(November 12-13)- Page 545
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Remembering Frank Harary
Discrete Mathematics Letters Discrete Math. Lett. 6 (2021) 1–7 www.dmlett.com DOI: 10.47443/dml.2021.s101 Editorial Remembering Frank Harary On March 11, 2005, at a special session of the 36th Southeastern International Conference on Combinatorics, Graph The- ory, and Computing held at Florida Atlantic University in Boca Raton, the famous mathematician Ralph Stanton, known for his work in combinatorics and founder of the Institute of Combinatorics and Its Applications, stated that the three mathematicians who had the greatest impact on modern graph theory have now all passed away. Stanton was referring to Frenchman Claude Berge of France, Canadian William Tutte, originally from England, and a third mathematician, an American, who had died only 66 days earlier and to whom this special session was being dedicated. Indeed, that day, March 11, 2005, would have been his 84th birthday. This third mathematician was Frank Harary. Let’s see what led Harary to be so recognized by Stanton. Frank Harary was born in New York City on March 11, 1921. He was the oldest child of Jewish immigrants from Syria and Russia. He earned a B.A. degree from Brooklyn College in 1941, spent a graduate year at Princeton University from 1943 to 1944 in theoretical physics, earned an M.A. degree from Brooklyn College in 1945, spent a year at New York University from 1945 to 1946 in applied mathematics, and then moved to the University of California at Berkeley, where he wrote his Ph.D. Thesis on The Structure of Boolean-like Rings, in 1949, under Alfred Foster. -
RM Calendar 2017
Rudi Mathematici x3 – 6’135x2 + 12’545’291 x – 8’550’637’845 = 0 www.rudimathematici.com 1 S (1803) Guglielmo Libri Carucci dalla Sommaja RM132 (1878) Agner Krarup Erlang Rudi Mathematici (1894) Satyendranath Bose RM168 (1912) Boris Gnedenko 1 2 M (1822) Rudolf Julius Emmanuel Clausius (1905) Lev Genrichovich Shnirelman (1938) Anatoly Samoilenko 3 T (1917) Yuri Alexeievich Mitropolsky January 4 W (1643) Isaac Newton RM071 5 T (1723) Nicole-Reine Etable de Labrière Lepaute (1838) Marie Ennemond Camille Jordan Putnam 2002, A1 (1871) Federigo Enriques RM084 Let k be a fixed positive integer. The n-th derivative of (1871) Gino Fano k k n+1 1/( x −1) has the form P n(x)/(x −1) where P n(x) is a 6 F (1807) Jozeph Mitza Petzval polynomial. Find P n(1). (1841) Rudolf Sturm 7 S (1871) Felix Edouard Justin Emile Borel A college football coach walked into the locker room (1907) Raymond Edward Alan Christopher Paley before a big game, looked at his star quarterback, and 8 S (1888) Richard Courant RM156 said, “You’re academically ineligible because you failed (1924) Paul Moritz Cohn your math mid-term. But we really need you today. I (1942) Stephen William Hawking talked to your math professor, and he said that if you 2 9 M (1864) Vladimir Adreievich Steklov can answer just one question correctly, then you can (1915) Mollie Orshansky play today. So, pay attention. I really need you to 10 T (1875) Issai Schur concentrate on the question I’m about to ask you.” (1905) Ruth Moufang “Okay, coach,” the player agreed. -
An Explicit Approach to Hypothesis H for Polynomials Over a Finite Field
AN EXPLICIT APPROACH TO HYPOTHESIS H FOR POLYNOMIALS OVER A FINITE FIELD PAUL POLLACK Abstract. Schinzel's Hypothesis H predicts that a family of irre- ducible polynomials over the integers satisfying certain necessary local conditions simultaneously assumes prime values in¯nitely of- ten. Here we consider an analogue of Hypothesis H for one-variable polynomials over the q-element ¯nite ¯eld Fq and show that it holds whenever q is large compared to the degree of the product of the polynomials involved. We also show that for ¯xed q, the conclu- sion of our Hypothesis H holds for \almost all" single-polynomial families. Along the way we propose a new polynomial analogue of the Hardy-Littlewood/Bateman-Horn conjectures. 