Bercovici, H. / Foias, C.I., Indiana
University, Bloomington, USA (Ed.)
International Workshop on Operator Theory and Applications, IWOTA
96
1999. Approx. 312 pages. Hardcover
ISBN 3-7643-6229-4
Due in December 1999
Operator Theory: Advances and Applications 115
Systems and control theories use sophisticated operator
theoretical methods. They also provide new ideas
and problems in operator theory. As a consequence, the biannual
MTNS (Mathematical Theory of Networks and
Systems) conference is attended by many operator theorists.
At the initiative of J.W. Helton and I. Gohberg, an International
Workshop on Operator Theory
and Applications (IWOTA) has been organized since the early 80s,
as a satellite of MTNS.
The articles in this volume originated from the IWOTA conference
held at Indiana University,
Bloomington, in June 1996. They represent most of the areas that
were discussed at the
workshop with some emphasis on modern interpolation theory, a
topic which has seen
much progress in recent years. The contributions were, as usual,
subject to a
thorough refereeing process and will bring the reader to the
forefront of current research in this area.
Birget, J.-C., Dalhousie University,
Halifax, Canada / Margolis, S.,
Bar-Ilan University, Ramat Gan,
Israel / Meakin, J., University of
Nebraska-Lincoln, USA / Sapir, M.,
Vanderbilt University, USA (Ed.)
1999. Approx. 352 pages. Hardcover
ISBN 3-7643-4130-0
Due in January 2000
Trends in Mathematics
The stimulus for this volume was provided by the international
conference on Algorithmic Problems in
Groups and Semigroups, held in May of 1998 at the University of
Nebraska-Lincoln.
New results, interesting techniques, and often overlapping ideas
from diverse fields are
reflected in this collection of largely expository articles which
cover topics in
algorithmic group and semigroup theory, and computer science.
Contributors to the volume:
J. Almeida, K. Auinger, G. Baumslag, K.
Bencsath, B. Fine, A.M. Gaglione, V.S. Guba,
K. Henckell, S.V. Ivanov, Y. Kobayashi, S.I.
Kublanovskii, A. Myasnikov, F. Otto, J.-E. Pin,
S.J. Pride, J.-F. Raymond, V. Remeslennikov,
F. Roehl, G. Rosenberger, N. Ruskuc, L.M.
Shneerson, D. Spellman, P.E. Schupp, B.
Steinberg, H. Straubing, P. Tesson, D. Th?rien,
J. Wang, P. Weil.
This book can serve as a good introduction to algorithmic
problems in groups and semigroups
for graduate students and as a useful reference text for
researchers in that area.
Contents
Preface / 1. Syntactic and Global Semigroup
Theory: A Synthesis Approach / 2.
Semigroups with Central Idempotents / 3.
Algebraic Geometry over Groups / 4. Aspects
of the Theory of Free Groups / 5. Polynomial
Isoperimetric Inequalities for Richard
Thompson's Groups F, T and V / 7. A Remark
on Finitely Generated Subgroups of Free
Groups / 8. Homotopy Reduction Systems for
Monoid Presentations II: The Guba--Sapir
Reduction and Homotopy Modules / 9.
Algorithmic Problems for Finite Groups and
Finite Semigroups / 10. A Survey on the
Computational Power of Some Classes of
Finite Monoid Presentations / 11. Rewriting
Systems, Finiteness Conditions, and
Associated Functions / 12. Multiparty
Communication Complexity of Finite Monoids
/ 13. Presentations for Monoids, their Maximal
Subgroups and Schutzenberger Groups / 14.
On the Growth of Relatively Free Semigroups
/ 15. When Can One Finite Monoid Simulate
Another? / 16. Computing Closures of Finitely
Generated Subgroups of the Free Group
Enns, R., Simon Fraser University,
Burnaby, Canada / McGuire, G.,
University College of the Fraser
Valley, Abbotsford, Canada
Second Edition
1999. Approx. 656 pages. Hardcover
ISBN 3-7643-4119-X
Due in January 2000
Nonlinear physics continues to be an area of dynamic modern
research, with applications to physics, engineering,
chemistry, mathematics, computer science, biology, medicine and
economics.
