Matrix-analytic Methods in Stochastic Models

This book, the first in the Cambridge Nonlinear Science Series, presents the fundamentals of chaos theory in conservative systems, providing a systematic study of the theory of transitional states of physical systems which lie between deterministic and chaotic behaviour. The authors' treatment of transitions to chaos, the theory of stochastic layers and webs, and the numerous applications of this theory, particularly to pattern symmetry, will make the book of importance to scientists from many disciplines.The authors have been meticulous in providing a detailed presentation of the material, enabling the reader to learn the necessary computational methods and to apply them in other problems. The inclusion of a significant amount of computer graphics is also an important aid to understanding. The final section of the book contains a fascinating collection of patterns in art and living nature. The book will be of interest to graduate students and researchers in physics and mathematics who

This book provides an introduction to the methods employed in forecasting the future state of the economy. It provides a comprehensive coverage of methods and applications in this fast-growing area and is intended for use in postgraduate and upper-level undergraduate courses. Part I outlines the available techniques, particularly those used in business forecasting and econometric forecasting. The state of the art in time series modelling is reviewed and includes a discussion of Box-Jenkins models, the vector autogressive approach and cointegration. Ways of combining forecasts are also examined in detail. Part II considers the most important applications of forecasting. Applications in microeconomics include demand and sales forecasting, the use of anticipations data, leading indicators and scenario analysis. In macroeconomics the emphasis is on why errors occur in forecasting asset market prices, including implications of the efficient markets hypothesis for foreign markets, stock mark

This classic book, now re-issued in paperback, presents a detailed account of the mathematical theory of viscosity, thermal conduction and diffusion in non-uniform gases based on the solution of the Maxwell–Boltzmann equations. The theory of Chapman and Enskog, describing work on dense gases, quantum theory of collisions and the theory of conduction and diffusion in ionized gases in the presence of electric and magnetic fields, is extended in the later chapters. The third edition was first published in 1970 and included revisions to take account of extensions of the theory to fresh molecular models and of new methods used in discussing dense gases and plasmas. This reprint will therefore be of value to mathematicians, theoretical physicists and chemical engineers interested in gas theory and its applications.

Time Series: Theory and Methods is a systematic account of linear time series models and their application to the modelling and prediction of data collected sequentially in time. The aim is to provid

This book presents a novel approach to the teaching of dynamic aspects of the operation of semiconductor and opto-electronic devices. Such dynamic aspects often determine the steady state conditions. Also, the dynamical operation of such devices is of increasing importance as modern methods of communicating data and information require electronic devices that switch electrical or optical signals at ever faster rates. The author discusses the rates at which electrons and holes can reach equilibrium, the rates at which transistors and diodes can switch, and the rates at which electrons and holes can interact with photons, and with protons. He also applies the rate equations in a unified way to models of light-emitting diodes, injection lasers and photodiodes. Finally, the author discusses more-advanced topics on the photon statistics of injection lasers, mode-locking and the application of rate equations and Maxwell's equations to opto-electronic devices.

The advent of electronic computing permits the empirical analysis of economic models of far greater subtlety and rigour than before, when many interesting ideas were not followed up because the calculations involved made this impracticable. The estimation and testing of these more intricate models is usually based on the method of Maximum Likelihood, which is a well-established branch of mathematical statistics. Its use in econometrics has led to the development of a number of special techniques; the specific conditions of econometric research moreover demand certain changes in the interpretation of the basic argument. This book is a self-contained introduction to this field. It consists of three parts. The first deals with general features of Maximum Likelihood methods; the second with linear and nonlinear regression; and the third with discrete choice and related micro-economic models. Readers should already be familiar with elementary statistical theory, with applied econometric res

This collection of essays, written between 1975 and 1987, covers the doctrine of analogy; the Trinity; 'theological realism'; the problems of evil and suffering; the doctrine of God, tragedy and Christian life; the doctrine of the atonement, christology, the theology of religions, ecclesiology, discipleship and the so-called theistic 'proofs'. The earlier essays reflect the author's training as a philosopher in the Anglo-American 'analytic' tradition. Later essays have a more explicitly theological focus, and they represent an attempt to come to terms with, and to proceed beyond, this tradition. More importance is attached to issues in hermeneutics and literary and social theory in the later essays. This collection therefore tends to address a wider list of topics than is usual in works of philosophical theology, and it is also distinctive in respect of the methods and approaches used in considering these topics.