1. Introduction 1.1. Hypothesis H: From Z[T ] to Fq[T ]. In 1854, Bouniakowsky [4] put forward a conjectural characterization of those polynomials over Z which assume in¯nitely many prime values. A century later, Schinzel (in a joint paper [22] with Sierpi¶nski)proposed the analogous conjecture for ¯nite families of integer polynomials; this conjecture, bearing the sadly nondescript title \Hypothesis H," contains (implicitly or more or less explicitly) many of the classical conjectures of number theory. In this article we investigate the following analogue of Hypothesis H for polynomials over a ¯nite ¯eld: Conjecture 1 (A function ¯eld analogue of Hypothesis H). Let f1(T ), ::: , fr(T ) be irreducible polynomials belonging to Fq[T ]. Suppose that there is no prime P 2 Fq[T ] for which every g(T ) 2 Fq[T ] satis¯es (1) f1(g(T )) ¢ ¢ ¢ fr(g(T )) ´ 0 (mod P ): Then the specializations f1(g(T )); : : : ; fr(g(T )) are simultaneously ir- reducible for in¯nitely many monic polynomials g(T ) 2 Fq[T ]. -
Decompositions and Graceful Labelings (Supplemental Material for Intro to Graph Theory)
Decompositions and Graceful Labelings (Supplemental Material for Intro to Graph Theory) Robert A. Beeler∗ December 17, 2015 1 Introduction A graph decomposition is a particular problem in the field of combinatorial designs (see Wallis [22] for more information on design theory). A graph decomposition of a graph H is a partition of the edge set of H. In this case, the graph H is called the host for the decomposition. Most graph decomposition problems are concerned with the case where every part of the partition is isomorphic to a single graph G. In this case, we refer to the graph G as the prototype for the decomposition. Further, we refer to the parts of the partition as blocks. As an example, consider the host graph Q3 as shown in Figure 1. In this case, we want to find a decomposition of Q3 into isomorphic copies of the path on three vertices, P3. We label the vertices of P3 as an ordered triple (a, b, c). where ab and bc are the edges of P3. The required blocks in the decompositions are (0, 2, 4), (1, 0, 6), (1, 3, 2), (1, 7, 5), (3, 5, 4), and (4, 6, 7). Usually, the goal of a combinatorial design is to determine whether the particular design is possible. The same is true for graph decompositions. Namely, given a host graph H and a prototype G, determine whether there exist a decomposition of H into isomorphic copies of G. Often, this is a difficult problem. In fact, there are entire books written on the subject (for ∗Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614-1700 USA email: [email protected] 1 2 0 1 2 3 4 5 6 7 Figure 1: A P3-decomposition of a Q3 example, see Bos´ak [1] and Diestel [5]). -
Mathematics Throughout the Ages. II
Mathematics throughout the ages. II Helena Durnová A history of discrete optimalization In: Eduard Fuchs (editor): Mathematics throughout the ages. II. (English). Praha: Výzkumné centrum pro dějiny vědy, 2004. pp. 51–184. Persistent URL: http://dml.cz/dmlcz/401175 Terms of use: © Jednota českých matematiků a fyziků Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz MATHEMATICS THROUGHOUT THE AGES II A History of Discrete Optimization Helena Durnová PRAGUE 2004 This is a Ph.D. thesis written under the supervision of Prof. Eduard Fuchs, defended at the Department of Mathematics of the Faculty of Science of Masaryk University in Brno on 24st May 2001. Contents 1 Introduction 57 1.1 Optimality and Mathematics . 58 1.2 GraphTheory......................... 64 1.3 ObjectivesoftheThesis . 69 2 Mathematical Background 71 2.1 Basic Definitions in Graph Theory . 71 2.1.1 Directed and undirected graphs . 71 2.1.2 Weighted graphs . 74 2.1.3 Description of graphs . 75 2.2 Algorithms, Heuristics, Complexity . 77 2.2.1 Algorithms and heuristics . 77 2.2.2 Complexity ...................... 78 3 Shortest Path Problem 81 3.1 SpecificBackground . 82 3.2 Origins and Development of Shortest Path Problems . 83 3.3 Early Shortest Path Algorithms . 85 3.3.1 Shimbel,1954. .. .. .. .. .. 85 3.3.2 G. B. -
