Alexander Tolstonogov
Institute of Systems Dynamics and Control Theory, Siberian Branch of
the Russian Academy of Sciences, Irkutsk, Russia

Differential Inclusions in a Banach Space

MATHEMATICS AND ITS APPLICATIONS Volume 524

This monograph is devoted to the development of a unified approach for studying differential inclusions in a Banach space with non-convex right-hand side, a new branch of the classical theory of ordinary differential equations. Differential inclusions are now a mature field of mathematical activity, with their own methods, techniques, and applications, which range
from economics to physics and biology. The current approach relies on ideas and methods from modern functional analysis, general topology, the theory of multifunctions, and continuous selectors.

Audience: This volume will be of interest to researchers and postgraduate student whose work involves differential equations, functional analysis, topology, and the theory of set-valued functions.

Contents
Preface. 1. Multi-Valued Differential Equation Generated by a Differential Inclusion. 2. Differential Inclusions. Existence of Solutions. 3. Properties of Solutions. 4. Integral Funnel of the Differential Inclusion. 5. Inclusions with Non-Compact Right Hand Side. Appendices. References. Index. Symbols.

Hardbound, ISBN 0-7923-6618-2
October 2000, 320 pp.

edited by Semen S. Kutateladze
Sobolev Institute of Mathematics, Siberian Division of the Russian
Academy of Sciences, Novosibirsk, Russia

Nonstandard Analysis and Vector Lattices

MATHEMATICS AND ITS APPLICATIONS Volume 525

This book collects applications of nonstandard methods to the theory of vector lattices. Primary attention is paid to combining infinitesimal and Boolean-valued constructions of use in the classical problems of representing abstract analytical objects, such as Banach-Kantorovich
spaces, vector measures, and dominated and integral operators. This book is a complement to Volume 358 of "Mathematics and Its Applications": Vector Lattices and Integral Operators, printed in 1996.

Audience: The book is intended for the reader interested in the modern tools of nonstandard models of set theory as applied to problems of contemporary functional analysis. It will also be of use to mathematicians, students and postgraduates interested in measure and integration, operator theory, and mathematical logic and foundation.

Contents and Contributors
Foreword. 1. Nonstandard Methods and Kantorovich Spaces; A.G. Kusraev, S.S. Kutateladze. 2. Functional Representation of a Boolean Valued Universe; A.E. Gutman, G.A. Losenkov. 3. Dual Banach Bundles; A.E. Gutman, A.V. Koptev. 4. Infinitesimals in Vector Lattices; ﾈ.Yu.
Emel'yanov. 5. Vector Measures and Dominated Mappings; A.G. Kusraev, S.A. Malyugin. Notation Index. Subject Index.

Hardbound, ISBN 0-7923-6619-0
October 2000, 320 pp.

Aram V. Arutyunov
Peoples' Friendship University, Moscow, and Moscow State University,
Dept. of Computational Mathematics and Cybernetics, Russia

Optimality Conditions: Abnormal and Degenerate Problems

MATHEMATICS AND ITS APPLICATIONS Volume 526

This book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem.
Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed.

Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students.

Contents
Preface. 1. Extremal Problems with Constraints. 2. Optimal Control Problem. Pontryagin Maximum Principle. 3. Degenerate Quadratic Forms of the Calculus of Variations. 4. Study of Mappings in a Neighborhood of an Abnormal Point. References. Index. List of Notation.

Hardbound, ISBN 0-7923-6655-7
November 2000, 312 pp.

Aurel Bejancu / Hani Reda Farran
Dept. of Mathematics and Computer Science, Kuwait University

Geometry of Pseudo-Finsler Submanifolds

MATHEMATICS AND ITS APPLICATIONS Volume 527

This book begins with a new approach to the geometry of pseudo-Finsler manifolds. It also discusses the geometry of pseudo-Finsler manifolds and presents a comparison between the induced and the intrinsic Finsler connections. The Cartan, Berwald, and Rund connections are all
investigated. Included also is the study of totally geodesic and other special submanifolds such as curves, surfaces, and hypersurfaces.

Audience: The book will be of interest to researchers working on pseudo-Finsler geometry in general, and on pseudo-Finsler submanifolds in particular.

Contents
Preface. 1. Pseudo-Finsler Manifolds. 2. Pseudo-Finsler Submanifolds. 3. Special Immersions of Pseudo-Finsler Manifolds. 4. Geometry of Curves in Finsler Manifolds. 5. Pseudo-Finsler Hypersurfaces. 6. Finsler Surfaces. Basic Notations and Terminology. References. Subject Index.

