7634", MRclass = "00B25", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", series = "Proc. Symp. Appl. Math.", ZMnumber = "0103.39704", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fseries = "Proceedings of Symposia in Applied Mathematics", ZBmath = "3169208", } @Proceedings{Birkhoff:1961:NRT, editor = "Garrett Birkhoff and Eugene P. (Eugene Paul) Wigner", booktitle = "{Nuclear reactor theory: [proceedings of the 11th Symposium in Applied Mathematics of the American Mathematical Society held at the Hotel New Yorker, April 23--25, 1959]}", title = "{Nuclear reactor theory: [proceedings of the 11th Symposium in Applied Mathematics of the American Mathematical Society held at the Hotel New Yorker, April 23--25, 1959]}", volume = "11", publisher = pub-AMS, address = pub-AMS:adr, bookpages = "v + 339", pages = "v + 339", year = "1961", ISSN = "0160-7634", LCCN = "QC787.N8 S9 1959", MRclass = "00B25", bibdate = "Tue Jun 28 07:04:40 MDT 2011", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", series = "Proceedings of Symposia in Applied Mathematics", ZMnumber = "0098.23302", acknowledgement = ack-nhfb, editor-dates = "Eugene Wigner (17 November 1902--1 January 1995); Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3160315", } @Book{Taub:1961:JNCa, editor = "A. H. Taub", booktitle = "{John von Neumann}: Collected Works: {Volume I}: {Logic}, Theory of Sets and Quantum Mechanics", title = "{John von Neumann}: Collected Works: {Volume I}: {Logic}, Theory of Sets and Quantum Mechanics", publisher = pub-PERGAMON, address = pub-PERGAMON:adr, pages = "x + 654", year = "1961", LCCN = "????", bibdate = "Wed Jun 01 16:58:29 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "See also volumes II--VI \cite{Taub:1961:JNCb,Taub:1961:JNCc,Taub:1962:JNC,Taub:1963:JNCa,Taub:1963:JNCb}.", ZMnumber = "0188.00102", acknowledgement = ack-nhfb, } @Book{Taub:1961:JNCb, editor = "A. H. Taub", booktitle = "{John von Neumann}: Collected Works. {Volume II}: {Operators}, Ergodic Theory and Almost Periodic Functions in a Group", title = "{John von Neumann}: Collected Works. {Volume II}: {Operators}, Ergodic Theory and Almost Periodic Functions in a Group", publisher = pub-PERGAMON, address = pub-PERGAMON:adr, pages = "x + 568", year = "1961", LCCN = "????", bibdate = "Wed Jun 01 16:58:29 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "See also volumes I, III--VI \cite{Taub:1961:JNCa,Taub:1961:JNCc,Taub:1962:JNC,Taub:1963:JNCa,Taub:1963:JNCb}.", ZMnumber = "0188.00102", acknowledgement = ack-nhfb, } @Book{Taub:1961:JNCc, editor = "A. H. Taub", booktitle = "{John von Neumann}: Collected Works. {Volume III}: Rings of Operators", title = "{John von Neumann}: Collected Works. {Volume III}: Rings of Operators", publisher = pub-PERGAMON, address = pub-PERGAMON:adr, pages = "ix + 574", year = "1961--1963", LCCN = "????", bibdate = "Wed Jun 01 16:58:29 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "See also volumes I--II, IV--VI \cite{Taub:1961:JNCa,Taub:1961:JNCb,Taub:1962:JNC,Taub:1963:JNCa,Taub:1963:JNCb}.", ZMnumber = "0188.00102", acknowledgement = ack-nhfb, } @Proceedings{Birkhoff:1962:HIP, editor = "Garrett Birkhoff and Richard Bellman and C. C. Lin", booktitle = "Hydrodynamic instability. {Proceedings of the Thirteenth Symposium in Applied Mathematics of the American Mathematical Society, Hotel New Yorker, New York, USA, April 14--15, 1960}", title = "Hydrodynamic instability. {Proceedings of the Thirteenth Symposium in Applied Mathematics of the American Mathematical Society, Hotel New Yorker, New York, USA, April 14--15, 1960}", volume = "13", publisher = pub-AMS, address = pub-AMS:adr, pages = "vii + 319", year = "1962", ISSN = "0160-7634", MRclass = "00B25", bibdate = "Sat Mar 31 07:49:19 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/u/ulam-stanislaw-m.bib", series = "Symposia in Applied Mathematics", ZMnumber = "0107.42003", acknowledgement = ack-nhfb, editor-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", fseries = "Proceedings of Symposia in Applied Mathematics", ZBmath = "3175906", } @Book{Taub:1962:JNC, editor = "A. H. Taub", booktitle = "{John von Neumann}: Collected Works. {Volume IV}: {Continuous} Geometry and Other Topics", title = "{John von Neumann}: Collected Works. {Volume IV}: {Continuous} Geometry and Other Topics", publisher = pub-PERGAMON, address = pub-PERGAMON:adr, pages = "x + 516", year = "1962", LCCN = "????", bibdate = "Wed Jun 01 16:58:29 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "See also volumes I--III, V--VI \cite{Taub:1961:JNCa,Taub:1961:JNCb,Taub:1961:JNCc,Taub:1963:JNCa,Taub:1963:JNCb}.", ZMnumber = "0188.00102", acknowledgement = ack-nhfb, } @Book{Frank:1963:SPR, editor = "Ph. Frank and S. Goldstein and M. Kac and W. Prager and G. Szeg{\H{o}} and G. Birkhoff", booktitle = "Selected papers of {Richard von Mises}. {Vol. I}: {Geometry}, mechanics, analysis", title = "Selected papers of {Richard von Mises}. {Vol. I}: {Geometry}, mechanics, analysis", publisher = pub-AMS, address = pub-AMS:adr, pages = "xxiii + 626", year = "1963", MRclass = "01A75", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0138.24202", acknowledgement = ack-nhfb, editor-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3224519", } @Book{Taub:1963:JNCa, editor = "A. H. Taub", booktitle = "{John von Neumann}: Collected Works. {Volume V}: {Design} of Computers, Theory of Automata and Numerical Analysis", title = "{John von Neumann}: Collected Works. {Volume V}: {Design} of Computers, Theory of Automata and Numerical Analysis", publisher = pub-PERGAMON, address = pub-PERGAMON:adr, pages = "ix + 784", year = "1963", LCCN = "????", bibdate = "Wed Jun 01 16:58:29 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "See also volumes I--IV, VI \cite{Taub:1961:JNCa,Taub:1961:JNCb,Taub:1961:JNCc,Taub:1962:JNC,Taub:1963:JNCb}.", ZMnumber = "0188.00102", acknowledgement = ack-nhfb, } @Book{Taub:1963:JNCb, editor = "A. H. Taub", booktitle = "{John von Neumann}: Collected Works. {Volume VI}: {Theory} of Games, Astrophysics, Hydrodynamics and Meteorology", title = "{John von Neumann}: Collected Works. {Volume VI}: {Theory} of Games, Astrophysics, Hydrodynamics and Meteorology", publisher = pub-PERGAMON, address = pub-PERGAMON:adr, pages = "x + 538", year = "1963", LCCN = "????", bibdate = "Wed Jun 01 16:58:29 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib; https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib; https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib; https://www.math.utah.edu/pub/tex/bib/einstein.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib", note = "See also volumes I--V \cite{Taub:1961:JNCa,Taub:1961:JNCb,Taub:1961:JNCc,Taub:1962:JNC,Taub:1963:JNCa}.", ZMnumber = "0188.00102", acknowledgement = ack-nhfb, } @Proceedings{Garabedian:1965:AFP, editor = "Henry L. Garabedian", booktitle = "{Approximation of Functions (Proceedings of the Symposium on Approximation of Functions, General Motors Research Laboratories, Warren, Michigan, 1964)}", title = "{Approximation of Functions (Proceedings of the Symposium on Approximation of Functions, General Motors Research Laboratories, Warren, Michigan, 1964)}", publisher = pub-ELSEVIER, address = pub-ELSEVIER:adr, pages = "220", year = "1965", LCCN = "????", bibdate = "Sun Dec 30 18:29:06 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib", acknowledgement = ack-nhfb, tableofcontents = "1. The convergence of sequences of rational functions of best approximation with some free poles (Walsh) \\ 2. Uses of Hilbert space in approximation (Sard) \\ 3. Applications of duality in approximation theory (Buck) \\ 4. Inclusion