DOCSLIB.ORG

The American Mathematical Society

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The American Mathematical Society AMERICAN MATHEMATICAL SOCIETY VOLUME 8, NUMBER 3 ISSUE NO. 54 JUNE 1961 THE AMERICAN MATHEMATICAL SOCIETY Edited by GORDON L. WALKER CONTENTS MEETINGS Calendar of Meetings ••••• , •• , • , • , ••• , • , ••••••••• , • , • , ••• , • 196 Program of the June Meeting in Seattle • • • • • • • • • • • • • • • • • • • • • • • • • • 197 Abstracts for the Meeting - pages 247-259 PRELIMINARY ANNOUNCEMENT OF MEETING. • • • • • • • • • • • • • • • • • • • • • • 204 ACTIVITIES OF OTHER ASSOCIATIONS • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 207 MATHEMATICS IN CONTINENTAL CHINA, 1949-1960- By Marshall Stone •••••• 209 FROM THE AMS SECRETARY •••••••••••••••••••••••••••••••••••• 216 NEWS ITEMS AND ANNOUNCEMENTS ••••••••••••••••••••••••••• 21.5,217 PERSONAL ITEMS •••••••••••••••••••••••••••••••••••••••••••• 223 LETTERS TO THE EDITOR ....................................... 226 MEMORANDA TO MEMBERS The Employment Register • • • • • • • • • • .. • • • • • • • • • • • • • • • • • • • • • • • 230 Reciprocity Agreement with the Edinburgh Mathematical Society •••••••• , 230 Addresses of Authors of Abstracts • • • • • • • • • • • • • • • • • • • • • • • • • • • • . 230 Retired Mathematicians Available for Employment • • • • • • • • • • • • • • • • • • 230 NEW PUBLICATIONS •••••••••••••••••••••••••••••••••••••••••• 231 CATALOG OF LECTURE NOTES •••••••••••••••••••••••••••••••••• 233 SUPPLEMENTARY PROGRAM Number 4. • • • • • • • • • • • • • • • • • • • • • . • • • • • 234 ABSTRACTS OF CONTRIBUTED PAPERS •••••••••••••••••••••••••••• 237 ERRATA ••••••••••••••••••••••••••••••••••••••• o......... 280 RESERVATIONS FORM •••••••••• o ••••••••••••••••••••••••••••• 287 MEETINGS CALENDAR OF MEETINGS Note: This Calendar lists all of the meetings which have been approved by the Council up to the date at which this issue of the NOTICES was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change. This is particularly true of the meetings to which no numbers have yet been assigned. Meet- Deadline ing Date Place for No. Abstracts* 582 August 2 9 - September 1, 1961 (66th Summer Meeting) Stillwater, Oklahoma July 14 583 October 28, 1961 Cambridge, Massachusetts Sept. 14 584 November 17-18, 1961 Milwaukee, Wisconsin Oct. 3 585 November 17-18, 1961 Gainesville, Florida Oct. 3 586 November 18, 1961 Santa Barbara, California Oct. 3 587 January, 22-26, 1962 Cincinnati, Ohio Nov. 17 (68th Annual Meeting) 588 February 22, 1962 New York, New York August 27-31, 1962 Vancouver, British Columbia (67th Summer Meeting) January 24-28, 1963 Berkeley, California (69th Annual Meeting) August 26-30, 1963 Boulder, Colorado (68th Summer Meeting) August, 1965 Ithaca, New Yorlc August, 1 966 New Brunswick, New Jersey * The abstracts of papers to be presented in person at the meetings must be received in the Head­ quarters Offices of the Society in Providence, Rhode Island, on or before these deadlines. The dead­ lines also apply to news items. The next two deadlines dates for by title abstracts are July 7, and September 7. The NOTICES of the American Mathematical Society is published by the Society seven times a year, in February, April, June, August, October, November, and December. Price per annual vol­ ume is $7.00. Price per copy, $2.00. Special price for copies sold at registration desks of meetings of the Society, $1.00 per copy. Subscriptions, orders for back numbers (none available before 1958), and inquiries should be addressed to the American Mathematical Society, 13 50 Main Street, Ann Arbor, Michigan, or to 190 Hope Street, Providence 6, Rhode Island. Second-class postage paid at Ann Arbor, Michigan. Authorization is granted under the author­ ity of the act of August 24, 1912, as amended by the act of August 4, 1947 (Sec. 34.21, P. L. and R.). Accepted for mailing at the special rate of postage provided for in section 34.40, paragraph (d). Olpyright © 1961 by the American Mathematical Society Printed in the Ulited States of America 196 Five Hundred Eighty-First Meeting University