Halanay, A. / Rasvan, V.
Stability and Stable Oscillations in Discrete Time Systems
Aristide Halanay (1924-1997), Department of Mathematics, Bucharest University, Romania and Vladimir Rasvan, Department of Automatic Control, Craiova University, Romania
The expertise of a professional mathematician and a theoretical engineer provides a fresh perspective of stability and stable oscillations. The current state of affairs in stability theory,
absolute stability of control systems, and stable oscillations of both periodic and almost periodic discrete systems is presented, including many applications in engineering such as stability of
digital filters, digitally controlled thermal processes, neurodynamics, and chemical kinetics. This book will be an invaluable reference source for those whose work is in the area of discrete dynamical systems, difference equations and control theory or applied areas that use discrete time models.
Contents: Chapter 1. Introduction ・Models with Discrete Storage of the Information ・Discrete-Time Models Induced by Impulses Occurring in Continuous Time Systems ・Discrete
Systems Occurring from Sampled Data Control Systems ・ Numerical Treatment of Continuous-Time Systems ・Chapter 2. Stability Theory ・Linear Discrete Time Systems with Constant Coefficients ・General Properties of Linear Systems ・Stability by the First Approximation ・Linear Discrete-Time Systems with Periodic Coefficients ・Liapunov Functions ・Invariance Principle. Barbashin-Krasovskii-La Salle Theorem ・Stability in Discrete Models of Chemical Kinetics ・Stability Results in Neurodynamics ・Stability via Input/Output Properties ・Chapter 3. Absolute Stability of Control Systems ・The Simplest Absolute Stability Criterion of Ya. Z. Tsypkin ・More Special Classes of Nonlinearities; Quadratic Constraints of Yakubovich
Type ・An Absolute Stability Criterion for the Case of Nondecreasing Nonlinearity ・The Brockett-Willems Type Criterion for Systems with Nondecreasing Nonlinearity ・ Liapunov Functions and Frequency Domain Inequalities in Absolute Stability. The Lemma of Kalman-Szeg・Popov-Yakubovich (Single Input Case) ・A New Condition of Absolute Stability for Systems with Slope Restricted Nonlinearity ・The Kalman-Szeg・Popov-Yakubovich Result for Multi-Input Systems ・Absolute Stability Conditions for Systems with Several Nonlinearities ・Chapter 4. Stable Oscillations ・Periodic Solutions of Forced Linear Systems with Periodic Coefficients (Forced Oscillations) ・Almost Periodic Sequences ・Forced Almost Periodic Oscillations ・Linear
Systems in a Product Space. Stable Invariant Surfaces ・ Nonlinear Periodic and Almost Periodic Oscillations ・Invariant Manifolds for Nonlinear Systems in a Product Space ・ Frequency Domain Conditions for Stable Oscillations
Readership: Researchers and graduate students in applied mathematics and electrical and systems engineering.
Series Part: Advances in Discrete Mathematics and Aplications, Volume 2
Kiselev, V. / Shnir, Y. / Tregubovich, A.
Introduction to Quantum Field Theory
V.G. Kiselev, Department of Diagnostic Radiology, University of Freiburg, Germany, Y.M. Shnir, Institut f・ Theoretische Physik, Universitet zu Koln, Germany and A.Ya. Tregubovich, Institute of Physics, National Academy of Sciences of Belarus
This text aims to provide an introduction to the subject of quantum field theory without the complication of introducing its application areas such as elementary particle physics or
statistical physics at the same time.
It explains those features of quantum and statistical field systems that result from their field-theoretic nature and are therefore common to different physical contexts. The reader is
supplied with practical tools for carrying out calculations as well as a discussion of the meaning of the results.
An approach emphasizing the simplest models is used, progressing to discussion of real systems before mentioning more general and rigorous conclusions. The book is structured
around carefully selected problems, which are solved in detail. The central concept is that of effective action (or free energy in statistical physics), and the main technical tool is the path
integral, although other formalisms are also mentioned. A knowledge of particle physics phenomenology is not required. The book stops short of advanced topics, and can be regarded
in a sense as a crash course in quantum field theory for anyone who needs it.
Contents: I. THE PATH INTEGRAL IN QUANTUM MECHANICS: Action in Classical Mechanics ・The Path Integral in Quantum Mechanics ・The Euclidean Path Integral ・II. INTRODUCTION TO QUANTUM FIELD THEORY: Classical and Quantum Fields ・Vacuum Energy in 4 Theory ・The
Effective Action in 4 Theory ・Renormalization of the Effective Action ・Renomalization Group ・Concluding Remarks ・III. MORE COMPLEX FIELDS AND OBJECTS: Second Quantization: from Particles to Fields ・Path Integral For Fermions ・Gauge Fields ・Topological Objects ・Some Integrals and Products ・Splitting of Levels in Double-Well Potential ・Lie Algebras
Readership: Advanced graduates with an interest in theoretical physics, professors and researchers in the area of field theory.
