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Now in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. Thoroughly updated, it also includes two brand new chapters surveying recent developments in the area.

Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference introduces the theory and applications of sub-Riemannian geometry for graduate students and researchers in pure and applied mathematics, theoretical physics, control theory, and thermodynamics. Potential applications include quantum mechanics and quantum field theory.

This unique book covers most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields and finitely generated fields. Also included are results based on recent work of E. Bombieri and U. Zannier.

Structural graph theory uses ideas of 'connectivity' to explore various aspects of graph theory and vice versa. Written by acknowledged international experts in the field, this reference for researchers and graduate students in graph theory and network flows also serves as a quick introduction for mathematicians in other fields.

For over a century lattice sums have been studied by mathematicians and scientists in diverse areas of science, in some cases unwittingly duplicating previous work. Here, at last, is a comprehensive overview of the substantial body of knowledge that now exists on lattice sums and their applications.

The first book in the literature devoted to ellipsoidal harmonics includes topics drawn from geometry, physics, biosciences and inverse problems. It serves as a reference for applied mathematicians and for anyone else who needs to know the current state of the art in this fascinating subject.

Now in its second edition, this classic text has been expanded to reflect significant developments in Brunn-Minkowski theory over the past two decades. It gives a complete presentation from basics to the exposition of current research, with full proofs, pointers to other fields and a fully updated reference list.

This first volume in a series provides a graduate-level introduction to the many facets of aperiodic order. Special attention is given to methods from algebra, discrete geometry and harmonic analysis, while the main focus is on topics motivated by physics and crystallography. Numerous illustrations and examples are included.

This third volume of four describes all the most important techniques, mainly based on Groebner bases. It covers the 'standard' solutions (Gianni-Kalkbrener, Auzinger-Stetter, Cardinal-Mourrain) as well as the more innovative (Lazard-Rouillier, Giusti-Heintz-Pardo). The author also explores the historical background, from Bezout to Macaulay.

An extensive synthesis of recent work in the study of endomorphism rings and their modules, this book considers direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization.

Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions and offers a unique in-depth treatment that provides emphasis on algorithms and applications.

Singularities are a common feature of the qualitative side of mathematics. In this monograph, the authors present some powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities, which will appeal to researchers and graduate students interested in analysis.

Mora covers the classical theory of finding roots of a univariate polynomial, emphasising computational aspects. He shows that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.

A collection of papers written by prominent experts that examine a variety of advanced topics related to Boolean functions and expressions.

This monograph systematically develops and returns to the topological and geometrical origins of absolute measurable space. The existence of uncountable absolute null space and extension of the Purves theorem are among the many topics discussed. The exposition will suit researchers and graduate students of real analysis, set theory and measure theory.

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.

This concise and elementary introduction to stochastic control and mathematical modelling is designed for researchers in stochastic control theory studying its application in mathematical economics, and for interested economics researchers. Also suitable for graduate students in applied mathematics, mathematical economics, and non-linear PDE theory.

This collaborative volume presents trends arising from the fruitful interaction between combinatorics on words, automata and number theory. Graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, fractals, tilings and stringology will find much of interest in this book.

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).

This 2010 comprehensive overview of relational mathematics provides an easy introduction to the topic, but is nevertheless theoretically sound and up-to-date. Assuming a minimum of prerequisites, it is suitable for applied scientists, explaining all of the necessary mathematics from scratch.

The second volume of this comprehensive treatise focusses on Buchberger theory and its application to the algorithmic view of commutative algebra. Aiming to be a complete survey on Groebner bases and their applications, the book will be essential for all workers in commutative algebra, computational algebra and algebraic geometry.

This book presents results on and applications of extremal problems in finite sets and finite posets from a unified point of view. The emphasis is on the powerful methods arising from the fusion of combinatorial techniques with programming, linear algebra, eigenvalue methods, and probability theory.

The theory of matroids is unique in the extent to which it connects such disparate branches of combinatorial theory and algebra as graph theory, lattice theory, design theory, combinatorial optimization, linear algebra, group theory, ring theory and field theory. Furthermore, matroid theory is alone among mathematical theories because of the number and variety of its equivalent axiom systems.

The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature.

Aggregation is the process of combining several numerical values into a single representative value, and an aggregation function performs this operation. This readable book provides a comprehensive, rigorous and self-contained exposition of aggregation functions. It is ideal for graduate students and a unique resource for researchers.

This comprehensive text develops the notion of symmetric generation from scratch and goes on to describe how the technique can be used to define and construct many of the sporadic simple groups (including the Mathieu groups, the Janko groups and the Higman-Sims group) in a uniform and accessible way.

The first book devoted exclusively to existence questions, constructive algorithms, enumeration questions, and other properties concerning classes of matrices of combinatorial significance. Combinatorial Matrix Classes is a natural sequel to the author's previous book Combinatorial Matrix Theory written with H. J. Ryser, and is likely to achieve similar classic status.

This book tells how continued fractions, studied even in Ancient Greece, only became a powerful tool in the hands of Euler, how he introduced the idea of orthogonal polynomials and combined the two subjects. The approach of Wallis, Brouncker and Euler is revived to illustrate its continuing significance on mathematics today.

Spline functions are universally recognized as highly effective tools in approximation theory, computer-aided geometric design, image analysis, and numerical analysis. A detailed mathematical treatment of polynomial splines on triangulations is outlined in this text, providing a basis for developing practical methods for using splines in numerous application areas.

Multiple scattering is the mathematical theory needed to understand the interaction of waves with obstacles; this book is the first devoted to it. The author covers a variety of techniques, and shows how to apply them to different types of problems. A 1400 item bibliography rounds off this essential reference.