Growth of Algebras and Gelfand-Kirillov Dimension: Revised Edition

Gunter R. Krause, University of Manitoba, Winnipeg, MB, Canada,
and Thomas H. Lenagan, University of Edinburgh, Scotland

Description

During the two decades that preceded the publication of the first edition of this book, the Gelfand-Kirillov
dimension had emerged as a very useful and powerful tool for investigating non-commutative algebras.
At that time, the basic ideas and results were scattered throughout various journal articles.
The first edition of this book provided a much-needed reliable and coherent single source of information.
Since that time, the book has become the standard reference source for researchers.
For this edition, the authors incorporated the original text with only minor modifications. Errors have been corrected,
items have been rephrased, and more mathematical expressions have been displayed for the purpose of clarity.
The newly added Chapter 12 provides broad overviews of the new developments that have surfaced in the last
few years, with references to the literature for details.The bibliography has been updated and accordingly,
almost double the size of the original one.
The faithful revision and contemporary design of this work offers time-honored expertise with modern functionality.
A keenly appealing combination. So, whether for the classroom, the well-tended mathematical books collection,
or the research desk, this book holds unprecedented relevance.

Contents

Growth of algebras
Gelfand-Kirillov dimension of algebras
Gelfand-Kirillov dimension of related algebras
Localization
Modules
Graded and filtered algebras and modules
Almost commutative algebras
Weyl algebras
Enveloping algebras of solvable Lie algebras
Polynomial identitiy algebras
Growth of groups
New developments
Bibliography
Index
Details:

Series: Graduate Studies in Mathematics,
Publication Year: 2000
ISBN: 0-8218-0859-1
Paging: 212 pp.
Binding: Hardcover


Renormalized Self-Intersection Local Times and
Wick Power Chaos Processes

Michael B. Marcus, City College of New York, NY,
and Jay Rosen, College of Staten Island, NY

Description

Sufficient conditions are obtained for the continuity of renormalized self-intersection local times for the multiple
intersections of a large class of strongly symmetric Levy processes in $R^m$, $m=1,2$. In $R^2$ these include Brownian
motion and stable processes of index greater than 3/2, as well as many processes in theirdomains of attraction. In $R^1$
these include stable processes of index $3/4<\beta\le 1$ and many processes in their domains of attraction.
Let $(\Omega,\cal F(t),X(t), P^{x})$ be one of these radially symmetric Levy processes with 1-potential density $u^1(x,y)$.
Let $\cal G^{2n}$ denote the class ofpositive finite measures $\mu$ on $R^m$ for which $\int\!\!\int (u^1(x,y))^{2n}\,d\mu(x)\,
d\mu(y)<\infty.$ For $\mu\in\cal G^{2n}$, let$\alpha_{n,\epsilon}(\mu,\lambda) \overset\text{def}\to=\int\!\!\int_{\{0\leq t_1\leq
\cdots \leq t_n\leq \lambda\}} f_{\epsilon}(X(t_1)-x)\prod_{j=2}^n f_{\epsilon}(X(t_j)- X(t_{j-1}))\,dt_1\cdots\,dt_n \,d\mu(x)$ where
$f_{\epsilon}$ is an approximate $\delta-$function at zero and $\lambda$ is an randomexponential time, with mean one, independent
of $X$, with probability measure $P_\lambda$. The renormalized self-intersection local time of $X$ with respect tothe measure
$\mu$ is defined as $\gamma_{n}(\mu)=\lim_{\epsilon\to 0}\,\sum_{k=0}^{n-1}(-1)^{k} {n-1 \choose k}(u^1_{\epsilon}(0))^{k}
\alpha_{n-k,\epsilon}(\mu,\lambda)$ where $u^1_{\epsilon}(x)\overset\text{def}\to= \int f_{\epsilon}(x-y)u^1(y)\,dy$, with
$u^1(x)\overset\text{def}\to=u^1(x+z,z)$ for all $z\in R^m$. Conditions are obtained under which this limit exists in $L^2
(\Omega\times R^+,P^y_\lambda)$ for all $y\in R^m$, where$P^y_\lambda\overset\text{def}\to= P^y\times P_\lambda$.
Let $\{\mu_x,x\in R^m\}$ denote the set of translates of the measure $\mu$. The main result in this paper is a sufficient condition
for the continuity of$\{\gamma_{n}(\mu_x),\,x\in R^m\}$ namely that this process is continuous $P^y_\lambda$ almost surely
for all $y\in R^m$, if the corresponding 2$n$-th Wick power chaos process, $\{:G^{2n}\mu_x:,\,x\in R^m\}$ is continuous almost
surely. This chaos process is obtained in the following way. A Gaussian process $G_{x,\delta}$ is defined which has covariance
$u^1_\delta(x,y)$, where $\lim_{\delta\to 0}u_\delta^1(x,y)=u^1(x,y)$. Then $:G^{2n}\mu_x:\overset\text{def}\to= \lim_{\delta\to
0}\int :G_{y,\delta}^{2n}:\,d\mu_x(y)$ where the limit is taken in $L^2$. ($:G_{y,\delta}^{2n}:$ is the 2$n$-th Wick power of $G_{y,
\delta}$, that is, a normalized Hermite polynomial of degree 2$n$ in $G_{y,\delta}$). This process has a natural metric
$d(x,y)\overset\text{def}\to= \frac1{(2n)!}\(E(:G^{2n}\mu_x:-:G^{2n}\mu_y:)^2\)^{1/2} =\(\int\!\! \int \(u^1(u,v)\)^{2n} \left
( d(\mu_x(u)-\mu_y(u)) \right) \left(d(\mu_x(v)-\mu_y(v)) \right)\)^{1/2}$. A well known metric entropy condition with respect
to $d$ gives a sufficient condition for the continuity of$\{:G^{2n}\mu_x:,\,x\in R^m\}$ and hence for $\{\gamma_{n}(\mu_x),\,x\in R^m\}$.

