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This book provides a detailed study of nonlinear partial differential equations satisfying certain nonstandard growth conditions which simultaneously extend polynomial, inhomogeneous and fully anisotropic growth.

The book describes how curvature measures can be introduced for certain classes of sets with singularities in Euclidean spaces. Its focus lies on sets with positive reach and some extensions, which include the classical polyconvex sets and piecewise smooth submanifolds as special cases.

This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Overall, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces.

In this new text, Steven Givant-the author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarski-develops three theories of duality for Boolean algebras with operators.

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.

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

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.

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.

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.

This monograph presents an introduction to some geometric and analytic aspects of the maximum principle.

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).

This volume provides an introduction to dessins d'enfants and embeddings of bipartite graphs in compact Riemann surfaces.

This monograph is about monotone complete C*-algebras, their properties and the new classification theory.

This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms.

Written by one of the subject's foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist.

This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups.

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;

Combinatorial Algebra: Syntax and Semantics

The featured review of the AMS describes the author's earlier work in the field of approach spaces as, 'A landmark in the history of general topology'. The theory is then illustrated in such varied fields as topology, functional analysis, probability theory, hyperspace theory and domain theory.

The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties.

Based on the author's lectures at Cornell Probability Summer School in 2012, this book links the concept of superconcentration with probability theory. Includes a number of open problems for professional mathematicians and exercises for graduate students.

This book covers dimension theory, ANR theory (theory of retracts) and related topics, connecting with various fields in geometric and general topology. Many proofs are illustrated by figures or diagrams, making it easier to understand the underlying concepts.

Presenting current results on analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes, this book covers distribution of points on the sphere, the reconstruction algorithm in computerized tomography and more.

This book introduces the notion of an E-semigroup, a generalization of the known concept of E_O-semigroup. These objects are families of endomorphisms of a von Neumann algebra satisfying certain natural algebraic and continuity conditions. Its thorough approach is ideal for graduate students and research mathematicians.

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.