of Washington Seattle, Washington June 13-16, 1961 PROGRAM The five hundred eighty-first meeting Book Exhibits will be located in the lobby of the American Mathematical Society will of Bagley Hall. be held on Tuesday, Wednesday, Thursday A banquet will be held on Friday and Friday, June 13-16, 1961 at the Uni­ evening, costing approximately $3.00 per versity of Washington inSeattle, Washing­ person. There will be a Social Evening for ton. This meeting will be in conjunction members of any of the five mathematical with meetings of the Mathematical Asso­ organizations on Thursday from 9:00P.M. ciation of America on June 17, the Institute to 11:00 P.M. The location of this event of Mathematical Statistics on June 14-17, will be announced at registration time. A the Institute of Management Sciences on tea at the University of Washington Faculty June 16-17, and the American Statistical Club will be presented on Saturday from Association on June 14-15. For information 4:30 to 6:00 P.M. All persons attending the concerning the programs of the meetings meetings are cordially invited to these of these organizations, see the section on events. Activities of Other Associations, page 207 There are two hotels and one motel of these NOTICES. within walking distance of the campus: By invitation of the Committee to Hotel Edmund Meany, E. 45th and Brook­ Select Hour Speakers for Far Western lyn Avenue, $8.00 - $9.00 (single room), Sectional Meetings, and with the financial $9.50 - $12.50 (double room); Wilsonian support of the Air Force Office of Scienti­ Hotel, E. 47th and University Way, $5.00- fie Research, a Symposium on Convexity $6.00 (single room), $7.00 - $9.00 (double will be held on Tuesday, Wednesday and room); Coach House, 4701 24th North East, Thursday, June 13-15. $10.00 (one bedroom suite), $14.00 (two By invitation of the same Committee, bedroom suite). Hotel reservations should there will be an address at 2:00 P.M. on be sent directly to the chosen hotel, men­ Friday in Room 131, Bagley Hall, byPro­ tioning the mathematics meeting at the feasor T. M. Apostol of the California In­ University of Washington. stitute of Technology on "Some lattice Breakfast and lunch will be available point problems in the theory ofnumbers." Tuesday through Friday in the Cafeteria Sessions for contributed papers will of the Husky Union Building (HUB) on cam­ be held on Saturday at 9:00 A.M. and at pus, beginning at 8:15 A.M. Dinner will 3:30 P.M. Abstracts of the papers to be also be served on Wednesday and Thurs­ presented at these sessions appear on day from 5:00 to 6:30 P.M. Information pages 237- 280 of these NOTICES. There concerning restaurants in Seattle will be are cross references to the abstracts in available at the Registration Desk. the program. For example, the title of Seattle is served by United, Western, paper ( 1) in the program is followed by West Coast and Northwest Airlines, the (581-42) indicating that the abstract can be Northern Pacific, Union Pacific, Great found under the designation 581-42 among Northern and Milwaukee Railroads, and the the published abstracts. There will be a Greyhound and Continental Trailways Bus session for late papers on Friday after­ Lines. To get to the campus from the noon if necessary. Information concerning Seattle-Tacoma Airport, take the Air­ late papers will be available at the Regis­ porter Bus to the Olympic Hotel in down­ tration Desk. town Seattle. Then take a Seattle Transit All sessions of the meeting will be in bus, or a taxi (cost -- about $2.50) to the Bagley Hall. The Registration Desk and University district. Members who drive to 197 the meeting can park on campus for 25 Residence Halls, 1201 Campus Parkway, cents per day. Those who stay in the Men's can park there for 25 cents per day. PROGRAM OF THE SYMPOSIUM ON CONVEXITY The Organizing Committee for the Symposium consists of Professor Victor K1ee, Chairman, Pro­ fessor David Gale, Professor Branko Grunbaum, and Dr. Merle Andrew (member for liaison with the A.F .O.S.R.). All sessions of the Symposium will be held in Room 140, Bagley Hall. TUESDAY, 9:00 A.M. First Session. Chairman: