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This second edition updates and expands the acclaimed first edition, adding a new chapter on a family of symmetric functions depending rationally on two parameters and also a chapter on zonal polynomials. It is available for the first time in paperback.

This book gives a complete and self-contained account of what is known about this subject and is written from a geometrical and analytical point of view, with quantum field theory very much in mind.

This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.

This book lies at the interface between mathematics and quantum theory. It provides a mathematically precise development of certain heuristic ideas originated by Richard Feynman in a profoundly influential 1951 paper.

This unique monograph brings together important material in the field of noncommutative rings and modules. It provides an up-to-date account of the topic of cyclic modules and the structure of rings which will be of particular interest to those working in abstract algebra and to graduate students who are exploring potential research topics.

A simple introduction to several important fields of modern mathematics. The exposition is based on an interplay between hyperbolic geometry, stochastic calculus, special relativity and chaotic dynamics. It is suitable for anyone with some solid background in linear algebra, calculus, and probability theory.

This text is the first to deal with the general theory of traces and determinants of operators on manifolds in a broad context, encompassing a number of the principle applications and backed up by specific computations which set out in detail to newcomers the nuts-and-bolts of the basic theory.

The aim of pattern theory is to create mathematical knowledge representations of complex systems, analyse the mathematical properties of the resulting regular structures, and to apply them to practically occuring patterns in nature and the man-made world.

The central theme of this book is the study of self-dual connections on four-manifolds. The authors' aim is to present moduli space techniques applied to four-manifolds and to study vector bundles over four-manifolds whose structure group is SO(3).

This book deals with fundamental number theoretic questions and their interplay with finite group theory. It reports on the great progress achieved since 1970 through the joint effort of researchers in both areas. The book allows access to the results achieved so far and aims to increase the scientific exchange between number theory and group theory.

This book develops the basic theory of elliptic operators on Lie groups and thereby extends the conventional theory of parabolic evolution equations to a natural non-commutative context.

This book studies problems of viscoplasticity using various and different mathematical methods. The mathematical results obtained are carefully interpreted from a mechanical point of view. The theory is developed to deal with numerical results from practical problems in industry and technology.

This study develops the theory of the complexity of the solution to differential and integral equations and discusses the relationship between the worst-case setting and two related problems - the average-case setting and the probalistic setting.

The arithmetic of polynomials over a finite field possesses deep and fascinating parallels with classical number theory. This volume develops all the tools needed to provide modern, "adelic" proofs of the polynomial analogs to two of the most famous theorems of classical additive number theory: Vinogradov's 3-Primes Theorem and the Waring Problem.

The aim of this monograph is to present an account of the advances in the oscillation theory of delay differential equations - considering applications as diverse as the populations of blowflies, logistic equations in ecology and the survival of red blood cells in animals.

Hypergeometric functions have occupied a significant position in mathematics for over two centuries. This monograph is concerned with the Boyarsky principle which expresses the analytic properties of a certain proto-gamma function.

Based in part on a lecture course, this book gives an authoritative and up-to-date overview of recent research on the behaviour of waves in crystalline solids. It covers aspects of plasticity, fracture, and nonlinear wave propagation.

A general introduction to the initial value problem for Einstein's equations coupled to collisionless matter. The book contains a proof of future stability of models of the universe consistent with the current observational data and a discussion of the restrictions on the possible shapes of the universe imposed by observations.

This book provides an introduction to surgery theory; the standard classification method for high dimension manifolds.

This book presents a survey of the geometric quantization theory of Kostant and Souriau and was first published in 1980. It has been extensively rewritten and brought up to date, with the addition of many new examples.

A unique monograph in a fast developing field of generalized thermoelasticity, an area of active research in continuum mechanics, focusing on thermoelasticity governed by hyperbolic equations, rather than on a wide range of continuum theories.

This work examines how the study of operator alegbras took a new turn with the introduction of subfactor theory, and how remarkable connections were found with knot theory, 3-manifolds, quantum groups and integrable systems in statistical mechanics and conformal theory. In the OXFORD MATHEMATICAL MONOGRAPHS series.

Starts with a survey of the standard theory of black holes. Then studies, analytically, the interaction of a black hole with another strongly self-gravitating system (such as the extra universe on and through black holes).

Wavelet analysis is a growing field of active research, and applications exist in all areas of mathematics, physics, and engineering. This book provides an easy-to-read introduction to the subject, laying the mathematical foundations of the theory and showing the variety of applications by means of examples.

Written by a leading scholar in mathematics, this monograph discusses the Radon transform. This topic has wide ranging applications, in particular X-ray technology, partial differential equations, nuclear magnetic resonance scanning, and tomography.

Suitable for mathematicians, mathematical physicists and theoretical physicists, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus. It also provides detailed proofs of the central results.

This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions.

This unique reference illustrates how different methods of finite group theory including representation theory, cohomology theory, combinatorial group theory and local analysis are combined to construct one of the last of the sporadic finite simple groups - the fourth Janko group J_4.

The study of the symmetric groups forms one of the basic building blocks of modern group theory. This book presents information currently known on the projective representations of the symmetric and alternating groups. Special emphasis is placed on the theory of Q-functions and skew Q-functions.

Building on the work of Ciarlet and Destuynder, this book provides a systematic coverage of these methods in multi-structures, for example, domains which are dependent on a small parameter e in such a way that the limit region consists of subsets of different space dimensions.