A Verschoren's Books

Localization and Sheaves

A Relative Point of View

By: Jara Pascual,Conchi Vidal,A Verschoren

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Localization and Sheaves

A Relative Point of View

By: Jara Pascual,Conchi Vidal,A Verschoren

This book completely solves the problem of representing rings (and modules over them), which are locally noetherian over subsets of their prime spectrum by structure sheaves over this subset. In order to realise this, one has to develop the necessary localization theory as well as to study local equivalents of familiar concepts like the Artin-Rees property, Ore sets and the second layer condition. The first part of the book is introductory and self-contained, and might serve as a starting course (at graduate level) on localization theory within Grothendieck categories. The second part is more specialised and provides the basic machinery needed to effectively these structure sheaves, as well as to study their functorial behaviour. In this way, the book should be viewed as a first introduction to what should be called relative noncommutative algebraic geometry.

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260

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CRC Press

Published Date

ISBN 10

0582273722

ISBN 13

9780582273726

Foundations of Generic Optimization

Volume 1: A Combinatorial Approach to Epistasis

By: M. Iglesias,B. Naudts,A. Verschoren,C. Vidal

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Foundations of Generic Optimization

Volume 1: A Combinatorial Approach to Epistasis

By: M. Iglesias,B. Naudts,A. Verschoren,C. Vidal

The success of a genetic algorithm when applied to an optimization problem depends upon several features present or absent in the problem to be solved, including the quality of the encoding of data, the geometric structure of the search space, deception or epistasis. This book deals essentially with the latter notion, presenting, for the first time, a complete state-of-the-art of research on this notion, in a structured, completely self-contained and methodical way. In particular, it contains a refresher on the linear algebra used in the text as well as an elementary introductory chapter on genetic algorithms aimed at readers unacquainted with this notion. In this way, the monograph aims to serve a broad audience consisting of graduate and advanced undergraduate students in mathematics and computer science, as well as researchers working in the domains of optimization, artificial intelligence, theoretical computer science, combinatorics and evolutionary algorithms.

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Page Count

303

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402036655

ISBN 13

9781402036651

Compatibility, Stability, and Sheaves

By: J.L. Bueso,P. Jara,A Verschoren

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Compatibility, Stability, and Sheaves

By: J.L. Bueso,P. Jara,A Verschoren

Integrates fundamental techniques from algebraic geometry, localization theory and ring theory, and demonstrates how each topic is enhanced by interaction with others, providing new results within a common framework. Technical conclusions are presented and illustrated with concrete examples.

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296

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CRC Press

Published Date

ISBN 10

082479589X

ISBN 13

9780824795894

Algorithmic Methods in Non-Commutative Algebra

Applications to Quantum Groups

By: J.L. Bueso,José Gómez-Torrecillas,A. Verschoren

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Algorithmic Methods in Non-Commutative Algebra

Applications to Quantum Groups

By: J.L. Bueso,José Gómez-Torrecillas,A. Verschoren

The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups. One of the fundamental properties of quantum groups is that they are modelled by associative coordinate rings possessing a canonical basis, which allows for the use of algorithmic structures based on Groebner bases to study them. This book develops these methods in a self-contained way, concentrating on an in-depth study of the notion of a vast class of non-commutative rings (encompassing most quantum groups), the so-called Poincaré-Birkhoff-Witt rings. We include algorithms which treat essential aspects like ideals and (bi)modules, the calculation of homological dimension and of the Gelfand-Kirillov dimension, the Hilbert-Samuel polynomial, primality tests for prime ideals, etc.

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Page Count

307

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401702853

ISBN 13

9789401702850

Elementary Boundary Value Problems

By: Theodore A. Bick

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Elementary Boundary Value Problems

By: Theodore A. Bick

This textbook elucidates the role of BVPs as models of scientific phenomena, describes traditional methods of solution and summarizes the ideas that come from the solution techniques, centering on the concept of orthonormal sets of functions as generalizations of the trigonometric functions. To reinforce important concepts, the book contains exercises that range in difficulty from routine applications of the material just covered to extensions of that material.;Emphasizing the unifying nature of the material, this book: constructs physical models for both bounded and unbounded domains using rectangular and other co-ordinate systems; develops methods of characteristics, eigenfunction expansions, and transform procedures using the traditional fourier series, D'Alembert's method , and fourier integral transforms; makes explicit connections with linear algebra, analysis, complex variables, set theory, and topology in response to the need to solve BVP's employing Sturm-Liouville ststems as the primary vehicle; and presents illustrative examples in science and engineering, such as versions of the wave, diffusion equations and Laplace's equations.;Providing fundamental definitions for students with no prior experience in this topic other than differential equations, this text is intended as a resource for upper-level undergraduates in mathematics, physics and engineering, and students on courses on boundary value problems.