Professor Roemer's goal in this book is to give a rigorous view of classical Marxian economic theory by presenting specific analytic models. The theory is not extended to deal with new problems, but it is deepened: Marxian theory is given micro-foundations and upon those foundations the author begins to rebuild a tightly constructed Marxian economics. The book begins, after a methodological introduction, with an examination of the Marxian notion of equilibrium and the theory of exploitation, and goes on to deal with the theory of the falling rate of profit. The next section explores one of the points made in the first section of the book, that the Marxian theory of exploitation can be constructed completely independently of the labor theory of value as a theory of exchange. Technical study of this problem allows comment on various issues, such as the relative importance of 'marginal utilities' and 'class struggle' in determining relative prices. The final part examines models of variou

Papers of the April 1988, Reno, Nevada meeting. They deal with: novel processing methods for metal based composites; deformation mechanisms in metal matrix composites; ceramic composite mechanical per

This is a concise graduate level introduction to analytical functional methods in quantum field theory. Functional integral methods provide relatively simple solutions to a wide range of problems in quantum field theory. After introducing the basic mathematical background, this book goes on to study applications and consequences of the formalism to the study of series expansions, measure, phase transitions, physics on spaces with nontrivial topologies, stochastic quantisation, fermions, QED, non-abelian gauge theories, symmetry breaking, the effective potential, finite temperature field theory, instantons and compositeness. Serious attention is paid to the shortcomings of the conventional formalism (e.g. problems of measure) as well as detailed appraisal of the ambiguities of series summation. This book will be of great use to graduate students in theoretical physics wishing to learn the use of functional integrals in quantum field theory. It will also be a useful reference for researc

The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and non-space-clamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex in this volume than in the first volume and involves numerical methods of solution of partial differential equations and the statistical analysis of point processes.

Although the complexity and capability of flight simulators have matched the growth of aerospace technology, there has until now been no textbook dealing specifically with the design and construction of flight simulators. This is a primary purpose of Flight Simulation. Written in collaboration with a number of internationally known specialists, the book considers the subject in three sections. Firstly it introduces the concept of simulation in order to identify the essential elements which make up the modern flight simulator. The development of these elements is also traced through the historical evolution of flight simulation. The main section of the book commences with an exposition of the mathematical models into dynamic physical devices capable of representing the response of a specific aircraft and its systems. The simulation of the flight environment is also covered in relation to cockpit motion systems and methods of representing the external visual scene. Another important aspe

This book represents a comprehensive examination of interest-group politics in France. Rather than the narrow case studies usually employed to study group politics, the book focuses on the overall pattern of interaction between interest groups and government. Drawing upon extensive interviews with French interest-group leaders and politicians, Wilson examines the structures and methods of group politics, the perspectives and attitudes of group leaders, and the place of interest groups in the broader pattern of French politics. He concludes that neither of the two major conceptualizations of interest-group/government relations is adequate to explain group politics in France. He suggests that the French state is much more powerful than recognized by these or other models of interest-group politics. Political influence is difficult for groups to develop and, once achieved, is fleeting. Consequently, groups engage in a wide range of activities, some of which are pluralist, others corporati

This 1987 book is a self-contained text on the probabilistic modelling method. It provides the reader with an understanding of the available results as well as with examples of their application. The only background assumed is a knowledge of basic calculus. The necessary fundamentals of probability are presented followed by an introduction to stochastic processes. The remainder of the book is devoted to the treatment of various single-station and their application to uni-programmed and multi-programmed systems and local and wide-area networks. Both exact and approximate solution methods are discussed, with as much emphasis on explaining the ideas and providing information, as on derivations and proofs. This book will still be of use for anyone with an interest in the history of computer science.

