Advanced Topics in Relation Algebras

Relation Algebras

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Author: Steven Givant

Publisher: Springer

ISBN: 3319659456

Category: Mathematics

Page: 605

View: 3924

The second volume of a pair that charts relation algebras from novice to expert level, this text brings the well-grounded reader to the frontiers of research. Building on the foundations established in the preceding Introduction to Relation Algebras, this volume advances the reader into the deeper mathematical results of the past few decades. Such material offers an ideal preparation for research in relation algebras and Boolean algebras with operators. Arranged in a modular fashion, this text offers the opportunity to explore any of several areas in detail; topics include canonical extensions, completions, representations, varieties, and atom structures. Each chapter offers a complete account of one such avenue of development, including a historical section and substantial number of exercises. The clarity of exposition and comprehensive nature of each module make this an ideal text for the independent reader entering the field, while researchers will value it as a reference for years to come. Collecting, curating, and illuminating over 75 years of progress since Tarski's seminal work in 1941, this textbook in two volumes offers a landmark, unified treatment of the increasingly relevant field of relation algebras. Clear and insightful prose guides the reader through material previously only available in scattered, highly-technical journal articles. Students and experts alike will appreciate the work as both a textbook and invaluable reference for the community. Note that this volume contains numerous, essential references to the previous volume, Introduction to Relation Algebras. The reader is strongly encouraged to secure at least electronic access to the first book in order to make use of the second.

Introduction to Relation Algebras

Relation Algebras

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Author: Steven Givant

Publisher: Springer

ISBN: 3319652354

Category: Mathematics

Page: 572

View: 4124

The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field. The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naïve set theory. The measured pace and outstanding clarity are particularly suited to independent study, and provide an unparalleled opportunity to learn from one of the leading authorities in the field. Collecting, curating, and illuminating over 75 years of progress since Tarski's seminal work in 1941, this textbook in two volumes offers a landmark, unified treatment of the increasingly relevant field of relation algebras. Clear and insightful prose guides the reader through material previously only available in scattered, highly-technical journal articles. Students and experts alike will appreciate the work as both a textbook and invaluable reference for the community.

Algebra

Volume II: Fields with Structure, Algebras and Advanced Topics

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Author: Falko Lorenz

Publisher: Springer Science & Business Media

ISBN: 0387724877

Category: Mathematics

Page: 340

View: 3120

This is Volume II of a two-volume introductory text in classical algebra. The text moves methodically with numerous examples and details so that readers with some basic knowledge of algebra can read it without difficulty. It is recommended either as a textbook for some particular algebraic topic or as a reference book for consultations in a selected fundamental branch of algebra. The book contains a wealth of material. Amongst the topics covered in Volume are the theory of ordered fields and Nullstellen Theorems. Known researcher Lorenz also includes the fundamentals of the theory of quadratic forms, of valuations, local fields and modules. What’s more, the book contains some lesser known or nontraditional results – for instance, Tsen's results on the solubility of systems of polynomial equations with a sufficiently large number of indeterminates.

Quantum Cosmology - The Supersymmetric Perspective - Vol. 2

Advanced Topic

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Author: Paulo Vargas Moniz

Publisher: Springer Science & Business Media

ISBN: 3642115691

Category: Science

Page: 300

View: 7952

We read in order to know we are not alone, I once heard, and perhaps it could also be suggested that we write in order not to be alone, to endorse, to promote continuity. The idea for this book took about 10 years to materialize, and it is the author’s hope that its content will constitute the beginning of further explorations beyond current horizons. More speci cally, this book appeals to the reader to engage upon and persevere with a journey, moving through the less well explored territories in the evolution of the very early universe, and pushing towards new landscapes. P- haps, during or after consulting this book, this attitude and this willingness will be embraced by someone, somewhere, and this person will go on to enrich our quantum cosmological description of the early universe, by means of a clearer supersymm- ric perspective. It is to these creative and inquisitive ‘young minds’ that the book is addressed. The reader will not therefore nd in this book all the answers to all the problems regarding a supersymmetric and quantum description of the early universe, and this remark is substantiated in the book by a list of unresolved and challenging problems, itself incomplete.

Representations of Algebras and Related Topics

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Author: Ragnar-Olaf Buchweitz,Helmut Lenzing

Publisher: American Mathematical Soc.

ISBN: 9780821885925

Category: Mathematics

Page: 396

View: 4730

This proceedings volume resulted from the Tenth International Conference on Representations of Algebras and Related Topics held at The Fields Institute (Toronto, ON, Canada). The collection of research and survey articles, honoring Vlastimil Dlab's seventieth birthday, reflects state-of-the-art research on the topic. Leading experts contributed papers, demonstrating the interaction between representation theory of finite dimensional algebras and neighboring subjects. A wide range of topics are covered, including quantum groups, the theory of Lie algebras, the geometry and combinatorics of tilting theory, commutative algebra, algebraic geometry, homology theories, and derived and triangulated categories. The book is suitable for graduate students and researchers interested in the theory of algebras.