Contents

Introduction
Wick products
Wick power chaos processes
Isomorphism theorems
Equivalence of two versions of renormalized self-intersection local times
Continuity
Stable mixtures
Examples
A large deviation result
Appendix A. Necessary conditions
Appendix B. The case $n=3$
Bibliography

Details:

Series: Memoirs of the American Mathematical Society,Volume: 142
Publication Year: 1999
ISBN: 0-8218-1340-4
Paging: 125 pp.
Binding: Softcover


Asymptotics for Solutions of Linear Differential Equations
Having Turning Points with Applications

S. Strelitz, University of Haifa, Israel

Description

Asymptotics are built for the solutions $y_j(x,\lambda)$, $y_j^{(k)}(0,\lambda)=\delta_{j\,n-k}$,
$0\le j,k+1\le n$ of the equation $L(y)=\lambda p(x)y,\quad x\in[0,1],$ where $L(y)$ is a linear differential
operator of whatever order $n\ge 2$ and $p(x)$ is assumed to possess a finite number of turning points.
The established asymptotics are afterwards applied to the study of: 1) the existence of infinite eigenvalue
sequences for various multipoint boundary problems posed on $L(y)=\lambda p(x)y,\quad x\in [0,1],$, especially
as $n=2$ and $n=3$ (let us be aware that the same method can be successfully applied on many occasions in
case $n>3$ too) and 2) asymptotical distribution of the corresponding eigenvalue sequences on the complex plane.

Contents

The construction of asymptotics
Application: Existence and asymptotics of eigenvalues

Details:

Series: Memoirs of the American Mathematical Society, Volume: 142
Publication Year: 1999
ISBN: 0-8218-1352-8
Paging: 89 pp.
Binding: Softcover


The Theory of Generalized Dirichlet Forms and Its Applications
in Analysis and Stochastics

Wilhelm Stannat, Universität Bielefeld, Germany

Contents

Introduction
Functional analytic background
Examples
Analytic potential theory of generalized Dirichlet forms
Generalized Dirichlet forms and their probabilistic counterpart
References

Details:

Series: Memoirs of the American Mathematical Society, Volume: 142
Publication Year: 1999
ISBN: 0-8218-1384-6
Paging: 101 pp.
Binding: Softcover


Handbook of Combinatorial Optimization ,Supplement Volume A

edited by
Ding-Zhu Du
University of Minnesota, Minneapolis, USA
Panos M. Pardalos
Dept. of Industrial & Systems Engineering, University of Florida,
Gainesville, USA

This volume can be considered as a supplementary volume to the majorthree-volume Handbook of Combinatorial
Optimization published by Kluwer. It can also be regarded as a stand-alone volume which presents chapters dealing
with various aspects of the subject including optimization problems and algorithmic approaches for discrete problems.

Audience: All those who use combinatorial optimization methods to model and solve problems.

