81. From Kirk@cs.pitt.edu Sun Mar 1 181307 1998 Received From Gomez FRED B. 115 255 220 5 33 JOO, ISTVAN 204 221 243 420 424 221 1 0 JOO, MIKLOS ISTVAN 220 222 7 37 kac, mark 36 72 86 329 423 446 464 223 3 6 KAINEN, http://www.cs.sunysb.edu/~algorith/biblio/testdata/erdos-number

From kirk@cs.pitt.edu Sun Mar 1 18:13:07 1998 Received: from gomez.cs.pitt.edu (gomez.cs.pitt.edu [136.142.79.193]) by cs.sunysb.edu (8.6.12/8.6.9) with ESMTP id SAA19649 for ; Sun, 1 Mar 1998 18:13:04 -0500 Received: from bucky.cs.pitt.edu (bucky.cs.pitt.edu [136.142.79.11]) by gomez.cs.pitt.edu (8.8.7/8.8.7) with ESMTP id SAA30354 for ; Sun, 1 Mar 1998 18:13:50 -0500 (EST) Received: from bucky (localhost [127.0.0.1]) by bucky.cs.pitt.edu (8.8.3/8.8.3) with SMTP id SAA12786 for ; Sun, 1 Mar 1998 18:13:49 -0500 (EST) Sender: kirk@cs.pitt.edu Message-ID: Date: Sun, 01 Mar 1998 18:13:48 -0500 From: Kirk Pruhs

82. Untitled Translate this page Marc Battier. marc.battier@paris4.sorbonne.fr. mark Beam Eduardo kac est un artiste et auteur qui travaille avec des médias électronique et photonique, http://www.olats.org/olats/comites_scientifiques.shtml

QUI SOMMES-NOUS ? COMITES SCIENTIFIQUES L'association Leonardo/Olats est gouvernée par un Conseil d'Administration assorti d'un Conseil Scientifique. Le Conseil d'Administration est composé de : Roger Malina , Président Christine Maxwell , Trésorière - Samuel Okoshken, Secrétaire Le Conseil Scientifique est composé de : Personnalités ès qualité Marc Battier , Président (2003 - ) Jean-Daniel Gardère Jean-Paul Longavesne Roger Malina Ramuntcho Matta ... Christine Maxwell Maarten Noyons - Vincent Winter (2003 - ) Personnels de l'association Annick Bureaud Julien Knebusch Pour ses différents projets, Leonardo/Olats s'est en outre doté de comités scientifiques d'experts internationaux : le Groupe Frieda Ackerman pour le projet et le Comité de lecture pour les Etudes , ainsi que du Comité d'organisation et du Conseil scientifique pour Space and the Arts . Les biographies des membres de ces comités sont disponibles ci-dessous. La composition de chaque comité est disponible dans la rubrique concernée. Nom Email Site Web Marc Battier marc.battier@paris4.sorbonne.fr Mark Beam http://www.beaming.com Paul Brown paul@paul-brown.com

83. Index To Scientists And Engineers Biographical File (Library Of Congress) kac, mark BIB, P. KALCKAR, HERMAN M. BIB. KAMAN, CHARLES H. P, BIO. KANTROWITZ, ARTHUR P, BIB. KAPLAN, JOSEPH BIO. KATCHALSKI, EPHRAIM P, BIB http://www.loc.gov/rr/scitech/sci-eng-em.html

Index to the Scientists and Engineers Biographical File About the Scientists and Engineers Biographical File What is the Scientists and Engineers Biographical File? It is a collection of hard copy files with information on scientists who were prominent in the early 1970s. It consists of folders containing photographs, biographical information and bibliographies of 1200 American and 100 foreign scientists and engineers. How was the collection formed? The collection was formed during the years 1972 - 75. The Science and Technology Division contacted well known and lesser known scientists and engineers of the mid-twentieth century, and asked them to donate the materials. Those asked included: Members of the National Academy of Sciences and the National Academy of Engineers Scientists listed in Who's Who in Science and Engineers of Distinction Nobel Prize recipients and winners of the National Medal for Science Members of Scientists in Search of Their Consciences. Who should use the The Scientists and Engineers Biographical File?