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274

Publisher

CRC Press

Published Date

ISBN 10

0824788990

ISBN 13

9780824788995

Methods for Solving Inverse Problems in Mathematical Physics

By: Global Express Ltd. Co.,Aleksey I. Prilepko,Dmitry G. Orlovsky,Igor A. Vasin

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Methods for Solving Inverse Problems in Mathematical Physics

By: Global Express Ltd. Co.,Aleksey I. Prilepko,Dmitry G. Orlovsky,Igor A. Vasin

Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, app

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732

Publisher

CRC Press

Published Date

ISBN 10

148229298X

ISBN 13

9781482292985

A Unified Signal Algebra Approach to Two-Dimensional Parallel Digital Signal Processing

By: Louis A. D'Alotto,Charles R. Giardina,Hua Luo

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A Unified Signal Algebra Approach to Two-Dimensional Parallel Digital Signal Processing

By: Louis A. D'Alotto,Charles R. Giardina,Hua Luo

Aims to bridge the gap between parallel computer architectures and the creation of parallel digital signal processing (DSP) algorithms. This work offers an approach to digital signal processing utilizing the unified signal algebra environment to develop naturally occurring parallel DSP algorithms.;College or university book shops may order five or more copies at a special student price. Price is available on request.

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Page Count

312

Publisher

CRC Press

Published Date

ISBN 10

0824700252

ISBN 13

9780824700256

Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes

By: Aleksand Janicki,A. Weron

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Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes

By: Aleksand Janicki,A. Weron

Presents new computer methods in approximation, simulation, and visualization for a host of alpha-stable stochastic processes.

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376

Publisher

CRC Press

Published Date

ISBN 10

1000445070

ISBN 13

9781000445077

Semigroups

An Introduction to the Structure Theory

By: Pierre A. Grillet

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Semigroups

An Introduction to the Structure Theory

By: Pierre A. Grillet

This work offers concise coverage of the structure theory of semigroups. It examines constructions and descriptions of semigroups and emphasizes finite, commutative, regular and inverse semigroups. Many structure theorems on regular and commutative semigroups are introduced.;College or university bookstores may order five or more copies at a special student price which is available upon request from Marcel Dekker, Inc.

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Page Count

417

Publisher

Routledge

Published Date

ISBN 10

1351417029

ISBN 13

9781351417020

The Theory of Difference Schemes

By: Alexander A. Samarskii

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The Theory of Difference Schemes

By: Alexander A. Samarskii

The Theory of Difference Schemes emphasizes solutions to boundary value problems through multiple difference schemes. It addresses the construction of approximate numerical methods and computer algorithms for solving mathematical physics problems. The book also develops mathematical models for obtaining desired solutions in minimal time using direct or iterative difference equations. Mathematical Reviews said it is "well-written [and] an excellent book, with a wealth of mathematical material and techniques.

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Page Count

796

Publisher

CRC Press

Published Date

ISBN 10

0203908511

ISBN 13

9780203908518

Noncommutative Distributions

Unitary Representation of Gauge Groups and Algebras

By: Sergio Albeverio,Raphael J. Hoegh-Krohn,Jean A. Marion,D. Testard,B. Torresani

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Noncommutative Distributions

Unitary Representation of Gauge Groups and Algebras

By: Sergio Albeverio,Raphael J. Hoegh-Krohn,Jean A. Marion,D. Testard,B. Torresani

Covering important aspects of the theory of unitary representations of nuclear Lie groups, this self-contained reference presents the general theory of energy representations and addresses various extensions of path groups and algebras.;Requiring only a general knowledge of the theory of unitary representations, topological groups and elementary st

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Page Count

207

Publisher

CRC Press

Published Date

ISBN 10

1482277573

ISBN 13

9781482277579

Quantum Mechanics

By: D. A. Dubin,Mark A. Hennings

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Quantum Mechanics

By: D. A. Dubin,Mark A. Hennings

These notes present a rigorous mathematical formulation of quantum mechanics based on the algebraic framework of observables and states. The underlying mathematics is that of topological algebras, locally convex spaces and distribution theory.

