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This second edition comprehensively presents important tools of
linear systems theory, including differential and difference
equations, Laplace and Z transforms, and more.
Linear Systems Theory discusses:
Nonlinear and linear systems in the state space form and through
the transfer function method
Stability, including marginal stability, asymptotical stability,
global asymptotical stability, uniform stability, uniform
exponential stability, and BIBO stability
Controllability
Observability
Canonical forms
System realizations and minimal realizations, including state space
approach and transfer function realizations
System design
Kalman filters
Nonnegative systems
Adaptive control
Neural networks
The book focuses mainly on applications in electrical engineering,
but it provides examples for most branches of engineering,
economics, and social sciences.
What's New in the Second Edition?
Case studies drawn mainly from electrical and mechanical
engineering applications, replacing many of the longer case
studies
Expanded explanations of both linear and nonlinear systems as well
as new problem sets at the end of each chapter
Illustrative examples in all the chapters
An introduction and analysis of new stability concepts
An expanded chapter on neural networks, analyzing advances that
have occurred in that field since the first edition
Although more mainstream than its predecessor, this revision
maintains the rigorous mathematical approach of the first edition,
providing fast, efficient development of the material.
Linear Systems Theory enables its reader to develop his or her
capabilities for modeling dynamic phenomena, examining their
properties, and applying them to real-life situations.
In two editions spanning more than a decade, The Electrical
Engineering Handbook stands as the definitive reference to the
multidisciplinary field of electrical engineering. Our knowledge
continues to grow, and so does the Handbook. For the third edition,
it has expanded into a set of six books carefully focused on a
specialized area or field of study. Each book represents a concise
yet definitive collection of key concepts, models, and equations in
its respective domain, thoughtfully gathered for convenient access.
Circuits, Signals, and Speech and Image Processing presents all of
the basic information related to electric circuits and components,
analysis of circuits, the use of the Laplace transform, as well as
signal, speech, and image processing using filters and algorithms.
It also examines emerging areas such as text-to-speech synthesis,
real-time processing, and embedded signal processing. Each article
includes defining terms, references, and sources of further
information. Encompassing the work of the world's foremost experts
in their respective specialties, Circuits, Signals, and Speech and
Image Processing features the latest developments, the broadest
scope of coverage, and new material on biometrics.
This book focuses on the latest advances in nonlinear dynamic
modeling in economics and finance, mainly-but not solely-based on
the description of strategic interaction by using concepts and
methods from dynamic and evolutionary game theory. The respective
chapters cover a range of theoretical issues and examples
concerning how the qualitative theory of dynamical systems is used
to analyze the local and global bifurcations that characterize
complex behaviors observed in social systems where heterogeneous
and boundedly rational economic agents interact. Nonlinear
dynamical systems, represented by difference and differential and
functional equations, are extensively used to simulate the behavior
of time-evolving economic systems, also in the presence of time
lags, discontinuities, and hysteresis phenomena. In addition, some
theoretical issues and particular applications are discussed, as
well. The contributions gathered here offer an up-to-date review of
the latest research in this rapidly developing research area.
Modeling Uncertainty: An Examination of Stochastic Theory, Methods,
and Applications, is a volume undertaken by the friends and
colleagues of Sid Yakowitz in his honor. Fifty internionally known
scholars have collectively contributed 30 papers on modeling
uncertainty to this volume. Each of these papers was carefully
reviewed and in the majority of cases the original submission was
revised before being accepted for publication in the book. The
papers cover a great variety of topics in probability, statistics,
economics, stochastic optimization, control theory, regression
analysis, simulation, stochastic programming, Markov decision
process, application in the HIV context, and others. There are
papers with a theoretical emphasis and others that focus on
applications. A number of papers survey the work in a particular
area and in a few papers the authors present their personal view of
a topic. It is a book with a considerable number of expository
articles, which are accessible to a nonexpert - a graduate student
in mathematics, statistics, engineering, and economics departments,
or just anyone with some mathematical background who is interested
in a preliminary exposition of a particular topic. Many of the
papers present the state of the art of a specific area or represent
original contributions which advance the present state of
knowledge. In sum, it is a book of considerable interest to a broad
range of academic researchers and students of stochastic systems.
