DOCSLIB.ORG

Download: PDF, 0,6 MB

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Download: PDF, 0,6 MB CONTENTS EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY EDITOR-IN-CHIEF ROBIN WILSON Department of Pure Mathematics The Open University Milton Keynes MK7 6AA, UK e-mail: [email protected] ASSOCIATE EDITORS STEEN MARKVORSEN Department of Mathematics Technical University of Denmark NEWSLETTER No. 40 Building 303 DK-2800 Kgs. Lyngby, Denmark June 2001 e-mail: [email protected] KRZYSZTOF CIESIELSKI EMS Agenda ................................................................................................. 2 Mathematics Institute Jagiellonian University Editorial - David Salinger ............................................................................ 3 Reymonta 4 30-059 Kraków, Poland SIAM-EMS Conference .................................................................................. 4 e-mail: [email protected] KATHLEEN QUINN Executive Committee Meeting ....................................................................... 6 The Open University [address as above] e-mail: [email protected] The Institute for Industrial Mathematics ..................................................... 8 SPECIALIST EDITORS Workshop on Applied Mathematics in Europe ...............................................9 INTERVIEWS Steen Markvorsen [address as above] GAMM Annual Scientific Conference 2001 ................................................ 11 SOCIETIES Krzysztof Ciesielski [address as above] The Methodology of Mathematics ................................................................ 12 EDUCATION Tony Gardiner Interview with Björn Engquist .................................................................... 15 University of Birmingham Birmingham B15 2TT, UK Interview with Manuel Valdivia .................................................................. 16 e-mail: [email protected] MATHEMATICAL PROBLEMS Mathematical Societies: France ................................................................. 18 Paul Jainta Werkvolkstr. 10 Mathematical Societies: Romania ............................................................. 20 D-91126 Schwabach, Germany e-mail: [email protected] Personal Column ......................................................................................... 23 ANNIVERSARIES Forthcoming Conferences ............................................................................ 25 June Barrow-Green and Jeremy Gray Open University [address as above] Recent Books ............................................................................................... 30 e-mail: [email protected] and [email protected] and CONFERENCES Designed and printed by Armstrong Press Limited Kathleen Quinn [address as above] Crosshouse Road, Southampton, Hampshire SO14 5GZ, UK RECENT BOOKS telephone: (+44) 23 8033 3132 fax: (+44) 23 8033 3134 Ivan Netuka and Vladimir Sou³ek Published by European Mathematical Society Mathematical Institute ISSN 1027 - 488X Charles University Sokolovská 83 The views expressed in this Newsletter are those of the authors and do not necessarily 18600 Prague, Czech Republic represent those of the EMS or the Editorial team. e-mail: [email protected] and [email protected] ADVERTISING OFFICER NOTICE FOR MATHEMATICAL SOCIETIES Vivette Girault Labels for the next issue will be prepared during the second half of August 2001. Laboratoire d’Analyse Numérique Please send your updated lists before then to Ms Tuulikki Mäkeläinen, Department of Mathematics, P.O. Box 4, FIN-00014 University of Helsinki, Finland; e-mail: Boite Courrier 187, Université Pierre [email protected] et Marie Curie, 4 Place Jussieu 