Phillip Augustus Griffiths 1962 Princeton University
Pyung-Lyun Kang 1988 University of Pennsylvania Lakshmi Modali 1996 Syracuse University J. Travis Lee Tony Horowitz 2004 Syracuse University 1982 Brown University Nicolò Fontana Tartaglia Philip Joseph Lynn Steven P. Diaz 2006 Syracuse University 1982 Brown University Thomas Bleier 2011 Syracuse University Ostilio Ricci Seonja Kim Universita' di Brescia 1989 Seoul National University Seong Suk Park 2002 Seoul National University Changho Keem 1983 Brown University Galileo Galilei Young Rock Kim 1585 Università di Pisa Vittorio Perduca 2003 Seoul National University 2009 Università di Torino Antonella Grassi Colin Diemer 1990 Duke University 2010 University of Pennsylvania Dong-Kwan Shin Benedetto Castelli 1990 Duke University 1610 Università degli Studi di Padova Qi Zhang 1990 Duke University Yun-Gang Ye Evangelista Torricelli Marin Mersenne Nora Youngs 1991 Duke University Università di Roma La Sapienza 1611 Université de Paris 2014 University of Nebraska-Lincoln Yiannis Vlassopoulos Caitlyn Parmelee 1998 Duke University 2016 University of Nebraska-Lincoln Richard Paul Horja 1999 Duke University Christopher Austin Frederick Vincenzo Viviani Gilles Personne de Roberval 2008 Colorado State University Carina Curto David Robert Morrison 1642 Università di Pisa Elin Rose Smith 2005 Duke University 1980 Harvard University Russell Richins 2010 University of Utah 2010 Colorado State University Charlie Ronald Beil Justin D. Marks 2010 University of California, Santa Barbara Cheryl B. Percell Hwan Yong Lee 1989 Rice University 2010 University of -
Hodge Theory on Metric Spaces
Hodge Theory on Metric Spaces Laurent Bartholdi∗ Georg-August-Universit¨atG¨ottingen Deutschland Thomas Schick∗ Nat Smale Georg-August-Universit¨atG¨ottingen University of Utah Deutschland Steve Smaley City University of Hong Kong With an appendix by Anthony W. Baker z Mathematics and Computing Technology The Boeing Company. Last compiled December 1, 2009; last edited December 1, by LB Abstract Hodge theory is a beautiful synthesis of geometry, topology, and anal- ysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the math- ematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step towards understanding the geometry of vision. The appendix by Anthony Baker provides a separable, compact metric space with infinite dimensional α-scale homology. 1 Introduction Hodge Theory [21] studies the relationships of topology, functional analysis and geometry of a manifold. It extends the theory of the Laplacian on domains of Euclidean space or on a manifold. ∗email: [email protected] and [email protected] www: http://www.uni-math.gwdg.de/schick Laurent Bartholdi and Thomas Schick were partially supported by the Courant Research Center \Higher order structures in Mathematics" of the German Initiative of Excellence ySteve Smale was supported in part by the NSF, and the Toyota Technological Institute, Chicago zemail: [email protected] 1 2 Laurent Bartholdi, Thomas Schick, Nat Smale, Steve Smale However, there are a number of spaces, not manifolds, which could ben- efit from an extension of Hodge theory, and that is the motivation here. -
RM Calendar 2019
