Meetings of the MAA Ken Ross and Jim Tattersall
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View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Caltech Authors PROOF OF THE STRONG SCOTT CONJECTURE FOR CHANDRASEKHAR ATOMS RUPERT L. FRANK, KONSTANTIN MERZ, HEINZ SIEDENTOP, AND BARRY SIMON Dedicated to Yakov Sinai on the occasion of his 85th birthday. Abstract. We consider a large neutral atom of atomic number Z, taking rel- ativistic effects into account by assuming the dispersion relation pc2p2 + c4. We study the behavior of the one-particle ground state density on the length scale Z−1 in the limit Z; c ! 1 keeping Z=c fixed and find that the spher- ically averaged density as well as all individual angular momentum densities separately converge to the relativistic hydrogenic ones. This proves the gen- eralization of the strong Scott conjecture for relativistic atoms and shows, in particular, that relativistic effects occur close to the nucleus. Along the way we prove upper bounds on the relativistic hydrogenic density. 1. Introduction 1.1. Some results on large Z-atoms. The asymptotic behavior of the ground state energy and the ground state density of atoms with large atomic number Z have been studied in detail in non-relativistic quantum mechanics. Soon after the advent of quantum mechanics it became clear that the non- relativistic quantum multi-particle problem is not analytically solvable and of in- creasing challenge with large particle number. This problem was addressed by Thomas [51] and Fermi [11, 12] by developing what was called the statistical model of the atom. The model is described by the so-called Thomas{Fermi functional (Lenz [28]) Z ZZ TF 3 5=3 Z 1 ρ(x)ρ(y) (1) EZ (ρ) := 10 γTFρ(x) − ρ(x) dx + dx dy ; 3 jxj 2 3 3 jx − yj R R ×R | {z } =:D[ρ] 2 2=3 where γTF = (6π =q) is a positive constant depending on the number q of spin states per electron, i.e., physically 2. -
Northeastern Section Newsletter Fall 2007
1 NORTHEASTERN SECTION NEWSLETTER FALL 2007 Volume 29 Number 2 Web Page: http:/www.maa.org/northeastern Webmaster: Tommy Ratliff, Wheaton College 2 EXECUTIVE COMMITTEE CHAIR: GOVERNOR Tommy Ratliff Ockle Johnson Department of Mathematics Department of Mathematics and Computer Science Keene State College Wheaton College Keene, NH 03435-2001 Norton, MA 02766 (603)358-2585 (508)286-3968 [email protected] [email protected] PAST CHAIR CHAIR-ELECT Sarah L. Mabrouk Jason J. Moliterno Department of Mathematics Department of Mathematics Framingham State College Academic Building SC 207 100 State Street, PO Box 9101 Sacred Heart University Framingham, MA 01701-9101 5151 Park Avenue (508)626-4785 Fairfield, CT 06825 [email protected] (203)396-8324 [email protected] SECRETARY-TREASURER TWO-YEAR COLLEGE REP. Ann Kizanis Lois Martin Mathmatics Department Mathematics Department Western New England College Massasoit Community CollegeSpringfield, MA 01119 Brockton, MA 02302 (413)782-1784 (508)588-9100, x 1621 [email protected] [email protected] NEWSLETTER EDITOR Frank Ford Department of Mathematics/CS Providence College Providence, RI 02918 (401)865-2635 [email protected] 2 NEXT SECTION MEETING November 16 and 17, 2007 Fall Section Meeting Framingham State College, Framingham, MA Program Chair: Sarah Mabrouk, Framingham State College Local Chair: Sarah Mabrouk, Framingham State College FUTURE SECTION MEETINGS May 30 and 31, 2008 Spring Section Meeting St. Michael’s College, Colchester, VT Fall 2008 Bentley College, Waltham, -
The Association for Women in Mathematics: How and Why It Was