75252 Paris Cedex 05, France INSTITUTIONAL SUBSCRIPTIONS FOR THE EMS NEWSLETTER e-mail: [email protected] Institutes and libraries can order the EMS Newsletter by mail from the EMS Secretariat, OPEN UNIVERSITY Department of Mathematics, P. O. Box 4, FI-00014 University of Helsinki, Finland, or by e- PRODUCTION TEAM mail: ([email protected]). Please include the name and full address (with postal code), tele- Liz Scarna, Kathleen Quinn phone and fax number (with country code) and e-mail address. The annual subscription fee (including mailing) is 60 euros; an invoice will be sent with a sample copy of the Newsletter. EMS June 2001 1 EMS NEWS EMS Committee EMS Agenda EXECUTIVE COMMITTEE PRESIDENT (1999–2002) 2001 Prof. ROLF JELTSCH 19-21 June Seminar for Applied Mathematics EMS lectures at the University of Heraklion, Crete (Greece) ETH, CH-8092 Zürich, Switzerland Lecturer: Prof. George Papanicolaou (Stanford, USA) e-mail: [email protected] Title: Time Reversed Acoustics VICE-PRESIDENTS Contact: David Brannan, e-mail: [email protected] Prof. LUC LEMAIRE (1999–2002) 9-25 July Department of Mathematics EMS Summer School at St Petersburg (Russia) Université Libre de Bruxelles Title: Asymptotic combinatorics with applications to mathematical physics C.P. 218 – Campus Plaine Organiser: Anatoly Vershik, e-mail: [email protected] Bld du Triomphe B-1050 Bruxelles, Belgium 15 August e-mail: [email protected] Deadline for proposals for 2003, 2004 and 2005 EMS Summer Schools Prof. BODIL BRANNER (2001–2004) Contact: Renzo Piccinini, e-mail: [email protected] Department of Mathematics Deadline for submission of material for the September issue of the EMS Newsletter Technical University of Denmark Contact: Robin Wilson, e-mail: [email protected] Building 303 19-31 August DK-2800 Kgs. Lyngby, Denmark EMS Summer School at Prague (Czech Republic) e-mail: [email protected] Title: Simulation of fluid and structure interaction SECRETARY (1999–2002) Organiser: Miloslav Feistauer, e-mail: [email protected] Prof. DAVID BRANNAN Department of Pure Mathematics 24-30 August The Open University EMS lectures in Malta, as part of the 10th International Meeting of European Women in Walton Hall Mathematics Milton Keynes MK7 6AA, UK Lecturer: Michèle Vergne (Ecole Polytechnique, Palaiseau, France) e-mail: [email protected] Title: Convex polytopes TREASURER (1999–2002) Contact: Dr. Tsou Sheung Tsun, e-mail: [email protected] Prof. OLLI MARTIO 1-2 September Department of Mathematics EMS Executive Committee meeting, Berlin (Germany) P.O. Box 4 3-6 September FIN-00014 University of Helsinki Finland 1st EMS-SIAM conference, Berlin (Germany) e-mail: [email protected] Organiser: Peter Deuflhard, e-mail: [email protected] ORDINARY MEMBERS 15 November Prof. VICTOR BUCHSTABER (2001–2004) Deadline for submission of material for the December issue of the EMS Newsletter Department of Mathematics and Mechanics Contact: Robin Wilson, e-mail: [email protected] Moscow State University 19-21 November 119899 Moscow, Russia EMS lectures at Università degli Studi, Tor Vergata, Rome (Italy) e-mail: [email protected] Lecturer: Michèle Vergne (Ecole Polytechnique, Palaiseau, France) Prof. DOINA CIORANESCU (1999–2002) Laboratoire d’Analyse Numérique Title: Convex Polytopes Université Paris VI Contact: Prof. Maria Welleda Baldoni, e-mail:[email protected] 4 Place Jussieu 22-23 November 75252 Paris Cedex 05, France Fifth Diderot Mathematical Forum e-mail: [email protected] Title: Mathematics and Telecommunications Prof. RENZO PICCININI (1999–2002) Venues: Eindhoven (Netherlands) Helsinki (Finland) and Lausanne (Switzerland) Dipartimento di Matematica e Applicazioni Contact: Jean-Pierre