This book deals with boundary value problems for analytic functions with applications to singular integral equations. New and simpler proofs of certain classical results such as the Plemelj formula, the Privalov theorem and the Poincare-Bertrand formula are given. Nearly one third of this book contains the author's original works, most of which were not published in English and, hence, were previously unknown to most readers in the world. This book consists of seven chapters together with an appendix: chapter 1 describes the basic knowledge on Cauchy-type integrals and Cauchy principal value...

This volume contains selected papers of Dr Morikazu Toda. The arrangement of papers is in chronological order of publishing dates. Among Dr. Toda's many contributions, his works on liquids and nonlinear lattice dynamics should be mentioned. The one-dimensional lattice where nearest neighbouring particles interact through an exponential potential is called the Toda lattice. The papers in this volume can be grouped into five subjects: statistical mechanics, theory of liquids and solutions, lattice dynamics, Toda lattice and soliton theory and its applications.

This book gives a fundamental study of the subject including the following special features: a classification of almost complex (and similarly, almost Hermitian) structures together with inclusion relations; discussions about various known almost Hermitian structures; a necessary and sufficient condition for a general almost Hermitian manifold to have constant holomorphic sectional (or bisectional) curvature and similar conditions for various special almost Hermitian manifolds; some complex Laplacians together with some of their relationships with the real Laplacian; the spectral geometry of...

This title aims to describe in simple terms the new area of statistical mechanics known as "spin-glasses", encompassing systems in which quenched disorder is the dominant factor. The book begins with a non-mathematical explanation of the problem, and the modern understanding of the physics of the spin-glass state is formulated in general terms. Following this, the "magic" of the replica symmetry breaking scheme is demonstrated and the physics behind it discussed. Recent experiments on real spin-glass materials are briefly described to demonstrate how this somewhat abstract physics can be...

This edited and reviewed volume consists of papers that were originally presented at a workshop in the Scientific Center at Schloss Dagstuhl, Germany. It gives an overview of the field and presents the latest developments in the areas of modelling and planning for sensor based robots. The particular topics addressed include active vision, sensor fusion, environment modelling, motion planning, robot navigation, distributed control architectures, reactive behaviour, and others. Key contributors to this volume are: S. Arimoto, R. Bolles, H. Bunke, H. Christensen, R. Dillmann, T. Henderson, R....

This book is based on the teaching experience of the authors, and therefore some of the topics are presented in a new form. For instance, the multi-valued properties of the argument function are discussed in detail so that the beginner may readily grasp the elementary multi-valued analytic functions. The residue theorem is extended to the case where poles of analytic functions considered may occur on the boundary of a region -- which is very useful in applications but not seen in textbooks written in English.

This book provides a detailed description of a most important unsolved mathematical problem -- the Goldbach conjecture. Raised in 1742 in a letter from Goldbach to Euler, this conjecture attracted the attention of many mathematical geniuses. Several great achievements were made, but only until the 1920's. The book gives an exposition of these results and their impact on mathematics, particularly, number theory. It also presents (partly or wholly) selections from important literature, so that readers can get a full picture of the conjecture.

Translation generalized quadrangles play a key role in the theory of generalized quadrangles, comparable to the role of translation planes in the theory of projective and affine planes. The notion of translation generalized quadrangle is a local analog of the more global "Moufang Condition," a topic of great interest, also due to the classification of all Moufang polygons. Attention is thus paid to recent results in that direction, but also many of the most important results in the general theory of generalized quadrangles that appeared since 1984 are treated. Translation Generalized...