Lorenzo Magnani / University of Pavia, Italy and Georgia Institute of Technology, Atlanta, USA

Philosophy and Geometry
Theoretical and Historical Issues

THE WESTERN ONTARIO SERIES IN PHILOSOPHY OF SCIENCE Volume 66

Philosophers have studied geometry since ancient times. Geometrical knowledge has often played the role of a laboratory for the philosopher's conceptual experiments dedicated to the ideation of powerful theories of knowledge. Lorenzo Magnani's new book Philosophy and Geometry illustrates the rich intrigue of this fascinating story of human knowledge, providing a new analysis of the ideas of many scholars (including Plato, Proclus, Kant, and Poincare), and discussing conventionalist and neopositivist perspectives and the problem of the origins of geometry. The book also ties together the concerns of philosophers of science and cognitive scientists, showing, for example, the connections between geometrical reasoning and cognition as well as the results of recent logical and computational models of geometrical reasoning. All the topics are dealt with using a novel combination of both historical and contemporary perspectives. Philosophy and Geometry is a valuable contribution to the renaissance of research in the field.

Contents
1. At the Origins of Geometrical Knowledge. 2. Geometry: the Model of Knowledge. 3. Constructions, Logic, Categories. 4. The Fantasia in Ancient Geometrical Knowledge. 5. Geometry and Convention. 6. Geometry, Problem Solving, Abduction. 7. Geometry and Cognition. References. Author Index. Subject Index.

Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6933-5
May 2001, 272 pp.

Philippe Baptiste /Centre National de la Recherche Scientifique, France
Claude Le Pape ,Wim Nuijten /ILOG, Gentilly, France

Constraint-Based Scheduling
Applying Constraint Programming to Scheduling Problems

INTERNATIONAL SERIES IN OPERATIONS RESEARCH AND MANAGEMENT SCIENCE Volume 39

Constraint Programming is a problem-solving paradigm that establishes a clear distinction between two pivotal aspects of a problem: (1) a precise definition of the constraints that define the problem to be solved and (2) the algorithms and heuristics enabling the selection of decisions to solve the problem.

It is because of these capabilities that Constraint Programming is increasingly being employed as a problem-solving tool to solve scheduling problems. Hence the development of Constraint-Based Scheduling as a field of study.

The aim of this book is to provide an overview of the most widely used Constraint-Based Scheduling techniques. Following the principles of Constraint Programming, the book consists of three distinct parts:

Contents
Foreword. Preface. Acknowledgements. 1. Introduction. 2. Propagation of the One-Machine Resource Constraint. 3. Propagation of Cumulative Constraints. 4. Comparison of Propagation Techniques. 5. Propagation of Objective Functions. 6. Resolution of Disjunctive Problems. 7. Cumulative Scheduling Problems. 8. Min-Sum Scheduling Problems. 9. Conclusion. 10. Summary of Notation. References. Index.

Kluwer Academic Publishers, Boston
Hardbound, ISBN 0-7923-7408-8
July 2001, 216 pp.

Gennadi Puninski / Dept. of Mathematics, Moscow State Social University, Russia

Serial Rings

This book presents an exhaustive and up-to-date overview of the structure theory of serial rings, and the various methods of treating them. Results have been scattered throughout the literature, and the achievements of some schools, such as the Kiev school, seem little-known. This volume endeavours to unify the wide spectrum of tools used in this area and state the theory of serial rings based on two constructions: firstly, localisation with respect to a semi-prime Goldie ideal; and, secondly, a hidden 'blow-up' construction in a serial ring. Part of the work deals with the theory of modules over a serial ring, especially with finitely presented and pure injective modules. Other topics include noetherian serial rings and Artinian serial rings.

Audience: This volume can be used as a textbook in ring theory and in the model theory of modules, and will also be of interest to postgraduates and researchers whose work involves rings and algebras.

Contents

Introduction. 1. Basic Notions. 2. Finitely Presented Modules over Serial Rings. 3. Prime Ideals in Serial Rings. 4. Classical Localizations in Serial Rings. 5. Serial Rings with the A.C.C. on annihilators and Nonsingular Serial Rings. 6. Serial Prime Goldie Rings. 7. Noetherian Serial Rings. 8. Artinian Serial Rings. 9. Serial Rings with Krull Dimension. 10. Model Theory for Modules. 11. Indecomposable Pure Injective Modules over Serial Rings. 12. Super-Decomposable Pure Injective Modules over Commutative Valuation Rings. 13. Pure Injective Modules over Commutative Valuation Domains. 14. Pure Projective Modules over Nearly Simple Uniserial Domains. 15. Pure Projective Modules over Exceptional Uniserial Rings. 16. S-Pure Injective Modules over Serial Rings. 17. Endomorphism Rings of Artinian Modules. Bibliography. Notations. Index.

Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-7187-9
September 2001, 236 pp.

