Vladimir Belinski, Enric Verdaguer

Gravitational Solitons

Description
This book gives a self-contained exposition of the theory of gravitational solitons and provides a comprehensive review of exact soliton solutions to Einstein?s equations. The text begins with a detailed discussion of the extension of the Inverse Scattering Method to the theory of gravitation, starting with pure gravity and then extending it to the coupling of gravity with the electromagnetic field. There follows a systematic review of the gravitational soliton solutions based on their symmetries. These solutions include some of the most interesting in gravitational physics such as those describing inhomogeneous cosmological models, cylindrical waves, the collision of exact gravity waves, and the Schwarzschild and Kerr black holes. A valuable reference for researchers and graduate students in the fields of general relativity, string theory and cosmology, this book will also be of interest to mathematical physicists in general.

Chapter Contents
Preface; 1. Inverse scattering technique in gravity; 2. General properties of gravitational solitons; 3. Einstein-Maxwell fields; 4. Cosmology: diagonal metrics from Kasner; 5. Cosmology: nondiagonal metrics and perturbed FLRW; 6. Cylindrical symmetry; 7. Plane waves and colliding plane waves; 8. Axial symmetry; Bibliography; Index.

ISBN: 0-521-80586-4
Binding: Hardback
Size: 255 x 182 mm
Pages: 272
Weight: 0.628kg
Published: 19 July 2001

Alexander S. Galperin, Evgeny A. Ivanov, Victor I. Ogievetsky, Emery S. Sokatchev

Harmonic Superspace

Description
This is the first pedagogical introduction to the harmonic superspace method in extended supersymmetry. Inspired by exciting developments in superstring theory, it provides a systematic treatment of the quantum field theories with N=2 and N=3 supersymmetry in harmonic superspace. The authors present the harmonic superspace approach as a means of providing an off-shell description of the N=2 supersymmetric theories, both at the classical and quantum levels. Furthermore, they show how it offers a unique way to construct an off-shell formulation of a theory with higher supersymmetry, namely the N=3 supersymmetric Yang-Mills theory. Harmonic superspace makes manifest many remarkable geometric properties of the N=2 theories, for example, the one-to-one correspondence between N=2 supersymmetric matter, and hyper-Kdhler and quaternionic manifolds. This book will be of interest to researchers and graduate students working in the areas of supersymmetric quantum field theory, string theory and complex geometries.

Chapter Contents
Preface; 1. Introductory overview; 2. Elements of supersymmetry; 3. Superspace; 4. Harmonic analysis; 5. N=2 matter with infinite sets of auxiliary fields; 6. N=2 matter multiplets with a finite number of auxiliary fields: N=2 duality transformations; 7. Supersymmetric Yang-Mills theories; 8. Harmonic supergraphs; 9. Conformal invariance in N=2 harmonic superspace; 10. Supergravity; 11. Hyper-Kdhler geometry in harmonic superspace; 12. N=3 supersymmetric Yang-Mills theory; 13. Conclusions; Appendices 1-5. Notations, conventions and useful formulae; Index.

Series: Cambridge Monographs on Mathematical Physics
ISBN: 0-521-80164-8
Binding: Hardback
Pages: 260
available from September 2001

James F. Epperson

An Introduction to Numerical Methods and Analysis

ISBN: 0-471-31647-4
Hardcover
576 Pages
Published July 2001

The objective of the book is for the reader to learn where approximation methods come from, why they work, why they sometimes don't work, and when to use which of many techniques that are available, and to do all this in a style that emphasizes readability and usefulness to the numerical methods novice. Each chapter and each section begins with the basic, elementary material and gradually builds up to more advanced topics.

Table Of Contents:

Preface.
Introductory Concepts and Calculus Review.
A Survey of Simple Methods and Tools.
Root-Finding.
Interpolation and Approximation.
Numerical Intergration.
Numerical Methods for Ordinary Differential Equations.
Numerical Methods for the Solution of Systems of Equations.
Approximate Solution of the Algebraic Eigenvalue Program.
Finite Difference Methods for PDE's.
Appendix: Proofs of Selected Theorems, and Other Additional Material.

Janusz Czelakowski
Institute of Mathematics, Opole University, Poland

Protoalgebraic Logics

TRENDS IN LOGIC Volume 10

The main aim of this monograph is to provide a structured study of the algebraic method in metalogic. In contrast to traditional algebraic logic, where the focus is on the algebraic forms of specific deductive systems, abstract algebraic logic is concerned with the process of algebraization itself. This book presents in a systematic way recent ideas in abstract algebraic logic centered around the notion of the Leibniz operator. The stress is put on the taxonomy of deductive systems. Isolating a list of plausible properties of the Leibniz operator serves as a basis for distinguishing certain natural classes of sentential logics. The hierarchy of deductive systems presented in the book comprises, among others, the following classes: protoalgebraic logics, equivalential logics, algebraizable logics, and Fregean logics. Because of the intimate connection between algebraic and logical structures, the book also provides a uniform treatment of various topics concerning deduction theorems and quasivarieties of algebras.

The presentation of the above classes of logics is accompanied by a wealth of examples illustrating the general theory. An essential part of the book is formed by the numerous exercises integrated into the text.

This book is both suitable for logically and algebraically minded graduate and advanced graduate students of mathematics, computer science and philosophy, and as a reference work for the expert.

Contents
Introduction. On the book. Mathematical Prerequisites. Exercises. Notes for Mathematical Prerquisites. 0. Basic definitions and facts. Part I: Protoalgebraic Logics. The Leibniz Operator. 1. Protoalgebraic logics. 2. Protoalgebraicity and the Deduction Theorem. 3. Equivalential logics. Part II: Algebraizable Sentential Logics. Q. Quasivarieties of algebras. 4. Algebraizable logics. 5. Regularly algebraizable logics. 6. Fregean logics. Bibliography. Symbol Index. Index of definitions.

Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6940-8
May 2001, 464 pp.

Ren-Hong Wang
Institute of Applied Mathematics, Dalian University of Technology, PR of China

Multivariate Spline Functions and Their Applications

MATHEMATICS AND ITS APPLICATIONS Volume 529

This book deals with the algebraic geometric method of studying multivariate splines. Topics treated include: the theory of multivariate spline spaces, higher-dimensional splines, rational splines, piecewise algebraic variety (including piecewise algebraic curves and surfaces) and applications in the finite element method and computer-aided geometric design. Many new results are given.

Audience: This volume will be of interest to researchers and graduate students whose work involves approximations and expansions, numerical analysis, computational geometry, image processing and CAD/CAM.

Contents
1. Introduction to Multivariate Spline Functions. 2. Multivariate Spline Spaces. 3. Other Methods for Studying Multivariate Spline Functions. 4. Higher-Dimensional Spline Spaces. 5. Rational Spline Functions. 6. Piecewise Algebraic Curves and Surfaces. 7. Applications of multivariate Spline Functions in Finite Element Method and CAGD. References. Index.

Co-publication with Science Press, Beijing, PR of China
Hardbound, ISBN 0-7923-6967-X
May 2001, 512 pp.