Mathematical Communities t’s 2011 and the Association for Women in Mathematics The Association (AWM) is celebrating 40 years of supporting and II promoting female students, teachers, and researchers. It’s a joyous occasion filled with good food, warm for Women conversation, and great mathematics—four plenary lectures and eighteen special sessions. There’s even a song for the conference, titled ‘‘((3 + 1) 9 3 + 1) 9 3 + 1 Anniversary in Mathematics: How of the AWM’’ and sung (robustly!) to the tune of ‘‘This Land is Your Land’’ [ICERM 2011]. The spirit of community and and Why It Was the beautiful mathematics on display during ‘‘40 Years and Counting: AWM’s Celebration of Women in Mathematics’’ are truly a triumph for the organization and for women in Founded, and Why mathematics. It’s Still Needed in the 21st Century SARAH J. GREENWALD,ANNE M. LEGGETT, AND JILL E. THOMLEY This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of ‘‘mathematical community’’ is Participants from the Special Session in Number Theory at the broadest: ‘‘schools’’ of mathematics, circles of AWM’s 40th Anniversary Celebration. Back row: Cristina Ballantine, Melanie Matchett Wood, Jackie Anderson, Alina correspondence, mathematical societies, student Bucur, Ekin Ozman, Adriana Salerno, Laura Hall-Seelig, Li-Mei organizations, extra-curricular educational activities Lim, Michelle Manes, Kristin Lauter; Middle row: Brooke Feigon, Jessica Libertini-Mikhaylov, Jen Balakrishnan, Renate (math camps, math museums, math clubs), and more. Scheidler; Front row: Lola Thompson, Hatice Sahinoglu, Bianca Viray, Alice Silverberg, Nadia Heninger. (Photo Cour- What we say about the communities is just as tesy of Kiran Kedlaya.) unrestricted. -
LA/MS MAA Newsletter
Mathematical Association of America Newsletter Winter 2001/2002 Volume 24, No. 2 Executive Committee 2001-2002 Chair: Frank Serio, Northwestern State University of Louisiana [email protected] (318) 357-4308 Mississippi Vice Chair/Internet Coordinator: John Travis, Mississippi College [email protected] (601) 925-3817 Louisiana Vice Chair: Judith Covington, Louisiana State University- Shreveport [email protected] 318-797-5354 Secretary/Treasurer: Leigh Ann Myers, Northwestern State University of Louisiana [email protected] (318) 357-4308 Newsletter Editor: Bonnie Oppenheimer, Mississippi University for Women [email protected] (662) 329-7239 Immediate Past Chair: Gerard Buskes, University of Mississippi [email protected] (662) 915-7425 Section Governor: Connie Campbell, Millsaps, [email protected] (601) 974-1371 Section Info on the Web http://www.mc.edu/campus/users/travis/maa/ Past newsletter as well as an electronic version of this one: http://www.mc.edu/campus/users/travis/maa/newsletters/index.html SPRING 2002 MEETING INFORMATION 1 of 11 Dates for the Spring 2002 LA-MS Section meeting are March1-2, 2002.Northwestern State University of Louisiana, under the direction of Section Chair Frank Serio, will be the hosting institution.A registration form, Call for Papers, and Hotel Information for the meeting in Natchitoches, Louisiana, is available on our section web site: http://www.mc.edu/campus/users/travis/maa/.A registration form and tentative schedule are included in this printed version of the newsletter. Section Chair’s Report Frank Serio It has been an honor to serve as your Chair for the past year. Planning the spring sectional meeting has been a rewarding task. -
BERNOULLI NEWS, Vol 24 No 1 (2017)
Vol. 24 (1), May 2017 Published twice per year by the Bernoulli Society ISSN 1360–6727 CONTENTS News from the Bernoulli Society p. 1 Awards and Prizes p. 2 New Executive Members A VIEW FROM THE PRESIDENT in the Bernoulli Society Dear Members of the Bernoulli Society, p. 3 As we all seem to agree, the role and image of statistics has changed dramatically. Still, it takes ones breath when realizing the huge challenges ahead. Articles and Letters Statistics has not always been considered as being very necessary. In 1848 the Dutch On Bayesian Measures of Ministry of Home Affairs established an ofŮice of statistics. And then, thirty years later Uncertainty in Large or InŮinite minister Kappeyne van de Coppelo abolishes the “superŮluous” ofŮice. The