Bourgignon, e-mail: [email protected] Università di Milano-Bicocca Via Bicocca degli Arcimboldi, 8 20126 Milano, Italy 2002 e-mail: [email protected] 9-10 February Prof. MARTA SANZ-SOLÉ (1997–2000) Executive Committee Meeting in Brussels, at the invitation of the Belgian Facultat de Matematiques Mathematical Society and the Université Libre de Bruxelles Universitat de Barcelona 24 February-1 March Gran Via 585 EMS Summer School in Eilat (Israel) E-08007 Barcelona, Spain Title: Algebraic Geometry, Computations and Applications e-mail: [email protected] Contact: Mina Teicher, e-mail: [email protected] Prof. MINA TEICHER (2001–2004) 1 March Department of Mathematics and Computer Deadline for Proposals for 2003 EMS Lectures. Science Bar-Ilan University Contact: David Brannan, e-mail: [email protected] Ramat-Gan 52900, Israel 31 May e-mail: [email protected] Executive Committee meeting in Oslo (Norway) EMS SECRETARIAT 1-2 June Ms. T. MÄKELÄINEN EMS Council Meeting, Oslo Department of Mathematics 3-8 June P.O. Box 4 Abel Bicentennial Conference, Oslo. FIN-00014 University of Helsinki Finland tel: (+358)-9-1912-2883 2004 fax: (+358)-9-1912-3213 25-27 June telex: 124690 EMS Council Meeting, Stockholm (Sweden) e-mail: [email protected] 27 June - 2 July website: http://www.emis.de 4th European Congress of Mathematicians (4ecm), Stockholm (Sweden) 2 EMS June 2001 EDITORIAL possible outcome of a reform that has been imposed from above without consultation with the academic disciplines. Indeed, the picture could be even bleaker: the ominous EditorialEditorial phrase ‘a European dimension to quality assurance’ conjures up a vision of philistine David Salinger bureaucratic control, and maybe the impo- sition of a common curriculum. The Bologna Declaration: a Bachelor’s degree for all To be fair, the Bologna Declaration declares specifically that it is aiming for convergence, not uniformity, and the evi- On 19 June 1999, 29 European Education dence so far is that each country is inter- Ministers signed a document that has preting the Declaration in its own way. become known as the Bologna Declaration. One of the strengths of European Higher Education is its diversity
Load more

Recommended publications
  • Summary As Preparation for the Final Exam
    UUnnddeerrsstatannddiinngg ththee UUnniivveerrssee Summary Lecture Volker Beckmann Joint Center for Astrophysics, University of Maryland, Baltimore County & NASA Goddard Space Flight Center, Astrophysics Science Division UMBC, December 12, 2006 OOvveerrvviieeww ● What did we learn? ● Dark night sky ● distances in the Universe ● Hubble relation ● Curved space ● Newton vs. Einstein : General Relativity ● metrics solving the EFE: Minkowski and Robertson-Walker metric ● Solving the Einstein Field Equation for an expanding/contracting Universe: the Friedmann equation Graphic: ESA / V. Beckmann OOvveerrvviieeww ● Friedmann equation ● Fluid equation ● Acceleration equation ● Equation of state ● Evolution in a single/multiple component Universe ● Cosmic microwave background ● Nucleosynthesis ● Inflation Graphic: ESA / V. Beckmann Graphic by Michael C. Wang (UCSD) The velocity- distance relation for galaxies found by Edwin Hubble. Graphic: Edwin Hubble (1929) Expansion in a steady state Universe Expansion in a non-steady-state Universe The effect of curvature The equivalent principle: You cannot distinguish whether you are in an accelerated system or in a gravitational field NNeewwtotonn vvss.. EEiinnssteteiinn Newton: - mass tells gravity how to exert a force, force tells mass how to accelerate (F = m a) Einstein: - mass-energy (E=mc²) tells space time how to curve, curved space-time tells mass-energy how to move (John Wheeler) The effect of curvature A glimpse at EinsteinThe effect’s field of equationcurvature Left side (describes the action
