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Scattering theory deals with the interactions of waves with obstacles in their path, and low frequency scattering occurs when the obstacles involved are very small. This book gives an overview of the subject for graduates and researchers, for the first time unifying the theories covering acoustic, electromagnetic and elastic waves.

The 1995 work of Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book, by a leading researcher, covers both this general area and that of Iwasawa Theory, which is currently enjoying a resurgence in popularity.

Succinct representation and fast access to large amounts of data are challenges of our time. This unique book suggests general approaches of 'complexity of descriptions'. It deals with a variety of concrete topics and bridges between them, while opening new perspectives and providing promising avenues for the 'complexity puzzle'.

This work on division space integration theory is intended to present a unified account of many classes of integrals including the Lebesgue-Bochner, Denjoy-Perron gauge, Denjoy-Hincin, Cesaro-Perron and Marcinkiewicz-Zygmund integrals.

The thermodynamic limit is a mathematical technique which permits to consider crystals (or other macroscopic objects) as infinitely sized periodically arranged molecules. It allows to derive models in solid state physics from models in quantum chemistry. Based on this technique, the book presents established as well as new mathematical results for a large class of models in quantum chemistry.

This monograph provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heat equation usually called the Porous Medium Equation. Each chapter is supplied with a section of notes providing comments, historical notes or recommended reading, and exercises for the reader.

Authored by leading scholars, this text presents the state of the art in multi-dimensional hyperbolic PDEs, with an emphasis on problems in which modern tools of analysis are used. Ordered in sections of gradually increasing difficulty and with an extensive bibliography, the text is ideal for graduates and researchers in applied mathematics.

This book offers an extensive modern treatment of Sasakian geometry, which is of importance in many different fields in geometry and physics.

This book is a systematic presentation of the solution of one of the fundamental problems of the theory of random dynamical systems - the problem of topological classification and structural stability of linear hyperbolic random dynamical systems.

Aimed at graduate students and researchers in mathematics, this book takes homological themes, such as Koszul complexes and their generalizations, and shows how these can be used to clarify certain problems in selected parts of algebra, as well as their success in solving a number of them.

Triple systems are among the simplest combinatorial designs. They have applications in coding theory, cryptography, computer science, statistcs, and many other areas. This book provides the first systematic and comprehensive treatment of triple systems. It gives an accurate picture of an incredibly rich and vibrant area of combinatorial mathematics.

Aimed at researchers in mathematics and physics, this monograph, in which the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field.

This monograph treats the analysis of symmetric cones in a systematic way. It discusses harmonic analysis and special functions associated with symmetric cones; it also tries these results together with the study of holomorphic functions on bounded symmetric domains of tube type.

This seminal text by a leading researcher is based on a course given at the Institut de Mathematiques de Jussieu. Aimed at students with a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. Full proofs are given and exercises aid the reader throughout.

The wide application of technologies in mechanical, electronic and biomedical systems calls for materials and structures with non-conventional properties. This text discusses the mathematical modelling used with these types of electromagnetic materials and provides a comprehensive treatment of electromagnetism of continuous media.

This volume explores the connections between the geometry of mappings and many important areas of modern mathematics such as Harmonic and non-linear Analysis, the theory of Partial Differential Equations, Conformal Geometry and Topology. It provides a comprehensive and up to date account and an overview of the subject as a whole.

Covers all the major areas including finitely generated soluble groups, soluble groups of finite rank, modules over group rings, algorithmic problems, applications of cohomology, finitely presented groups, whilst remaining fairly strictly within the boundaries of soluble group theory.

This book describes a completely novel mathematical development which has already influenced probability theory, and has potential for application to engineering and to areas of pure mathematics.

Presenting the topic of special functions in a different perspective, the authors have based the special functions on the theory of second-order ordinary differential equations in the complex domain. Several physical applications are presented, along with many tables and figures that help the readers find their way through the subject.

Summability is a mathematical topic with a long tradition and many applications. This work aims to introduce the reader to the wide field of summability and its applications, and provides an overview of the most important classical and modern methods used.

This is a combination of a graduate textbook on Riemannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin (7). It is the first book on compact manifolds with exceptional holonomy, and contains much new research material and many new examples.

Provides an accessible account to the modern study of the geometry of four-manifolds. This title is suitable for postgraduates and research workers. The central theme is that the appropriate geometrical tools for investigating these questions come from mathematical physics: the Yang-Mills theory and anti-self dual connections over four-manifolds.

This is a complete reworking of the out-of-print first volume of a three-volume treatise on finite projective spaces. There are numerous articles in journals, but this is the only extended work in the area. It also includes a comprehensive bibliography of more than 3000 items.

A wide-ranging introduction to a field of mathematics combining functional analysis with the perspectives of global geometry.

This book is a comprehensive guide to theories of Kleinian groups from the viewpoints of both geometry and analysis. Studies of Kleinian groups have been in an active area in mathematics concerned with many interesting theories. This book provides fundamental results and important theorems which are needed for access to the frontiers of the theory from a modern viewpoint.

This book represents a new attempt to classify homotopy types of simply connected CW-complexes. It provides methods and examples of explicit homotopy classification and includes applications to the classification of manifolds.

This text deals with fractal geometries which have features similar to ones of ordinary Euclidean spaces, while at the same time being different from Euclidean spaces in other ways. A basic type of feature being considered is the presence of Sobolev or Poincare inequalities.

Summability methods are concerned with transforming series of numbers to other series. It is an area that has seen applications in number theory as well as in other parts of mathematics. This book covers both the theory and some of the applications of Borel summability.

The geometry of complex hyperbolic space has not, so far, been given a comprehensive treatment in the literature. This book seeks to address this by providing an overview of this particularly rich area of research, and is largely motivated by the wide applications in other areas of mathematics and physics.

This text provides an up-to-date account of Banach and locally convex algebras with emphasis on general theory, representations and homology. This approach leads Helemskii to consider topics not covered at this level in any other book.