84. On Some Isospectral Second Order Differential Operators Kac And Copyright © 1974 by the National Academy of Sciences. On Some Isospectral Second Order Differential Operators. mark kac and Pierre Van Moerbeke http://www.pnas.org/cgi/content/abstract/71/6/2350

85. By Mark Kac Author - New And Used Books By mark kac Author new and used books - by mark kac Author, Books, new and used books, isbn, price compare, shops. http://www.isbn.pl/C-32/A-by-Mark-Kac-Author/

BY MARK KAC AUTHOR - all books, old, new and used Language: English Deutsch Fran§ais Top searches: Colin Spedding C R W Spedding Shay Art Art Shay Photography H K Colebatch Hal K Colebatch Axelrod Alan Phillips Charles ... ISBN By Mark Kac Author - new and used books Keyword: Author: Title: ISBN: Book location: UK Ireland Germany France USA Canada Results: 1-1 by Mark Kac (Author) Mathematics and Logic ISBN: by Mark Kac (Author) - Mathematics and Logic Price: CDN$ 13.20 Seller: Amazon.ca

86. By Mark Kac (author) - Mathematics And Logic (isbn 0486670856) - New And Used Bo By mark kac (author) Mathematics And Logic (isbn 0486670856) - new and used books - 0486670856, Books, new and used books, isbn, price compare, shops. http://www.isbn.pl/C-32/I-0486670856/Mathematics-and-Logic.html

by Mark Kac (Author) - Mathematics and Logic (ISBN 0486670856) Language: English Deutsch Fran§ais Top searches: Lester R Brown Christopher Flavin Hilary French Katharine Andres Loss Mcgraw Katherine Andres Lewis Carroll Loss Mcgraw Illustrator Browd Victor L M D Introduction Robert West Ph D ... ISBN By Mark Kac (author) - Mathematics And Logic (isbn 0486670856) - new and used books Keyword: Author: Title: ISBN: Book location: UK Ireland Germany France USA Canada Results: 1-1 by Mark Kac (Author) Mathematics and Logic ISBN: 0486670856 by Mark Kac (Author) - Mathematics and Logic Price: CDN$ 13.20 Seller: Amazon.ca

87. USP/SIBi - DEDALUS Translate this page Mostra, 1, kac, mark 1914-. Mostra, 1, kac, Michael B. Mostra, 2, kac, VG. Mostra, 6, kac, Victor G. 1943-. Mostra, 1, kacelmtc, Alejandro http://dedalus.usp.br:4500/ALEPH/POR/USP/USP/MONO/SCAN-F/2452377

Kac, Mark Kac, Mark 1914- Kac, Michael B. Kac, V G Kac, Victor G. 1943- Kacelmtc, Alejandro Kacelnik, Joyce Kacelnik, Zilda Kacew, Sam Kachaniwsky, George Kachanov, L M Kachanov, L. M. (Lazar§ Markovich)

88. The DIAS-APG Members Summary Page Under the influence of mark kac, whom he met in 1969, he specialized in the use of probabilistic methods in statistical mechanics. http://www.stp.dias.ie/APG/members_summary.html

Dublin Institute for Advanced Studies - Applied Probability Group MEMBERS OF THE APPLIED PROBABILITY GROUP Prof. John T. Lewis Thermodynamic Probability: Some Aspects of Large Deviations, written in collaboration with Charles Pfister of EPF, Lausanne, appeared in a special issue of Russian Mathematical Surveys dedicated to A.N.Kolmogorov; this is a systematic exposition of Large Deviation theory from the point of view of Ruelle and Lanford. it paved the way for Entropy, Concentration of Probability and Conditional Limit Theorems , a joint paper with Charles Pfister and Wayne Sullivan, which appeared in Markov Processes and Related Fields in 1995. Much of the work of the Applied Probability Group, both basic and applied, has its origins in this paper. His participation in the Dobrushin-Minlos-Sinai seminar in Moscow in 1985 was a formative experience; the example Dobrushin gave by working in both basic science and in applications to telecommunications inspired the formation of the Applied Probability Group with its distinctive character. In 1998, he gave the Andrejewski Lectures Dr. Raymond Russell

