Bøger i Springer Monographs in Mathematics serien

Absolute values and their completions - such as the p-adic number fields - play an important role in number theory. In valuation theory, the notion of completion must be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the skills of a standard graduate course in algebra.

This book presents a self-contained exposition of the theory of cellular automata on groups and explores its deep connections with recent developments in geometric group theory and other branches of mathematics and theoretical computer science.

This book classifies all families of orthogonal polynomials satisfying a second-order differential or difference equation with polynomial coefficients, which leads to the families of hypergeometric orthogonal polynomials belonging to the Askey scheme.

The book is aimed at people working in number theory or at least interested in this part of mathematics. It is hoped that this may be helpful in preventing rediscoveries of old results, and might also inspire the reader to look at the work done earlier, which may hide some ideas which could be applied in contemporary research.

Among others, this monograph presents the most successful existence theorems known and construction methods for Galois extensions as well as solutions for embedding problems combined with a collection of the existing Galois realizations.

The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. a formula for Bernoulli numbers by Stirling numbers; congruences between some class numbers and Bernoulli numbers;

Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature.

This introduction to modern set theory opens the way to advanced current research. Coverage includes the axiom of choice and Ramsey theory, and a detailed explanation of the sophisticated technique of forcing. Offers notes, related results and references.

This book provides an overview of the main approaches used to analyze the dynamics of cellular automata. Pattern formation is related to linear cellular automata, to the Bar-Yam model for the Turing pattern, and Greenberg-Hastings automata for excitable media.

This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume).

In a revised edition, this book presents basic results of the theory of convex sets and functions in infinite-dimensional spaces. Includes new results on advanced concepts of subdifferential for convex functions and new duality results in convex programming.

It features three chapters dealing with point distributions on the sphere, including an extensive treatment of Delsarte-Yudin-Levenshtein linear programming methods for lower bounding energy, a thorough treatment of Cohn-Kumar universality, and a comparison of 'popular methods' for uniformly distributing points on the two-dimensional sphere.

This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums.

This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy. The structure of the book is designed to be flexible enough to serve a variety of readers.

Fully supported with underlying mechanical concepts, this revised new edition includes exercises and examples throughout in its concise and accessible introduction to functional analysis, including new material on essential inequalities and imbedding results.

This unique book on the subject addresses fundamental problems and will be the standard reference for a long time to come. The authors have different scientific origins and combine these successfully, creating a text aimed at graduate students and researchers that can be used for courses and seminars.

This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curva ture -1, which is traditionally called hyperbolic 3-space.

In this regard, we refer to the works of Pironneau [1984], Haslinger and Neittaanmaki [1988], [1996], Sokolowski and Zolksio [1992], Litvinov [2000], Allaire [2001], Mohammadi and Pironneau [2001], Delfour and Zolksio [2001], and Makinen and Haslinger [2003].

An invaluable summary of research work done in the period from 1978 to the present