Modeling Uncertainty: An Examination of Stochastic Theory, Methods,
and Applications, is a volume undertaken by the friends and
colleagues of Sid Yakowitz in his honor. Fifty internationally
known scholars have collectively contributed 30 papers on modeling
uncertainty to this volume. Each of these papers was carefully
reviewed and in the majority of cases the original submission was
revised before being accepted for publication in the book. The
papers cover a great variety of topics in probability, statistics,
economics, stochastic optimization, control theory, regression
analysis, simulation, stochastic programming, Markov decision
process, application in the HIV context, and others. There are
papers with a theoretical emphasis and others that focus on
applications. A number of papers survey the work in a particular
area and in a few papers the authors present their personal view of
a topic. It is a book with a considerable number of expository
articles, which are accessible to a nonexpert - a graduate student
in mathematics, statistics, engineering, and economics departments,
or just anyone with some mathematical background who is interested
in a preliminary exposition of a particular topic. Many of the
papers present the state of the art of a specific area or represent
original contributions which advance the present state of
knowledge. In sum, it is a book of considerable interest to a broad
range of academic researchers and students of stochastic systems.
This is the first book to comprehensively examine the asymptotic
behavior of dynamic monopolies, duopolies, and oligopolies where
firms face information and implementation delays. It considers
discrete and continuous timescales, continuously distributed
delays, as well as single and multiple delays. It also discusses
models with linear and hyperbolic price functions in three types of
oligopolies: Cournot competition with quantity-adjusting firms,
Bertrand competition with price-adjusting firms, and mixed
oligopolies with both types of firms. In addition to the
traditional Cournot-Nash equilibria, it introduces cases of partial
cooperation are also introduced, leading to the analysis of
cartelizing groups of firms and possible governmental actions
against antitrust behavior. Further, the book investigates special
processes for firms learning about the uncertain price function
based on repeated market information. It addresses asymptotic
properties of the associated dynamic systems, derives stability
conditions, identifies stability switching curves, and presents in
global analyses of cases of instability. The book includes both
theoretical results and computer studies to illustrate and verify
the theoretical findings.
This book reflects the state of the art in nonlinear economic
dynamics, providing a broad overview of dynamic economic models at
different levels. The wide variety of approaches ranges from
theoretical and simulation analysis to methodological study. In
particular, it examines the local and global asymptotical behavior
of both macro- and micro- level mathematical models, theoretically
as well as using simulation. It also focuses on systems with one or
more time delays for which new methodology has to be developed to
investigate their asymptotic properties. The book offers a
comprehensive summary of the existing methodology with extensions
to the more complex model variants, since considerations on bounded
rationality of complex economic behavior provide the foundation
underlying choice-theoretic and policy-oriented studies of macro
behavior, which impact the real macro economy. It includes 13
chapters addressing traditional models such as monopoly, duopoly
and oligopoly in microeconomics and Keynesian, Goodwinian, and
Kaldor-Kaleckian models in macroeconomics. Each chapter presents
new aspects of these traditional models that have never been seen
before. This work renews the past wisdom and reveals tomorrow's
knowledge.
This book reflects the state of the art in nonlinear economic
dynamics, providing a broad overview of dynamic economic models at
different levels. The wide variety of approaches ranges from
theoretical and simulation analysis to methodological study. In
particular, it examines the local and global asymptotical behavior
of both macro- and micro- level mathematical models, theoretically
as well as using simulation. It also focuses on systems with one or
more time delays for which new methodology has to be developed to
investigate their asymptotic properties. The book offers a
comprehensive summary of the existing methodology with extensions
to the more complex model variants, since considerations on bounded
rationality of complex economic behavior provide the foundation
underlying choice-theoretic and policy-oriented studies of macro
behavior, which impact the real macro economy. It includes 13
chapters addressing traditional models such as monopoly, duopoly
and oligopoly in microeconomics and Keynesian, Goodwinian, and
Kaldor-Kaleckian models in macroeconomics. Each chapter presents
new aspects of these traditional models that have never been seen
before. This work renews the past wisdom and reveals tomorrow's
knowledge.