ofŮice was Dimensional Models p. 4 quite rightly put back in place in 1899, as “Centraal Bureau voor de Statistiek” (CBS). Statistics at the CBS has evolved from “simple” counting to an art requiring a broad range On the Probability of Co-primality of competences. Of course counting remains important. For example the CBS reports in of two Natural Numbers Chosen February 2017 that almost 1 out of 4 people entitled to vote in the Netherlands is over the at Random p. 7 age of 65. But clearly, knowing this generates questions. What is the inŮluence of this on the outcome of the elections? This calls for more data. Demographic data are combined with survey data and nowadays also with data from other sources, in part to release the “survey pressure” that Ůirms and individuals are facing. -
The Meaning of Probability
CHAPTER 2 THE MEANING OF PROBABILITY INTRODUCTION by Glenn Shafer The meaning of probability has been debated since the mathematical theory of probability was formulated in the late 1600s. The five articles in this section have been selected to provide perspective on the history and present state of this debate. Mathematical statistics provided the main arena for debating the meaning of probability during the nineteenth and early twentieth centuries. The debate was conducted mainly between two camps, the subjectivists and the frequentists. The subjectivists contended that the probability of an event is the degree to which someone believes it, as indicated by their willingness to bet or take other actions. The frequentists contended that probability of an event is the frequency with which it occurs. Leonard J. Savage (1917-1971), the author of our first article, was an influential subjectivist. Bradley Efron, the author of our second article, is a leading contemporary frequentist. A newer debate, dating only from the 1950s and conducted more by psychologists and economists than by statisticians, has been concerned with whether the rules of probability are descriptive of human behavior or instead normative for human and machine reasoning. This debate has inspired empirical studies of the ways people violate the rules. In our third article, Amos Tversky and Daniel Kahneman report on some of the results of these studies. In our fourth article, Amos Tversky and I propose that we resolve both debates by formalizing a constructive interpretation of probability. According to this interpretation, probabilities are degrees of belief deliberately constructed and adopted on the basis of evidence, and frequencies are only one among many types of evidence. -
Transactions American Mathematical Society
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY EDITED BY A. A. ALBERT OSCAR ZARISKI ANTONI ZYGMUND WITH THE COOPERATION OF RICHARD BRAUER NELSON DUNFORD WILLIAM FELLER G. A. HEDLUND NATHAN JACOBSON IRVING KAPLANSKY S. C. KLEENE M. S. KNEBELMAN SAUNDERS MacLANE C. B. MORREY W. T. REID O. F. G. SCHILLING N. E. STEENROD J. J. STOKER D. J. STRUIK HASSLER WHITNEY R. L. WILDER VOLUME 62 JULY TO DECEMBER 1947 PUBLISHED BY THE SOCIETY MENASHA, WIS., AND NEW YORK 1947 Reprinted with the permission of The American Mathematical Society Johnson Reprint Corporation Johnson Reprint Company Limited 111 Fifth Avenue, New York, N. Y. 10003 Berkeley Square House, London, W. 1 First reprinting, 1964, Johnson Reprint Corporation PRINTED IN THE UNITED STATES OF AMERICA TABLE OF CONTENTS VOLUME 62, JULY TO DECEMBER, 1947 Arens, R. F., and Kelley, J. L. Characterizations of the space of con- tinuous functions over a compact Hausdorff space. 499 Baer, R. Direct decompositions. 62 Bellman, R. On the boundedness of solutions of nonlinear differential and difference equations. 357 Bergman, S. Two-dimensional subsonic flows of a compressible fluid and their singularities. 452 Blumenthal, L. M. Congruence and superposability in elliptic space.. 431 Chang, S. C. Errata for Contributions to projective theory of singular points of space curves. 548 Day, M. M. Polygons circumscribed about closed convex curves. 315 Day, M. M. Some characterizations of inner-product spaces. 320 Dushnik, B. Maximal sums of ordinals. 240 Eilenberg, S. Errata for Homology of spaces with operators. 1. 548 Erdös, P., and Fried, H. On the connection between gaps in power series and the roots of their partial sums. -