In this second edition extensive use is made of the computer
algebra system, Maple V. No
prior knowledge of Maple or of programming is assumed. The
authors have provided 74 Maple
files on a CD-ROM, all classroom tested, as well as 60 annotated
Maple worksheets. These
files and worksheets may be used to both solve and explore the
text's 400 problems.
This book includes 30 experimental activities which are intended
to deepen and broaden
the reader's understanding of the nonlinear physics. These
activities are correlated with
Part I, the theoretical framework of the text.
Contents
Preface
Part I: THEORY
1. Introduction / 2. Nonlinear Systems, Part I
/ 3. Nonlinear Systems, Part II / 4. Topological
Analysis / 5. Analytic Methods / 6. The
Numerical Approach / 7. Limit Cycles / 8.
Forced Oscillators / 9. Nonlinear Maps / 10.
Nonlinear PDE Phenomena / 11. Numerical
Simulation / 12. Inverse Scattering Method
Part II: EXPERIMENTAL ACTIVITIES
Introduction to Nonlinear Experiments / 1.
Spin Toy Pendulum / 2. Driven Eardrum / 3.
Nonlinear Damping / 4. Anaharmonic Potential
/ 5. Iron Core Conductor / 6. Nonlinear LRC
Circuit / 7. Tunnel Diode Negative Resistance
Curve / 8. Tunnel Diode Self-Excited
Oscillator / 9. Forced Duffing Equation / 10.
Focal Point Instability / 11. Compound
Pendulum / 12. Stable Limit Cycle / 13. Van
der Pol Limit Cycle / 14. Relaxation
Oscillations: Neon Bulb / 15. Relaxation
Oscillations: Drinking Bird / 16. Relaxation
Oscillations: Tunnel Diode / 17. Hard Spring /
18. Nonlinear Resonance Curve: Mechanical /
19. Nonlinear Resonance Curve: Electrical /
20. Nonlinear Resonance Curve: Magnetic /
21. Subharmonic Response: Period Doubling /
22. Diode: Period Doubling / 23. Five-Well
Magnetic Potential / 24. Power Spectrum /
25. Entrainment and Quasiperiodicity / 26.
Quasiperiodicity / 27. Chua's Butterfly / 28.
Route to Chaos / 29. Driven Spin Toy / 30.
Mapping
Index
Features
* Maple code updated to Maple V, Release 5
* 74 example files of Maple provided on
CD-ROM, all classroom tested * 60 annotated Maple worksheets
included
* no prior knowledge of Maple or of programming required
* 30 experimental "hands on" activities to deepen and
broaden the understanding of
material covered in the first part of the text
* 400 problems presented with solutions manual available to
instructors
* Accessible to students in engineering, physics, chemistry,
mathematics, computer
science, and biology
Filar, J.A. / Gaitsgory, V., Univ. of
South Australia, Mawson Lake,
Australia / Mizukami, K., Hiroshima
University, Japan (Ed.)
1999. Approx. 432 pages. Hardcover
ISBN 3-7643-4002-9
Due in January 2000
Modern game theory has evolved enormously since its inception in
the 1920s in the works of Borel and
Neumann. The branch of game theory known as dynamic games
descended from the pioneering work on differential
games by Isaacs. Since those early development decades, game
theory has had significant impact in such diverse
disciplines as applied mathematics, economics, systems theory,
control engineering, operations research,
ecology and the environmental sciences.
This new edited book focuses on various aspects of dynamic game
theory, providing authoritative, state-of-the-art information
and serving as a guide to the vitality of the field and its
applications. The chapters are based on presentations at the 7th
International Symposium on Dynamic Games and Applications held in
Kanagawa, Japan. A variety of topics of current interest are
presented.
The book offers an ideal survey of recent developments and
advances in dynamic games and their applications. It is a
valuable
resource for all dynamic game practitioners, researchers and
professionals in the fields of applied mathematics, operations
research,
economics, systems and control and environmental sciences.