This book integrates the fundamentals, methodology, and major
application fields of noncooperative and cooperative games
including conflict resolution. The topics addressed in the book are
discrete and continuous games including games represented by finite
trees; matrix and bimatrix games as well as oligopolies;
cooperative solution concepts; games under uncertainty; dynamic
games and conflict resolution. The methodology is illustrated by
carefully chosen examples, applications and case studies which are
selected from economics, social sciences, engineering, the military
and homeland security. This book is highly recommended to readers
who are interested in the in-depth and up-to-date integration of
the theory and ever-expanding application areas of game theory.
This book integrates the fundamentals, methodology, and major
application fields of noncooperative and cooperative games
including conflict resolution. The topics addressed in the book are
discrete and continuous games including games represented by finite
trees; matrix and bimatrix games as well as oligopolies;
cooperative solution concepts; games under uncertainty; dynamic
games and conflict resolution. The methodology is illustrated by
carefully chosen examples, applications and case studies which are
selected from economics, social sciences, engineering, the military
and homeland security. This book is highly recommended to readers
who are interested in the in-depth and up-to-date integration of
the theory and ever-expanding application areas of game theory.
Oligopoly theory is one of the most intensively studied areas of
mathematical economics. On the basis of the pioneering works of
Cournot (1838), many res- rchers have developed and extensively
examined the different variants of oligopoly models. Initially, the
existence and uniqueness of the equilibrium of the different types
of oligopolies was the main concern, and later the dynamic
extensions of these models became the focus. The classical result
of Theocharis (1960) asserts that under discrete time scales and
static expectations, the equilibrium of a sing- product oligopoly
without product differentiation and with linear price and cost
functions is asymptotically stable if and only if it is a duopoly.
In the continuous time case, asymptotic stability is guaranteed for
any number of ?rms. In these cases the resulting dynamical systems
are also linear, where local and global asymptotic stability are
equivalent to each other. The classical book of Okuguchi (1976)
gives a comprehensive summary of the earlier results and
developments. The multipr- uct extensionshave been discussed in
Okuguchiand Szidarovszky(1999);however, nonlinear features were
barely touched upon in these contributions.
WiththedevelopmentofthecriticalcurvemethodbyGumowskiandMira(1980)
(see also Mira et al. (1996))fordiscrete time systemsand the
introductionof cont- uously distributed information lags by
Invernizzi and Medio (1991) in continuous time systems, increasing
attention has been given to the global dynamics of n- linear
oligopolies. The authors of this book have devoted a great deal of
research effort to this area.
Multicriteria analysis is one of the most important fields of
decision science. This book gives an outline of the formulation of
an appropriate model and presents a comprehensive summary of the
most popular methods for solving multicriteria decision problems.
In addition to the classical approach the book introduces fuzzy and
stochastic methodology, models with uncertainty, social choice and
conflict resolution. All methods are illustrated with easy to
follow simple examples. At the end of each chapter detailed case
studies are given in water and environment management including
inter-basin water transfer, urban water management, water
allocation, groundwater quality management, forest treatment,
ranking water resources projects, reservoir planning, water
distribution network design and long-term watershed management. The
new methodology and the wide variety of case studies are not easily
accessible elsewhere.
In the mid 1960's both authors undertook independent works in
oligopoly.and game theory. However, it was not until 1983 that they
formally met. Since then, they have continued meeting either in
Budapest or Tokyo. Their collaboration has resulted in numerous
publications as well as in this work. Essentially, this book has
two origins. First, it originated in previous results, either
published or circulated in mimeograph form. Finely sifting their
results, the authors constructed a concise reinterpretation of
their achievement to date. However, this unifying process led to
the second origin. Reconsideration, particularly in this
comprehensive approach, generated new results. This was especially
true in the analysis of the existence, uniqueness and global
stability of the Cournot-Nash equilibrium for oligopoly with
multi-product flrms, and for several modilled Cournot and related
models. This book should be ideal for graduate students in
economics or mathematics. However, as the authors have firmly
grounded their ideas in the formal language of mathematics, the
student should possess some background in calculus, linear algebra,
and ordinary differential and difference equations. Additionally,
the book should be useful to researchers in oligopoly and game
theory as well as to mathematically oriented economists. The
methodology developed for analyzing the existence and stability of
oligopoly equilibrium should prove useful also in theoretical
analysis of other economic models. Weare both very grateful to
Professor Wilhelm Krelle for his careful review and helpful
suggestions. In addition, Koji Okuguchi wishes to thank Professors
W.