89. Mark Kac, “GLI ENIGMI DEL CASO – Vicissitudini Di Un Matematico” Translate this page Si tratta dell’autobiografia di mark kac, “figura di spicco di quella scuola di matematici polacchi che annovera tra i suoi esponenti Steinhaus, http://www.maecla.it/bibliotecaMatematica/go_file/KAC.htm

Ultimo aggiornamento: Mark Kac, “GLI ENIGMI DEL CASO – Vicissitudini di un matematico” traduzione di Umberto Sampieri, Bollati Boringhieri, 1986 Si tratta dell’autobiografia di Mark Kac, “figura di spicco di quella scuola di matematici polacchi che annovera tra i suoi esponenti Steinhaus, Banach e Smoluckowski ” Nato in Polonia nel 1914, Kac emigrò negli Stati Uniti nel 1939, dove morì nel 1984. “A lui si devono fondamentali contributi nel campo dell’analisi matematica, della teoria della probabilità e della fisica matematica”. Il libro comprende una prefazione, un’introduzione, sette capitoli, un poscritto e le note. Nel prologo “Come divenni un matematico”, l’autore racconta come nell’estate del 1930 venne colpito “da un attacco acuto di quella malattia che, a intervalli irregolari, affligge tutti i matematici, anzi tutti gli scienziati: l’ossessione per un problema. I sintomi, così noti alle mogli dei colpiti dal virus, sono facilmente riconoscibili: comportamento antisociale, insonnia, perdita di appetito ” Nelle pagina 22 e 23 scrive: “Il problema che mi tormentava riguardava la soluzione delle equazioni algebriche di terzo grado, e la risposta era ben nota dal 1545, anno in cui Cardano pubblicò le sue formule risolutive. Ciò che io non sapevo era come dedurre tali formule! [ ]

90. Mark R Gregory - ResearchIndex Document Query problem both of which are associated with the name mark kac, though most likely he never made the The road from kac s matrix to kac s random polynomials http://citeseer.ist.psu.edu/cis?q=Mark R. Gregory

91. Mark G Kelly - ResearchIndex Document Query problem both of which are associated with the name mark kac, though most likely he never made the matrix kac nj 0 BBBBBBBB @0 n 1 0 n \Gamma 1 2 0 n \Gamma http://citeseer.ist.psu.edu/cis?q=Mark G. Kelly

92. DBLP: Eduardo Kac Eduardo kac. List of publications from the DBLP Bibliography Server FAQ Eduardo kac, Kenneth Y. Goldberg, mark Pauline Interfacing reality exploring http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/k/Kac:Eduardo.html

Eduardo Kac List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL ACM Guide CiteSeer CSB ... John F. Canny , Eduardo Kac, Kenneth Y. Goldberg Mark Pauline : Interfacing reality: exploring emerging trends between humans and machines (panel). SIGGRAPH 1997 Coauthor Index John F. Canny Kenneth Y. Goldberg Mark Pauline Eric Paulos DBLP: [ Home Author Title Conferences ... Michael Ley (ley@uni-trier.de) Thu Sep 1 17:37:14 2005

93. DBLP: Mark Pauline mark Pauline. List of publications from the DBLP Bibliography Server FAQ Eduardo kac, Kenneth Y. Goldberg, mark Pauline Interfacing reality http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/p/Pauline:Mark.html