    [Show full text]
  • Boletín De La RSME
    Boletín de la RSME Número 297, 16 de enero de 2012 Sumario Noticias de la RSME Noticias de la RSME Encuentro Conjunto RSME-SMM. Antonio Campillo. Torremolinos, Málaga, 17-20 de enero El programa científico consta de veinticuatro • Encuentro Conjunto RSME- La Real Sociedad Matemática Española y la sesiones especiales, ocho conferencias ple- SMM. Torremolinos, Málaga, Sociedad Matemática Mexicana celebran el narias y la conferencia de clausura del profe- 17-20 de enero Segundo Encuentro Conjunto RSME-SMM en sor Federico Mayor Zaragoza con el título preciso “La comunidad científica ante los de- • Noticias del CIMPA el Hotel Meliá Costa del Sol de Torremolinos (Málaga) los próximos días 17, 18, 19 y 20 de safíos presentes”. Como en la primera edi- • Acuerdo entre cuatro insti- enero. El Primer Encuentro Conjunto se ce- ción, el congreso ha programado alrededor tuciones para la creación del lebró en Oaxaca en julio de 2009 y la serie de doscientas conferencias invitadas, la mitad IEMath. Documento de In- continuará cada tres años a partir de 2014, de las cuales corresponden a la parte mexi- cana y la otra mitad a la española. vestigación de la RSME año en el que está prevista la tercera edición en México. El comité organizador está presi- Las conferencias plenarias están a cargo de • Ampliación del orden del dido por Daniel Girela, e integrado por José Samuel Gitler, José Luis Alías, José María día de la Junta General Ordi- Luis Flores, Cristóbal González, Francisco Pérez Izquierdo, Jorge Velasco, María Emilia naria de la RSME Javier Martín Reyes, María Lina Martínez, Caballero, Javier Fernández de Bobadilla, Francisco José Palma, José Ángel Peláez y • Noticia de la COSCE: Nue- Xavier Gómez-Mont y Eulalia Nulart.
    [Show full text]
  • Abstract Generalized Natural Inflation and The
    ABSTRACT Title of dissertation: GENERALIZED NATURAL INFLATION AND THE QUEST FOR COSMIC SYMMETRY BREAKING PATTERS Simon Riquelme Doctor of Philosophy, 2018 Dissertation directed by: Professor Zackaria Chacko Department of Physics We present a two-field model that generalizes Natural Inflation, in which the inflaton is the pseudo-Goldstone boson of an approximate symmetry that is spon- taneously broken, and the radial mode is dynamical. Within this model, which we designate as \Generalized Natural Inflation”, we analyze how the dynamics fundamentally depends on the mass of the radial mode and determine the size of the non-Gaussianities arising from such a scenario. We also motivate ongoing research within the coset construction formalism, that aims to clarify how the spontaneous symmetry breaking pattern of spacetime, gauge, and internal symmetries may allow us to get a deeper understanding, and an actual algebraic classification in the spirit of the so-called \zoology of con- densed matter", of different possible \cosmic states", some of which may be quite relevant for model-independent statements about different phases in the evolution of our universe. The outcome of these investigations will be reported elsewhere. GENERALIZED NATURAL INFLATION AND THE QUEST FOR COSMIC SYMMETRY BREAKING PATTERNS by Simon Riquelme Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2018 Advisory Committee: Professor Zackaria Chacko, Chair/Advisor Professor Richard Wentworth, Dean's Representative Professor Theodore Jacobson Professor Rabinda Mohapatra Professor Raman Sundrum A mis padres, Kattya y Luis. ii Acknowledgments It is a pleasure to acknowledge my adviser, Dr.
