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A comprehensive introduction to the theory of J-contractive and J-inner matrix valued functions with respect to the open upper half-plane and a number of applications of this theory. It will be of particular interest to those with an interest in operator theory and matrix analysis.

This book presents a complete account of the theory of dynamical systems with nonzero Lyapunov exponents. It serves as a rigorous mathematical foundation for one of the greatest discoveries of the twentieth century: deterministic chaos - the appearance of 'chaotic' motions in pure deterministic dynamical systems.

Abstract regular polytopes are highly symmetric combinatorial structures with distinctive geometric, algebraic or topological properties. This comprehensive up-to-date account of the subject meets a critical need for a text in this area; no book has been published in this topic since Coxeter's Regular Polytopes (1948) and Regular Complex Polytopes (1974).

The book gives a categorical introduction to some of the key areas of modern mathematics. Researchers, teachers and graduate students in algebra and topology familiar with the very basic notions of category theory will find all the advanced tools needed for their subjects, without being forced to study category theory for its own sake.

This volume, the third in a sequence that began with The Theory of Matroids and Combinatorial Geometries, concentrates on the applications of matroid theory to a variety of topics from engineering (rigidity and scene analysis), combinatorics (graphs, lattices, codes and designs), topology and operations research (the greedy algorithm).

A revised version of McEliece's classic, this volume is a self-contained introduction to the basic results in the theory of information and coding. It is ideal either for self-study, or for a graduate/undergraduate level course at university. The text includes dozens of worked examples and several hundred problems for solution.

The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). Other books cover portions of this material, but none of these have such a wide scope.

Much of the material that the author presents is original and many results have never appeared in book form before. A comprehensive bibliography completes this work which will be indispensable to all working in systems theory, operator theory, delay equations and partial differential equations.

Explains how to solve highly non-trivial nonlinear partial and ordinary differential equations using methods from contact and symplectic geometry. Combining the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia, it contains applications to problems ranging from Lie's classification problem to analysis of laser beams.

Asymptotics and Mellin-Barnes Integrals, first published in 2001,provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics.

This is the second volume in a two-volume set, which will provide the complete proof of classification of two important classes of geometries, closely related to each other: Petersen and tilde geometries. It is an essential purchase for researchers into finite group theory, finite geometries and algebraic combinatorics.

This is a revised edition of McEliece's classic, published with students in mind. It is a self-contained introduction to all basic results in the theory of information and coding. Includes dozens of worked examples and several hundred problems for solution. Ideal as a text for a graduate or undergraduate course.

A comprehensive account of the theory and applications of regular variation. It is concerned with the asymptotic behaviour of a real function of a real variable x which is 'close' to a power of x.

Minkowski geometry is a type of non-Euclidean geometry in a finite number of dimensions in which distance is not 'uniform' in all directions. This first comprehensive treatment of the subject since the 1940's is suitable for graduate students and researchers in geometry, convexity theory, and functional analysis.

This book is a continuation of Theory of Matroids (also edited by Neil White), and again consists of a series of related surveys that have been contributed by authorities in the area. The volume has been carefully edited to ensure a uniform style and notation throughout.