Mark Pauline List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL ACM Guide CiteSeer CSB ... Kenneth Y. Goldberg , Mark Pauline: Interfacing reality: exploring emerging trends between humans and machines (panel). SIGGRAPH 1997 Coauthor Index John F. Canny Kenneth Y. Goldberg Eduardo Kac Eric Paulos DBLP: [ Home Author Title Conferences ... Michael Ley (ley@uni-trier.de) Thu Sep 1 17:37:14 2005

94. Fine Hall In Its Golden Age: Remembrances Of Princeton In The Early Fifties, By He was particularly harsh with mark kac. Kitty kac once related to me an He painted a grim picture of kac s future, unless mark followed Willy s advice http://libweb.princeton.edu/libraries/firestone/rbsc/finding_aids/mathoral/pmcxr

A Century of Mathematics in America, Part III, History of Mathematics, Volume 3, P. Duren, Ed., pp.223-236, American Mathematical Society, 1989. Gian-Carlo Rota was born in Italy, where he went to school through the ninth grade. He attended high school in Quito, Ecuador, and entered Princeton University as a freshman in 1950. Three years later, he graduated summa cum laude and went to Yale, where he received a Ph.D. in 1956 with a thesis in functional analysis under the direction ofJ. T. Schwartz. After a position at Harvard, in 1959 he moved to MIT, where he is now professor of mathematics and philosophy. He has made basic contributions to operator theory, ergodic theory, and combinatorics. The AMS recently honored him with a Steele Prize for his seminal work in algebraic combinatorics. He is a senior fellow of the Los Alamos National Laboratory and a member of the National Academy of Sciences. Fine Hall in its golden age: Remembrances of Princeton in the early fifties* GIAN-CARLO ROTA [*The present article is a draft for a chapter of a book which the author is under contract to write for the Sloan science series. ]

95. Zygmunt William Birnbaum Papers - Special Collections, UW Libraries 5/77, Review of Enigmas of Chance, an Autobiography, by mark kac, 1987 5/80, Hugo Steinhaus A Reminiscence and a Tribute, by mark kac, 1974 http://www.lib.washington.edu/specialcoll/findaids/docs/uarchives/UA19_14_5266Bi

Archival Finding Aids Home Page University Archives Home Page Biographical Note Scope and Content ... Subject Terms Guide to the Zygmunt William Birnbaum Papers Record Group No. : Accession No. : Creator: Birnbaum, Zygmunt William, 1903-, creator Title: Zygmunt William Birnbaum Papers Date Span: Quantity: 6.9 cubic ft. (8 boxes, one oversize folder) Location : C2724e-2725e (boxes 1-8); T0643 (misc. oversize box 6) Languages: Collection materials are in English, with a significant portion of the collection in Polish and German, and some in French. Z.W. Birnbaum, 1958. Special Collections, UW Libraries, UW235260z Funding for encoding this finding aid was partially provided through a grant awarded by the National Endowment for the Humanities. Biographical Note Zygmunt William “Bill” Birnbaum (1903-2000), was for thirty-five years professor of mathematics and statistics at the University of Washington (1939-1974). Zygmunt William Birnbaum was born in Lw³w, Austria-Hungary, on October 18, 1903, to Ignacy and Lina Birnbaum. He attended grade and high schools (gymnasium) in Lw³w and Vienna, and then, in deference to his family's wishes that he pursue a "practical" degree, he obtained a master of law degree from the University of Lw³w in 1925. He practiced law for a year, but during that time he resumed his studies in mathematics. In 1926 Birnbaum received a teaching certificate in mathematics. He taught at a gymnasium in Lw³w from 1925 to 1929 while continuing his graduate studies in mathematics under Hugo Steinhaus and Stefan Banach, among others. He received his Ph.D. in 1929, with Steinhaus as his major professor.

