On Certain Unitary Representations of an Infinite Group of Transformations
On Certain Unitary Representations of an Infinite Group of Transformations

Author: L‚on Hove

Publisher: World Scientific

Published: 2001

Total Pages: 108

ISBN-13: 9789810246433

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On April 20, 1951, L‚on Van Hove presented his thesis ?Sur certaines repr‚sentations unitaires d'un groupe infini de transformations' to the Universit‚ libre de Bruxelles (Free University of Brussels), two days before the University of Grenoble had approved the creation of L'Ecole d'‚t‚ de physique th‚orique at Les Houches (Haute Savoie, France). The first session of the ?Ecole des Houches? began on July 15, 1951, with a month-long course by Van Hove on quantum mechanics. The lecture notes for this course were written for the benefit of physicists who ? like most of their colleagues outside the US, Canada, and England at that time ? did not know quantum mechanics but wanted to learn it seriously. Van Hove's course met their expectations fully. The physics course benefitted from the mathematical expertise of the lecturer, which is also apparent in this thesis. Without his own research as scaffolding, Van Hove could not have built the short and beautiful course which provided the participants with a solid, useful foundation in modern physics.The lecture notes are in French. If they had been in English they would have been published together with the translation of the thesis. The first three pages of the notes are reproduced at the end of this book. The set of notes was reproduced by stencils and distributed to the participants at the beginning of the course.The translation of L‚on Van Hove's thesis was initiated in late 2000, when Bob Hermann, formerly in the Department of Mathematics at MIT, sent to Van Hove's son Michel his view on the thesis: ?I would consider it as one of the most important mathematical physics papers of the past fifty years, containing the key ideas for what has become known as ?geometric quantization.?? Indeed, the thesis is interesting both to historians of science and to theoretical physicists and mathematicians exploring the relationships between quantum and classical physics, based on the Hilbert-space approach to classical mechanics.

Sums of Squares of Integers
Sums of Squares of Integers

Author: Carlos J. Moreno

Publisher: CRC Press

Published: 2005-12-09

Total Pages: 368

ISBN-13: 1584884568

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Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's elementary methods with the analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares of integers for any s and n. It is also the first book to give a proof of Szemeredi's theorem, and is the first number theory book to discuss how the modern theory of modular forms complements and clarifies the classical fundamental results about sums of squares. The book presents several existing, yet still interesting and instructive, examples of modular forms. Two chapters develop useful properties of the Bernoulli numbers and illustrate arithmetic progressions, proving the theorems of van der Waerden, Roth, and Szemeredi. The book also explains applications of the theory to three problems that lie outside of number theory in the areas of cryptanalysis, microwave radiation, and diamond cutting. The text is complemented by the inclusion of over one hundred exercises to test the reader's understanding.

On Certain Unitary Representations Of An Infinite Group Of Transformations - Thesis By Leon Van Hove
On Certain Unitary Representations Of An Infinite Group Of Transformations - Thesis By Leon Van Hove

Author: Marcus Berg

Publisher: World Scientific

Published: 2001-05-17

Total Pages: 103

ISBN-13: 981449089X

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On April 20, 1951, Léon Van Hove presented his thesis “Sur certaines représentations unitaires d'un groupe infini de transformations' to the Université libre de Bruxelles (Free University of Brussels), two days before the University of Grenoble had approved the creation of L'Ecole d'été de physique théorique at Les Houches (Haute Savoie, France). The first session of the “Ecole des Houches” began on July 15, 1951, with a month-long course by Van Hove on quantum mechanics. The lecture notes for this course were written for the benefit of physicists who — like most of their colleagues outside the US, Canada, and England at that time — did not know quantum mechanics but wanted to learn it seriously. Van Hove's course met their expectations fully. The physics course benefitted from the mathematical expertise of the lecturer, which is also apparent in this thesis. Without his own research as scaffolding, Van Hove could not have built the short and beautiful course which provided the participants with a solid, useful foundation in modern physics.The lecture notes are in French. If they had been in English they would have been published together with the translation of the thesis. The first three pages of the notes are reproduced at the end of this book. The set of notes was reproduced by stencils and distributed to the participants at the beginning of the course.The translation of Léon Van Hove's thesis was initiated in late 2000, when Bob Hermann, formerly in the Department of Mathematics at MIT, sent to Van Hove's son Michel his view on the thesis: “I would consider it as one of the most important mathematical physics papers of the past fifty years, containing the key ideas for what has become known as ‘geometric quantization.’” Indeed, the thesis is interesting both to historians of science and to theoretical physicists and mathematicians exploring the relationships between quantum and classical physics, based on the Hilbert-space approach to classical mechanics.

Cohen-Macaulay Representations
Cohen-Macaulay Representations

Author: Graham J. Leuschke

Publisher: American Mathematical Soc.

Published: 2012-05-02

Total Pages: 390

ISBN-13: 0821875817

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This book is a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative algebra, singularity theory, and representations of groups and algebras. Two introductory chapters treat the Krull-Remak-Schmidt Theorem on uniqueness of direct-sum decompositions and its failure for modules over local rings. Chapters 3-10 study the central problem of classifying the rings with only finitely many indecomposable MCM modules up to isomorphism, i.e., rings of finite CM type. The fundamental material--ADE/simple singularities, the double branched cover, Auslander-Reiten theory, and the Brauer-Thrall conjectures--is covered clearly and completely. Much of the content has never before appeared in book form. Examples include the representation theory of Artinian pairs and Burban-Drozd's related construction in dimension two, an introduction to the McKay correspondence from the point of view of maximal Cohen-Macaulay modules, Auslander-Buchweitz's MCM approximation theory, and a careful treatment of nonzero characteristic. The remaining seven chapters present results on bounded and countable CM type and on the representation theory of totally reflexive modules.