Contents and Contributors

Preface. The Maximum Clique Problem; I.M. Bomze, et al. Linear
Assignment Problems and Extensions; R.E. Burkard, E. Çela. Bin Packing
Approximation Algorithms: Combinatorial Analysis; E.G. Coffman, et al.
Feedback Set Problems; P. Festa, et al. Neural Networks Approaches
for Combinatorial Optimization Problems; T.B. Trafalis, S. Kasap.
Frequency Assignment Problems; R.A. Murphey, et al. Algorithms for the
Satisfiability (SAT) Problem; J. Gu, et al. The Steiner Ratio of Lp-planes;
J. Albrecht, D. Cieslik. A Cogitative Algorithm for Solving the Equal
Circles Packing Problem; W. Huang, et al. Author Index. Subject Index.

Hardbound, ISBN 0-7923-5924-0
November 1999, 656 pp.


Number Theory and Its Applications

edited by
Shigeru Kanemitsu
Dept. of Liberal Arts, Kinki University, Iizuka, Japan
Kálmán Gyory
University of Debrecen, Hungary

DEVELOPMENTS IN MATHEMATICS ,Volume 2

The contents of this volume range from expository papers on several aspects of number theory,
intended for general readers (Steinhaus property of planar regions; experiments with computers; Diophantine
approximation; number field sieve), to a collection of research papers for specialists, whichare at prestigious
journal level. Thus the book leads the reader in many ways not only to the state of the art of number theory
but also to its rich garden.

Audience: Researchers and graduate students interested in recent developments in number theory.

Contents and Contributors

Preface. A problem of Steinhaus concerning the existence of a plane setwith a certain property;
S.D. Adhikari. Self affine tiling and Pisotnumeration system; S. Akiyama. A fundamental but unexploited partition
invariant; K. Alladi. On Algebraic independence of certain functions related to the elliptic modular function;
M. Amou. Fragments by Ramanujan on Lambert Series; B.C. Berndt. Metric theory of Diophantine approximation
in the field of complex numbers; V.I. Bernik, M.M. Dodson. The Davenport-Heilbronn Fourier transform method,
and some diophantine inequalities; J. BrEern. On the probabilistic complexity of numerically checking the binary
Goldbach conjecture in certain intervals; J.M. Deshouillers, H. te Riele. On the mean square of Hecke L-functions
associated to holomorphic cusp forms; S. Egami. Mean Square of an Error Term Related to a Certain Exponential
Sum Involving the Divisor Function; J. Furuya. On zeros of the Lerch zeta-function; R. Garunkstis, A.Laurincikas.
Power values of products of consecutive integers and binomial coefficients; K. Gyory. A note on Hilbert modular threefolds;
Y. Hamahata. Inverse Galois Problem for Dihedral Groups; K. Hashimoto, K. Miyake. On Ramachandra's method for
the mean value problems of various L-functions; Y. Kamiya. On the zeros of certain modular forms; M.Kaneko.
A weighted integral approach to the mean square of Dirichlet L-functions; M. Katsurada, K. Matsumoto.
The mean value theorem ofthe Riemann zeta-function in the critical strip for short intervals; I. Kuchi, Y.Tanigawa.
On inhomogeneous Diophantine approximation and the NST-algorithm; T. Komatsu. Selberg zeta functions of PGL
and PSL over function fields; S. Koyama. A Survey on the Number Field Sieve; K. Nakamula. Non-normal class number
one problem and the least prime power-residue; R. Okazaki. Higher dimensional modular equations of degree 7;
R. Sasaki. Exponential congruences; A. Schinzel. Pade approximation for words generated by certain substitutions,
and Hankel determinants; J. Tamura. On Sturmian Sequences which are invariant under some substitutions; S. Yasutomi.
Kluwer Academic Publishers, Dordrecht

Hardbound, ISBN 0-7923-5952-6
October 1999, 388 pp.


Fuzzy Sets, Logics and Reasoning about Knowledge

edited by
Didier Dubois
IRIT, UniversitEPaul Sabatier, Toulouse, France
Henri Prade
IRIT, UniversitEPaul Sabatier, Toulouse, France
Erich Peter Klement
Institute of Mathematics, Johannes Kepler University, Linz, Austria

APPLIED LOGIC SERIES ,Volume 15

Fuzzy Sets, Logics and Reasoning about Knowledge reports recentresults concerning the genuinely logical
aspects of fuzzy sets in relation to algebraic considerations, knowledge representation and commonsense
reasoning. It takes a state-of-the-art look at multiple-valued and fuzzy set-based logics, in an artificial intelligence
perspective. The papers, all of which are written by leading contributors in their respective fields, are
grouped into four sections.