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260

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CRC Press

Published Date

ISBN 10

0582067766

ISBN 13

9780582067769

Nonlinear Dynamics and Pattern Formation in the Natural Environment

By: A. Van Harten,A. Doelman

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Nonlinear Dynamics and Pattern Formation in the Natural Environment

By: A. Van Harten,A. Doelman

This Research Note aims to provide an insight into recent developments in the theory of pattern formation. In the last decade there has been considerable progress in this field, both from a theoretical and a practical point of view. Recent mathematical developments concern the study of the nonlinear stability of systems at near-critical conditions by an appropriate system of modulation equations. The complexity of the original problem can be reduced drastically by this approximation. Moreover, it provides unifying point of view for a wide range of problems. New applications of the theory arise in a multitude of scientific areas such as hydrodynamics, reaction-diffusion problems, oceanography, meteorology, combustion, geophysical and biological morphodynamics and semi-conductors.This book is intended to show the interactions between the mathematical theory of nonlinear dynamics and the study of pattern generating phenomena in the natural environment. There is an intimate relationship between new insights in the mathematical aspects of nonlinear pattern formation and the comprehension of such phenomena. Therefore there are two partly overlapping main themes: one in which the emphasis is on generally applicable mathematical theories and techniques and one in which the phenomenology of pattern evolution in various areas is discussed.The book comprises 19 contributions by experts in the field. Although the emphasis changes considerably from paper to paper, in each contribution the same two themes are present; all the authors have aimed to achieve a suitable balance between the mathematical theory and the physical phenomena.

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Page Count

344

Publisher

Taylor & Francis

Published Date

ISBN 10

1351428276

ISBN 13

9781351428279

Geometry and Topology

Manifolds: Varieties, and Knots

By: Martin A. Mccrory

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Geometry and Topology

Manifolds: Varieties, and Knots

By: Martin A. Mccrory

This book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and algebraic geometry. It also discusses other topics such as three-manifolds, group actions, and algebraic varieties.

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Page Count

370

Publisher

CRC Press

Published Date

ISBN 10

1000153932

ISBN 13

9781000153934

Nonlinear Partial Differential Equations

By: A Benkirane,J P Gossez

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Nonlinear Partial Differential Equations

By: A Benkirane,J P Gossez

This book presents a collection of selected contributions on recent results in nonlinear partial differential equations from participants to an international conference held in Fes, Morocco in 1994. The emphasis is on nonlinear elliptic boundary value problems, but there are also papers deveoted to related areas such as monotone operator theory, calculus of variations, Hamiltonian systems and periodic solutions. Some of the papers are exhaustive surveys, while others contain new results,published here for the first time. This book will be of particular interest to graduate or postgraduate students as well as to specialists in these areas.

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Page Count

220

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CRC Press

Published Date

ISBN 10

0582292131

ISBN 13

9780582292130

Progress in Elliptic and Parabolic Partial Differential Equations

By: A Alvino,P Buonocore,V Ferone,E Giarrusso,G Trombetti,S Matarasso

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Progress in Elliptic and Parabolic Partial Differential Equations

By: A Alvino,P Buonocore,V Ferone,E Giarrusso,G Trombetti,S Matarasso

This Research Note collects reports of the invited plenary addresses given during the conference Elliptic and Parabolic Partial Differential Equations and Applications held in Capri, Italy, 19-23 September 1994. The conference was devoted to new developments in partial differential equations of elliptic and parabolic type and to their applications in various fields.

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Page Count

236

Publisher

CRC Press

Published Date

ISBN 10

0582259703

ISBN 13

9780582259706

Complex Analysis, Harmonic Analysis and Applications

By: Robert Deville,J Esterle,V Petkov,A Sebbar,A Yger

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Complex Analysis, Harmonic Analysis and Applications

By: Robert Deville,J Esterle,V Petkov,A Sebbar,A Yger

Multivariable complex analysis and harmonic analysis provide efficient techniques to study many applied mathematical problems. The main objective of a conference held in Bordeaux in June 1995, in honour of Professor Roger Gay, was to connect these mathematical fields with some of their applications. This was also the guideline for the fourteen contributions collected in this volume. Besides presenting new results, each speaker made a substantial effort in order to present an up to date survey of his field of research. All the subjects presented here are very active domains of research: integral geometry (with its relation to X-ray tomography), classical harmonic analysis and orthogonal polynomials, pluricomplex potential theory (with its deep connection with polynomial approximation), complex analytic methods in the theory of partial differentiable operators with constant coefficients (in the spirit of those initiated by Leon Ehrenpreis), Calderon-Zygmund operators and nonlinear operators, oscillatory integrals and resonance, and finally multivariable residue theory in its most recent developments. It is hoped that the reader will find enough insight in the different survey papers presented here to become involved with one of these subjects or to pursue further applications.

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