2019 Symposium Schedule of Events and Abstracts
2019 AWM Research Symposium Schedule Rice University, Houston Texas Friday, April 5, 2019 5:00-8:00pm Informal Opening Reception Outside Valhalla Hall | Rice University Saturday, April 6, 2019 8:00-8:30am Registration and Continental Breakfast (Duncan Hall) 8:30-8.45am Welcoming Remarks: Ruth Haas, AWM President, and Ami Radunskaya, AWM Past-President (McMurtry Auditorium, Duncan Hall) 8:45-9:30am Plenary Lecture: Chelsea Walton, University of Illinois Title: Quantum Symmetry Location: McMurtry Auditorium, Duncan Hall 9:30-10:15 Exhibits and Coffee (Martel Atrium, Duncan Hall) 10:15-12:15 Research Sessions (expanded below) ACxx: Women in Algebraic Combinatorics, I (Keck 105) Analysis and Numerical Methods for Kinetic Transport and Related Models, I (Duncan Hall 1046) Applied and Computational Harmonic Analysis, I (Duncan Hall 1075) Combinatorial Commutative Algebra, I (Hermann Brown 227) WICA: Women in Commutative Algebra, I (Herzstein 212) Education Partnerships: University Mathematics Faculty and K-12 Mathematics Teachers (Herzstein 210) New Advances in Symplectic and Contact Topology, I (Hermann Brown 423) Topology of 3- and 4-Manifolds, I (Hermann Brown 427) WIC: Women in Control, I (Duncan Hall 1042) WIMM: Women in Mathematics of Materials, I (Herzstein 211) WINASC: Women in Numerical Analysis and Scientific Computing, I (Duncan Hall 1064) WinCompTop: Women in Computational Topology, I (Keck 100) WINART: Women in Noncommutative Algebra and Representation Theory, I (Keck 107) WIN: Women in Numbers, I (Herman Brown 453) WiSh: -
Contemporary Mathematics 78
CONTEMPORARY MATHEMATICS 78 Braids Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Artin's Braid Group held July 13-26. 1986 at the University of California, Santa Cruz, California Joan S. Birman Anatoly Libgober Editors http://dx.doi.org/10.1090/conm/078 Recent Titles in This Series 120 Robert S. Doran, Editor, Selfadjoint and nonselfadjoint operator algebras and operator theory, 1991 119 Robert A. Melter, Azriel Rosenfeld, and Prabir Bhattacharya, Editors, Vision geometry, 1991 118 Yan Shi-Jian, Wang Jiagang, and Yang Chung-chun, Editors, Probability theory and its applications in China, 1991 117 Morton Brown, Editor, Continuum theory and dynamical systems, 1991 116 Brian Harboume and Robert Speiser, Editors, Algebraic geometry: Sundance 1988, 1991 115 Nancy Flournoy an'il Robert K. Tsutakawa, Editors, Statistical multiple integration, 1991 114 Jeffrey C. Lagarias and Michael J. Todd, Editors, Mathematical developments arising from linear programming, 1990 113 Eric Grinberg and Eric Todd Quinto, Editors, Integral geometry and tomography, 1990 112 Philip J. Brown and Wayne A. Fuller, Editors, Statistical analysis of measurement error models and applications, 1990 Ill Earl S. Kramer and Spyros S. Magliveras, Editors, Finite geometries and combinatorial designs, I 990 II 0 Georgia Benkart and J. Marshall Osborn, Editors, Lie algebras and related topics, 1990 109 Benjamin Fine, Anthony Gaglione, and Francis C. Y. Tang, Editors, Combinatorial group theory, 1990 108 Melvyn S. Berger, Editor, Mathematics of nonlinear science, 1990 107 Mario Milman and Tomas Schonbek, Editors, Harmonic analysis and partial differential equations, 1990 I 06 Wilfried Sieg, Editor, Logic and computation, 1990 I 05 Jerome Kaminker, Editor, Geometric and topological invariants of elliptic operators, 1990 I 04 Michael Makkai and Robert Pare, Accessible categories: The foundations of categorical model theory, 1989 I 03 Steve Fisk, Coloring theories, 1989 I 02 Stephen McAdam, Primes associated to an ideal, 1989 101 S.-Y. -
