Bart, H., Rotterdam, Gohberg I.,Ramat Aviv, Ran, A.C.M.,Amsterdam

Operator Theory and Analysis
The M.A. Kaashoek Anniversary Volume. Workshop in Amsterdam, Nov.1997

Operator Theory vol.122

2001. 474 pages. Hardcover
ISBN 3-7643-6499-8
English

This volume is dedicated to M.A. Kaashoek, who made major contributions to operator theory
and its applications. Apart from biographical material, the book consists of original research
papers centered around factorization of matrix valued function, interpolation and spectral theory.

This book contains the proceedings of the international workshop organized at the Vrije Universiteit Amsterdam in November 1997 and dedicated to the sixtieth birthday of M.A. Kaashoek, one
of the leading experts in operator theory and its applications. The workshop focused on areas in
mathematical and functional analysis where the ideas and results of M.A. Kaashoek played an
important role. The papers of this volume cover a wide range of topics centered around
factorization of matrix valued functions, interpolation theory, and spectral theory. Other papers
deal with canonical systems of differential equations, operators in indefinite inner product spaces,
and the effect of small delays on stability and control of partial differential equations. The book starts
with biographical material and a list of publications of M.A. Kaashoek. The main part consists of original research papers, which contain new interesting results. The book will be of interest to a
wide range of readers in pure and applied mathematics and engineering.

Bojan Mohar and Carsten Thomassen

GRAPHS ON SURFACES

hardcover | 0-8018-6689-8
Johns Hopkins Studies in the Mathematical Sciences
in Association with the Department of Mathematical Sciences, The Johns Hopkins University
April 2001, 304 pp., 88 line drawings

"This is a long-awaited book by two of the most powerful practitioners in the field.
There is nothing else like it, and it will remain the definitive book on the subject for many, many years to come." --Thomas Tucker, Colgate University

Graph theory is one of the fastest growing branches of mathematics. Until recently, it was regarded as a branch of combinatorics and was best known by the famous four-color theorem stating that any map can be colored using only four colors such that no two bordering countries have the same color. Now graph
theory is an area of its own with many deep results and beautiful open problems. Graph theory has numerous applications in almost every field of science and has attracted new interest because of its relevance to such technological problems as computer and telephone networking and, of course, the internet. In this new
book in the Johns Hopkins Studies in the Mathematical Science series, Bojan Mohar and Carsten Thomassen look at a relatively new area of graph theory: that associated with curved surfaces.

Graphs on surfaces form a natural link between discrete and continuous mathematics. The book provides a rigorous and concise introduction to graphs on surfaces and surveys some of the recent developments in this area. Among the basic results discussed are Kuratowski's theorem and other planarity criteria, the
Jordan Curve Theorem and some of its extensions, the classification of surfaces, and the Heffter-Edmonds-Ringel rotation principle, which makes it possible to treat graphs on surfaces in a purely combinatorial way. The genus of a graph, contractability of cycles, edge-width, and face-width are treated purely combinatorially, and several results related to these concepts are included. The extension by Robertson and Seymour of Kuratowski's theorem to higher surfaces is discussed in detail, and a shorter proof is presented. The book concludes with a survey of recent developments on coloring graphs on surfaces.

Wu Wen-tsun
Mathematics Mechanization Research Center, Institute of
Systems Science, Chinese Academy of Sciences, Beijing, PRC

Mathematics Mechanization

Mechanical Geometry Theorem-Proving,
Mechanical Geometry Problem-Solving and
Polynomial Equations-Solving

MATHEMATICS AND ITS APPLICATIONS Volume 489

This book is a collection of essays centred around the subject of mathematical mechanization. It tries to deal with mathematics in a constructive and algorithmic manner so that reasoning becomes mechanical, automated and less laborious.

The book is divided into three parts. Part I concerns historical developments of mathematics mechanization, especially in ancient China. Part II describes the underlying principles of polynomial equation-solving, with polynomial coefficients in fields restricted to the case of characteristic 0. Based on the general principle, some methods of solving such arbitrary polynomial systems may be found. This part also goes back to
classical Chinese mathematics as well as treating modern works in this field. Finally, Part III contains applications and examples.