96. SULAIR: Mathematical & Computer Sciences Library: The Undergraduate Collection AUTHOR kac, mark. TITLE Statistical independence in probability, analysis and number theory. IMPRINT np Mathematical Association of America; http://www-sul.stanford.edu/depts/mathcs/collections/undergraduate.html

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97. Edpa2000.html In 1956 mark kac introduced a probabilistic model of N interacting particles. The velocity distribution is governed by a markov semi group and the evolution http://www.math.sciences.univ-nantes.fr/edpa/2000/

Journées Équations aux dérivées partielles Nantes, 5-9 juin GDR 1151 CNRS ... Ses participants Résumés / Abstracts I. Jean-Marie Barbaroux, François Germinet, Serguei Tcheremchantsev (Université de Nantes) Quantum diffusion and generalized Rényi dimensions of spectral measures We estimate the spreading of the solution of the Schrödinger equation asymptotically in time, in term of the fractal properties of the associated spectral measures. For this, we exhibit a lower bound for the moments of order p at time T for the state defined by We show that this lower bound can be expressed in term of the generalized Rényi dimension of the spectral measure associated to the Hamiltonian H and the state . We especially concentrate on continuous models. II. T. Christiansen, M. S. Joshi (University of Missouri) Recovering Asymptotics at Infinity of Perturbations of Stratified Media We consider perturbations of a stratified medium , where the operator studied is . The function c is a perturbation of c y y c , we give results on the Fourier integral operator structure of the scattering matrix. Moreover, we show that we can recover the asymptotic expansion at infinity of

98. [math-ph/0109003] Determination Of The Spectral Gap For Kac's Master Equation An In particular, the method yields the exact spectral gap in a model due to mark kac of energy conserving collisions with one dimensional velocities. http://arxiv.org/abs/math-ph/0109003

Mathematical Physics, abstract math-ph/0109003 From: Michael Loss [ view email ] Date: Mon, 3 Sep 2001 16:04:33 GMT (43kb) Determination of the Spectral Gap for Kac's Master Equation and Related Stochastic Evolutions Authors: Eric A. Carlen Maria C. Carvalho Michael Loss Comments: Plain TeX, 49 pages Subj-class: Mathematical Physics We present a method for bounding, and in some cases computing, the spectral gap for systems of many particles evolving under the influence of a random collision mechanism. In particular, the method yields the exact spectral gap in a model due to Mark Kac of energy conserving collisions with one dimensional velocities. It is also sufficiently robust to provide qualitatively sharp bounds also in the case of more physically realistic momentum and energy conserving collisions in three dimensions, as well as a range of related models. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers?

99. The Rockefeller Archive Center - Record Group Descriptions Griffin, Donald R. Hartline, H. Keffer; Holmes, Francis O. *; Hotchkiss, Rollin O. Jacobs, Walter A. Jesaitis, Margaris A. kac, mark Kaiser, Emil T. http://archive.rockefeller.edu/collections/ru/rgdescriptions.php?printer=1

100. Scientific Heroes -- C. Villani In 1959 the great mathematician mark kac wrote ``Boltzmann summarized not (but not all) of This is mark kac, one of the most famous probabilists ever. http://www.umpa.ens-lyon.fr/~cvillani/solutions.html

This of course is Ludwig Boltzmann , one of the fathers of Statistical Mechanics. Among other contributions, Boltzmann had the idea of the famous formula for the entropy S=k log W , identified its counterpart in kinetic theory and proved that it can only increase in time along solutions of the Boltzmann equation: this is the H -Theorem. This was the first time that one had obtained a justification of the second principle of thermodynamics starting from the basic laws of physics. It is well-known that Boltzmann had to fight continuously about the relevance of his equation and its probabilistic interpretation, about his conclusions, and about the existence of atoms as well. Apparently he believed that we would never have direct evidence of atoms, although he was aware of Brownian motion. He was depressive and committed suicide in 1906, a few years before the atomic hypothesis became accepted by most people. Usually Boltzmann is represented with a long beard and a frigthening look, but I prefer this portrait of him as a young scientist. More information, as well as pictures (including one of his grave with the entropy formula on it) can be found here . Carlo Cercignani recently wrote a nice biography: Ludwig Boltzmann, The Man Who Trusted Atoms

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