Language and Automata Theory and Applications

7th International Conference, LATA 2013, Bilbao, Spain, April 2-5, 2013, Proceedings

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Author: Adrian-Horia Dediu,Carlos Martín-Vide,Bianca Truthe

Publisher: Springer

ISBN: 3642370640

Category: Computers

Page: 580

View: 321

This book constitutes the refereed proceedings of the 7th International Conference on Language and Automata Theory and Applications, LATA 2013, held in Bilbao, Spain in April 2013. The 45 revised full papers presented together with 5 invited talks were carefully reviewed and selected from 97 initial submissions. The volume features contributions from both classical theory fields and application areas (bioinformatics, systems biology, language technology, artificial intelligence, etc.). Among the topics covered are algebraic language theory; algorithms for semi-structured data mining; algorithms on automata and words; automata and logic; automata for system analysis and program verification; automata, concurrency and Petri nets; automatic structures; cellular automata; combinatorics on words; computability; computational complexity; computational linguistics; data and image compression; decidability questions on words and languages; descriptional complexity; DNA and other models of bio-inspired computing; document engineering; foundations of finite state technology; foundations of XML; fuzzy and rough languages; grammars (Chomsky hierarchy, contextual, multidimensional, unification, categorial, etc.); grammars and automata architectures; grammatical inference and algorithmic learning; graphs and graph transformation; language varieties and semigroups; language-based cryptography; language-theoretic foundations of artificial intelligence and artificial life; parallel and regulated rewriting; parsing; pattern recognition; patterns and codes; power series; quantum, chemical and optical computing; semantics; string and combinatorial issues in computational biology and bioinformatics; string processing algorithms; symbolic dynamics; symbolic neural networks; term rewriting; transducers; trees, tree languages and tree automata; weighted automata.

Advanced Topics in Bisimulation and Coinduction

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Author: Davide Sangiorgi,Jan Rutten

Publisher: Cambridge University Press

ISBN: 1139502905

Category: Computers

Page: N.A

View: 4682

Coinduction is a method for specifying and reasoning about infinite data types and automata with infinite behaviour. In recent years, it has come to play an ever more important role in the theory of computing. It is studied in many disciplines, including process theory and concurrency, modal logic and automata theory. Typically, coinductive proofs demonstrate the equivalence of two objects by constructing a suitable bisimulation relation between them. This collection of surveys is aimed at both researchers and Master's students in computer science and mathematics and deals with various aspects of bisimulation and coinduction, with an emphasis on process theory. Seven chapters cover the following topics: history, algebra and coalgebra, algorithmics, logic, higher-order languages, enhancements of the bisimulation proof method, and probabilities. Exercises are also included to help the reader master new material.

Algebra in the Stone-Cech Compactification

Theory and Applications

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Author: Neil Hindman,Dona Strauss

Publisher: Walter de Gruyter

ISBN: 3110809222

Category: Mathematics

Page: 498

View: 2499

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Topics in Contemporary Mathematical Physics

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Author: Kai Shue Lam

Publisher: World Scientific

ISBN: 9789812384041

Category: Science

Page: 604

View: 9220

This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. Its main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics. Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; and (3) topology and differential geometry. The features of this work include: an exposition style which is a fusion of those common in the standard physics and mathematics literatures; a level of exposition that varies from quite elementary to moderately advanced, so that the text should be of interest to a wide audience; a strong degree of thematic unity, despite the diversity of the topics covered; and cross references, so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.

Introduction to Octonion and Other Non-Associative Algebras in Physics

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Author: Susumo Okubo

Publisher: Cambridge University Press

ISBN: 9780521472159

Category: Science

Page: 136

View: 7933

In this book, the author applies non-associative algebras to physics. Okubo covers topics ranging from algebras of observables in quantum mechanics and angular momentum and octonions to division algebra, triple-linear products and YangSHBaxter equations. He also discusses the non-associative gauge theoretic reformulation of Einstein's general relativity theory. Much of the material found in this volume is not available in other works. The book will therefore be of great interest to graduate students and research scientists in physics and mathematics.

Relative Homological Algebra

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Author: Edgar E. Enochs,Overtoun M. G. Jenda

Publisher: Walter de Gruyter

ISBN: 3110803666

Category: Mathematics

Page: 350

View: 548

Semigroups in Algebra, Geometry and Analysis

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Author: Karl H. Hofmann,Jimmie D. Lawson,Ernest B. Vinberg

Publisher: Walter de Gruyter

ISBN: 3110885581

Category: Mathematics

Page: 382

View: 6341

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Topics In Abstract Algebra (second Edition)

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Author: P. Mukhopadhyay,Shamik Ghosh,Mridul Kanti Sen

Publisher: Universities Press

ISBN: 9788173715518

Category:

Page: 436

View: 7071

This book covers the elements of Abstract Algebra, which is a major mathematics course for undergraduate students all over the country and also for first year postgraduate students of many universities. It is designed according to the new UGC syllabus prescribed for all Indian universities.