Contents
Part I. Robust Control Design and H-Infinity:
Worst-Case Rate-Based Flow Control with an
ARMA Model of the Available Bandwidth *
H-Infinity Output Feedback Control Problems
for Bilinear Systems * H-Infinity Control of a
Class of Infinite-Dimensional Systems with
Nonlinear Outputs * Nonstandard Extension of
H-Infinity Optimal Control for Singularly
Perturbed Systems
Part II. Pursuit-evasion (P-E) Games:
Geodesic Parallel Pursuit Strategy in a Simple
Motion Pursuit Game * Real-Time Collision
Avoidance: Differential Game, Numerical
Solution and Synthesis of Strategies *
Rendezvous-Evasion as Multi-Stage Game
with Observed Actions * Identification and
Construction of Singular Surfaces in
Pursuit-Evasion Games * On Numerical
Solution of a Class of Pursuit-Evasion Games
Part III. Coupled Dynamic and Stochastic
Games: Infinite Horizon Dynamic Games with
Coupled State Constraints * Constrained
Markov Games: Nash Equilibria *
Piecewise-Deterministic Differential Games
and Dynamic Teams with Hybrid Controls * A
Game Variant of Stopping Problem on Jump
Processes with a Monotone Rule
Part IV. General Game Theoretic
Developments: Refinement of Nash Solution
for the Games with Perfect Information * A
Perturbation on Two-Person Zero-Sum
Games * Linear Complementarity Problems in
Static and Dynamic Games * Weighted
Discounted Stochastic Games with perfect
Information * Stochatic Games with Complete
Information and Average Cost Criterion
Part V. Applications: Crime and Law
Enforcement: A Multistage Game * Global
Analysis of a Dynamic Duopoly Game with
Bounded Rationality * A Multistage
Supergame of Downstream Pollution *
Solution and Stability for a Simple Dynamic
Bottleneck Model * Cumulants and
Risk-Sensitive Control: A Cost Mean and
Variance Theory with Application to Seismic
Protection of Structures
Features
* Robust control design and H-infinity
* Pursuit-evasion games
* Coupled dynamic and stochastic games
* Recent game-theoretic developments
* Selected applications in ecology and environmental science The
book offers an
ideal survey of recent developments and advances in dynamic games
and their
applications. It is a valuable resource for all dynamic game
practitioners, researchers, and
professionals in the fields of applied mathematics, operations
research, economics,
systems and control and environmentalsciences.
Matveev, A., St. Petersburg
University, Russia / Savkin, A.,
University of Western Australia,
Nedlands, Australia
2000. Approx. 352 pages. Hardcover
ISBN 3-7643-4141-6
Due in January 2000
Hybrid dynamical systems, both continuous and discrete dynamics
and variables, have attracted considerable
interest recently. This emerging area is found at the interface
of control theory and computer engineering, focusing on
the analogue and digital aspects of systems and devices. They are
essential for advances in modern
digital-controller technology.
"Qualitative Theory of Hybrid Dynamical Systems"
provides a thorough development and systematic presentation of
the
foundations and framework for hybrid dynamical systems. The
presentation offers an accessible, but precise, development of
the
mathematical models, heuristic algorithms and stability criteria.
The book largely concentrates on the case of discretely
controlled continuous-time systems and their relevance for
modeling aspects of flexible manufacturing systems and
dynamically
routed queuing networks.
This new book is an excellent resource for the study and analysis
of hybrid dynamical systems used in systems and control
engineering. Researchers, postgraduates and professionals in
control engineering and computer engineering will find the book
an
up-to-date development of the relevant new concepts and tools.
