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The primary aim of this monograph is to achieve part of Beilinson's program on mixed motives using Voevodsky's theories of A1-homotopy and motivic complexes.

The aim of the present monograph is a thorough study of the adic-completion, its left derived functors and their relations to the local cohomology functors, as well as several completeness criteria, related questions and various dualities formulas.

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 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.

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.

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;

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 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.

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.

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.

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 is a translation of the earlier book written by Koji Doi and the author, who revised it substantially for this English edition. It offers the basic knowledge of elliptic modular forms necessary to understand recent developments in number theory. It also treats the unit groups of quaternion algebras, rarely dealt with in books;

This monograph covers the recent major advances in various areas of set theory. In three parts the author offers us what in his view every young set theorist should learn and master....This well-written book promises to influence the next generation of set theorists, much as its predecessor has done."

People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen ta, where we find a proof of their infinitude, now regarded as canonical.

The 1963 Goettingen notes of T. A. Springer are well known in the field but have been unavailable for some time. This book is a translation of those notes, completely updated and revised. The part of the book dealing with the algebraic structures is on a fairly elementary level, presupposing basic results from algebra.

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.

This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory.

In its Second Edition, this in-depth study of the vibrations of fractal strings interlinks number theory, spectral geometry and fractal geometry. Includes a geometric reformulation of the Riemann hypothesis and a new final chapter on recent topics and results.

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

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].

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.

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.

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 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).

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.

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.

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.

A long-awaited, updated introductory text by the world leaders in potential theory. This essential reference work covers all aspects of this major field of mathematical research, from basic theory and exercises to more advanced topological ideas. The largely self-contained presentation makes it basically accessible to graduate students.

The aim of this book is the classification of symplectic amalgams - structures which are intimately related to the finite simple groups. The classification touches on many important aspects of modern group theory: * p-local analysis * the amalgam method * representation theory over finite fields; and * properties of the finite simple groups.