    [Show full text]
  • Lecture Notes in Mathematics
    Lecture Notes in Mathematics Edited by A. Oold and B. Eckmann 1185 Group Theory, Beijing 1984 Proceedings of an International Symposium held in Beijing, Aug. 27-Sep. 8, 1984 Edited by Tuan Hsio-Fu Springer-Verlag Berlin Heidelberg New York Tokyo Editor TUAN Hsio-Fu Department of Mathematics, Peking University Beijing, The People's Republic of China Mathematics Subject Classification (1980): 05-xx, 12F-xx, 14Kxx, 17Bxx, 20-xx ISBN 3-540-16456-1 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-16456-1 Springer-Verlag New York Heidelberg Berlin Tokyo This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich. © by Springer-Verlag Berlin Heidelberg 1986 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210 PREFACE From August 27 to September 8, 1984 there was held in Peking Uni• versity, Beijing an International Symposium on Group Theory. As well said by Hermann Wey1: "Symmetry is a vast subject signi• ficant in art and nature. Whenever you have to do with a structure endowed entity, try to determine the group of those transformations which leave all structural relations undisturbed." This passage underlies that the group concept is one of the most fundamental and most important in modern mathematics and its applications.
    [Show full text]
  • Degree in Mathematics
    Degree in Mathematics Title: Singularities and qualitative study in LQC Author: Llibert Aresté Saló Advisor: Jaume Amorós Torrent, Jaume Haro Cases Department: Departament de Matemàtiques Academic year: 2017 Universitat Polit`ecnicade Catalunya Facultat de Matem`atiquesi Estad´ıstica Degree in Mathematics Bachelor's Degree Thesis Singularities and qualitative study in LQC Llibert Arest´eSal´o Supervised by: Jaume Amor´osTorrent, Jaume Haro Cases January, 2017 Singularities and qualitative study in LQC Abstract We will perform a detailed analysis of singularities in Einstein Cosmology and in LQC (Loop Quantum Cosmology). We will obtain explicit analytical expressions for the energy density and the Hubble constant for a given set of possible Equations of State. We will also consider the case when the background is driven by a single scalar field, obtaining analytical expressions for the corresponding potential. And, in a given particular case, we will perform a qualitative study of the orbits in the associated phase space of the scalar field. Keywords Quantum cosmology, Equation of State, cosmic singularity, scalar field. 1 Contents 1 Introduction 3 2 Einstein Cosmology 5 2.1 Friedmann Equations . .5 2.2 Analysis of the singularities . .7 2.3 Reconstruction method . .9 2.4 Dynamics for the linear case . 12 3 Loop Quantum Cosmology 16 3.1 Modified Friedmann equations . 16 3.2 Analysis of the singularities . 18 3.3 Reconstruction method . 21 3.4 Dynamics for the linear case . 23 4 Conclusions 32 2 Singularities and qualitative study in LQC 1. Introduction In 1915, Albert Einstein published his field equations of General Relativity [1], giving birth to a new conception of gravity, which would now be understood as the curvature of space-time.
    [Show full text]
  • An Invitation to Model-Theoretic Galois Theory
    AN INVITATION TO MODEL-THEORETIC GALOIS THEORY. ALICE MEDVEDEV AND RAMIN TAKLOO-BIGHASH Abstract. We carry out some of Galois’ work in the setting of an arbitrary first-order theory T . We replace the ambient algebraically closed field by a large model M of T , replace fields by definably closed subsets of M, assume that T codes finite sets, and obtain the fundamental duality of Galois theory matching subgroups of the Galois group of L over F with intermediate exten- sions F ≤ K ≤ L. This exposition of a special case of [11] has the advantage of requiring almost no background beyond familiarity with fields, polynomials, first-order formulae, and automorphisms. 1. Introduction. Two hundred years ago, Evariste´ Galois contemplated symmetry groups of so- lutions of polynomial equations, and Galois theory was born. Thirty years ago, Saharon Shelah found it necessary to work with theories that eliminate imaginar- ies; for an arbitrary theory, he constructed a canonical definitional expansion with this property in [16]. Poizat immediately recognized the importance of a theory already having this property in its native language; indeed, he defined “elimina- tion of imaginaries” in [11]. It immediately became clear (see [11]) that much of Galois theory can be developed for an arbitrary first-order theory that eliminates imaginaries. This model-theoretic version of Galois theory can be generalized be- yond finite or even infinite algebraic extensions, and this can in turn be useful in other algebraic settings such as the study of Galois groups of polynomial differential equations (already begun in [11]) and linear difference equations. On a less applied note, it is possible to bring further ideas into the model-theoretic setting, as is done in [10] for the relation between Galois cohomology and homogeneous spaces.