The first section presents a panorama of many-valued logics in connection with fuzzy sets. The second explores
algebraic foundations, with an emphasis on MV algebras. The third is devoted to approximate reasoningmethods and
similarity-based reasoning. The fourth explores connections between fuzzy knowledge representation, especially
possibilistic logic and prioritized knowledge bases.

Readership: Scholars and graduate students in logic, algebra, knowledgerepresentation, and formal aspects
of artificial intelligence.

Contents and Contributors
Editorial Preface; D.M. Gabby. Introduction. Part I: Advances in Multiple-valued Logics. The PoincarEParadox and Non-classical
Logics; U. Höhle. Propositional Fuzzy Logics based on Frank t-norms: A comparison; E.P. Klement, M. Navara. A Resolution-based
Axiomatisation of `Bold' Propositional Fuzzy Logic; S. Lehmke. How to Make Your Logic Fuzzy: Fibred Semantics and The Weaving
of Logics;D.M. Gabbay. Introducing Grade to Some Metalogical Notions; M.K.Chakraborty, S. Basu. Closure Operators, Fuzzy Logic and Constraints;G. Gerla. Part II: Algebraic Aspects of Multiple-valued Logics. UlamGame, the Logic of MaxSat, and Many-valued Partitions; D. Mundici. AMany-valued Generalisation of the Ultrapower Construction; C.A. Drossos. Gabriel Filters and the Spectrum of an MV-Algebra; P.
Karazeris. Conditional States in Finite-valued Logics; A. Di Nola, et al.Conditioning on MV-algebras and Additive Measures Efurther results; S.
Weber. Part III: Advances in Approximate Reasoning. TowardAdequacy Conditions for Inference Schemata in Approximate Reasoning:
The Case of the Rule of Syllogism; S. Gottwald. Formal Theories in FuzzyLogic; V. Novák. A Note on Fuzzy Inference as Deduction; L. Godo, P.
Hájek. The Role of Similarity in Fuzzy Reasoning; F. Klawonn.T-indistinguishability Operators and Approximate Reasoning via CRI; D.
Boixader, J. Jacas. About Similarity-based Logical Systems; F. Esteva,et al. On Similarity-based Fuzzy Clusterings; H. Thiele. Part IV:
Reasoning about Information and Knowledge. Informational Representability: Abstract Models versus Concrete Models; S. Demri, E.
Orlowska. From Possibilistic Information to Kleene's Strong Multi-valued Logics; G. De Cooman. A Roadmap of Qualitative Independence; D.
Dubois, et al. Truth Functionality and Measure-based Logics; L. Boldrin, C. Sossai. Logic Programs with Context-dependent Preferences; G.
Brewka. An Overview of Inconsistency-tolerant Inferences in Prioritized Knowledge Bases; S. Benferhat, et al. Index.


Hardbound, ISBN 0-7923-5977-1
November 1999, 436 pp.

@


Topological Fixed Point Theory of Multivalued Mappings

by
Lech Gorniewicz
Faculty of Mathematics and Computer Science, Nicolas Copernicus
University, Torun, Poland

MATHEMATICS AND ITS APPLICATIONS ,Volume 495

This volume presents a broad introduction to the topological fixed point
theory of multivalued (set-valued) mappings, treating both classical
concepts as well as modern techniques. A variety of up-to-date results is
described within a unified framework.

Topics covered include the basic theory of set-valued mappings with both
convex and nonconvex values, approximation and homological methods in
the fixed point theory together with a thorough discussion of various index
theories for mappings with a topologically complex structure of values,
applications to many fields of mathematics, mathematical economics and
related subjects, and the fixed point approach to the theory of ordinary
differential inclusions. The work emphasises the topological aspect of the
theory, and gives special attention to the Lefschetz and Nielsen fixed point
theory for acyclic valued mappings with diverse compactness assumptions
via graph approximation and the homological approach.

Audience: This work will be of interest to researchers and graduate
students working in the area of fixed point theory, topology, nonlinear
functional analysis, differential inclusions, and applications such as game
theory and mathematical economics.


Hardbound, ISBN 0-7923-6001-X
September 1999, 416 pp.