The place of money capital in the theory of the firm has remained a relatively neglected question in traditions of economic analysis. In this highly integrative work, issues in production, pricing, capital investment and financial theory are brought to new levels of interdependence. Developing a three-part argument, Money Capital in the Theory of the Firm deals successively with the theoretical issues and analytic motivation, the neoclassical tradition and postclassical perspectives. In doing so, it presents a self-contained foundation in the basic structures of microeconomic analysis relating to optimize decision making in the firm and in the accounting concepts and statistical apparatus of probability theory relevant to the neoclassical aspects of the argument. Additionally, the book provides the essential mathematical development of such advanced topics as utility functions defined over stochastic arguments, the equilibrium theory of financial asset prices and yields, the cost of mo

The papers in this volume, a multidisciplinary collaboration of anthropologists, linguists, and psychologists, explore the ways in which cultural knowledge is organized and used in everyday language and understanding. Employing a variety of methods, which rely heavily on linguistic data, the authors offer analyses of domains of knowledge ranging across the physical, social, and psychological worlds, and reveal the importance of tacit, presupposed knowledge in the conduct of everyday life. The authors argue that cultural knowledge is organized in 'cultural models' - storylike chains of prototypical events that unfold in simplified worlds - and explore the nature and role of these models. They demonstrate that cultural knowledge may take either proposition-schematic or image-schematic form, each enabling the performance of different kinds of cognitive tasks. Metaphor and metonymy are shown to have special roles in the construction of cultural models. The authors also demonstrates that so

This book is based on a course given at Massachusetts Institute of Technology. It is intended to be a reasonably self-contained introduction to stochastic analytic techniques that can be used in the study of certain problems. The central theme is the theory of diffusions. In order to emphasize the intuitive aspects of probabilistic techniques, diffusion theory is presented as a natural generalization of the flow generated by a vector field. Essential to the development of this idea is the introduction of martingales and the formulation of diffusion theory in terms of martingales. The book will make valuable reading for advanced students in probability theory and analysis and will be welcomed as a concise account of the subject by research workers in these fields.

This book presents a novel approach to the teaching of dynamic aspects of the operation of semiconductor and opto-electronic devices. Such dynamic aspects often determine the steady state conditions. Also, the dynamical operation of such devices is of increasing importance as modern methods of communicating data and information require electronic devices that switch electrical or optical signals at ever faster rates. The author discusses the rates at which electrons and holes can reach equilibrium, the rates at which transistors and diodes can switch, and the rates at which electrons and holes can interact with photons, and with protons. He also applies the rate equations in a unified way to models of light-emitting diodes, injection lasers and photodiodes. Finally, the author discusses more-advanced topics on the photon statistics of injection lasers, mode-locking and the application of rate equations and Maxwell's equations to opto-electronic devices.

This book delves into the rapidly changing area of combustion, in which asymptotic methods and bifurcation theory have made a significant impact as have the constant-density, small-heat-release models

This textbook describes the physics of the plastic deformation of solids at high temperatures. It is directed at geologists or geophysicists interested in the high-temperature behaviour of crystals who wish to become acquainted with the methods of materials science in so far as they are useful to earth scientists. It explains the most important models and recent experimental results without losing the reader in the primary literature of materials science. In turn the book deals with the essential solid-state physics; thermodynamics and hydrostatics of creep; creep models and their applications in the geological sciences; diffusion creep; superplastic deformation and deformation enhanced by phase transformations. Five concluding chapters give experimental results for metals, ceramics and minerals. There are extensive bibliographies to aid further study.

There has been a surge of interest in methods of analysing data that typically arise from surveys of various kinds of experiments in which the number of people, animals, places or objects occupying various categories are counted. Such observations are known variously as category counts, contingency tables, or cross-tabulated or cross-classified categorical data. In this textbook, first published in 1984, Dr Fingleton describes some techniques centred on the log-linear model from the perspective of the social, behavioural and environmental scientist. His aim is to provide a route from conceptual appreciation to the practicalities of fitting models to data, and he therefore gives some consideration to appropriate computer software. The emphasis throughout is on data analysis and interpretation. Recently developed methods are clearly explained and mathematics has been kept to a minimum.

