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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.

This book explores the fundamentals of total domination in graphs, the interplay with transversals in hypergraphs and the association with diameter-2-critical graphs. Includes several proofs, and a toolbox of proof techniques for attacking open problems.

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.

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].

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 gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. Its main goal is to provide complexity estimates by tracking numerically invariants of the structures that may occur.

This book examines algebraic number theory and the theory of semisimple algebras. It covers classification over an algebraic number field and classification over the ring of algebraic integers.

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 clearly written text is the first book on unitals embedded in finite projective planes. It provides a thorough survey of the research literature on embedded unitals. The book is well-structured with excellent diagrams and a comprehensive bibliography.

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;

The field of functional equations is an ever-growing branch of mathematics with far-reaching applications. This book presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations and their applications to related topics.

This book examines interactions of polyhedral discrete geometry and algebra. What makes this book unique is the presentation of several central results in all three areas of the exposition - from discrete geometry, to commutative algebra, and K-theory.

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.

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.

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.

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 volume provides readers with a detailed introduction to the amenability of Banach algebras and locally compact groups.

This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras.

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.

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.

Building on fundamental results in variational analysis, this monograph presents new and recent developments in the field as well as selected applications.

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.

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.

Authored by a ranking authority in Gaussian harmonic analysis, this book embodies a state-of-the-art entree at the intersection of two important fields of research: harmonic analysis and probability.

The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups.

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.