@


Software Prototyping in Data and Knowledge Engineering

by
Giovanni Guida
Dipartimento di Elettronica per l'Automzione, UniversitEdegli Studi di
Brescia, Italy
Gianfranco Lamperti
Dipt. di Elettronica per l'Automazione, UniversitEdegli Studi di
Brescia, Italy
Marina Zanella
Dipartimento di Elettronica per l'Automzione, UniversitEdegli Studi di
Brescia, Italy

MATHEMATICS AND ITS APPLICATIONS ,Volume 497

This monograph describes an innovative prototyping framework for data
and knowledge intensive systems. The proposed approach will prove
especially useful for advanced and research-oriented projects that aim to
develop a traditional database perspective into fully-fledged advanced
database approaches and knowledge engineering technologies.

The book is organised in two parts. The first part, comprising chapters 1 to
4, provides an introduction to the concept of prototyping, to database and
knowledge-based technologies, and to the main issues involved in the
integration of data and knowledge engineering. The second part, comprising
chapters 5 to 12, illustrates the proposed approach in technical detail.

Audience: This volume will be of interest to researchers in the field of
databases and knowledge engineering in general, and for software designers
and knowledge engineers who aim to expand their expertise in data and
knowledge intensive systems.

Contents
Preface. Acknowledgements. 1. The Prototyping Approach to Software
Development. 2. Overview of Database Technology. 3. Overview of
Knowledge-Based Technology. 4. Data and Knowledge Intensive
Systems. 5. The Prototyping Hierarchy. 6. The Relational Layer. 7. The
Extended Relational Layer. 8. The Deductive Layer. 9. The Object Layer.
10. The Active Layer. 11. Prototyping Techniques Integration. 12.
Mapping Prototypes to Relational Databases. References. Index.

Hardbound, ISBN 0-7923-6016-8
November 1999, 424 pp.


Applications of Fibonacci Numbers ,Volume 8

Proceedings of The Eighth International Research Conference onFibonacci Numbers
and Their Applications', Rochester Institute of Technology, NY, USA

edited by
Frederic T. Howard
Dept. of Mathematics and Computer Science, Wake Forest University,
Winston-Salem, NC, USA

This volume presents the Proceedings of the Eighth International
Conference on Fibonacci Numbers and their Applications, held in
Rochester, New York, in June 1998.

All papers have been carefully refereed for content and originality and
represent a continuation of the work of previous conferences. This book,
describing recent discoveries and encouraging future research, shows the
growing interest in and the importance of the pure and applied aspects of
Fibonacci Numbers in many different areas of science.

Audience: This volume will be of interest to graduate students and research
mathematicians whose work involves number theory, combinatorics,
algebraic number theory, field theory and polynomials, finite geometry and
special functions.

