DOCSLIB.ORG

February 1980 Table of Contents

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

•ces Mathematical Society < 2. c ~ ..N..... zc 3 lf N 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. Pirst 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. MEETING ABSTRACT NUMBER DATE PLACE DEADLINE ISSUE 775 April 11-1 2, 1980 Bloomington, Indiana FEBRUARY 11 776 April 17-18, 1980 Philadelphia, Pennsylvania FEBRUARY 14 April 1980 777 April 25-26, 1980 Davis, California FEBRUARY 18 778 June 20-21, 1980 Ellensburg, Washington APRIL 21 june 1980 779 August 18-22, 1980 Ann Arbor, Michigan JUNE 3 August 1980 (84th Summer Meeting) October 17-18, 1980 Storrs, Connecticut january 7-11, 1981 San Francisco, California (87th Annual Meeting) January 13-17, 1982 Cincinnati, Ohio (88th Annual Meeting) Notices DEADLINES ISSUE NEWS ADVERTISING April 1980 February 12 February 26 june 1980 April 18 April 29 August 1980 june 3 june 18 Deadlines for announcements intended for the Special Meetings section are the same as for News. Other Events Sponsored by the Society ANNOUNCEMENT APPEARS April 7-10, 1980 AMS Symposium on the Mathematical Heritage of This Issue, p. 1 50 Henri Poincare, Indiana University, Bloomington, Indiana April 1 5-16, 1980 AMS Symposium on Mathematical Psychology and This Issue, p. 1 55 Psychophysiology, Philadelphia, Pennsylvania june 15-27, 1980 AMS Summer Seminar on Mathematical Aspects of This Issue, p. 158 Physiology, University of Utah, Salt Lake City, Utah july 14-August 2, 1980 AMS Summer Institute on Operator Algebras and This Issue, p. 158 Applications, Queen's University, Kingston, Ontario, Canada Notices of the American Mathematical Society Volume 27, Number 2, February 1980 EDITORIAL COMMITTEE Ed Dubinsky, Richard j. Griego, Robion C. Kirby, Arthur P. Mattuck, 142 MEETINGS OF THE SOCIETY Susan Montgomery, Barbara L. Osofsky, Boulder, Colorado, March 27, 142 Everett Pitcher (Chairman} Bloomington, Indiana, April 11, 150 MANAGING EDITOR Philadelphia, Pennsylvania, April 17, 154 Lincoln K. Durst Davis, California, April 25, 156 ASSOCIATE EDITOR FOR QUERIES Ellensburg, Washington, june 29, 157 Hans Samelson Summer Seminar, Salt Lake City, june 15, 158 Summer Institute, Kingston, july 14, 158 SUBSCRIPTION ORDERS Notices is published eight times a Invited Speakers, 149; Special Sessions, 159 year (January, February, April, june, 160 August, October, November, and 1980 AMS ELECTIONS (Nominations by Petition) December}. Subscription for Vol. 27 164 COLE PRIZES FOR 1980 (1980}, $22.00 list, $11.00 member. The subscription price for members 168 1981 NSF BUDGET is included in the annual dues. Sub­ scriptions and orders for AMS publi· 170 23rd AMS SURVEY: Second Report cations should be addressed to the Employment and Faculty Mobility, 170; American Mathematical Society, Enrollments, P. 0. Box 1571, Annex Station, Teaching Loads, 176; Providence, R. I. 02901. All orders Two-Year Colleges, 178 must be prepaid. 179 QUERIES ADVERTISING & INQUIRIES 181 LETTERS The Notices publishes situations wanted and classified advertising, 183 NEWS & ANNOUNCEMENTS and display advertising for publishers and academic or scientific organiza­ 186 SPECIAL MEETINGS tions. Requests for information: Advertising: Elaine Lauble 193 NEW AMS PUBLICATIONS Change of address or subscriptions: 196 MISCELLANEOUS Virginia Biber To avoid interruption in service please Personal Items, 196; Deaths, 197; Visiting send address changes four to six Mathematicians (Supplement), 197; Assistant­ weeks in advance. It is essential ships and Fellowships (Supplement), 198; to include the member code which appears on the address label with Backlog, 202 all correspondence regarding subscriptions. Address correspondence 204 AMS REPORTS & COMMUNICATIONS to American Mathematical Society, Appointments, 204; Reports of Meetings: P. 0. Box 6248, Providence, Rl 02940. Washington, D.C., 205; Kent, 206; Birmingham, Telephone 401-272-9500. 206; Riverside, 207; San Antonio, 208 Second class postage paid at Providence, Rl, and additional 209 AMS BOOKS IN GLOBAL ANALYSIS mailing offices. U.S. Postal Service AND DIFFERENTIAL GEOMETRY Publication No. 398520. Copyright © 1980 by the 214 ADVERTISEMENTS American Mathematical Society, Printed in the United States of America. 