Rudi Mathematici x3 – 6’141 x2 + 12’569’843 x – 8’575’752’975 = 0 www.rudimathematici.com 1 T (1803) Guglielmo Libri Carucci dalla Sommaja RM132 (1878) Agner Krarup Erlang Rudi Mathematici (1894) Satyendranath Bose RM168 (1912) Boris Gnedenko 2 W (1822) Rudolf Julius Emmanuel Clausius (1905) Lev Genrichovich Shnirelman (1938) Anatoly Samoilenko 3 T (1917) Yuri Alexeievich Mitropolsky January 4 F (1643) Isaac Newton RM071 5 S (1723) Nicole-Reine Étable de Labrière Lepaute (1838) Marie Ennemond Camille Jordan Putnam 2004, A1 (1871) Federigo Enriques RM084 Basketball star Shanille O’Keal’s team statistician (1871) Gino Fano keeps track of the number, S( N), of successful free 6 S (1807) Jozeph Mitza Petzval throws she has made in her first N attempts of the (1841) Rudolf Sturm season. Early in the season, S( N) was less than 80% of 2 7 M (1871) Felix Edouard Justin Émile Borel N, but by the end of the season, S( N) was more than (1907) Raymond Edward Alan Christopher Paley 80% of N. Was there necessarily a moment in between 8 T (1888) Richard Courant RM156 when S( N) was exactly 80% of N? (1924) Paul Moritz Cohn (1942) Stephen William Hawking Vintage computer definitions 9 W (1864) Vladimir Adreievich Steklov Advanced User : A person who has managed to remove a (1915) Mollie Orshansky computer from its packing materials. 10 T (1875) Issai Schur (1905) Ruth Moufang Mathematical Jokes 11 F (1545) Guidobaldo del Monte RM120 In modern mathematics, algebra has become so (1707) Vincenzo Riccati important that numbers will soon only have symbolic (1734) Achille Pierre Dionis du Sejour meaning. -
An Interview with Martin Davis
Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Geometry Ramanujan‘s Lost Notebook An Introduction to Mathematical of the American Mathematical Society Selected Topics in Plane and Solid Part II Cryptography May 2008 Volume 55, Number 5 Geometry G. E. Andrews, Penn State University, University J. Hoffstein, J. Pipher, J. Silverman, Brown J. Aarts, Delft University of Technology, Park, PA, USA; B. C. Berndt, University of Illinois University, Providence, RI, USA Mediamatics, The Netherlands at Urbana, IL, USA This self-contained introduction to modern This is a book on Euclidean geometry that covers The “lost notebook” contains considerable cryptography emphasizes the mathematics the standard material in a completely new way, material on mock theta functions—undoubtedly behind the theory of public key cryptosystems while also introducing a number of new topics emanating from the last year of Ramanujan’s life. and digital signature schemes. The book focuses Interview with Martin Davis that would be suitable as a junior-senior level It should be emphasized that the material on on these key topics while developing the undergraduate textbook. The author does not mock theta functions is perhaps Ramanujan’s mathematical tools needed for the construction page 560 begin in the traditional manner with abstract deepest work more than half of the material in and security analysis of diverse cryptosystems. geometric axioms. Instead, he assumes the real the book is on q- series, including mock theta Only basic linear algebra is required of the numbers, and begins his treatment by functions; the remaining part deals with theta reader; techniques from algebra, number theory, introducing such modern concepts as a metric function identities, modular equations, and probability are introduced and developed as space, vector space notation, and groups, and incomplete elliptic integrals of the first kind and required. -
Coll032-Endmatter.Pdf
http://dx.doi.org/10.1090/coll/032 AMERICAN MATHEMATICAL SOCIETY COLLOQUIUM PUBLICATIONS VOLUME 32 Topology of Manifolds Raymond Louis Wilder American Mathematical Society Providence, Rhode Island International Standard Seria l Numbe r 0065-925 8 International Standar d Boo k Number 0-8218-1032- 4 Library o f Congress Catalog Card Numbe r 49-672 2 Copying an d reprinting . Individua l reader s o f thi s publication , an d nonprofi t librarie s actin g for them , ar e permitte d t o mak e fai r us e o f th e material , suc h a s t o cop y a chapte r fo r us e in teachin g o r research . Permissio n i s grante d t o quot e brie f passage s fro m thi s publicatio n i n reviews, provide d th e customary acknowledgmen t o f the source i s given. Republication, systematic