Professor H. S. M. Coxeter 9:00 - 9:45 Problem on a circle Professor A. S. Besicovitch, University of Pennsylvania and Cambridge University 10:00 - 10:45 Various notions of convexity for functions defined on matrix spaces Dr. Chandler Davis, American Mathematical Society ,Providence, Rhode Island 11:00 - 11:45 The dual cone and Helly type theorems Professor F. A. Valentine, University of California, Los Angeles TUESDAY, 1:30 P.M. Second Session, Chairman: Professor A. S. Besicovitch 1:30 - 2:15 Helly's theorem and its relatives Professor Ludwig Danzer, University of Washington and Univer­ sity of Munich 2:30 - 3:15 An upper bound for the number of equal nonoverlapping spheres that can touch another of the same size Professor H. S.M. Coxeter, University of Toronto 3:30- 4:15 Measures of asymmetry for convex sets Professor Branko Grunbaum, University of Washington and The Hebrew University, Jerusalem 4:30 - 5:15 Closedness under a set of linear combinations Professor T. S. Motzkin, University of California, Los Angeles WEDNESDAY, 9:00 A.M. Third Session. Chairman: Professor T. S. Motzkin 9:00 - 9:45 Cyclic and neighborly polytopes Professor David Gale, Brown University 10:00 - 10:45 Simplifications of linear programs Dr. Alan Hoffman, General Electric
Load more

Recommended publications
  • Lajos Takacs and His Work
    Yournal of Applied Mathematics and Stochastic Analysis 7, Number 3, 1994, 215-237 LAJOS TAKACS AND HIS WORK JEWGENI H. DSHALALOW Department of Applied Mathematics Florida Institute of Technology Melbourne, FL 32901, U.S.A. RYSZARD SYSKI Department of Mathematics University of Maryland College Park, MD 2072 (Received May, 1994; revised October, 1994) ABSTRACT This paper, written in honor of the 70th birthday of Lajos Takcs, addresses his life and work, and includes some personal observations and appreciation of his contributions. In particular, it includes a short biography, an informal discussion of some of his major research areas (queueing, fluctuations, waiting time proces- ses, and random rooted trees), and an account of the relationship of his work to that of F(lix Pollaczek. Key words: Lajos Takcs, fluctuations, queueing, semi-Markov processes, bi- nomial moments, M/G/i, GI/G/1, multi-server queues, Banach algebras, Takhcs process, Lindley integral equation, random rooted trees, random graphs. AMS (MOS) subject classifications: Primary: 01A70; Secondary: 60G50, 60G55, 60J15, 60K05, 60K15, 60K25, 90B22. 1. Biographical Sketches of Lajos Takcs 1.1 Introduction In the second half of 1994, many scientific institutions (including the Institute of Mathemati- cal Statistics, Operations Research Society of America, The Institute of Management Sciences, and Hungarian Academy of Sciences) celebrated Lajos Takcs' 70th birthday, which took place on August 21, 1994. In addition, a special volume, Studies in Applied Probability (31A of YAP, sec reference [B], edited by J. Galambos and J. Gani), appeared in the first half of 1994 honoring Professor Takcs. The authors of this paper were happy to participate in this honorable event by contributing a few essays on Lajos Takcs life and work, which at least in part complement the fine articles by Bingham [2] and Takcs [Tak, 183] himself.
    [Show full text]
  • Strength in Numbers: the Rising of Academic Statistics Departments In
    Agresti · Meng Agresti Eds. Alan Agresti · Xiao-Li Meng Editors Strength in Numbers: The Rising of Academic Statistics DepartmentsStatistics in the U.S. Rising of Academic The in Numbers: Strength Statistics Departments in the U.S. Strength in Numbers: The Rising of Academic Statistics Departments in the U.S. Alan Agresti • Xiao-Li Meng Editors Strength in Numbers: The Rising of Academic Statistics Departments in the U.S. 123 Editors Alan Agresti Xiao-Li Meng Department of Statistics Department of Statistics University of Florida Harvard University Gainesville, FL Cambridge, MA USA USA ISBN 978-1-4614-3648-5 ISBN 978-1-4614-3649-2 (eBook) DOI 10.1007/978-1-4614-3649-2 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012942702 Ó Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer.