228 REGISTRATION FORM (Philadelphia) BOULDER, March 27-29, 1980, University of Colorado Program for the 774th Meeting The seven hundred seventy-fourth meeting of Other Organizations. The MAA program will in­ the American Mathematical Society will be held at clude a banquet Friday evening; the dinner speaker the University of Colorado in Boulder, Colorado, on will be DOROTHY L. BERNSTEIN who will speak Thursday through Saturday, March 27-29, 1980. on A differential equation of literary criticism. The The meeting will be held jointly with the Rocky theme of the MAA program will be "Nontraditional Mountain section of the Mathematical Association uses of mathematics and computers" and will include of America (MAA) and the Association for Symbolic two panel discussions. The ASL program will include Logic (ASL). an invited hour address by WILLIAM j. MITCHELL; Invited Addresses other speakers will be STEWART BALDWIN, WILFRID A. HODGES, MATTHEW D. FOREMAN, By invitation of the Committee to Select Hour RICHMOND H. THOMASON, and W. HUGH WOODIN. Speakers for Far Western Sectional Meetings, there The ASL meeting is in honor of Frank P. Ramsey will be two invited one-hour addresses. ROBERT who died in 1930. FINN of Stanford University will lecture at 11:00 a.m., Saturday, on Capillary free surfaces. DOUGLAS REGISTRATION A. LIND of the University of Washington will lecture The registration area will be in the first floor at 11 :00 a.m., Friday, on Finitary ergodic theory. lobby of the Engineering Center. The registration Both lectures will be in Biology-Psychology E-050. desk will be open Thursday from 10:00 a.m. to 5:00 Special Sessions p.m.; on Friday from 8:00 a.m. to 5:00 p.m.; and on Saturday from 8:00 a.m. to 11 :00 a.m. Regis­ By invitation of the same committee, there will tration fees will be $3 for members of AMS, ASL, be three special sessions of selected papers: or MAA; $5 for nonmembers; and $1 for students Nonabelian harmonic analysis, organized by and unemployed persons. LAWRENCE W. BAGGETT and ARLAN B. RAMSAY; the list of speakers includes Louis ACCOMMODATIONS Auslander, Raymond C. Fabec, Eugene Gutkin, joe The following motels are located in Boulder, W. jenkins, Ray A. Kunze, Wesley Mitchell, Calvin Colorado, Zip Code 80303. The distances listed are C. Moore, Bent (t>rsted, Richard C. Penney, Marc A. the approximate distances from the registration area. Rieffel, Keith F. Taylor, Peter C. Trombi, and V. S. The rates given do not include an 8.5% room tax and Varadarajan. Sixty or seventy-five minute talks will may increase before the meeting. Participants should be given by Auslander, Moore and Varadarajan. make reservations directly with the motel and should Lattice theory and general algebra, organized by mention the mathematics conference, since some ALAN DAY and WALTER F. TAYLOR; the speakers rooms will be held for conference participants until will be Ralph S. Freese, H. Peter Gumm, William A. February 28. Lampe, Ralph N. McKenzie, Don L. Pigozzi, Robert Willis Quackenbush, Ivan Rival, and jonathan D. H. Boulder Inn (1 /2 mile) Smith. In addition, George A. Gratzer, Bjarni 770 28th Street j6nsson, and Rudolf Wille will organize problem Telephone: 303-449-3800 sessions. (1-800-528-1234 Best Western) Topics in mathematical physics, organized by Single $28 up Triple $39 up KARL E. GUSTAFSON and WILLIAM P. Double 31 up Quadruple 44 up REINHARDT; the speakers will be A. 0. Barut, Twin double 34 up Frank H. Brownell, jr., Charles L. Dolph, Volker Broker Inn Hotel (1 mile) Enss, Robert K. Goodrich, Karl E. Gustafson, R. L. 550 30th Street Hartman, Eric j. Heller, Ira W. Herbst, j. S. Howland, Telephone: 303-444-3330 (collect calls accepted) Robin L. Hudson, Guy johnson, Jr., William B. jones, Single $28 up Triple $41 up Richard B. Lavine, jean-Paul Marchand, C. William Double 35 up Quadruple 47 up McCurdy, Richard Mercer, William H. Miller, B. Twin double 35 up Misra, D. W. Noid, R. Ramaswamy, Alexander G. Ramm, William P. Reinhardt, Peter A. Rejto, R. D. Highlander Inn Motel (1 /4 mile) Richtmyer, Franklin E. Schroeck, j r., M. Seddigh in; 970 28th Street Randall B. Shirts, Israel M. Sigal, Kalyan B. Sinha, Telephone: 303-443-7800 Michael P. Strand, M. Tabor, Hamid Tadjeran, Tuong Single $25-$29 Double-double $30-$31 Ton-That, Ricardo A. Weder, and Daoxing Xia. Double 27- 32 Contributed Papers. There will be sessions of Hilton Harvest House \1/2 mile) contributed ten-minute papers scheduled on Saturday.
Recommended publications
  • Creating New Concepts in Mathematics: Freedom and Limitations. the Case of Category Theory

