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North Holland

Psychobiology and Early Development
1st Edition
Volume 46
H. Rauh + 1 more
English
This volume is the outcome of an international symposium held in Berlin, FRG, which brought together researchers in the field of infant development.The contributors are from Europe and North America, and have as their primary professional interest either pediatrics, biology or psychology. These fields, in spite of common involvement and large overlap, still have to overcome communication problems and differences in scientific approaches. The emphasis of this book is on the efforts of the participants towards reaching a mutual understanding. In spite of disciplinary diversity, the papers in this book complement each other, and set the scene for future multidisciplinary research and exchange in the field of infant development.
Geometry of Numbers
2nd Edition
Volume 37
C.G. Lekkerkerker + 1 more
English
This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc.This second edition was prepared jointly by P.M. Gruber and the author of the first edition. The authors have retained the existing text (with minor corrections) while adding to each chapter supplementary sections on the more recent developments. While this method may have drawbacks, it has the definite advantage of showing clearly where recent progress has taken place and in what areas interesting results may be expected in the future.
Difference Schemes
An Introduction to the Underlying Theory
1st Edition
Volume 19
S.K. Godunov + 1 more
English
Much applied and theoretical research in natural sciences leads to boundary-value problems stated in terms of differential equations. When solving these problems with computers, the differential problems are replaced approximately by difference schemes.This book is an introduction to the theory of difference schemes, and was written as a textbook for university mathematics and physics departments and for technical universities. Some sections of the book will be of interest to computations specialists.While stressing a mathematically rigorous treatment of model problems, the book also demonstrates the relation between theory and computer experiments, using difference schemes created for practical computations.
The Algebraic Structure of Crossed Products
1st Edition
Volume 142
G. Karpilovsky
English
In the past 15 years, the theory of crossed products has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings.The purpose of this monograph is to give, in a self-contained manner, an up-to-date account of various aspects of this development, in an effort to convey a comprehensive picture of the current state of the subject. It is assumed that the reader has had the equivalent of a standard first-year graduate course, thus familiarity with basic ring-theoretic and group-theoretic concepts and an understanding of elementary properties of modules, tensor products and fields. A chapter on algebraic preliminaries is included, which briefly surveys topics required later in the book.
The Jacobson Radical of Group Algebras
1st Edition
Volume 135
G. Karpilovsky
English
Let G be a finite group and let F be a field. It is well known that linear representations of G over F can be interpreted as modules over the group algebra FG. Thus the investigation of ring-theoretic structure of the Jacobson radical J(FG) of FG is of fundamental importance. During the last two decades the subject has been pursued by a number of researchers and many interesting results have been obtained. This volume examines these results.The main body of the theory is presented, giving the central ideas, the basic results and the fundamental methods. It is assumed that the reader has had the equivalent of a standard first-year graduate algebra course, thus familiarity with basic ring-theoretic and group-theoretic concepts and an understanding of elementary properties of modules, tensor products and fields. A chapter on algebraic preliminaries is included, providing a survey of topics needed later in the book. There is a fairly large bibliography of works which are either directly relevant to the text or offer supplementary material of interest.
Foundations of Analysis over Surreal Number Fields
1st Edition
Volume 141
N.L. Alling
English
In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are derived. A primer on Conway's field of surreal numbers is also given.Throughout the manuscript, great efforts have been made to make the volume fairly self-contained. Much exposition is given. Many references are cited. While experts may want to turn quickly to new results, students should be able to find the explanation of many elementary points of interest. On the other hand, many new results are given, and much mathematics is brought to bear on the problems at hand.
Solitons and Instantons
An Introduction to Solitons and Instantons in Quantum Field Theory
1st Edition
Volume 15
R. Rajaraman
English
This book offers an elementary and unified introduction to the non-perturbative results obtained in relativistic quantum field theory based on classical soliton and instanton solutions. Such solutions are derived for a variety of models and classified by topological indices. The methods are then developed for quantizing solitons to obtain quantum particles. Vacuum tunneling, &ugr;-vacua and the dilute-instanton-gas approximation are described in detail. Other instanton effects related to quark-quark forces, confinement, the U(1) problem and Borel summability are also discussed. The emphasis is on presenting the basic ideas in a simple pedagogical way. Technical tools like functional methods, Grassman integrals, homotopy classification, collective co-ordinates etc. are developed ab initio.The presentation of this work is kept at a fairly simple level and ideas are developed through illustrative examples. Techniques not covered in older field theory textbooks, such as functional integral methods, are presented in some detail to the necessary extent. These techniques are important in their own right. Although the book is mainly addressed to particle physicists and quantum field theorists, several portions will be of relevance to other branches of physics, particularly statistical mechanics. These include three chapters devoted to deriving classical soliton and instanton solutions and one on collective co-ordinates, as well as sections devoted to general techniques.
Neurophysiological and Neuropsychological Aspects of Spatial Neglect
1st Edition
Volume 45
M. Jeannerod
English
Spatial Neglect is one of the few areas in Neuropsychology where clinicians, psychologists and animal experimenters have succeeded in adopting a common language. The result of interaction between these three approaches has been some important new advances, which are presented in this volume.Apart from its clinical significance in neuropsychology, Spatial Neglect raises important questions in the field of behavioral neurosciences. In this volume, three aspects are examined: a) normal subjects, where new findings on spatial behavior are described. b) brain-lesioned subjects, where the classical studies on neglect are reconsidered in the light of new findings. c) animals, where new experimental situations allow a deeper understanding of the neural substrate.
Theory of Linear Operations
1st Edition
Volume 38
S. Banach
English
This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra.The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series.A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'') complements this important monograph.
Obstacle Problems in Mathematical Physics
1st Edition
Volume 134
J.-F. Rodrigues
English
The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics.The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitati... problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.

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