Abelian Groups and Representations of Finite Partially Ordered Sets
Abelian Groups and Representations of Finite Partially Ordered Sets

Author: David Arnold

Publisher: Springer Science & Business Media

Published: 2012-11-14

Total Pages: 256

ISBN-13: 1441987509

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The theme of this book is an exposition of connections between representations of finite partially ordered sets and abelian groups. Emphasis is placed throughout on classification, a description of the objects up to isomorphism, and computation of representation type, a measure of when classification is feasible. David M. Arnold is the Ralph and Jean Storm Professor of Mathematics at Baylor University. He is the author of "Finite Rank Torsion Free Abelian Groups and Rings" published in the Springer-Verlag Lecture Notes in Mathematics series, a co-editor for two volumes of conference proceedings, and the author of numerous articles in mathematical research journals.

Theorems of the 21st Century
Theorems of the 21st Century

Author: Bogdan Grechuk

Publisher: Springer

Published: 2019-06-15

Total Pages: 455

ISBN-13: 303019096X

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This book consists of short descriptions of 106 mathematical theorems, which belong to the great achievements of 21st century mathematics but require relatively little mathematical background to understand their formulation and appreciate their importance. The selected theorems of this volume, chosen from the famous Annals of Mathematics journal, cover a broad range of topics from across mathematics. Each theorem description is essentially self-contained, can be read independently of the others, and requires as little preliminary knowledge as possible. Although the sections often start with an informal discussion and toy examples, all the necessary definitions are included and each description culminates in the precise formulation of the corresponding theorem. Filling the gap between surveys written for mathematicians and popular mathematics, this book is intended for readers with a keen interest in contemporary mathematics.

Affine Representations of Grothendieck Groups and Applications to Rickart $C^\ast $-Algebras and $\aleph _0$-Continuous Regular Rings
Affine Representations of Grothendieck Groups and Applications to Rickart $C^\ast $-Algebras and $\aleph _0$-Continuous Regular Rings

Author: K. R. Goodearl

Publisher: American Mathematical Soc.

Published: 1980

Total Pages: 175

ISBN-13: 0821822349

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This paper is concerned with the structure of three interrelated classes of objects: partially ordered abelian groups with countable interpolation, [Hebrew]Aleph0-continuous regular rings, and finite Rickart C*-algebras. The connection from these rings and algebras to these groups is the Grothendieck group K0, which, for all [Hebrew]Aleph0-continuous regular rings and most finite Rickart C*-algebras, is a partially ordered abelian group with countable interpolation. Such partially ordered groups are shown to possess quite specific representations in spaces of affine continuous functions on Choquet simplices. The theme of this paper is to develop the structure theory of these groups and these representations, and to translate the results, via K0, into properties of [Hebrew]Aleph0-continuous regular rings and finite Rickart C*-algebras.

Encyclopaedia of Mathematics
Encyclopaedia of Mathematics

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 506

ISBN-13: 940151237X

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This ENCYCLOPAEDIA OF MA THEMA TICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Digital Electronics
Digital Electronics

Author: Dr. P. Kannan

Publisher: Sree kamalamani Publications

Published: 2018-10-01

Total Pages: 397

ISBN-13: 9385449052

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This book is extensively designed for the third semester ECE students as per Anna university syllabus R-2013. The following chapters constitute the following units Chapter 1, 2 and :-Unit 1Chapter 3 covers :-Unit 2 Chapter 4 and 5 covers:-Unit 3Chapter 6 covers :- Unit 4Chapter 7 covers :- Unit 5Chapter 8 covers :- Unit 5 CHAPTER 1: Introduces the Number System, binary arithmetic and codes. CHAPTER 2: Deals with Boolean algebra, simplification using Boolean theorems, K-map method , Quine McCluskey method, logic gates, implementation of switching function using basic Logical Gates and Universal Gates. CHAPTER 3: Describes the combinational circuits like Adder, Subtractor, Multiplier, Divider, magnitude comparator, encoder, decoder, code converters, Multiplexer and Demultiplexer. CHAPTER 4: Describes with Latches, Flip-Flops, Registers and Counters CHAPTER 5: Concentrates on the Analysis as well as design of synchronous sequential circuits, Design of synchronous counters, sequence generator and Sequence detector CHAPTER 6: Concentrates the Design as well as Analysis of Fundamental Mode circuits, Pulse mode Circuits, Hazard Free Circuits, ASM Chart and Design of Asynchronous counters. CHAPTER 7: Discussion on memory devices which includes ROM, RAM, PLA, PAL, Sequential logic devices and ASIC. CHAPTER 8: Concentrate on the comparison, operation and characteristics of RTL, DTL, TTL, ECL and MOS families. We have taken enough care to present the definitions and statements of basic laws and theorems, problems with simple steps to make the students familiar with the fundamentals of Digital Design.