    Creating New Concepts in Mathematics: Freedom and Limitations. the Case of Category Theory

    Creating new concepts in mathematics: freedom and limitations. The case of Category Theory Zbigniew Semadeni Institute of Mathematics, University of Warsaw Abstract In the paper we discuss the problem of limitations of freedom in mathematics and search for criteria which would differentiate the new concepts stemming from the historical ones from the new concepts that have opened unexpected ways of thinking and reasoning. We also investigate the emergence of category theory (CT) and its origins. In particular we explore the origins of the term functor and present the strong evidence that Eilenberg and Carnap could have learned the term from Kotarbinski´ and Tarski. Keywords categories, functors, Eilenberg-Mac Lane Program, mathematical cognitive transgressions, phylogeny, platonism. CC-BY-NC-ND 4.0 • 1. Introduction he celebrated dictum of Georg Cantor that “The essence of math- Tematics lies precisely in its freedom” expressed the idea that in mathematics one can freely introduce new notions (which may, how- Philosophical Problems in Science (Zagadnienia FilozoficzneNo w Nauce) 69 (2020), pp. 33–65 34 Zbigniew Semadeni ever, be abandoned if found unfruitful or inconvenient).1 This way Cantor declared his opposition to claims of Leopold Kronecker who objected to the free introduction of new notions (particularly those related to the infinite). Some years earlier Richard Dedekind stated that—by forming, in his theory, a cut for an irrational number—we create a new number. For him this was an example of a constructed notion which was a free creation of the human mind (Dedekind, 1872, § 4). In 1910 Jan Łukasiewicz distinguished constructive notions from empirical reconstructive ones.
  • Algebraic Properties of the Richard Thompson's Group F

    Algebraic Properties of the Richard Thompson's Group F

    ALGEBRAIC PROPERTIES OF THE RICHARD THOMPSON’S GROUP F AND ITS APPLICATIONS IN CRYPTOGRAPHY A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY BY HAKAN YETER IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN MATHEMATICS FEBRUARY 2021 Approval of the thesis: ALGEBRAIC PROPERTIES OF THE RICHARD THOMPSON’S GROUP F AND ITS APPLICATIONS IN CRYPTOGRAPHY submitted by HAKAN YETER in partial fulfillment of the requirements for the de- gree of Master of Science in Mathematics Department, Middle East Technical University by, Prof. Dr. Halil Kalıpçılar Dean, Graduate School of Natural and Applied Sciences Prof. Dr. Yıldıray Ozan Head of Department, Mathematics Assoc. Prof. Dr. Mustafa Gökhan Benli Supervisor, Mathematics Department, METU Examining Committee Members: Assoc. Prof. Dr. Fatih Sulak Mathematics Department, Atilim University Assoc. Prof. Dr. Mustafa Gökhan Benli Mathematics Department, METU Assist. Prof. Dr. Burak Kaya Mathematics Department, METU Date: I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work. Name, Surname: Hakan Yeter Signature : iv ABSTRACT ALGEBRAIC PROPERTIES OF THE RICHARD THOMPSON’S GROUP F AND ITS APPLICATIONS IN CRYPTOGRAPHY Yeter, Hakan M.S., Department of Mathematics Supervisor: Assoc. Prof. Dr. Mustafa Gökhan Benli February 2021, 69 pages Thompson’s groups F; T and V , especially F , are widely studied groups in group theory.
  • The Role of the Interval Domain in Modern Exact Real Airthmetic

