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Finslerian Geometries Fundamental Theories of Physics
Finslerian Geometries Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE, University of Denver, U.S.A. Editorial Advisory Board: LAWRENCE P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, u.K. CLIVE KILMISTER, University of London, U.K. PEKKA J. LAHTI, University of Turku, Finland GUNTER LUDWIG, Philipps-Universitiit, Marburg, Germany NATHAN ROSEN, Israel Institute of Technology, Israel ASHER PERES, Israel Institute of Technology, Israel EDUARD PRUGOVECKI, University of Toronto, Canada MENDEL SACHS, State University of New York at Buffalo, U.S.A. ABDUS SALAM, International Centre for Theoretical Physics, Trieste, Italy HANS-JURGEN TREDER, Zentralinstitut fur Astrophysik der Akademie der Wissenschaften, Germany Volume 109 Finslerian Geometries A Meeting of Minds edited by P.L. Antonell i DeJXlrlmem of Mathematical Sciences, University ofAlberta, EdmonlOn. Alberta, Canada SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A C .I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-94-010-5838-4 ISBN 978-94-011-4235-9 (eBook) DOI 10.1007/978-94-011-4235-9 Printed an arid1ree paper AH Rights Reserved © 2000 Springer Science+Business Media Dordrecht Originally published by K!uwer Academic Publishers in 2000 Soticovcr repri Il! of the hardcover l s( cd ition in 20()(} No part of the material protected by this copyright natice may be reproduced Of utilized in any farm Of by any means, electronic or mechanical, induding pholocopying, recording or by any informat ion slorage and relrieval system, withoUI wrinen permissian from the copyright owner. -
CRITERIA for FLATNESS and INJECTIVITY 3 Ring of R
CRITERIA FOR FLATNESS AND INJECTIVITY NEIL EPSTEIN AND YONGWEI YAO Abstract. Let R be a commutative Noetherian ring. We give criteria for flatness of R-modules in terms of associated primes and torsion-freeness of certain tensor products. This allows us to develop a criterion for regularity if R has characteristic p, or more generally if it has a locally contracting en- domorphism. Dualizing, we give criteria for injectivity of R-modules in terms of coassociated primes and (h-)divisibility of certain Hom-modules. Along the way, we develop tools to achieve such a dual result. These include a careful analysis of the notions of divisibility and h-divisibility (including a localization result), a theorem on coassociated primes across a Hom-module base change, and a local criterion for injectivity. 1. Introduction The most important classes of modules over a commutative Noetherian ring R, from a homological point of view, are the projective, flat, and injective modules. It is relatively easy to check whether a module is projective, via the well-known criterion that a module is projective if and only if it is locally free. However, flatness and injectivity are much harder to determine. R It is well-known that an R-module M is flat if and only if Tor1 (R/P,M)=0 for all prime ideals P . For special classes of modules, there are some criteria for flatness which are easier to check. For example, a finitely generated module is flat if and only if it is projective. More generally, there is the following Local Flatness Criterion, stated here in slightly simplified form (see [Mat86, Section 22] for a self-contained proof): Theorem 1.1 ([Gro61, 10.2.2]). -
Can Croatia Join Europe As Competitive Knowledge-Based Society by 2010?