theorems for the minimal distance in rational Tschebyscheff approximation with several variables (Collatz) \\ 5. Rational approximation on finite point sets (Fox, Goldstein, and Lastman) \\ 6. Phase methods for polynomial approximation (Stiefel) \\ 7. Optimal and nearly-optimal linear approximation (Golomb) \\ 8. Approximation by generalized rat ion a 1 functions (Cheney) \\ 9. Nonlinear approximation (Rice) \\ 10. Nonlinear sequence transformations (Bauer) \\ 11. Approximation theory in the first two decades of electronic computers (Davis) \\ 12. Piecewise polynomial interpolation and approximation (Birkhoff and de Boor) \\ 13. Russian literature on approximation in 1958--1964 (Lorentz)", } @Proceedings{Bellman:1969:TTP, editor = "R. Bellman and G. Birkhoff and I. Abu-Shumays", booktitle = "Transport theory. Proceedings of a symposium in applied mathematics of the {American Mathematical Society and the Society for Industrial and Applied Mathematics. Held in New York City, April 5--8, 1967}", title = "Transport theory. Proceedings of a symposium in applied mathematics of the {American Mathematical Society and the Society for Industrial and Applied Mathematics. Held in New York City, April 5--8, 1967}", publisher = pub-AMS, address = pub-AMS:adr, pages = "vii + 327", year = "1969", MRclass = "00B25 90-06", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0181.22903", acknowledgement = ack-nhfb, editor-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3288375", } @Proceedings{Abbott:1970:TLT, editor = "J. C. (James Crawford) Abbott", booktitle = "Trends in Lattice Theory", title = "Trends in Lattice Theory", publisher = pub-VAN-NOSTRAND-REINHOLD, address = pub-VAN-NOSTRAND-REINHOLD:adr, bookpages = "ix + 215", pages = "ix + 215", year = "1970", ISBN = "0-442-00215-7", ISBN-13 = "978-0-442-00215-2", LCCN = "QA171.5T74 1970", bibdate = "Wed Nov 01 07:41:38 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", note = "Written versions of four talks delivered to a symposium on trends in lattice theory held at the United States Naval Academy in May of 1966.", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", tableofcontents = "Preface / iii \\ \\ Part I: What Can Lattices Do for You? / Garrett Birkhoff \\ \\ Introduction / 1 \\ Boolean logic / 2 \\ Dedekind's work / 4 \\ Lattice theory begins / 6 \\ Lattices and groups / 7 \\ Universal algebra / 9 \\ Geometric lattices / 12 \\ Continuous geometries / 14 \\ Lattices and set theory / 19 \\ Current trends in set theory / 21 \\ Convergence in lattices / 24 \\ Lattice-ordered monoids / 27 \\ Lattice- ordered groups / 29 \\ Vector lattices / 31 \\ Directed vector spaces / 34 \\ Positive linear operators / 36 \\ Time- dependent case / 37 \\ Bibliography / 39 \\ \\ Part II: The Current Interest in Orthomodular Lattices / Samuel S. Holland, Jr. \\ \\ Introduction / 41 \\ The origin of orthomodular lattice theory / 46 \\ Some basic orthomodular lattice theory / 79 \\ The principal results / 95 \\ Some brief remarks on quantum mechanics / 114 \\ Bibliography / 117 \\ Part III: Geometric Lattices / Henry Crapo and Gian-Carlo Rota \\ \\ Introduction / 127 \\ Geometries and Geometric Lattices / 132 \\ Classical Examples / 141 \\ Span, bases, minors, and dependence / 150 \\ The extension theorem / 153 \\ The critical problem / 161 \\ Bibliography / 167 \\ \\ Part IV: Universal Algebra / George Gr{\"a}tzer \\ \\ Introduction / 173 \\ Basic concepts / 175 \\ From the Homomorphism theorem to the Jordan--H{\"o}lder theorem / 176 \\ Algebraic constructions / 178 \\ Related structures / 181 \\ Free algebras and identities / 185 \\ Bases of free algebras / 188 \\ The first order language of algebras / 193 \\ Free $\Sigma$-algebras / 199 \\ Some general comments and lattice-theoretic particulars / / 202 \\ Appendix / 