    The Role of the Interval Domain in Modern Exact Real Airthmetic

    The Role of the Interval Domain in Modern Exact Real Airthmetic Andrej Bauer Iztok Kavkler Faculty of Mathematics and Physics University of Ljubljana, Slovenia Domains VIII & Computability over Continuous Data Types Novosibirsk, September 2007 Teaching theoreticians a lesson Recently I have been told by an anonymous referee that “Theoreticians do not like to be taught lessons.” and by a friend that “You should stop competing with programmers.” In defiance of this advice, I shall talk about the lessons I learned, as a theoretician, in programming exact real arithmetic. The spectrum of real number computation slow fast Formally verified, Cauchy sequences iRRAM extracted from streams of signed digits RealLib proofs floating point Moebius transformtions continued fractions Mathematica "theoretical" "practical" I Common features: I Reals are represented by successive approximations. I Approximations may be computed to any desired accuracy. I State of the art, as far as speed is concerned: I iRRAM by Norbert Muller,¨ I RealLib by Branimir Lambov. What makes iRRAM and ReaLib fast? I Reals are represented by sequences of dyadic intervals (endpoints are rationals of the form m/2k). I The approximating sequences need not be nested chains of intervals. I No guarantee on speed of converge, but arbitrarily fast convergence is possible. I Previous approximations are not stored and not reused when the next approximation is computed. I Each next approximation roughly doubles the amount of work done. The theory behind iRRAM and RealLib I Theoretical models used to design iRRAM and RealLib: I Type Two Effectivity I a version of Real RAM machines I Type I representations I The authors explicitly reject domain theory as a suitable computational model.
  • SENATE—Wednesday, July 26, 2000

    SENATE—Wednesday, July 26, 2000

    July 26, 2000 CONGRESSIONAL RECORD—SENATE 16283 SENATE—Wednesday, July 26, 2000 The Senate met at 9:31 a.m. and was Again, if cloture is invoked on the mo- to be offered, the time for the debate, called to order by the President pro tion, postcloture debate will begin im- and some tangential but very impor- tempore [Mr. THURMOND]. mediately. tant issues such as the consideration of As a reminder, on Thursday the appointments of Federal district court PRAYER morning hour has been set aside for judges across America to fill vacancies. The Chaplain, Dr. Lloyd John those Senators who wish to make their These judgeships have been a source of Ogilvie, offered the following prayer: final statements in remembrance of great controversy in recent times be- Almighty God, take charge of the the life of our former friend and col- cause there is a clear difference of control centers of our brains. Think league, Senator Paul Coverdell. At the opinion between Democrats and Repub- Your thoughts through us and send to expiration of that time, a vote on the licans about how many judges should our nervous systems the pure signals of motion to proceed to the energy and be appointed this year. Your peace, power, and patience. Give water appropriations bill will occur. Of course, the Republicans in control us minds responsive to Your guidance. I thank my colleagues for their at- of the Senate are hopeful that their Take charge of our tongues so that tention. I yield the floor. I suggest the candidate for President will prevail in we may speak truth with clarity, with- absence of a quorum.
  • Alexandre Grothendieck Eléments De Biographie

    Alexandre Grothendieck Eléments De Biographie

    Alexandre Grothendieck Eléments de biographie « Ce qui vient au monde pour ne rien troubler ne mérite ni égards ni patience ». René Char, Fureur et mystère Le 14 novembre 2014, les journaux, les radios, les télévisions du monde entier ont annoncé la mort, à Saint-Girons, en Ariège, d’un mathématicien âgé de 86 ans, au nom imprononçable. Des millions de personnes ont ainsi appris l’existence de cet inconnu au lendemain même de sa disparition. Quant à la communauté mathématique, elle a appris la nouvelle avec émotion, une émotion que Cédric Villani résume par ces mots : « Aucun mathématicien vivant n’était plus révéré de ses pairs que lui. » Pendant trente-cinq ans, tous les ans ou presque, en début d’année, j’ai tenu à dire à mes élèves quelques mots sur ce mathématicien, que je croyais retiré dans une bergerie de l’Hérault. C’est de lui que je vais vous parler, ce soir 1. Alexandre Grothendieck fut l’un des plus grands mathématiciens du 20 e siècle. L’irruption de cet autodidacte dans le monde mathématique, en 1949, ses contributions décisives en analyse fonctionnelle et en géométrie algébrique au cours de vingt années de création ininterrompue, sa rupture spectaculaire avec le monde mathématique, en 1970, et sa longue retraite, ont fait de lui un personnage mythique : Grothendieck fut un génie solitaire au destin romanesque, comme la science pure aime à en produire, de temps en temps, depuis trois millénaires : Evariste Galois, Albert Einstein, Srinivasa Ramanujan, Ettore Majorana, Alan Turing, Stephen Hawking, Grigori Perelman… Solitaire,
  • Contemporary Mathematics 358