J´Ozef Marcinkiewicz
JOZEF¶ MARCINKIEWICZ: ANALYSIS AND PROBABILITY N. H. BINGHAM, Imperial College London Pozna¶n,30 June 2010 JOZEF¶ MARCINKIEWICZ Life Born 4 March 1910, Cimoszka, Bialystok, Poland Student, 1930-33, University of Stefan Batory in Wilno (professors Stefan Kempisty, Juliusz Rudnicki and Antoni Zygmund) 1931-32: taught Lebesgue integration and trigono- metric series by Zygmund MA 1933; military service 1933-34 PhD 1935, under Zygmund 1935-36, Fellowship, U. Lw¶ow,with Kaczmarz and Schauder 1936, senior assistant, Wilno; dozent, 1937 Spring 1939, Fellowship, Paris; o®ered chair by U. Pozna¶n August 1939: in England; returned to Poland in anticipation of war (he was an o±cer in the reserve); already in uniform by 2 September Second lieutenant, 2nd Battalion, 205th In- fantry Regiment Defence of Lwo¶w12 - 21 September 1939; Lwo¶wsurrendered to Red (Soviet) Army Prisoner of war 25 September ("temporary in- ternment" by USSR); taken to Starobielsk Presumed executed Starobielsk, or Kharkov, or Kozielsk, or Katy¶n;Katy¶nMassacre commem- orated on 10 April Work We outline (most of) the main areas in which M's influence is directly seen today, and sketch the current state of (most of) his areas of in- terest { all in a very healthy state, an indication of M's (and Z's) excellent mathematical taste. 55 papers 1933-45 (the last few posthumous) Collaborators: Zygmund 15, S. Bergman 2, B. Jessen, S. Kaczmarz, R. Salem Papers (analysed by Zygmund) on: Functions of a real variable Trigonometric series Trigonometric interpolation Functional operations Orthogonal systems Functions of a complex variable Calculus of probability MATHEMATICS IN POLAND BETWEEN THE WARS K. -
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. -
Hyberbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves CBMS-NSF REGIONAL CONFERENCE SERIES in APPLIED MATHEMATICS
Hyberbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS A series of lectures on topics of current research interest in applied mathematics under the direction of the Conference Board of the Mathematical Sciences, supported by the National Science Foundation and published by SIAM. GARRETT BIRKHOFF, The Numerical Solution of Elliptic Equations D. V. LINDLEY, Bayesian Statistics, A Review R. S. VARGA, Functional Analysis and Approximation Theory in Numerical Analysis R. R. BAHADUR, Some Limit Theorems in Statistics PATRICK BILLINGSLEY, Weak Convergence of Measures: Applications in Probability J. L. LIONS, Some Aspects of the Optimal Control of Distributed Parameter Systems ROGER PENROSE, Techniques of Differential Topology in Relativity HERMAN CHERNOFF, Sequential Analysis and Optimal Design J. DURBIN, Distribution Theory for Tests Based on the Sample Distribution Function SOL I. RUBINOW, Mathematical Problems in the Biological Sciences P. D. LAX, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves I. J. SCHOENBERG, Cardinal Spline Interpolation IVAN SINGER, The Theory of Best Approximation and Functional Analysis WERNER C. RHEINBOLDT, Methods of Solving Systems of Nonlinear Equations HANS F. WEINBERGER, Variational Methods for Eigenvalue Approximation R. TYRRELL ROCKAFELLAR, Conjugate Duality and Optimization SIR JAMES LIGHTHILL, Mathematical Biofluiddynamics GERARD SALTON, Theory of Indexing CATHLEEN S. MORAWETZ, Notes on Time Decay and Scattering for Some Hyperbolic Problems F. HOPPENSTEADT, Mathematical Theories of Populations: Demographics, Genetics and Epidemics RICHARD ASKEY, Orthogonal Polynomials and Special Functions L. E. PAYNE, Improperly Posed Problems in Partial Differential Equations S. ROSEN, Lectures on the Measurement and Evaluation of the Performance of Computing Systems HERBERT B.