    [Show full text]
  • 13Th International Workshop on Matrices and Statistics Program And
    13th International Workshop on Matrices and Statistics B¸edlewo, Poland August 18–21, 2004 Program and abstracts Organizers • Stefan Banach International Mathematical Center, Warsaw • Committee of Mathematics of the Polish Academy of Sciences, Warsaw • Faculty of Mathematics and Computer Science, Adam Mickiewicz Uni- versity, Pozna´n • Institute of Socio-Economic Geography and Spatial Management, Faculty of Geography and Geology, Adam Mickiewicz University, Pozna´n • Department of Mathematical and Statistical Methods, Agricultural Uni- versity, Pozna´n This meeting has been endorsed by the International Linear Algebra Society. II Sponsors of the 13th International Workshop on Matrices and Statistics III Mathematical Research and Conference Center in B¸edlewo IV edited by A. Markiewicz Department of Mathematical and Statistical Methods, Agricultural University, Pozna´n,Poland and W. Wo ly´nski Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Pozna´n,Poland Contents Part I. Introduction Poetical Licence The New Intellectual Aristocracy ............ 3 Richard William Farebrother Part II. Local Information Part III. Program Part IV. Ingram Olkin Ingram Olkin, Statistical Statesman .......................... 21 Yadolah Dodge Why is matrix analysis part of the statistics curriculum ...... 25 Ingram Olkin A brief biography and appreciation of Ingram Olkin .......... 31 A conversation with Ingram Olkin ............................ 34 Bibliography .................................................. 58 Part V. Abstracts Asymptotic
    [Show full text]
  • Obituary: FELIX POLLACZEK Felix Pollaczek Was Born on 1 December
    Obituary: FELIX POLLACZEK Felix Pollaczek was born on 1 December 1892 in Vienna, Austria; he was the descendant of a well-known mid-European Jewish family which for several centuries had counted many learned men amongst its members. He became a Frenchman by naturalization in 1947. He obtained his scientific education and training at the Latin grammar school of Vienna, and at the Technical Univer- sities of Vienna and Brno (Czechoslovakia); he later studied mathematics at the University of Berlin. A master's degree in electrical engineering in 1920 from Brno was followed by a doctoral degree in mathematics in 1922 from Berlin with a thesis on number theory. This was concerned with the fields generated by the Ith and 12th roots of one, I being an irregular prime number. His first paper, on number theory, dates from 1917. He was employed in 1921 as an engineer by A.E.G. in Berlin. Then, in 1923, he became scientific adviser to the German Postal, Telephone and Telegraph Services at Reichspost-Zentralamt Berlin-Tempelhof. As a result of the political situation in Germany in 1933, he was dismissed from his post and then left the country. In Paris he made his living as a consulting engineer for the Societe d'Etudes pour Liaisons Telephoniques et Telegraphiques. In 1939-1940 and again from 1944 on, he held the position of Maitre de Recherches at the Centre National de la Recherche Scientifique in Paris. Felix Pollaczek's fruitful life came to an end on 29 April 1981 at Boulogne- Billancourt. In 1977 Pollaczek was awarded the John von Neumann Theory Prize by the ORSA-TIMS prize committee.