November, 2000 / 452 pp / Cloth / 90-5699-237-6 / R
Rothmaler, P.
Introduction to Model Theory
Philipp Rothmaler, Christian-Albrechts-University, Kiel, Germany
Model theory investigates mathematical structures by means of formal languages. These so-called first-order languages have proved particularly useful. The text introduces the reader to the
model theory of first-order logic, avoiding syntactical issues that are not too relevant to model-theory. In this spirit, the compactness theorem is proved via the algebraically useful
ultraproduct technique, rather than via the completeness theorem of first-order logic. This leads fairly quickly to algebraic applications, like Malcev's local theorems (of group theory) and,
after a little more preparation, also to Hilbert's Nullstellensatz (of field theory). Steinitz' dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal sets.
The final chapter is on the models of the first-order theory of the integers as an abelian group. This material appears here for the first time in a textbook of introductory level, and is used to
give hints to further reading and to recent developments in the field, such as stability (or classification) theory. The latter itself is not touched upon. The undergraduate or graduate, is assumed to be familiar with some general algebraic background as provided by a few semesters of mathematical studies.
Contents: I: Basics ・Structures ・Languages ・Semantics ・II: Beginnings of Model Theory ・The Finiteness Theorem ・First Consequences of Finiteness Theorem ・Malcev's Applications to
Group Theory ・Some Theory of Orderings ・III: Basic Properties of Theories ・Elementary Maps ・Elimination ・ Chains ・IV: Theories and Types ・Types ・Thick and Thin Models ・Countable Complete Theories ・V: Two Applications ・ Strong Minimal Theories ・Z ・Hints to Selected Exercises ・ Solutions for Selected Exercises ・Bibliography and Hints for Further Reading ・Symbols ・Index
Readership: Undergraduates and graduates primarily in mathematics with some general algebraic knowledge.
Series Part: Algebra, Logic and Applications, Volume 15
November, 2000 / 328 pp / Cloth / 90-5699-287-2
2000 / 328 pp / Paper / 90-5699-313-5
Richard O. Duda / Peter E. Hart / David G. Stork
Pattern Classification, 2nd Edition
ISBN: 0-471-05669-3
Hardcover
Pages: 680
Copyright: 2001
Pattern recognition is the construction of algorithms to create a decoding so that discriminations can be made by a computer. While the best-selling first edition of this book provided the basic theory underlying pattern recognition by computers, this new edition presents a systematic account of the major topics in pattern recognition today, reflecting the growth of neural networks research in artificial intelligence and its influence on pattern recognition.
Table of Contents
Bayesian Decision Theory.
Maximum Likelihood and Bayesian Estimation.
Nonparametric Techniques.
Linear Discriminant Functions.
Multilayer Neural Networks.
Stochastic Methods.
Non-Metric Methods.
Algorithm-Independent Machine Learning.
Unsupervised Learning and Clustering.
Epilog: The Future.
Appendices.
Bibliography.
Index.
Shayle R. Searle (Cornell Univ.)
Charles E. McCulloch (Univ. of California, San Francisco)Generalized, Linear, and Mixed Models
ISBN: 0-471-19364-X
Hardcover
Pages: 358
Copyright: 2001
Wiley Series in Probability and Statistics
A modern perspective on mixed models
The availability of powerful computing methods in recent decades has thrust linear and nonlinear mixed models into the mainstream of statistical application. This volume offers a modern perspective on generalized, linear, and mixed models, presenting a unified and accessible treatment of the newest statistical methods for analyzing correlated, nonnormally distributed data.
As a follow-up to Searle痴 classic, Linear Models, and Variance Components by Searle, Casella, and McCulloch, this new work
progresses from the basic one-way classification to generalized linear mixed models. A variety of statistical methods are explained and
illustrated, with an emphasis on maximum likelihood and restricted maximum likelihood. An invaluable resource for applied statisticians
and industrial practitioners, as well as students interested in the latest results, Generalized, Linear, and Mixed Models features:
A review of the basics of linear models and linear mixed models
Descriptions of models for nonnormal data, including generalized linear and nonlinear models
Analysis and illustration of techniques for a variety of real data sets
Information on the accommodation of longitudinal data using these models
Coverage of the prediction of realized values of random effects
A discussion of the impact of computing issues on mixed models
Subject: Statistics / Applied Probability & Statistics / Models
Series Title: Wiley Series in Probability and Statistics: Texts and References Section