    Contemporary Mathematics 358

    ! CONTEMPORARY MATHEMATICS 358 Stark/ s Conjectures: Recent Work and New Directions An International Conference on Stark's Conjectures and Related Topics August 5-9, 2002 Johns Hopkins University David Burns Cristian Popescu Jonathan Sands David Solomon Editors http://dx.doi.org/10.1090/conm/358 CoNTEMPORARY MATHEMATICS 358 Stark's Conjectures: Recent Work and New Directions An International Conference on Stark's Conjectures and Related Topics August 5-9, 2002 Johns Hopkins University David Burns Cristian Popescu Jonathan Sands David Solomon Editors American Mathematical Society Providence, Rhode Island Editorial Board Dennis DeTurck, managing editor Andreas Blass Andy R. Magid Michael Vogelius This volume contains articles based on talks given at the International Conference on Stark's Conjectures and Related Topics, held August 5-9, 2002, at Johns Hopkins University, Baltimore, Maryland. 2000 Mathematics Subject Classification. Primary 11G40, 11R23, 11R27, 11R29, 11R33, 11R42, 11840, 11 Y 40. Library of Congress Cataloging-in-Publication Data International Conference on Stark's Conjectures and Related Topics (2002 : Johns Hopkins Uni- versity) Stark's conjectures : recent work and new directions : an international conference on Stark's conjectures and related topics, August 5-9, 2002, Johns Hopkins University / David Burns ... [et a!.], editors. p. em. -(Contemporary mathematics, ISSN 0271-4132; 358) Includes bibliographical references. ISBN 0-8218-3480-0 (soft : acid-free paper) 1. Stark's conjectures-Congresses. I. Burns, David, 1963- II. Title. III. Contemporary mathematics (American Mathematical Society) ; v. 358. QA246 .!58 2002 512.7'4-dc22 2004049692 Copying and reprinting. Material in this book may be reproduced by any means for edu- cational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledg- ment of the source is given.
  • Fundamental Algebraic Geometry

    Fundamental Algebraic Geometry

    http://dx.doi.org/10.1090/surv/123 hematical Surveys and onographs olume 123 Fundamental Algebraic Geometry Grothendieck's FGA Explained Barbara Fantechi Lothar Gottsche Luc lllusie Steven L. Kleiman Nitin Nitsure AngeloVistoli American Mathematical Society U^VDED^ EDITORIAL COMMITTEE Jerry L. Bona Peter S. Landweber Michael G. Eastwood Michael P. Loss J. T. Stafford, Chair 2000 Mathematics Subject Classification. Primary 14-01, 14C20, 13D10, 14D15, 14K30, 18F10, 18D30. For additional information and updates on this book, visit www.ams.org/bookpages/surv-123 Library of Congress Cataloging-in-Publication Data Fundamental algebraic geometry : Grothendieck's FGA explained / Barbara Fantechi p. cm. — (Mathematical surveys and monographs, ISSN 0076-5376 ; v. 123) Includes bibliographical references and index. ISBN 0-8218-3541-6 (pbk. : acid-free paper) ISBN 0-8218-4245-5 (soft cover : acid-free paper) 1. Geometry, Algebraic. 2. Grothendieck groups. 3. Grothendieck categories. I Barbara, 1966- II. Mathematical surveys and monographs ; no. 123. QA564.F86 2005 516.3'5—dc22 2005053614 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA.
  • The Rebirth of Cosmology: from the Static to the Expanding Universe