    [Show full text]
  • Mathematicians Fleeing from Nazi Germany
    Mathematicians Fleeing from Nazi Germany Mathematicians Fleeing from Nazi Germany Individual Fates and Global Impact Reinhard Siegmund-Schultze princeton university press princeton and oxford Copyright 2009 © by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved Library of Congress Cataloging-in-Publication Data Siegmund-Schultze, R. (Reinhard) Mathematicians fleeing from Nazi Germany: individual fates and global impact / Reinhard Siegmund-Schultze. p. cm. Includes bibliographical references and index. ISBN 978-0-691-12593-0 (cloth) — ISBN 978-0-691-14041-4 (pbk.) 1. Mathematicians—Germany—History—20th century. 2. Mathematicians— United States—History—20th century. 3. Mathematicians—Germany—Biography. 4. Mathematicians—United States—Biography. 5. World War, 1939–1945— Refuges—Germany. 6. Germany—Emigration and immigration—History—1933–1945. 7. Germans—United States—History—20th century. 8. Immigrants—United States—History—20th century. 9. Mathematics—Germany—History—20th century. 10. Mathematics—United States—History—20th century. I. Title. QA27.G4S53 2008 510.09'04—dc22 2008048855 British Library Cataloging-in-Publication Data is available This book has been composed in Sabon Printed on acid-free paper. ∞ press.princeton.edu Printed in the United States of America 10 987654321 Contents List of Figures and Tables xiii Preface xvii Chapter 1 The Terms “German-Speaking Mathematician,” “Forced,” and“Voluntary Emigration” 1 Chapter 2 The Notion of “Mathematician” Plus Quantitative Figures on Persecution 13 Chapter 3 Early Emigration 30 3.1. The Push-Factor 32 3.2. The Pull-Factor 36 3.D.
    [Show full text]
  • A Class of Null Sets Associated with Convex Functions on Banach Spaces
    BULL. AUSTRAL. MATH. SOC. 26E15, 28AO5, 46B20, 46GO5 VOL. 42 (1990) [315-322] A CLASS OF NULL SETS ASSOCIATED WITH CONVEX FUNCTIONS ON BANACH SPACES JOHN RAINWATER A generalisation of the notion of "sets of measure zero" for arbitrary Banach spaces is defined so that continuous convex functions are automatically Gateaux differen- tiable "almost everywhere". It is then shown that this class of sets satisfies all the properties that one expects of sets of measure zero. Moreover (in a certain large class of Banach spaces, at least) nonempty open sets are not of "measure zero". There are several different substitutes for sets of measure zero in infinite dimen- sional spaces (where tr-finite translation invariant measures do not exist); see, for in- stance, [1, 3, 5, 6]. These have all been defined in separable Banach spaces and have generally been motivated by theorems which assert that locally Lipschitzian maps are Gateaux differentiable "almost everywhere", where the latter means "outside of a null set". In what follows we define a new class of null sets in arbitrary Banach spaces, with the motivation being Gateaux differentiability of convex functions. DEFINITIONS: Let / be a real-valued continuous convex function defined on a real Banach space E. We denote by N(f) the set of all points x £ E where / fails to be Gateaux differentiable. That is, for some y € E, the limit (1) [f( + y)f()] fails to exist. By a null set we mean any subset of M[f), for some / as above. This definition changes the focus of attention from functions to sets: rather than attempting to show that convex continuous (hence locally Lipschitzian) functions are Gateaux differentiable almost everywhere (with respect to some given class of null sets), this property is guaranteed by the very definition of "null set".
    [Show full text]
  • Geometrical Implications of Upper Semi-Continuity of the Duality Mapping on a Banach Space
    Pacific Journal of Mathematics GEOMETRICAL IMPLICATIONS OF UPPER SEMI-CONTINUITY OF THE DUALITY MAPPING ON A BANACH SPACE JOHN R. GILES,DAVID ALLAN GREGORY AND BRAILEY SIMS Vol. 79, No. 1 May 1978 PACIFIC JOURNAL OF MATHEMATICS Vol. 79, No. 1, 1978 GEOMETRICAL IMPLICATIONS OF UPPER SEMI-CONTINUITY OF THE DUALITY MAPPING ON A BANACH SPACE J. R. GILES, D. A. GREGORY AND BRAILEY SIMS For the duality mapping on a Banach space the relation between lower semi-continuity and upper semi-continuity properties is explored, upper semi-continuity is characterized in terms of slices of the ball and upper semi-continuity properties are related to geometrical properties which imply that the space is an Asplund space. The duality mapping is a natural set-valued mapping from the unit sphere of a normed linear space into subsets of its dual sphere, and which for an inner product space is the mapping associating an element of the unit sphere with the corresponding continuous linear functional given by the inner product. It is an example of a sub- differential mapping of a continuous convex function (in this case, the norm), which is in turn a special kind of maximal monotone mapping. Cudia [4, p. 298] showed that the duality mapping is always upper semi-continuous when the space has the norm and the dual space has the weak* topology, and Kenderov [10, p. 67] extended this to maximal monotone mappings. Bonsall, Cain, and Schneider [3] used the property to prove the connectedness of the numerical range of an operator on a normed linear space.