Game theory, defined in the broadest sense, is a collection of
mathematical models designed for the analysis of strategic aspects
of situations of conflict and cooperation in a broad spectrum of
fields including economics, politics, biology, engineering, and
operations research. This book, besides covering the classical
results of game theory, places special emphasis on methods of
determining 'solutions' of various game models. Generalizations
reaching beyond the 'convexity paradigm' and leading to nonconvex
optimization problems are enhanced and discussed in more detail
than in standard texts on this subject. The development is
theoretical-mathematical interspersed with elucidating
interpretations and examples. Audience: The material in the book is
accessible to PhD and graduate students and will also be of
interest to researchers. Solid knowledge of standard undergraduate
mathematics is required to read the book.
Oligopoly theory is one of the most intensively studied areas of
mathematical economics. On the basis of the pioneering works of
Cournot (1838), many res- rchers have developed and extensively
examined the different variants of oligopoly models. Initially, the
existence and uniqueness of the equilibrium of the different types
of oligopolies was the main concern, and later the dynamic
extensions of these models became the focus. The classical result
of Theocharis (1960) asserts that under discrete time scales and
static expectations, the equilibrium of a sing- product oligopoly
without product differentiation and with linear price and cost
functions is asymptotically stable if and only if it is a duopoly.
In the continuous time case, asymptotic stability is guaranteed for
any number of ?rms. In these cases the resulting dynamical systems
are also linear, where local and global asymptotic stability are
equivalent to each other. The classical book of Okuguchi (1976)
gives a comprehensive summary of the earlier results and
developments. The multipr- uct extensionshave been discussed in
Okuguchiand Szidarovszky(1999);however, nonlinear features were
barely touched upon in these contributions.
WiththedevelopmentofthecriticalcurvemethodbyGumowskiandMira(1980)
(see also Mira et al. (1996))fordiscrete time systemsand the
introductionof cont- uously distributed information lags by
Invernizzi and Medio (1991) in continuous time systems, increasing
attention has been given to the global dynamics of n- linear
oligopolies. The authors of this book have devoted a great deal of
research effort to this area.
Game theory, defined in the broadest sense, is a collection of
mathematical models designed for the analysis of strategic aspects
of situations of conflict and cooperation in a broad spectrum of
fields including economics, politics, biology, engineering, and
operations research. This book, besides covering the classical
results of game theory, places special emphasis on methods of
determining `solutions' of various game models. Generalizations
reaching beyond the `convexity paradigm' and leading to nonconvex
optimization problems are enhanced and discussed in more detail
than in standard texts on this subject. The development is
theoretical-mathematical interspersed with elucidating
interpretations and examples. Audience: The material in the book is
accessible to PhD and graduate students and will also be of
interest to researchers. Solid knowledge of standard undergraduate
mathematics is required to read the book.
It is an incontestable fact that numerical analysis techniques are
used rou tinely (although not always effectively) in virtually
every quantitative field of scientific endeavor. In this book,
which is directed toward upper-division and graduate level students
in engineering and mathematics, we have selected for discussion
subjects that are traditionally found in numerical analysis texts.
But our choice of methodology rejects the traditional where
analysis and experience clearly warrant such a departure, and one
of our primary aspirations in this work is to equip the reader with
the wherewithal to apply numerical analysis thinking to
nontraditional subjects. For there is a plethora of
computer-oriented sciences such as optimization, statistics, and
system analysis and identification that are sorely in need of
methods comparable to those related here for classical numerical
analysis problems. Toward uncovering for the reader the structure
of numerical methods we have, for example, devoted a chapter to a
metric space theory for iter ative application of operators. In
this chapter, we have collected those definitions and concepts of
real and functional analysis that are requisite to a modern
intermediate-level exposition of the principles of numerical anal
ysis. Further, we derive the abstract theory (most notably, the
contraction mapping theorem) for iteration processes.