Hardbound, ISBN 0-7923-6664-6
November 2000, 256 pp.

Cathy Gorini, Editor

Geometry at Work
Papers in Applied Geometry

Series: MAA Notes

As the study of shape and form, geometry is able to model the space around us and the forms inhabiting this space. For this reason, geometry has always been highly regarded for its practical value, and geometry and its applications have long been a central part of the study of mathematics. Centuries ago, in prescribing geometry to be a part of the standard educational program for youth, Plato recognized that "for the better apprehension of any branch of knowledge, it makes all the difference whether a man has a grasp of geometry or not." Since then, geometry has grown to include many different theories, techniques, and points of view, each of which has found a role, of one sort or another, for the better apprehension of other branches of knowledge.

While there are many textbooks presenting a pure or theoretical approach to geometry and many monographs investigating a single aspect of applied geometry, it is difficult to find a wide-angle view of applied geometry. The purpose of this collection is to give as broad a picture as possible of the applications of geometry. At the same time, since the papers in this collection have been written by pioneers and leading experts in each of the fields represented, the reader is assured of seeing the creativity, depth, and rigor that is an essential part of any successful application of mathematical knowledge.

This collection will be a rich resource for the geometry instructor, whether as a supplement to standard textbook material, reference material for student reports and projects, or as the starting point for a research program. The papers vary in difficulty, but are accessible to anyone having a college-level acquaintance with geometry. It is hoped that this volume will open many new worlds for all lovers of geometry.

Contents:

1.Art and Architecture
Spirals and the Rosette in Architectural Ornament, Kim Williams
Sun, Disk, Moon Disk, Paul Calter
Facade Measurement by Trigonometry, Paul Calter
A Secret of Ancient Geometry Jay Kappraff

2.Vedic Civilization
Square Roots in the Sulba Sultras, David W. Henderson
Applied Geometry in the Sulba Sultras, John F. Price

3.The Classroom
Ethnomathematics for the Geometry Curriculum, Marcia Ascher
Education with Fascination: Teaching Descriptive Geometry with Applications Marina V. Pokrovskaya

4.Engineering
Making Measurements on Curved Surfaces, James Casey
Mathematics to the Aid of Surgeons, Ramin Shahidi
The Geometry of Frameworks: Rigidity, Mechanisms and CAD, Brigitte Servatius
Geometry and Geographical Information Systems, George Nagy
On the Other Hand: Geometric Ideas in Robotics, Bud Mishra

5.Decision Making Processes
Decisions through Triangles, Donald G. Saari
Geometry in Learning, Kristin P. Bennett and Erin J. Bredensteiner

6.Mathematics and Science
The Geometry of Numbers, Antonie Boerkoel
Statistical Symmetry, Charles Radin
Three-Dimensional Topology and Quantum Physics, Louis H. Kauffman
Bridges between Geometry and Graph Theory Tomaz Pisanski and Milan Randic
Polytopes in Combinatorial Optimization, Thomas Burger and Peter Gritzmann

Catalog Code: NTE-53
250 pp., Paperbound, 2000
ISBN 0-88385-164-4

Titu Andreescu and Zuming Feng, Editors

Mathematical Olympiads Problems and Solutions
from Around the World 1998-1999

This book is a continuation of "Mathematical Olympiads: Problems and Solutions from around the world 1997-1998". It contains solutions to challenging problems from algebra, geometry, combinatorics and number theory featured in the earlier book, together with selected questions (without solutions) from 30 national and regional Olympiads given during 1999.

This collection is intended as practice for the serious student who wishes to improve their performance on the USA Mathematical Olympiad (USAMO). Some of the problems are comparable to the USAMO in that they come from national contests. Others are harder, as some countries first have a national Olympiad, and later one ore more exams to select a team for the International Mathematical Olympiad (IMO). And some problems are easier, coming from regional international contests ("mini-IMOs").

Different nations have different mathematical cultures, so you will find some of these questions extremely difficult and some rather easy. We have included a wide variety of problems, especially from those countries that have often done well at the IMO. You will have the chance to work on beautiful mathematical questions. Take them on!

Catalog Code: OPW/W
280 pp., Paperbound, 2000
ISBN 0-88385-803-7