Audience: This volume will be of interest to research and applied mathematicians, computer scientists and historians in mathematics.

Contents
Preface. Part I: Historical Developments. 1. Polynomial Equations-Solving in Ancient Times, Mainly in Ancient China. 2. Historical Development of Geometry Theorem-Proving and Geometry Problem-Solving in Ancient Times. Part II: Principles and Methods. 3. Algebraic Varieties as Zero-Sets and Characteristic-Set Method. 4. Some Topics in Computer Algebra. 5. Some Topics in Computational Algebraic Geometry. Part III: Applications and Examples. 6. Applications to Polynomial Equations-Solving. 7. Applications to Geometry Theorem-Proving. 8. Diverse Applications. Bibliography. Index.

Kluwer Academic Publishers, Dordrecht
Co-publication with Science Press, Beijing, PR of China

Hardbound, ISBN 0-7923-5835-X
December 2000, 432 pp.

Maria do R. Grossinho
ISEG, Universidade T?cnica de Lisboa, CMAF, Universidade de
Lisboa, Portugal Stepan Agop Tersian University of Rousse, Bulgaria

An Introduction to Minimax Theorems and Their Applications
to Differential Equations

NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 52

The book is intended to be an introduction to critical point theory and its applications to differential equations. Although the related material can be found in other books, the authors of this volume have had the following goals in mind:

To present a survey of existing minimax theorems, To give applications to elliptic differential equations in
bounded domains, To consider the dual variational method for problems with continuous and discontinuous nonlinearities, To present some elements of critical point theory for locally Lipschitz functionals and give applications to fourth-order differential equations with discontinuous nonlinearities,
To study homoclinic solutions of differential equations via the variational methods.

The contents of the book consist of seven chapters, each one divided into several sections.

Audience: Graduate and post-graduate students as well as specialists in the fields of differential equations, variational methods and optimization.

Contents
Preface. 1. Minimization and Mountain-Pass Theorems. 2. Saddle-Point and Linking Theorems. 3. Applications to Elliptic Problems in Bounded Domains. 4. Periodic Solutions for Some Second-Order Differential Equations. 5. Dual Variational Method and Applications. 6. Minimax Theorems for Locally Lipschitz Functionals and Applications. 7. Homoclinic Solutions of Differential Equations. Notations. Index.

Kluwer Academic Publishers, Dordrecht

Hardbound, ISBN 0-7923-6832-0
January 2001, 288 pp.

edited by
Eric Goles Dep. de Ingenieria Matematica, F.C.F.M., Universidad de Chile, Santiago, Chile
Servet Martinez Dep. de Ingenieria Matematica, F.C.F.M., Universidad de Chile, Santiago, Chile

Complex Systems

NONLINEAR PHENOMENA AND COMPLEX SYSTEMS Volume 6

This volume contains the courses given at the Sixth Summer School on Complex Systems held at the Faculty of Physical and Mathematical Sciences, University of Chile at Santiago, Chile, 14-18 December 1998.

The contributions, which in some cases have been structured as surveys, treat recoding Sturmian sequences on a subshift of finite type chaos from order; Lyapunov exponents and synchronisation of cellular automata; dynamical systems and biological regulations; cellular automata and artificial life; Kolmogorov complexity; and
cutoff for Markov chains.

Audience: This book will be of interest to graduate students and researchers whose work involves mathematical modelling and industrial mathematics, statistical physics, thermodynamics,
algorithms and computational theory, statistics and probability, and
discrete mathematics.

Contents and Contributors
Foreword. Recoding Sturmian Sequences on a Subshift of Finite Type Chaos from Order: A Worked out Example; P. Arnoux. Lyapunov Exponents and Synchronization of Cellular Automata; F. Bagnoli, R. Rechtman. Dynamical Systems and Biological Regulations; J. Demongeot, et al. Cellular Automata and Artificial
Life; K. Morita. Why Kolmogorov Complexity?; V.A. Uspensky. Cutoff for Markov Chains: Some Examples and Applications; B. Ycart.

Kluwer Academic Publishers, Dordrecht

Hardbound, ISBN 0-7923-6830-4
February 2001