Wilfried Hazod / Mathematical Dept., University of Dortmund, Germany
Eberhard Siebert†

Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups : Structural Properties and Limit Theorems

MATHEMATICS AND ITS APPLICATIONS Volume 531

Generalising classical concepts of probability theory, the investigation of operator (semi)-stable laws as possible limit distributions of operator-normalized sums of i.i.d. random variable on finite-dimensional vector space started in 1969. Currently, this theory is still in progress and promises interesting applications. Parallel to this, similar stability concepts for probabilities on groups were developed during recent decades. It turns out that the existence of suitable limit distributions has a strong impact on the structure of both the normalizing automorphisms and the underlying group. Indeed, investigations in limit laws led to contractable groups and ? at least within the class of connected groups ? to homogeneous groups, in particular to groups that are topologically isomorphic to a vector space. Moreover, it has been shown that (semi)-stable measures on groups have a vector space counterpart and vice versa.

The purpose of this book is to describe the structure of limit laws and the limit behaviour of normalized i.i.d. random variables on groups and on finite-dimensional vector spaces from a common point of view. This will also shed a new light on the classical situation. Chapter 1 provides an introduction to stability problems on vector spaces. Chapter II is concerned with parallel investigations for homogeneous groups and in Chapter III the situation beyond homogeneous Lie groups is treated. Throughout, emphasis is laid on the description of features common to the group- and vector space situation.

Chapter I can be understood by graduate students with some background knowledge in infinite divisibility. Readers of Chapters II and III are assumed to be familiar with basic techniques from probability theory on locally compact groups.

Contents

Preface. Introduction. I. Probabilities on vector spaces. II. Probabilities on simply connected nilpotent Lie groups. III. (Semi-) stability and limit theorems on general locally compact groups. Epilogue. Bibliography. List of Symbols. Index.

Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 1-4020-0040-5
September 2001, 632 pp.

Vyacheslav L. Girko / Dept. of Statistics and Probability, Michigan State University

Theory of Stochastic Canonical Equations
Volumes I and II

MATHEMATICS AND ITS APPLICATIONS Volume 535

Theory of Stochastic Canonical Equations collects the major results of thirty years of the author's work in the creation of the theory of stochastic canonical equations. It is the first book to completely explore this theory and to provide the necessary tools for dealing with these equations. Included are limit phenomena of sequences of random matrices and the asymptotic properties of the eigenvalues of such matrices. The book is especially interesting since it gives readers a chance to study proofs written by the mathematician who discovered them.

All fifty-nine canonical equations are derived and explored along with their applications in such diverse fields as probability and statistics, economics and finance, statistical physics, quantum mechanics, control theory, cryptography, and communications networks. Some of these equations were first published in Russian in 1988 in the book Spectral Theory of Random Matrices, published by Nauka Science, Moscow.

An understanding of the structure of random eigenvalues and eigenvectors is central to random matrices and their applications. Random matrix analysis uses a broad spectrum of other parts of mathematics, linear algebra, geometry, analysis, statistical physics, combinatories, and so forth. In return, random matrix theory is one of the chief tools of modern statistics, to the extent that at times the interface between matrix analysis and statistics is notably blurred.

Volume I of Theory of Stochastic Canonical Equations discusses the key canonical equations in advanced random matrix analysis. Volume II turns its attention to a broad discussion of some concrete examples of matrices. It contains in-depth discussion of modern, highly-specialized topics in matrix analysis, such as unitary random matrices and Jacoby random matrices.

The book is intended for a variety of readers: students, engineers, statisticians, economists and others.

Kluwer Academic Publishers, Dordrecht
Hardbound Set only of 2 volumes, ISBN 1-4020-0075-8
September 2001, 1016 pp.

edited by
Norair Arakelian /National Academy of Sciences of Armenia, Yerevan, Armenia
Paul M. Gauthier / Gert Sabidussi / Dept. de math. et de statistique, Universite de Montreal,

Approximation, Complex Analysis, and Potential Theory
Proceedings of the Nato Advanced Study Institute on Modern Methods in Scientific Computing and Applications, Montreal, Quebec, Canada, from 3 to 14 July 2000

NATO SCIENCE SERIES: II: Mathematics, Physics and Chemistry Volume 37

Hermann Weyl considered value distribution theory to be the greatest mathematical achievement of the first half of the 20th century. The present lectures show that this beautiful theory is still growing. An important tool is complex approximation and some of the lectures are devoted to this topic. Harmonic approximation started to flourish astonishingly rapidly towards the end of the 20th century, and the latest development, including approximation manifolds, are presented here.

Since de Branges confirmed the Bieberbach conjecture, the primary problem in geometric function theory is to find the precise value of the Bloch constant. After more than half a century without progress, a breakthrough was recently achieved and is presented. Other topics are also presented, including Jensen measures.

A valuable introduction to currently active areas of complex analysis and potential theory. Can be read with profit by both students of analysis and research mathematicians.

Contents and Contributors


Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 1-4020-0028-6
October 2001, 288 pp.

Paperback, ISBN 1-4020-0029-4
October 2001, 288 pp.