Editorial Can Croatia Join Europe as Competitive Knowledge-based Society by 2010? Mladen Petrovečki1, Vladimir Paar2, Dragan Primorac1 1Ministry of Science, The 21st century has brought important changes in the paradigms of eco- Education and Sports of the nomic development, one of them being a shift toward recognizing knowl- Republic of Croatia, Zagreb, Croatia edge and information as the most important factors of today. The European 2Croatian Academy of Union (EU) has been working hard to become the most competitive knowl- Sciences and Arts, edge-based society in the world, and Croatia, an EU candidate country, has Zagreb, Croatia been faced with a similar task. To establish itself as one of the best knowl- edge-based country in the Eastern European region over the next four years, Croatia realized it has to create an education and science system correspon- dent with European standards and sensitive to labor market needs. For that purpose, the Croatian Ministry of Science, Education, and Sports (MSES) has created and started implementing a complex strategy, consisting of the following key components: the reform of education system in accordance with the Bologna Declaration; stimulation of scientific production by sup- porting national and international research projects; reversing the “brain drain” into “brain gain” and strengthening the links between science and technology; and informatization of the whole education and science sys- tem. In this comprehensive report, we describe the implementation of these > Correspondence to: measures, whose coordination with the EU goals presents a challenge, as well as an opportunity for Croatia to become a knowledge-based society Mladen Petrovečki Assistant Minister for Science by 2010. -
Lectures on Local Cohomology
Contemporary Mathematics Lectures on Local Cohomology Craig Huneke and Appendix 1 by Amelia Taylor Abstract. This article is based on five lectures the author gave during the summer school, In- teractions between Homotopy Theory and Algebra, from July 26–August 6, 2004, held at the University of Chicago, organized by Lucho Avramov, Dan Christensen, Bill Dwyer, Mike Mandell, and Brooke Shipley. These notes introduce basic concepts concerning local cohomology, and use them to build a proof of a theorem Grothendieck concerning the connectedness of the spectrum of certain rings. Several applications are given, including a theorem of Fulton and Hansen concern- ing the connectedness of intersections of algebraic varieties. In an appendix written by Amelia Taylor, an another application is given to prove a theorem of Kalkbrenner and Sturmfels about the reduced initial ideals of prime ideals. Contents 1. Introduction 1 2. Local Cohomology 3 3. Injective Modules over Noetherian Rings and Matlis Duality 10 4. Cohen-Macaulay and Gorenstein rings 16 d 5. Vanishing Theorems and the Structure of Hm(R) 22 6. Vanishing Theorems II 26 7. Appendix 1: Using local cohomology to prove a result of Kalkbrenner and Sturmfels 32 8. Appendix 2: Bass numbers and Gorenstein Rings 37 References 41 1. Introduction Local cohomology was introduced by Grothendieck in the early 1960s, in part to answer a conjecture of Pierre Samuel about when certain types of commutative rings are unique factorization 2000 Mathematics Subject Classification. Primary 13C11, 13D45, 13H10. Key words and phrases. local cohomology, Gorenstein ring, initial ideal. The first author was supported in part by a grant from the National Science Foundation, DMS-0244405. -
Introduction to Soliton Theory: Applications to Mechanics Fundamental Theories of Physics
Introduction to Soliton Theory: Applications to Mechanics Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE, University of Denver, U.S.A. Editorial Advisory Board: GIANCARLO GHIRARDI, University of Trieste, Italy LAWRENCE P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, U.K. CLIVE KILMISTER, University of London, U.K. PEKKA J. LAHTI, University of Turku, Finland ASHER PERES, Israel Institute of Technology, Israel EDUARD PRUGOVECKI, University of Toronto, Canada FRANCO SELLERI, Università di Bara, Italy TONY SUDBURY, University of York, U.K. HANS-JÜRGEN TREDER, Zentralinstitut für Astrophysik der Akademie der Wissenschaften, Germany Volume 143 Introduction to Soliton Theory: Applications to Mechanics by Ligia Munteanu Institute of Solid Mechanics, Romanian Academy, Bucharest, Romania and Stefania Donescu Technical University of Civil Engineering, Department of Mathematics, Bucharest, Romania KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBook ISBN: 1-4020-2577-7 Print ISBN: 1-4020-2576-9 ©2005 Springer Science + Business Media, Inc. Print ©2004 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Springer's eBookstore at: http://ebooks.kluweronline.com and the Springer Global Website Online at: http://www.springeronline.com Contents Preface ix Part 1. INTRODUCTION TO SOLITON THEORY 1. MATHEMATICAL METHODS 1 1.1 Scope of the chapter 1 1.2 Scattering theory 1 1.3 Inverse scattering theory 12 1.4 Cnoidal method 17 1.5 Hirota method 25 1.6 Linear equivalence method (LEM) 31 1.7 Bäcklund transformation 39 1.8 Painlevé analysis 46 2. -