    [Show full text]
  • PREFACE in Honor and Memory Of
    Available at http://pvamu.edu/aam Applications and Appl. Appl. Math. Applied Mathematics: ISSN: 1932-9466 An International Journal (AAM) Vol. 10, Issue 2 (December 2015), pp. 634 - 666 PREFACE In Honor and Memory of Professor Lajos Takács August 21, 1924 - December 4, 2015 Professor Emeritus of Mathematics & Statistics Case Western Reserve University, Cleveland, Ohio, USA & An elected member of the Hungarian Academy of Sciences A World Leading Mathematician, a Pioneer in the field of Queueing Theory, Author of 225 Original Papers and three clelbrated volumes in English language: Introduction to the Theory of Queues Combinatorial Methods in the Theory of Stochastic Processes Stochastic Processes, Problems and Solutions 634 AAM: Intern. J., Vol. 10, Issue 2 (December 2015) Preface 635 This issue of AAM is dedicated to honoring and remembering Professor Lajos Takács. While wrapping up the manuscript of my book (co-authored by Dr. Dimitar Mishev): Delayed and Network Queues, I went back to celebrate his 1962 book, Introduction to the Theory of Queues, where he gives an example illustrating a waiting time paradox, where the waiting time of a passenger waiting for a bus at a bus stop is infinite, while, in reality, he will wait a finite unit of time before a bus arrive. I sent Professor Takács an e-mail on December 4, 2015, inquiring if he had come up with a solution to resolve this paradox. In response, I received an e-mail from Dalma, his wife, that broke down me to tears by the sad news she broke that he passed away on the day I sent my e-mail.
    [Show full text]
  • Gazette 31 Vol 3
    Volume 31 Number 5 2004 283 Editorial 284 President’s column M. Cowling 285 Math matters P. Taylor 288 Mathellaneous N. Do 295 The 8th problem A. Molev 298 The 48th annual meeting of the Australian Mathematical Society 301 Acceptance speech on the award of the George Szekeres medal B. Anderssen 309 Obituary S. Fitzpatrick C. Praeger 311 ICMI Study 16: Challenging mathematics in and beyond the classroom P. Taylor 314 Higher degrees and honours bachelor degrees in mathematics and statistics completed in Australia in 2003 P. Johnston 320 A mathematician goes to hospital T. Mills 328 Wallis sequence estimated through the Euler-Maclarin formula: even from the Wallis product π could be computed fairly accurately V. Lampret 340 More terms of the asymptotic solution of a difference equation consid- ered by Ramanujan H. Prodinger 342 Book reviews 351 News 359 AustMS bulletin board Often, we mathematicians are asked that dreaded question: “What is it you actually do all day?” A few of us are perhaps brave (or is it foolish?) enough to respond with an exposition on elliptic curves, homotopy theory, pde’s or Markov processes, but most of us will give a deep sigh, look sheepish, and begin to stutter “Uhhhhh . , well . , hmmm . , you see . ,” to finally blurt out in what seems like a super-human effort, “It is kind of complicated,” hoping this will satisfy our inquisitor. Perhaps a reasonable response would be to explain that mathematics is much like art or music, with ‘beautiful theorems’, ‘amazing proofs’ and ‘stunning conjectures’, but that unfortunately the wonderland of mathematics can only be fully appreciated by those initiated into the art.