    [Show full text]
  • Prizes and Awards Session
    PRIZES AND AWARDS SESSION Wednesday, July 12, 2021 9:00 AM EDT 2021 SIAM Annual Meeting July 19 – 23, 2021 Held in Virtual Format 1 Table of Contents AWM-SIAM Sonia Kovalevsky Lecture ................................................................................................... 3 George B. Dantzig Prize ............................................................................................................................. 5 George Pólya Prize for Mathematical Exposition .................................................................................... 7 George Pólya Prize in Applied Combinatorics ......................................................................................... 8 I.E. Block Community Lecture .................................................................................................................. 9 John von Neumann Prize ......................................................................................................................... 11 Lagrange Prize in Continuous Optimization .......................................................................................... 13 Ralph E. Kleinman Prize .......................................................................................................................... 15 SIAM Prize for Distinguished Service to the Profession ....................................................................... 17 SIAM Student Paper Prizes ....................................................................................................................
    [Show full text]
  • Fundamental Theorems in Mathematics
    SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635].
    [Show full text]
  • UT Austin Professor, Luis Caffarelli, Wins Prestigious Wolf Prize Porto Students Conduct Exploratory Visits
    JANUARY//2012 NUMBER//41 UT Austin Professor, Luis Caffarelli, wins prestigious Wolf Prize Luis Caffarelli, a mathematician, Caffarelli’s research interests include Professor at the Institute for Compu- nonlinear analysis, partial differential tational Engineering and Sciences equations and their applications, (ICES) at the University of Texas at calculus of variations and optimiza- Austin and Director of CoLab tion. The ICES Professor is also widely Mathematics Program, has been recognized as the world’s leading named a winner of Israel’s prestigious specialist in free-boundary problems Wolf Prize, in the mathematics for nonlinear partial differential category. equations. This prize, which consists of a cer- Each year this prize is awarded to tificate and a monetary award of specialists in the fields of agriculture, $100,000, “is further evidence of chemistry, mathematics, physics Luis’ huge impact”, according to and the arts. Caffarelli will share the Alan Reid (Chair of the Department 2012 mathematics prize with of Mathematics). “I feel deeply Michael Aschbacher, a professor at honored”, states Caffarelli, who joins the California Institute of Technology. the UT Austin professors John Tate (Mathematics, 2002) and Allen Bard Link for Institute for Computational UT Austin Professor, Luis Caffarelli (Chemistry, 2008) as a Wolf Prize Engineering and Sciences: winner. http://www.ices.utexas.edu/ Porto Students Conduct Exploratory Visits UT Austin welcomed several visitors at the end of the Fall animation. Bastos felt he benefited greatly from the visit, 2011 semester, including Digital Media doctoral students commenting, “The time I spent in Austin and in College Pedro Bastos, Rui Dias, Filipe Lopes, and George Siorios of Station was everything I expected and more.
    [Show full text]
  • A Sketch of the History and State of Automated Deduction
    A Sketch of the History and State of Automated Deduction David A. Plaisted October 19, 2015 Introduction • Ed Reingold influenced me to do algorithms research early in my career, and this led to some good work. However, my main research area now is automatic theorem proving, so I will discuss this instead. • This talk will be a survey touching on some aspects of the state of the field of automated deduction at present. The content of the talk will be somewhat more general than the original title indicated; thus the change in title. This talk should be about 20 minutes long. I’m planning to put these notes on the internet soon. There is a lot to cover in 20 minutes, so it is best to leave most questions until the end. Proofs in Computer Science • There is a need for formal proofs in computer science, for example, to prove the correctness of software, or to prove theorems in a theoretical paper. • There is also a need for proofs in other areas such as mathematics. • It can be helpful to have programs that check proofs or even help to find the proofs. 1 Automated Deduction • This talk emphasizes systems that do a lot of proof search on their own, either to find the whole proof automatically or large parts of it, without the user specifying each application of each rule of inference. • There are also systems that permit the user to construct a proof and check that the rules of inference are properly applied. History of Automated Deduction Our current state of knowledge in automated deduction came to us by a long and complicated process of intellectual development.