This book focuses on the latest advances in nonlinear dynamic
modeling in economics and finance, mainly-but not solely-based on
the description of strategic interaction by using concepts and
methods from dynamic and evolutionary game theory. The respective
chapters cover a range of theoretical issues and examples
concerning how the qualitative theory of dynamical systems is used
to analyze the local and global bifurcations that characterize
complex behaviors observed in social systems where heterogeneous
and boundedly rational economic agents interact. Nonlinear
dynamical systems, represented by difference and differential and
functional equations, are extensively used to simulate the behavior
of time-evolving economic systems, also in the presence of time
lags, discontinuities, and hysteresis phenomena. In addition, some
theoretical issues and particular applications are discussed, as
well. The contributions gathered here offer an up-to-date review of
the latest research in this rapidly developing research area.
Experience has shown that structural solutions for water diversion, conservation, and transfer are not always the most efficient and economically sound alternatives. New, non-structural means of solving problems must be used to guarantee safe and efficient allocation of water to domestic, agricultural, and industrial customers.
Focusing on conflict resolution, Water Resources Systems Analysis discusses systematic approaches for the mathematical modeling of various water resources issues, helping decision-makers allocate water effectively and efficiently. Readers will gain an understanding of simulation, optimization, multi-criterion-decision-making, as well as engineering economics and time series analysis, all necessary for successful water resources systems analysis. The book explores recent developments in surface and groundwater systems optimization and modeling, and relates these to real field applications and case studies.
Supported by essential mathematical tools, this book gives current and future hydrologists, water resources managers, and civil engineers a logical reference for prioritizing and addressing critical issues such as flood control, power generation, and water quality management.
Multicriteria analysis is one of the most important fields of
decision science. This book gives an outline of the formulation of
an appropriate model and presents a comprehensive summary of the
most popular methods for solving multicriteria decision problems.
In addition to the classical approach the book introduces fuzzy and
stochastic methodology, models with uncertainty, social choice and
conflict resolution. All methods are illustrated with easy to
follow simple examples. At the end of each chapter detailed case
studies are given in water and environment management including
inter-basin water transfer, urban water management, water
allocation, groundwater quality management, forest treatment,
ranking water resources projects, reservoir planning, water
distribution network design and long-term watershed management. The
new methodology and the wide variety of case studies are not easily
accessible elsewhere.
Linear algebra and matrix theory are among the most important and
most frequently applied branches of mathematics. They are
especially important in solving engineering and economic models,
where either the model is assumed linear, or the nonlinear model is
approximated by a linear model, and the resulting linear model is
examined.This book is mainly a textbook, that covers a one semester
upper division course or a two semester lower division course on
the subject.The second edition will be an extended and modernized
version of the first edition. We added some new theoretical topics
and some new applications from fields other than economics. We also
added more difficult exercises at the end of each chapter which
require deep understanding of the theoretical issues. We also
modernized some proofs in the theoretical discussions which give
better overview of the study material. In preparing the manuscript
we also corrected the typos and errors, so the second edition will
be a corrected, extended and modernized new version of the first
edition.
Linear algebra and matrix theory are among the most important and
most frequently applied branches of mathematics. They are
especially important in solving engineering and economic models,
where either the model is assumed linear, or the nonlinear model is
approximated by a linear model, and the resulting linear model is
examined.This book is mainly a textbook, that covers a one semester
upper division course or a two semester lower division course on
the subject.The second edition will be an extended and modernized
version of the first edition. We added some new theoretical topics
and some new applications from fields other than economics. We also
added more difficult exercises at the end of each chapter which
require deep understanding of the theoretical issues. We also
modernized some proofs in the theoretical discussions which give
better overview of the study material. In preparing the manuscript
we also corrected the typos and errors, so the second edition will
be a corrected, extended and modernized new version of the first
edition.
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