    [Show full text]
  • Chapter 6 the Brézis-Browder Ordering Principle and Its Applications
    Chapter 6 The Brézis-Browder Ordering Principle and its Applications This chapter is based on a basic optimization theorem, namely, the Brézis-Browder Ordering Principle, which can be established using only the rudiments of order theory. Loosely speaking, this result identi…es a large collection of preordered sets on which, starting from anywhere, we can construct an increasing sequence that leads us to a point beyond which the value of an order-preserving real function cannot increase. As we shall see, this principle, and its generalizations, serve to unify various results of nonlinear analysis on …xed point theory and optimization. It is thus a brilliant illustration of how order theory may serve when dealing with problems that have, at face value, little to do with preorders. Put speci…cally, we begin this chapter by introducing the Brézis-Browder Ordering Principle, and then consider one of its important generalizations, namely, Altman’sOr- dering Principle. The major part of the chapter is, however, concerned with “using” these optimization theorems within the broad context of nonlinear analysis. In partic- ular, we use here Altman’sOrdering Principle to deduce a number of important metric …xed point theorems, each generalizing the all important Contraction Mapping Theorem in di¤erent ways. We then move on to optimization theory, and use the Brézis-Browder Ordering Principle to deduce the Ekeland Variational Principle, a pillar of nonlinear analysis. We conclude the present chapter with another application, this time to con- vex analysis, by proving the fundamental Bishop-Phelps Theorem on the denseness of support points of a closed convex set in its boundary.
    [Show full text]
  • Matical Society Was Held at the University of Washington in Seattle, Washington, on Tuesday, Wednesday, Thursday, and Friday, June 13-16, 1961
    THE JUNE MEETING IN SEATTLE The five hundred eighty-first meeting of the American Mathe­ matical Society was held at the University of Washington in Seattle, Washington, on Tuesday, Wednesday, Thursday, and Friday, June 13-16, 1961. There were 447 registrants at this meeting, 238 of whom were members of the Society. This meeting wras held in con­ junction with meetings of the Institute of Mathematical Statistics, the American Statistical Association, the Biométrie Society, the Institute of Management Sciences, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics. By invitation of the Committee to Select Hour Speakers for Far Western Sectional Meetings, and sponsored by the Society with the financial aid of the Air Force Office of Scientific Research, a Sym­ posium on Convexity was held on Tuesday, Wednesday, and Thurs­ day. The program committee for this symposium consisted of Profes­ sor V. L. Klee, Chairman, Professor David Gale, Professor Branko Grünbaum, and Dr. Merle Andrew. The chairmen of the six sessions of the Symposium were Professors H. S. M. Coxeter, A. S. Besico- vitch, T. S. Motzkin, Vlastimil Ptâk, Mahlon Day, and Ky Fan. The following addresses were presented at these sessions: Problem on a circle, Professor A. S. Besicovitch, University of Pennsylvania, and Cambridge University; Various notions of convexity f or functions de­ fined on matrix spaces, Dr. Chandler Davis, American Mathematical Society, Providence, Rhode Island; The dual cone and Kelly type theo­ rems, Professor F. A. Valentine, University of California, Los Angeles; Hetty's theorem and its relatives, Professor Ludwig Danzer, University of Washington and University of Munich; An upper bound for the number of equal nonoverlapping spheres that can touch another of the same size, Professor H.
    [Show full text]
  • UC Berkeley Electronic Theses and Dissertations
    UC Berkeley UC Berkeley Electronic Theses and Dissertations Title Suburbs of Last Resort: Landscape, Life, and Ruin on the Edges of San Francisco Bay Permalink https://escholarship.org/uc/item/6c87q28k Author Ekman, Peter Publication Date 2016 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California Suburbs of Last Resort: Landscape, Life, and Ruin on the Edges of San Francisco Bay by Peter Sheldon Read Ekman A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Geography in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Emeritus Paul Groth, Chair Associate Professor Jake Kosek Professor Louise Mozingo Fall 2016 Abstract Suburbs of Last Resort: Landscape, Life, and Ruin on the Edges of San Francisco Bay by Peter Sheldon Read Ekman Doctor of Philosophy in Geography University of California, Berkeley Professor Emeritus Paul Groth, Chair This study surveys the historical geography of suburban landscapes built and abandoned over the course of the United States’ long twentieth century. Diverse thinkers and actors, it shows, have understood the edges of the American metropolis to be laboratories of a sort, experimental sites where the forms of a reordered city might be glimpsed in microcosm and put on display. Suburbs have also served as laboratories where questions of landscape’s animacy — not what landscape means, the focus of a generation of scholarship in cultural geography, but what landscape does — came vividly to the fore, provoking much debate and speculation. Drawing on archival sources, visual materials, maps, plans, and field study of the built environment, this work recasts debates that have long been central to cultural geography, geographic thought, urban and suburban studies, and the intellectual histories of planning and urbanism.
    [Show full text]