Contents
1. Introduction
2. Qualitative Analysis of Some Simple Hybrid
Dynamical Systems
3. General Theory of Differential Automata
4. Two-Dimensional Hybrid Dynamical
Systems
5. Limit Cycles in Hybrid Dynamical Systems
with Constant Derivatives
6. Limit Cycles in Hybrid Dynamical Systems
with Constant Derivatives--Examples
7. Globally Periodic Behavior of Switched
Single-Server Flow Networks
8. Regularizability of Switched Multiple-Server
Flow Networks
9. Open Problems
References
Index
Features
* Differential automata
* Development and use of the concept "cyclic linear
differential automata" (CLDA)
* Switched single-server flow networks coverage
* Application to specific models of manufacturing systems and
queuing networks
* Select collection of open problems for the subject
* Self-contained presentation of topics, with the necessary
background
Frankenhuysen, M. van / Lapidus,
M.L., University of California,
Riverside, USA
1999. Approx. 280 pages. Hardcover
ISBN 3-7643-4098-3
Due in January 2000
Number theory and fractal geometry are combined in this study of
the vibrations of fractal strings, that is,
one-dimensional drums with fractal boundary, and of the zeros of
zeta functions. The notion of complex
dimension, hinted at in an earlier work on fractal and spectral
geometry which examined connections with the
Riemann zeta function, is precisely defined in this work. An
explicit formula, originally developed for the
proof of the Prime Number Theorem, is extended here to apply to
the zeta functions associated with fractals.
This theory of complex dimensions enables a precise description
of the oscillations in the geometry or in the spectrum of a
fractal
string.
In the context of vibrating fractal strings, the Riemann
Hypothesis is given a geometric setting. This conjecture becomes
an inverse
spectral problem, and its interpretation in the language of
fractal strings, which have complex dimensions with real part
between 0
and 1, is: "One can hear if a fractal string is Minkowski
measurable, provided that its fractal dimension is not 1/2."
This is of course
an allusion to a central problem in contemporary mathematics,
often expressed as "Can one hear the shape of a drum?"
A
combination of analytical and geometric methods is used to also
establish new results about the vertical distribution of zeros of
number-theoretic and many other zetafunctions.
The new approach and results on the important problems
illuminated in this work will appeal to researchers and graduate
students
in number theory, fractal geometry, dynamical systems, spectral
geometry, and mathematical physics.
Contents
Overview / Introduction / 1. Complex
Dimensions of Ordinary Fractal Strings / 2.
Complex Dimensions of Self-Similar Fractal
Strings * 3. Generalized Fractal Strings
Viewed as Measures / 4. Explicit Formulas for
Generalized Fractal Strings / 5. The
Geometry and the Spectrum of Fractal
Strings / 6. Tubular Neighborhoods and
Minkowski Measurability / 7. The Riemann
Hypothesis and Inverse Spectral Problems /
8. Generalized Cantor Strings and their
Oscillations / 9. The Critical Zeros of Zeta
Functions / 10. Concluding Comments /
Appendix A: Zeta Functions in Number Theory
/ Appendix B: The Zeta Function of a
Laplacian and Spectral Asymptotics /
References / Conventions / Symbol Index /
Index / List of Figures / Acknowledgements
Description
Group representation theory is both elegant and practical, with
important applications to quantum mechanics, spectroscopy,
crystallography, and other fields in the physical sciences. Until
now, however, there have been virtually no accessible treatments
of group theory that include representations and characters. The
classic works in the field require a high level of mathematical
sophistication, and other texts omit representations and
characters.
Groups and Characters offers an easy-to-follow introduction to
the theory of groups and of group characters. Designed as a rapid
survey of the subject, this unique text emphasizes examples and
applications of the theorems, and avoids many of the longer and
more difficult proofs. The author presents group theory through
the Sylow Theorems and includes the full subgroup structure of
A5. Representations and characters are worked out with numerous
character tables, along with real andinduced characters that lead
to the table for S5.
The text includes specific sections that provide the mathematical
basis for some of the important applications of group theory in
spectroscopy and molecular structure. It also offers numerous
exercises-some stressing computation of concrete examples, others
stressing development of the mathematical theory.
Groups and Characters provides the ideal grounding for more
advanced studies with the classic texts, and for more broad-based
work in abstract algebra.
Furthermore, physical scientists-whose experience with groups and
characters may not be rigorous-will find Groups and Characters
the ideal means for gaining asense of the mathematics lying
behind the techniques used in applications.