Contents and Contributors
A Report on the Eighth International Conference. List of Contributors to
this Proceedings. Foreword. The Organizing Committees. List of
Contributors to the Conference. Introduction. On the Generalized Binomial
Coefficients Defined by Strong Divisibility Sequences; S. Ando, D. Sato.
On Triangles and Squares Marked with Goldpoints-Studies of Golden
Tiles; V.K. Anatassova, J.C. Turner. Multivariate Pascal Polynomials or
order K with Probability Applications; D.L. Antzoulakos, A.N. Philippou.
Fibonacci Planes and Spaces; K.T. Atanassov, A.G. Shannon. The
Smallest Positive Integer Having Fk Representations as Sums of Distinct
Fibonacci Numbers; M. Bicknell-Johnson. The Zeckendorf-Wythoff
Array Applied to Counting the Number of Representations of N as Sums of
Distinct Fibonacci Numbers; M. Bicknell-Johnson. Composing with
Sequences: ...Cut is it Art? J.A. Biles. Invariants for Linear Recurrences;
M. Caragiu, W. Webb. Base 10 Rats Cycles and Arbitrarily Long Base 10
Rats Cycles; C. Cooper, R.E. Kennedy. Quintics x5 E5x Ek, the Golden
Section, and Square Lucas Numbers; M. Elia, P. Filipponi. The
Pascal-De Moivre Moments and their Generating Functions; L. Ericksen.
Investigating Special Binary Sequences with some Computer Help; D.C.
Fielder, C.O. Alford. Integration Sequences of Jacobsthal and
Jacobsthal-Lucas Polynomials; P. Filipponi, A.F. Horadam. A Property
of the Unit Digits of Recursive Sequences; H.T. Freitag, et al. On General
Divisibility of Sums of Integral Powers of the Golden Ratio; H.T. Freitag,
D.C. Fielder. Sylvester's Algorithm and Fibonacci Numbers; H.T.
Freitag, G.M. Phillips. On the Characteristic Polynomial of the J-TH
Order Fibonacci Sequence; G.W. Grossman and S.K. Narayan. Quasi
Morgan-Voyce Polynomials and Pell Convolutions; A.F. Horadam. On a
Symptotic Maximality of the Fibonacci Tree; Y. Horibe. Generalizations of
a Fibonacci Identity; F.T. Howard. Some Generalizations of
Wolstenholme's Theorem; W.A. Kimball and W.A. Webb. Card Sorting
Related to Fibonacci Numbers; C. Kimberling. On the Inhomogeneous
Geometric Line-Sequence; J. Lee. Fibonacci Numbers of the Form k2 + k
+ 2; F. Luca. On Certain Polynomials of Even Subscripted Lucas
Numbers; R.S. Melham. On the Rank of Appearance of Lucas Sequences;
S. MEler. Algorithmic Simplification of Reciprocal Sums; S. Rabinowitz.
Solved and Unsolved Problems on Pseudoprime Numbers and their
Generalizations; A. Rotkiewicz. Some Relationships among Vieta,
Morgan-Voyce and Jacobsthal Polynomials; A.G. Shannon, A.F.
Horadam. Special Multipliers of Lucas Sequences Modulo pr; L. Somer.
Digital Halftoning Using Error Diffusion and Linear Pixel Shuffling; J.
Szybist and P.G. Anderson. On Vector Sequence Recurrence Equations
in Fibonacci Vector Geometry; J.C. Turner. Constructing Identities
Involving Kth-Order F-L Numbers by using The Characteristic Polynomial;
C. Zhou. Subject Index.

Hardbound, ISBN 0-7923-6027-3
November 1999, 408 pp.


Introduction to Discrete Event Systems

by
Christos G. Cassandras
Dept. of Manufacturing Engineering, Boston University, MA, USA
Stéphane Lafortune
Dept. of Electrical Engineering and Computer Science, The University
of Michigan, Ann Arbor, USA

THE KLUWER INTERNATIONAL SERIES ON DISCRETE EVENT
DYNAMIC SYSTEMS ,Volume 11

The rapid evolution of computing, communication, and sensor technologies
has brought about the proliferation of `new' dynamic systems, mostly
technological and often highly complex. Examples are all around us:
computer and communication networks; automated manufacturing systems;
air traffic control systems; and distributed software systems. The `activity' in
these systems is governed by operational rules designed by humans; their
dynamics are therefore characterized by asynchronous occurrences of
discrete events. These features lend themselves to the term discrete event
system for this class of dynamic systems.

A substantial portion of this book is a revised version of Discrete Event
Systems: Modeling and Performance Analysis (1993), written by the first
author and recipient of the 1999 International Federation of Automatic
Control Triennial Control Engineering Textbook Prize. This new expanded
book is intended to be a comprehensive introduction to the field of discrete
event systems, emphasizing breadth of coverage and accessibility of the
material to readers with possibly different backgrounds. Its key feature is
the emphasis placed on a unified modeling framework that transcends
specific application areas and allows linking of the following topics in a
coherent manner: language and automata theory, supervisory control, Petri
net theory, (max,+) algebra, Markov chains and queueing theory,
discrete-event simulation, perturbation analysis, and concurrent estimation
techniques. Until now, these topics had been treated in separate books or in
the research literature only.

Introduction to Discrete Event Systems is written as a textbook for
courses at the senior undergraduate level or the first-year graduate level. It
will be of interest to students in a variety of disciplines where the study of
discrete event systems is relevant: control, communications, computer
engineering, computer science, manufacturing engineering, operations
research, and industrial engineering.

Contents
Preface. 1. Systems and Models. 2. Languages and Automata. 3.
Supervisory Control. 4. Petri Nets. 5. Timed Models. 6. Stochastic Times
Automata. 7. Markov Chains. 8. Introduction to Queueing Theory. 9.
Controlled Markov Chains. 10. Introduction to Discrete-Event Simulation.
11. Sensitivity Analysis and Concurrent Estimation. I. Review of Probability
Theory. II. IPA Estimator. Index. About the Authors.

Hardbound, ISBN 0-7923-8609-4
September 1999, 848 pp.