211", } @Proceedings{Birkhoff:1970:NSF, editor = "Garrett Birkhoff and Richard S. Varga", booktitle = "Numerical solution of field problems in continuum physics: proceedings of a {Symposium in applied mathematics of the American Mathematical Society and the Society for Industrial and Applied Mathematics held in Durham, North Carolina, April 5--6, 1968}", title = "Numerical solution of field problems in continuum physics: proceedings of a {Symposium in applied mathematics of the American Mathematical Society and the Society for Industrial and Applied Mathematics held in Durham, North Carolina, April 5--6, 1968}", volume = "2", publisher = pub-AMS, address = pub-AMS:adr, bookpages = "viii + 280", pages = "viii + 280", year = "1970", ISBN = "0-8218-1321-0", ISBN-13 = "978-0-8218-1321-8", LCCN = "QA1 .A5217 n.s. v.2 1968; QC174.45.S96 1968", MRclass = "00B25 74-06 76-06", bibdate = "Wed Apr 20 17:21:32 MDT 2022", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib", series = "SIAM-AMS proceedings", ZMnumber = "0207.00201", acknowledgement = ack-nhfb, author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", editor-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Richard S. Varga (8 October 1928--25 February 2022)", subject = "Kontinuumsphysik; Numerisches Verfahren", xxbooktitle = "Numerical Solution of Field Problems in Continuum Physics ({Proceedings of the Symposium Appl. Math., Durham, NC, 1968}), {SIAM-AMS Proc., Vol. II}", ZBmath = "3328977", } @Proceedings{Birkhoff:1970:SNA, editor = "G. Birkhoff and R. S. Varga", booktitle = "Studies in Numerical Analysis, 2: Numerical Solutions of Nonlinear Problems ({Symposia, SIAM, Philadelphia, Pa., 21--23 October 1968})", title = "Studies in Numerical Analysis, 2: Numerical Solutions of Nonlinear Problems ({Symposia, SIAM, Philadelphia, Pa., 21--23 October 1968})", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "143", year = "1970", LCCN = "QA297 .S95 1968", bibdate = "Wed Apr 20 14:10:28 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib", acknowledgement = ack-nhfb, editor-dates = "Garrett Birkhoff (19 January 1911--22 November 1996); Richard S. Varga (8 October 1928--25 February 2022)", xxeditor = "James M. Ortega and Werner C. Rheinboldt.", } @Proceedings{Birkhoff:1971:CAN, editor = "Garrett Birkhoff and Marshall {Hall, Jr.}", booktitle = "Computers in Algebra and Number Theory. {Proceedings} of a symposium in applied mathematics of the {American Mathematical Society and the Society for Industrial and Applied Mathematics. Held in New York City, March 25--26, 1970}", title = "Computers in Algebra and Number Theory. {Proceedings} of a symposium in applied mathematics of the {American Mathematical Society and the Society for Industrial and Applied Mathematics. Held in New York City, March 25--26, 1970}", publisher = pub-AMS, address = pub-AMS:adr, pages = "vii + 200", year = "1971", MRclass = "00B25 11-06 20-06 68-06 05-06", bibdate = "Sun Oct 29 10:49:01 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib", ZMnumber = "0236.00006", acknowledgement = ack-nhfb, editor-dates = "Garrett Birkhoff (19 January 1911--22 November 1996)", ZBmath = "3373679", } @Proceedings{Tarwater:1977:BTA, editor = "Dalton Tarwater", booktitle = "The bicentennial tribute to {American} mathematics 1776--1976. {Papers} presented at the fifty-nineth annual meeting of the {Mathematical Association of America} commemorating the nation's bicentennial", title = "The bicentennial tribute to {American} mathematics 1776--1976. {Papers} presented at the fifty-nineth annual meeting of the {Mathematical Association of America} commemorating the nation's bicentennial", publisher = pub-MATH-ASSOC-AMER, address = pub-MATH-ASSOC-AMER:adr, pages = "vii + 225", year = "1977", MRclass = "01A60 01A50 01A55", bibdate = "Sun Oct 29 10:49:01 2023",