Audience
Students in mathematics (upper level undergraduate or graduate),
chemistry, physics, or geology; Physical Scientists
Contents
Introductory Examples
Groups and Subgroups
Point Groups and Cosets
Homomorphisms and Normal Subgroups
Isomorphisms and Automorphisms
Factor Groups
Sylow Subgroups
Permutation Groups
Matrix Groups
Group Representations
Regular Representations
Irreducible Representations
Representations of Abelian Groups
Group Characters
Orthogonality Relations and Character Tables
Reducible Characters
The Burnside Counting Theorem
Real Characters
Induced Representations and Characters
The Character Table for S5
Space Groups and Semi-Direct Products
Proofs of the Sylow Theorems
References
Bibliography
Index
Index of Symbols.
Features
Uses specific examples throughout the book and includes
references to applications of group theory in physical chemistry
Provides numerous applications of the Sylow theorems, including
the full subgroup structure of A5
Contains many worked-out character tables, including A5 and S5
Links space groups (chemistry) to semi-direct products
(mathematics)
Groups and Characters
ISBN: 1584880384
Publication Date: 11/10/99
Ivanoff; B G
Merzbach; Ely
Description
Set Indexed Martingales offers a unique, comprehensive
development of a general theory of martingales indexed by a
family of sets. The authors establish-for the first time-an
appropriate framework that provides a suitable structure for a
theory of martingales with enough generality to include many
interesting examples.
Developed from first principles, the theory brings together the
theories of martingales with a directed index set and set-indexed
stochastic processes. Part One presents several classical
concepts extended to this setting, including: stopping,
predictability, Doob-Meyer decompositions, martingale
characterizations of the set-indexed Poisson process, and
Brownian motion. Part Two addresses convergence of sequences of
set-indexed processes and introduces functional convergence for
processes whose sample paths live in a Skorokhod-type space and
semi-functional convergence for processes whose sample paths may
be badly behaved.
Completely self-contained, the theoretical aspects of this work
are rich and promising. With its many important
applications-especially in the theory of spatial statistics and
in stochastic geometry- Set Indexed Martingales will undoubtedly
generate great interest and inspire further research and
development of the theoryand applications.
Contents
Introduction
General Theory
Generalities. Predictability. Martingales. Decompositions and
Quadratic Variation
Martingale Characterizations. Generalizations of Martingales
Weak Convergence.
Weak Convergence of Set-Indexed Processes
Limit Theorems for Point Processes
Martingale Central Limit Theorems
References
Index.
Features
+ Offers a unique, self-contained development of the theory of
set-indexed martingales
+ Leads readers from first principles to fundamental results and
through to applications
+ Includes numerous examples throughout the book to illustrate
theoretical concepts
+ Contains an extensive bibliography-to date, the most
comprehensive bibliography of the subject available
ISBN: 1584880821
Publication Date: 10/27/99
Description
Until recently, acquiring a background in the basic
methodological principles that apply to most types of
investigations meant struggling to obtain results through
laborious calculations. The advent of statistical software
packages has removed much of the tedium and many of the errors of
manual calculations and allowed a marked increase in the depth
and sophistication of analyses. Although most statistics classes
now incorporate some instruction in using a statistics package,
most introductory texts do not.
Quantitative Investigations in the Biosciences using MINITAB
fills this void by providing an introduction to investigative
methods that, in addition to outlining statistical principles and
describing methods of calculations, also presents essential
commands and interprets output from the statistics package
MINITAB.
The author introduces the three basic elements of
investigations-design, analysis, and reporting-using an extremely
accessible approach that keeps mathematical detail to a minimum.
He groups statistical tests according to the type of problem they
are used to examine, such as comparisons, sequential
relationships, andassociations.
Quantitative Investigations in the Biosciences using MINITAB
draws techniques and examples from a variety of subjects, ranging
from physiology and biochemistry through to ecology, behavioral
sciences, medicine, agriculture and horticulture, and complements
the mathematical results with formal conclusions for all of the
worked examples. It thus provides an ideal handbook for anyone in
virtually any field who wants to apply statistical techniques to
their investigations.