    [Show full text]
  • Observational Cosmology - 30H Course 218.163.109.230 Et Al
    Observational cosmology - 30h course 218.163.109.230 et al. (2004–2014) PDF generated using the open source mwlib toolkit. See http://code.pediapress.com/ for more information. PDF generated at: Thu, 31 Oct 2013 03:42:03 UTC Contents Articles Observational cosmology 1 Observations: expansion, nucleosynthesis, CMB 5 Redshift 5 Hubble's law 19 Metric expansion of space 29 Big Bang nucleosynthesis 41 Cosmic microwave background 47 Hot big bang model 58 Friedmann equations 58 Friedmann–Lemaître–Robertson–Walker metric 62 Distance measures (cosmology) 68 Observations: up to 10 Gpc/h 71 Observable universe 71 Structure formation 82 Galaxy formation and evolution 88 Quasar 93 Active galactic nucleus 99 Galaxy filament 106 Phenomenological model: LambdaCDM + MOND 111 Lambda-CDM model 111 Inflation (cosmology) 116 Modified Newtonian dynamics 129 Towards a physical model 137 Shape of the universe 137 Inhomogeneous cosmology 143 Back-reaction 144 References Article Sources and Contributors 145 Image Sources, Licenses and Contributors 148 Article Licenses License 150 Observational cosmology 1 Observational cosmology Observational cosmology is the study of the structure, the evolution and the origin of the universe through observation, using instruments such as telescopes and cosmic ray detectors. Early observations The science of physical cosmology as it is practiced today had its subject material defined in the years following the Shapley-Curtis debate when it was determined that the universe had a larger scale than the Milky Way galaxy. This was precipitated by observations that established the size and the dynamics of the cosmos that could be explained by Einstein's General Theory of Relativity.
    [Show full text]
  • On a Generalization of the Hadwiger-Nelson Problem
    On a generalization of the Hadwiger-Nelson problem Mohammad Bardestani, Keivan Mallahi-Karai October 15, 2018 Abstract For a field F and a quadratic form Q defined on an n-dimensional vector space V over F , let QGQ, called the quadratic graph associated to Q, be the graph with the vertex set V where vertices u; w 2 V form an edge if and only if Q(v − w) = 1. Quadratic graphs can be viewed as natural generalizations of the unit-distance graph featuring in the famous Hadwiger-Nelson problem. In the present paper, we will prove that for a local field F of characteristic zero, the Borel chromatic number of QGQ is infinite if and only if Q represents zero non-trivially over F . The proof employs a recent spectral bound for the Borel chromatic number of Cayley graphs, combined with an analysis of certain oscillatory integrals over local fields. As an application, we will also answer a variant of question 525 proposed in the 22nd British Combinatorics Conference 2009 [6]. 1 Introduction The celebrated Hadwiger-Nelson problem asks for the minimum number of colors required to color n R such that no two points at distance one from each other have the same color. Recall that the chromatic number of a graph G, denoted by χ(G), is the least cardinal c such that the vertices of G can be partitioned into c sets (called color classes) such that no color class contains an edge in G. Hence, the Hadwiger-Nelson problem is the question of finding χ(Gn), where Gn is the graph with vertex set n V (Gn) = R , where the adjacency of vertices x; y 2 V (Gn) is defined by the equation Q(x − y) = 1; 2 2 n here, Q(x1; : : : ; xn) = x1 + ··· + xn is the canonical positive-definite quadratic form on R .
    [Show full text]