    The Rebirth of Cosmology: from the Static to the Expanding Universe

    Physics Before and After Einstein 129 M. Mamone Capria (Ed.) IOS Press, 2005 © 2005 The authors Chapter 6 The Rebirth of Cosmology: From the Static to the Expanding Universe Marco Mamone Capria Among the reasons for the entrance of Einstein’s relativity into the scientific folklore of his and our age one of the most important has been his fresh and bold approach to the cosmological problem, and the mysterious, if not paradoxical concept of the universe as a three-dimensional sphere. Einstein is often credited with having led cosmology from philosophy to science: according to this view, he made it possible to discuss in the pro- gressive way typical of science what had been up to his time not less “a field of endless struggles” than metaphysics in Kant’s phrase. It is interesting to remember in this connection that the German philosopher, in his Critique of Pure Reason, had famously argued that cosmology was beyond the scope of science (in the widest sense), being fraught with unsolvable contradictions, inherent in the very way our reason functions. Of course not everybody had been impressed by this argument, and several nineteenth-century scientists had tried to work out a viable image of the universe and its ultimate destiny, using Newtonian mechanics and the principles of thermodynamics. However, this approach did not give unambiguous answers either; for instance, the first principle of thermodynamics was invoked to deny that the universe could have been born at a certain moment in the past, and the second principle to deny that its past could be infinite.
  • 1 Clifford Algebraic Computational Fluid Dynamics

    1 Clifford Algebraic Computational Fluid Dynamics

    Clifford Algebraic Computational Fluid Dynamics: A New Class of Experiments. Dr. William Michael Kallfelz 1 Lecturer, Department of Philosophy & Religion, Mississippi State University The Philosophy of Scientific Experimentation: A Challenge to Philosophy of Science-Center for Philosophy of Science, University of Pittsburgh October 15-16, 2010. October 24, 2010 Abstract Though some influentially critical objections have been raised during the ‘classical’ pre- computational simulation philosophy of science (PCSPS) tradition, suggesting a more nuanced methodological category for experiments 2, it safe to say such critical objections have greatly proliferated in philosophical studies dedicated to the role played by computational simulations in science. For instance, Eric Winsberg (1999-2003) suggests that computer simulations are methodologically unique in the development of a theory’s models 3 suggesting new epistemic notions of application. This is also echoed in Jeffrey Ramsey’s (1995) notions of “transformation reduction,”—i.e., a notion of reduction of a more highly constructive variety. 4 Computer simulations create a broadly continuous arena spanned by normative and descriptive aspects of theory-articulation, as entailed by the notion of transformation reductions occupying a continuous region demarcated by Ernest Nagel’s (1974) logical-explanatory “domain-combining reduction” on the one hand, and Thomas Nickels’ (1973) heuristic “domain- preserving reduction,” on the other. I extend Winsberg’s and Ramsey’s points here, by arguing that in the field of computational fluid dynamics (CFD) as well as in other branches of applied physics, the computer plays a constitutively experimental role—supplanting in many cases the more traditional experimental methods such as flow- visualization, etc. In this case, however CFD algorithms act as substitutes, not supplements (as the notions “simulation” suggests) when it comes to experimental practices.
  • Contemporary Mathematics 327

    Contemporary Mathematics 327

    CONTEMPORARY MATHEMATICS 327 Advances in Differential Equations and Mathematical Physics UAB International Conference Differential Equations and Mathematical Physics March 26-30, 2002 University of Alabama, Birmingham Yulia Karpeshina Gunter Stolz Rudi Weikard Yanni Zeng Editors http://dx.doi.org/10.1090/conm/327 CoNTEMPORARY MATHEMATICS 327 Advances in Differential Equations and Mathematical Physics UAB International Conference Differential Equations and Mathematical Physics March 26-30, 2002 University of Alabama, Birmingham Yulia Karpeshina Gunter Stolz Rudi Weikard Yanni Zeng Editors American Mathematical Society Providence, Rhode Island Editorial Board Dennis DeTurck, managing editor Andreas Blass Andy R. Magid Michael Vogelius This volume contains the proceedings of a UAB 2002 International Conference on Differential Equations and Mathematical Physics, held at the University of Alabama, Birmingham, from March 26-30, 2002. 2000 Mathematics Subject Classification. Primary 34-06, 35-06, 76-06, 81-06, 82-06. Library of Congress Cataloging-in-Publication Data International Conference on Differential Equations and Mathematical Physics (9th: 2002 : Uni- versity of Alabama, Birmingham). Advances in differential equations and mathematical physics : UAB international conference, differential equations and mathematical physics, March 26-30, 2002, University of Alabama, Birm- ingham/ Yulia Karpeshina... [et a!.], editors. p. cm.-(Contemporary mathematics, ISSN 0271-4132; 327) Includes bibliographical references. ISBN 0-8218-3296-4 (alk. paper)
  • Dyadic Rationals and Surreal Number Theory C