Relativity in Rotating Frames Fundamental Theories of Physics
Relativity in Rotating Frames Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE, University of Denver, U.S.A. Editorial Advisory Board: JAMES T. CUSHING, University of Notre Dame, U.S.A. GIANCARLO GHIRARDI, University of Trieste, Italy LAWRENCE P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, U.K. CLIVE KILMISTER, University of London, U.K. PEKKA J. LAHTI, University of Turku, Finland ASHER PERES, Israel Institute of Technology, Israel EDUARD PRUGOVECKI, University of Toronto, Canada TONY SUDBURY, University of York, U.K. HANS-JÜRGEN TREDER, Zentralinstitut für Astrophysik der Akademie der Wissenschaften, Germany Volume 135 Relativity in Rotating Frames Relativistic Physics in Rotating Reference Frames Edited by Guido Rizzi Politecnico di Torino and Istituto Nazionale di Fisica Nucleare, Torino, Italy and Matteo Luca Ruggiero Politecnico di Torino and Istituto Nazionale di Fisica Nucleare, Torino, Italy SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-90-481-6514-8 ISBN 978-94-017-0528-8 (eBook) DOI 10.1007/978-94-017-0528-8 Printed on acid-free paper All Rights Reserved © 2004 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2004 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. -
Introduction to Soliton Theory: Applications to Mechanics Fundamental Theories of Physics
Introduction to Soliton Theory: Applications to Mechanics Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE, University of Denver, U.S.A. Editorial Advisory Board: GIANCARLO GHIRARDI, University of Trieste, Italy LAWRENCE P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, U.K. CLIVE KILMISTER, University of London, U.K. PEKKA J. LAHTI, University of Turku, Finland ASHER PERES, Israel Institute of Technology, Israel EDUARD PRUGOVECKI, University of Toronto, Canada FRANCO SELLERI, Università di Bara, Italy TONY SUDBURY, University of York, U.K. HANS-JÜRGEN TREDER, Zentralinstitut für Astrophysik der Akademie der Wissenschaften, Germany Volume 143 Introduction to Soliton Theory: Applications to Mechanics by Ligia Munteanu Institute of Solid Mechanics, Romanian Academy, Bucharest, Romania and Stefania Donescu Technical University of Civil Engineering, Department of Mathematics, Bucharest, Romania KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBook ISBN: 1-4020-2577-7 Print ISBN: 1-4020-2576-9 ©2005 Springer Science + Business Media, Inc. Print ©2004 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Springer's eBookstore at: http://ebooks.kluweronline.com and the Springer Global Website Online at: http://www.springeronline.com Contents Preface ix Part 1. INTRODUCTION TO SOLITON THEORY 1. MATHEMATICAL METHODS 1 1.1 Scope of the chapter 1 1.2 Scattering theory 1 1.3 Inverse scattering theory 12 1.4 Cnoidal method 17 1.5 Hirota method 25 1.6 Linear equivalence method (LEM) 31 1.7 Bäcklund transformation 39 1.8 Painlevé analysis 46 2. -
Notices of the American Mathematical Society
OF THE AMERICAN MATHEMATICAL SOCIETY Edited by Everett Pitcher and Gordon L. Walker CONTENTS MEETINGS Calendar of Meetings ................ 578 Program for the june Meeting in Corvallis, Oregon 579 Abstracts for the Meeting: Pages 611-617 PRELIMINARY ANNOUNCEMENTS OF MEETINGS 583 NEWS ITEMS AND ANNOUNCEMENTS . 582, 589 MATHEMATICAL OFFPRINT SERVICE 590 LETTERS TO THE EDITOR . 592 SPECIAL MEETINGS INFORMATION CENTER 595 MEMORANDA TO MEMBERS . 600 Policy on Recruitment PERSONAL ITEMS 601 NEW AMS PUBLICATIONS .. 605 ABSTRACTS OF CONTRIBUTED PAPERS 608 ERRATA TO ABSTRACTS ........• 617 ABSTRACTS PRESENTED TO THE SOCIETY 618 INDEX TO ADVERTISERS. 687 RESERVATION FORM •.. 688 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 cJ{oticti) 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• 687 August 30-September 3, 1171 University Park, Pennsylvania July 7, I 'n I (76th Summer Meeting) 688 October 30, 1971 Cambridge, Massachusetts Sept. 9, 1971 689 November 19-20, I971 Auburn, Alabama Oct. 4, 1971 690 November 27, 1971 Milwaukee, Wisconsin Oct. 4, 1971 691 January 17-21, 1972 Las Vegas, Nevada Nov. 4, 1971 (78th Annual Meeting) March 29-April 1, 1972 St. Louis, Missouri August 28-September 1, 1972 Hanover, New Hampshire (77th Summer Meeting) January 25-29, 1973 Dallas, Texas (79:h Annual Meeting) August 20-24, 1973 Missoula, Montana (78th Summer Meeting) January 13-19, 1974 San Francisco, California (80th Annual Meeting) January 23-27, 1975 Washington, D.C. -