copying, or multiple reproduction o f any material i n this publicatio n (including abstracts ) i s permitte d onl y unde r licens e fro m th e America n Mathematica l Society . Requests fo r suc h permissio n shoul d b e addresse d t o th e Assistan t t o th e Publisher , America n Mathematical Society , P.O . Bo x 6248 , Providence , Rhod e Islan d 02940-6248 . Request s ca n als o be mad e b y e-mail t o reprint-permissionQmath.ams.org . Copyright © 1949 , 196 3 by the American Mathematica l Societ y Revised edition, 196 3 Revised edition , fourt h printing , with corrections, 197 9 The America n Mathematica l Societ y retain s al l right s except thos e grante d to the United States Government . -
NPRC) VIP List, 2009
Description of document: National Archives National Personnel Records Center (NPRC) VIP list, 2009 Requested date: December 2007 Released date: March 2008 Posted date: 04-January-2010 Source of document: National Personnel Records Center Military Personnel Records 9700 Page Avenue St. Louis, MO 63132-5100 Note: NPRC staff has compiled a list of prominent persons whose military records files they hold. They call this their VIP Listing. You can ask for a copy of any of these files simply by submitting a Freedom of Information Act request to the address above. The governmentattic.org web site (“the site”) is noncommercial and free to the public. The site and materials made available on the site, such as this file, are for reference only. The governmentattic.org web site and its principals have made every effort to make this information as complete and as accurate as possible, however, there may be mistakes and omissions, both typographical and in content. The governmentattic.org web site and its principals shall have neither liability nor responsibility to any person or entity with respect to any loss or damage caused, or alleged to have been caused, directly or indirectly, by the information provided on the governmentattic.org web site or in this file. The public records published on the site were obtained from government agencies using proper legal channels. Each document is identified as to the source. Any concerns about the contents of the site should be directed to the agency originating the document in question. GovernmentAttic.org is not responsible for the contents of documents published on the website. -
CHSA HP2010.Pdf
The Hawai‘i Chinese: Their Experience and Identity Over Two Centuries 2 0 1 0 CHINESE AMERICA History&Perspectives thej O u r n a l O f T HE C H I n E s E H I s T O r I C a l s OCIET y O f a m E r I C a Chinese America History and PersPectives the Journal of the chinese Historical society of america 2010 Special issUe The hawai‘i Chinese Chinese Historical society of america with UCLA asian american studies center Chinese America: History & Perspectives – The Journal of the Chinese Historical Society of America The Hawai‘i Chinese chinese Historical society of america museum & learning center 965 clay street san francisco, california 94108 chsa.org copyright © 2010 chinese Historical society of america. all rights reserved. copyright of individual articles remains with the author(s). design by side By side studios, san francisco. Permission is granted for reproducing up to fifty copies of any one article for educa- tional Use as defined by thed igital millennium copyright act. to order additional copies or inquire about large-order discounts, see order form at back or email [email protected]. articles appearing in this journal are indexed in Historical Abstracts and America: History and Life. about the cover image: Hawai‘i chinese student alliance. courtesy of douglas d. l. chong. Contents Preface v Franklin Ng introdUction 1 the Hawai‘i chinese: their experience and identity over two centuries David Y. H. Wu and Harry J. Lamley Hawai‘i’s nam long 13 their Background and identity as a Zhongshan subgroup Douglas D.