    Dyadic Rationals and Surreal Number Theory C

    IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 16, Issue 5 Ser. IV (Sep. – Oct. 2020), PP 35-43 www.iosrjournals.org Dyadic Rationals and Surreal Number Theory C. Avalos-Ramos C.U.C.E.I. Universidad de Guadalajara, Guadalajara, Jalisco, México J. A. Félix-Algandar Facultad de Ciencias Físico-Matemáticas de la Universidad Autónoma de Sinaloa, 80010, Culiacán, Sinaloa, México. J. A. Nieto Facultad de Ciencias Físico-Matemáticas de la Universidad Autónoma de Sinaloa, 80010, Culiacán, Sinaloa, México. Abstract We establish a number of properties of the dyadic rational numbers associated with surreal number theory. In particular, we show that a two parameter function of dyadic rationals can give all the trees of n-days in surreal number formalism. --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 07-10-2020 Date of Acceptance: 22-10-2020 --------------------------------------------------------------------------------------------------------------------------------------- I. Introduction In mathematics, from number theory history [1], one learns that historically, roughly speaking, the starting point was the natural numbers N and after a centuries of though evolution one ends up with the real numbers from which one constructs the differential and integral calculus. Surprisingly in 1973 Conway [2] (see also Ref. [3]) developed the surreal numbers structure which contains no only the real numbers , but also the hypereals and other numerical structures. Consider the set (1) and call and the left and right sets of , respectively. Surreal numbers are defined in terms of two axioms: Axiom 1. Every surreal number corresponds to two sets and of previously created numbers, such that no member of the left set is greater or equal to any member of the right set .
  • Adaptive Resonance Theory

    Adaptive Resonance Theory

    Adaptive Resonance Theory Jonas Jacobi, Felix J. Oppermann C.v.O. Universitat¨ Oldenburg Gliederung 1. Neuronale Netze 2. Stabilität - Plastizität 3. ART-1 4. ART-2 5. ARTMAP 6. Anwendung 7. Zusammenfassung Adaptive Resonance Theory – p.1/27 Neuronale Netze Künstliche neuronale Netze sind Modell für das Nervensystem Aufbau aus einzellnen Zellen Paralelle Datenverarbeitung Lernen implizit durch Gewichtsveränderung Sehr unterschiedliche Strukturen Adaptive Resonance Theory – p.2/27 Neuronale Netze Summation der Eingänge Vergleich mit einem Schwellenwert Erzeugen eines Ausgabesignals Adaptive Resonance Theory – p.3/27 Stabilität $ Plastizität Lernen mit fester Lernrate Die Lernrate gibt an wie stark ein neues Muster die Gewichte beeinflusst Lernen erfolgt bei überwachtem Lernen nur in einer Trainingsphase Im biologischen System wird das Lernen nicht beendet Meist kein direktes Fehlersignal Adaptive Resonance Theory – p.4/27 Stabilität $ Plastizität Stabilität Einmal Gelerntes soll gespeichert bleiben Das trainieren neuer Muster soll vermieden werden, da diese die Klassifikation stark verändern könnten Plastizität Neue Muster sollen kein vollständiges Neutrainieren erfordern Alte Klassifikation sollten beim Hinzufügen neuer Muster erhalten bleiben Adaptive Resonance Theory – p.5/27 Stabilität $ Plastizität Beide Anforderungen konkurrieren Hohe Stabilität oder hohe Plastizität Plastizitäts-Stabilitäts-Dilemma Adaptive Resonance Theory – p.6/27 Stabilität $ Plastizität Lösungsansätze: Kontrolle ob das neue Muster bereits bekannt ist Für neue Muster eine neue Klasse öffnen Bei hoher Ähnlichkeit zu bekannten Mustern Einordnung in diese Klasse Der Parameter der Kontrolle kann als Aufmerksamkeit betrachtet werden Adaptive Resonance Theory – p.7/27 Stephen Grossberg Stuyvesant High School, Manhattan, 1957 Rockefeller University, Ph.D., 1964-1967 Associate Professor of Applied Mathematics, M.I.T., 1969-1975.