In economic modeling and planning, as well as in business, most problems are linear, or approximated by linear models. Such problems are solved by matrix methods, so the material presented in this book is essential to these fields.
This book presents the latest trends, methods and results in nonlinear dynamics with a special focus on oligopolies. It contains a number of technical appendices that summarize techniques of global dynamics not easily accessible elsewhere.
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.
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 this book a rigorous, systematic, mathematical analysis is presented for oligopoly with multi-product firms in static as well as dynamic frameworks in the light of recent developments in theories of games, oligopoly and industrial organization. The general results derived in this book on oligopoly with multi-product firms contain, as special cases, all previous results on oligopoly with single product as well as oligopoly with product differentiation and single product firms. A constructive nu- merical method is given for finding the Cournot-Nash equilibrium, which may be extremely valuable to those who are interested in numerical analysis of the effects of various industrial policies. A sequential adjustment process is also formulated for finding the equilibrium. Dynamic adjustment processes have two versions, one with a discrete time scale and the other with a continuous time scale. The stability of the equilibrium is thoroughly investigated utilizing powerful mathematical results from the stability and linear algebra literature. The methodology developed for analyzing stability proves to be useful for dynamic analysis of economic models.
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 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.
The Theory and Applications of Iteration Methods focuses on an abstract iteration scheme that consists of the recursive application of a point-to-set mapping. Each chapter presents new theoretical results and important applications in engineering, dynamic economic systems, and input-output systems. At the end of each chapter, case studies and numerical examples are presented from different fields of engineering and economics. Following an outline of general iteration schemes, the authors extend the discrete time-scale Liapunov theory to time-dependent, higher order, nonlinear difference equations. The monotone convergence to the solution is examined in and comparison theorems are proven . Results generalize well-known classical theorems, such as the contraction mapping principle, the lemma of Kantorovich, the famous Gronwall lemma, and the stability theorem of Uzawa. The book explores conditions for the convergence of special single- and two-step methods such as Newton's method, modified Newton's method, and Newton-like methods generated by point-to-point mappings in a Banach space setting. Conditions are examined for monotone convergence of Newton's methods and their variants. Students and professionals in engineering, the physical sciences, mathematics, and economics will benefit from the book's detailed examples, step-by-step explanations, and effective organization.
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 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.
Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then It is that they can't see the problem. one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Min kowsky lemma, coding theory and the structure of water meet one another in packing and covering theory: quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.
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.
Focusing on conflict resolution, Water Resources Systems Analysis discusses systematic approaches to the mathematical modeling of various water resources issues, which helps decision-makers allocate water effectively and efficiently. Readers will gain an understanding of simulation, optimization, multi-criterion-decision-making, as well as engineer
A comprehensive guide to the application and processing of condition-based data to produce prognostic estimates of functional health and life. Prognostics and Health Management provides an authoritative guide for an understanding of the rationale and methodologies of a practical approach for improving system reliability using conditioned-based data (CBD) to the monitoring and management of health of systems. This proven approach uses electronic signatures extracted from conditioned-based electrical signals, including those representing physical components, and employs processing methods that include data fusion and transformation, domain transformation, and normalization, canonicalization and signal-level translation to support the determination of predictive diagnostics and prognostics. Written by noted experts in the field, Prognostics and Health Management clearly describes how to extract signatures from conditioned-based data using conditioning methods such as data fusion and transformation, domain transformation, data type transformation and indirect and differential comparison. This important resource: Integrates data collecting, mathematical modelling and reliability prediction in one volume Contains numerical examples and problems with solutions that help with an understanding of the algorithmic elements and processes Presents information from a panel of experts on the topic Follows prognostics based on statistical modelling, reliability modelling and usage modelling methods Written for system engineers working in critical process industries and automotive and aerospace designers, Prognostics and Health Management offers a guide to the application of condition-based data to produce signatures for input to predictive algorithms to produce prognostic estimates of functional health and life.
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.
The Theory and Applications of Iteration Methods focuses on an abstract iteration scheme that consists of the recursive application of a point-to-set mapping. Each chapter presents new theoretical results and important applications in engineering, dynamic economic systems, and input-output systems. At the end of each chapter, case studies and numerical examples are presented from different fields of engineering and economics. Following an outline of general iteration schemes, the authors extend the discrete time-scale Liapunov theory to time-dependent, higher order, nonlinear difference equations. The monotone convergence to the solution is examined in and comparison theorems are proven . Results generalize well-known classical theorems, such as the contraction mapping principle, the lemma of Kantorovich, the famous Gronwall lemma, and the stability theorem of Uzawa. The book explores conditions for the convergence of special single- and two-step methods such as Newton's method, modified Newton's method, and Newton-like methods generated by point-to-point mappings in a Banach space setting. Conditions are examined for monotone convergence of Newton's methods and their variants. Students and professionals in engineering, the physical sciences, mathematics, and economics will benefit from the book's detailed examples, step-by-step explanations, and effective organization.
In this book a rigorous, systematic, mathematical analysis is presented for oligopoly with multi-product firms in static as well as dynamic frameworks in the light of recent developments in theories of games, oligopoly and industrial organization. The general results derived in this book on oligopoly with multi-product firms contain, as special cases, all previous results on oligopoly with single product as well as oligopoly with product differentiation and single product firms. A constructive nu- merical method is given for finding the Cournot-Nash equilibrium, which may be extremely valuable to those who are interested in numerical analysis of the effects of various industrial policies. A sequential adjustment process is also formulated for finding the equilibrium. Dynamic adjustment processes have two versions, one with a discrete time scale and the other with a continuous time scale. The stability of the equilibrium is thoroughly investigated utilizing powerful mathematical results from the stability and linear algebra literature. The methodology developed for analyzing stability proves to be useful for dynamic analysis of economic models.
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.
Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then It is that they can't see the problem. one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Min kowsky lemma, coding theory and the structure of water meet one another in packing and covering theory: quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.
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