Relativistic Elementary Particles 47 1
Kinematical Theory of Spinning Particles Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE, University of Denver, U.S.A. Editorial Advisory Board: JAMES T. CUSHING, University of Notre Dame, U.S.A. GIANCARLO GHIRARDI, University of Trieste, Italy LAWRENCE P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, U.K. CLIVE KILMISTER, University of London, U.K. PEKKA J. LAHTI, University of Turku, Finland ASHER PERES, Israel Institute of Technology, Israel EDUARD PRUGOVECKI, University of Toronto, Canada TONY SUDBURY, University of York, U.K. HANS-JÜRGEN TREDER, Zentralinstitut für Astrophysik der Akademie der Wissenschaften, Germany Volume 116 Kinematical Theory of Spinning Particles Classical and Quantum Mechanical Formalism of Elementary Particles by Martin Rivas The University of the Basque Country, Bilbao, Spain KLUWER ACADEMIC PUBLISHERS NEW YORK,BOSTON, DORDRECHT,LONDON, MOSCOW eBook ISBN 0-306-47133-7 Print ISBN 0-792-36824-X ©2002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://www.kluweronline.com and Kluwer's eBookstore at: http://www.ebooks.kluweronline.com To Merche This page intentionally left blank. Contents List of Figures xi Acknowledgment xvii Introduction xix 1. GENERAL FORMALISM 1 1. Introduction 1 1 . 1 Kinematics and dynamics 3 2 . Variational versus Newtonian formalism 4 3. -
Notices of the American Mathematical Society
Notices of the American Mathematical Society November 1985, Issue 244 Volume 32, Number 6, Pages 737- 872 Providence, Rhode Island USA ISSN 0002-9920 Calendar of AMS Meetings THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to the 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 meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and supplementary announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meeting. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the headquarters office of the Society. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence. Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for abstracts for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcements and the list of organizers of special sessions. ABSTRACT MEETING# DATE PLACE DEADLINE ISSUE 825 January 7-11. -
Assistantships and Fellowships in the Mathematical Sciences in 1982-1983 Supplementary List
il16 and 17)-Page 257 ta~Aellnformation- Page 27 5 ematical Society < 2. c 3 II> J~ cz 3 i"... w Calendar of AMS Meetings THIS CALENDAR lists all meetings which have been approved by the Council prior to the date 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 Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab· stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcement and the list of organizers of special sessions. -
A Selected Bibliography of Publications By, and About, Paul Adrien Maurice Dirac
A Selected Bibliography of Publications by, and about, Paul Adrien Maurice Dirac Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 08 June 2021 Version 1.195 Title word cross-reference (1 + 1) [Das93]. (2 + 1) [JM99]. −1=2 [CT67a]. −1=2; 1=2; 3=2; 5=2 [Mac98]. − 1 1 2 ; 2 [CT67b]. 1 [CG07]. 1 + 1 [Fei02]. 1=2 [CT67a, FA01, Ogu96, dB51, dB52a]. 2:7◦ [Noe73]. $250.00 [War96]. $26.00 [Ryc17]. $29.95 [RS10, Dys10]. 3 [RRS06]. 3 + 1 [Nak00]. 3 + 2 [Dir63b]. 3=2 [CT67a]. $44.50 [Dre90]. $49.50 [Sch85]. $7.50 [Suc67]. 6 [DN96]. α [BM98, LT04]. α, β; γ; δ [Som36]. c [IC04, MBS02, Mag15]. D [DSP03]. δ ˇ 2 3 [DES89, IP56, IP57, Lut07, Sch72]. e [IC04, MBS02]. e [CP68]. [GGS04]. 2 + [CT67b]. G [AWW 81, Dir75f, Dir78b, Dir80g, Dir82f]. GF [FA10]. m+2 s 3 Gr2(C ) [Mil98].RH (R ) [EV97].h ¯ [IC04]. mp=me [BBSF10, FK07]. F ∞ p −η p(η)=1=Γ(p +1) 0 [ =(1 + e )]d [GFG01]. SU (2) [yRSBSV99]. H2 [SBK+08]. N [Ata89, KY01, MHN98, MB90, Mor85, Won90]. ∇2n=n [MHN98]. ∇n=n [MHN98]. π [JT10]. q [CPV10, JT10]. R [Szm98, Szm99]. Rn [Bet83]. rt [BBR85]. s>1 [EV97]. SL(2; C) [Hos82, Hos83]. SO(4) [LH86].