Introduction to Abstract Algebra

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Author: Jonathan D. H. Smith

Publisher: CRC Press

ISBN: 9781420063721

Category: Mathematics

Page: 344

View: 6437

Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles. A Quick Introduction to Algebra The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. The author also uses equivalence relations to introduce rational numbers and modular arithmetic as well as to present the first isomorphism theorem at the set level. The Basics of Abstract Algebra for a First-Semester Course Subsequent chapters cover orthogonal groups, stochastic matrices, Lagrange’s theorem, and groups of units of monoids. The text also deals with homomorphisms, which lead to Cayley’s theorem of reducing abstract groups to concrete groups of permutations. It then explores rings, integral domains, and fields. Advanced Topics for a Second-Semester Course The final, mostly self-contained chapters delve deeper into the theory of rings, fields, and groups. They discuss modules (such as vector spaces and abelian groups), group theory, and quasigroups.

Infinite Dimensional Lie Superalgebras

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Author: Yuri Bahturin,Alexander V. Mikhalev,Viktor M. Petrogradsky,Mikhail V. Zaicev

Publisher: Walter de Gruyter

ISBN: 3110851202

Category: Mathematics

Page: 260

View: 6112

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Commutative Algebra

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Author: Oscar Zariski,Pierre Samuel

Publisher: Springer Science & Business Media

ISBN: 3662292440

Category: Mathematics

Page: 416

View: 6315

This second volume of our treatise on commutative algebra deals largely with three basic topics, which go beyond the more or less classical material of volume I and are on the whole of a more advanced nature and a more recent vintage. These topics are: (a) valuation theory; (b) theory of polynomial and power series rings (including generalizations to graded rings and modules); (c) local algebra. Because most of these topics have either their source or their best motivation in algebraic geom etry, the algebro-geometric connections and applications of the purely algebraic material are constantly stressed and abundantly scattered through out the exposition. Thus, this volume can be used in part as an introduc tion to some basic concepts and the arithmetic foundations of algebraic geometry. The reader who is not immediately concerned with geometric applications may omit the algebro-geometric material in a first reading (see" Instructions to the reader," page vii), but it is only fair to say that many a reader will find it more instructive to find out immediately what is the geometric motivation behind the purely algebraic material of this volume. The first 8 sections of Chapter VI (including § 5bis) deal directly with properties of places, rather than with those of the valuation associated with a place. These, therefore, are properties of valuations in which the value group of the valuation is not involved.

Signal Processing for Neuroscientists, A Companion Volume

Advanced Topics, Nonlinear Techniques and Multi-Channel Analysis

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Author: Wim van Drongelen

Publisher: Elsevier

ISBN: 0123849160

Category: Medical

Page: 186

View: 1536

The popularity of signal processing in neuroscience is increasing, and with the current availability and development of computer hardware and software, it is anticipated that the current growth will continue. Because electrode fabrication has improved and measurement equipment is getting less expensive, electrophysiological measurements with large numbers of channels are now very common. In addition, neuroscience has entered the age of light, and fluorescence measurements are fully integrated into the researcher’s toolkit. Because each image in a movie contains multiple pixels, these measurements are multi-channel by nature. Furthermore, the availability of both generic and specialized software packages for data analysis has altered the neuroscientist’s attitude toward some of the more complex analysis techniques. This book is a companion to the previously published Signal Processing for Neuroscientists: An Introduction to the Analysis of Physiological Signals, which introduced readers to the basic concepts. It discusses several advanced techniques, rediscovers methods to describe nonlinear systems, and examines the analysis of multi-channel recordings. Covers the more advanced topics of linear and nonlinear systems analysis and multi-channel analysis Includes practical examples implemented in MATLAB Provides multiple references to the basics to help the student

Algebra

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Author: Siegfried Bosch

Publisher: Springer-Verlag

ISBN: 3642395678

Category: Mathematics

Page: 370

View: 1178

Eine verständliche, konzise und immer flüssige Einführung in die Algebra, die insbesondere durch ihre sorgfältige didaktische Aufbereitung bei vielen Studierenden Freunde findet. Die vorliegende Auflage bietet neben zahlreichen Aufgaben (mit Lösungshinweisen) sowie einführenden und motivierenden Vorbemerkungen auch Ausblicke auf neuere Entwicklungen. Auch selten im Lehrbuch behandelte Themen wie Resultanten, Diskriminanten, Kummer-Theorie und Witt-Vektoren werden angesprochen. Die berühmten Formeln aus dem 16. Jahrhundert zur Auflösung von Gleichungen dritten und vierten Grades werden ausführlich erläutert und in den Rahmen der Galois-Theorie eingeordnet. Ein klares, modernes und inhaltsreiches Lehrbuch, das für das Studium der Algebra unentbehrlich ist.

Basic Algebra

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Author: Anthony W. Knapp

Publisher: Springer Science & Business Media

ISBN: 0817632484

Category: Mathematics

Page: 717

View: 3083

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.