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
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
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
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
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.
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. BrEern. 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.
edited by
Didier Dubois
IRIT, UniversitEPaul Sabatier, Toulouse, France
Henri Prade
IRIT, UniversitEPaul 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 PoincarEParadox 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.
@
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.
@
by
Giovanni Guida
Dipartimento di Elettronica per l'Automzione, UniversitEdegli
Studi di
Brescia, Italy
Gianfranco Lamperti
Dipt. di Elettronica per l'Automazione, UniversitEdegli Studi
di
Brescia, Italy
Marina Zanella
Dipartimento di Elettronica per l'Automzione, UniversitEdegli
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.
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. MEler. 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.
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.