Audience
Researchers in biosciences
Professors and undergraduate students in biology, environment, or
statistics using MINITAB
Contents
Preface
Introduction
Introduction
The Process of Conducting an Investigation
Summary
DATA FAMILIARIZATION AND PRESENTATION
Exploring, Summarizing and Presenting Data
Introduction
Organizing Data using MINITAB
Numerical Methods of Data Description
Graphical Methods of Data Description
Summary of MINITAB Commands
Reliability, Probability and Confidence
Introduction
Reliability
Probability
Confidence Intervals
Graphical Representation of Reliability and Confidence
Summary of MINITAB Commands
Sampling
Introduction
Sampling Techniques
Sample Size Determination
QUESTIONS OF COMPARISON
General Introduction
Single Sample Comparisons
Introduction
Comparisons of a Large Sample (or where a population standard
deviation is known)
Comparison of a Small Sample
Comparisons of Samples that have not been Drawn from Normal
Distributions
Summary of MINITAB Commands
Comparing Two Samples
Introduction
Comparing Two Independent Samples
Comparison of Two Related (or Paired) Samples
Summary of MINITAB Commands
Multiple Comparisons
Introduction
Comparisons Involving Many Levels of a Single Factor
Comparisons Involving more than One Factor
Data Transformations
Summary of MINITAB Commands
SEQUENTIAL RELATIONSHIPS
General Introduction
Non-Causal and Causal Relationships
Introduction
Correlation
Regression
Summary of MINITAB Commands
QUESTIONS OF ASSOCIATION & AGREEMENT
General Introduction
Tabular Relationships
Introduction
The Contingency Table
Goodness-of-Fit
Summary of MINITAB Commands
Concluding Remarks
Solutions
Statistical Tables
References
Index
Plus each chapter contains a chapter summary and exercises
Features
+ Provides an introduction to statistics that minimizes the
drudgery of laborious calculation by integrating the text with
MINITAB-the statistical software package
+ Introduces the three basic elements of investigations: Design,
Analysis, and Reporting
+ Discusses principles in words before applying algebraic
terms-keeps mathematical detail to a minimum
+ Illustrates analyses with fully worked examples
+ Draws techniques and examples from a variety of subjects in
science, technology, and business
ISBN: 1584880333
Publication Date: 12/13/99
A.M. Mathai, McGill University, Department of
Mathematics and
Statistics, Montreal, Canada
There are...many areas of applications where one can benefit from
thecontent of this book.
? S. Panchapakesan, Department of Mathematics, Southern Illinois
University
A useful guide for researchers and professionals, graduate and
senior undergraduate students, this book provides an in-depth
look at applied
and geometrical probability with an emphasis on statistical
distributions.
A meticulous treatment of geometrical probability, kept at a
level to appeal to a wider audience including applied researchers
who will find the
book to be both functional and practical with the large number
ofproblems chosen from different disciplines
A few topics such as packing and covering problems that have a
vast literature are introduced here at a peripheral level for the
purpose of
familiarizing readers who are new to the area of research.
Contents: Buffon痴 Clean Tile Problem and the Needle Problem ?
Some Geometrical Objects ? Probability Measures and Invariance
Properties ?
Measures for Points of Intersection and Random Rotations ? Random
Points ? Random Distances on a Line and Some General Procedures ?
Random Distances in a Circle ? Random Points in a Plane and
Random Points in Rectangles ? Random Distances in a Convex Body ?
The
Content of a Random Parallelotope ? Random Volume, an Algebraic
Procedure ? Random Points in a n-Ball ? Convex Hulls Generated by
Random Points ? Random Simplex in a Given Simplex ? The Method of
Moments ? Uniformly Distributed Random Points in a Unit n-Ball ?
Type-1 Beta Distributed Random Points in Rn ? Type-2 Beta
Distributed Random Points in Rn ? Gaussian Distributed Random
Points in Rn ?
Approximations and Asymptotic Results ? Miscellaneous
RandomVolumes and Their Distributions
Readership: Researchers, professionals, senior undergraduate and
graduate students in probability and statistics. Also of interest
to
biostatisticians, geologists, applied physicists, electrical and
civilengineers, and crystallographers.
February, 2000 / 576 pp / Cloth / 90-5699-681-9