Structural Sensitivity in Econometric Models Edwin Kuh, John W. Neese and Peter Hollinger Provides a pathbreaking assessment of the worth of linear dynamic systems methods for probing the behavior of

For a number of years, French mathematicians have run regular number theory conferences to which they have invited number theorists from many countries. To repay their hospitality, the London Mathematical Society arranged for the 1980 'Journees Arithmeiques' to be held in Exeter. The papers published here are either based on the main invited lectures or on selected research talks given at the conference. They cover all branches of the subject: combinatorial and elementary methods; analytic number theory; transcendence theory; Galois module theory and algebraic number theory in general; elliptic curves and modular functions; local fields; additive number theory; Diophantine geometry, and uniform distribution. It will be necessary reading for all those undertaking research in number theory.

This introduction to mathematical methods that are useful for studying population phenomena is intended for advanced undergraduate and graduate students, and will be accessible to scientists who do not have a strong mathematics background. The material is graded in mathematical difficulty. The earlier parts of the book involve elementary diference equations while later chapters present topics that require more mathematical preparation. Models of total population and population age structure are first derived and studied, and then models of random population events are presented in terms of Markov chains. The last two chapters deal with mathematical methods used to uncover qualitative behaviour of more complicated difference equations. Each chapter begins with a simple model, usually of some historical interest, that defines the primary goals of the chapter. Exercises, for which solutions are provided, illustrate material in the text and also deal with models more advanced than those de

This book presents the major themes of the economic literature on natural resources and the environment. It is designed to bring the reader, in part with the aid of a unified model of optimal resource use, to the frontiers of the discipline, using only elementary mathematical models. Features special to exhaustible and renewable resources, including the problems posed by market imperfections, are treated as extensions of the basic model. The theoretical discussion is enriched with examples and applications, including a systematic investigation of the behaviour of resource reserves, costs, prices, and substitution possibilities. Substantial attention to environmental, as well as extractive, resources is a distinctive aspect of this book. The author describes methods of estimating the environmental costs of resource development and other projects, and presents some key empirical findings. Policy instruments to protect the environment, such as taxes, subsidies, marketable permits, and dir

An enormous amount of research into British field systems has been undertaken by historical geographers, economic historians and others since H. L. Gray's classic work on English Field Systems was published. Detailed local studies have been legion, generalized explanations of the origins and functioning of field systems few but influential in promoting further studies. This book both synthesises and advances our knowledge of field systems in the British Isles. An introduction by the editors outlines the sources and methods of studies of field systems. There then follow twelve chapters concerned with specific areas within the British Isles. In their own conclusion, the editors consider the problems and perspectives of field system studies in the context of the British Isles as a whole. This chapter is an attempt at generalisation in historical geography, generalization in relation to both existing models of British field systems and putative problems which only further research can reso

Offers students with an understanding of fundamental models in macroeconomics, and introduces them to the methods of formal macroeconomic analysis. This book focuses on macroeconomics for the long run

Probability models, statistical methods, and the information to be gained from them is vital for work in business, engineering, sciences (including social and behavioral), and other fields. Data must

This is a book about powerful mathematical methods rather than a mere catalogue of the properties of conics. The treatment is elegant and refreshing as well as systematic, and throughout the book the author is concerned to lay the foundations of future work. Consequently (unlike too many textbooks) there is little for the student to unlearn when he goes on to more advanced courses. A valuable feature is the large number of carefully selected and graded problems for solution (about 400 in all). When this book was first published, the reviewer in Science suggested that 'this scholarly work should be supplemented by a similar book on the analytic projective geometry of ordinary space'. His suggestion has since been adopted: and the companion volume, E.A. Maxwell's General Homogenous Coordinates in Space of Three Dimensions is now also available.

This textbook provides an introduction to Scientific Computing and algorithms that help solve computational problems in science and engineering. The book will be designed to serve both professionals

Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book has served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references.Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory （the possible branching of solutions as parameters vary）, including the proof of Rabinowitz's global bifurcation theorem. Stability of the branches is also studied. The book concludes with a presentation of some generalized implicit function theorems of Nash-Moser type with applications to Kolmogorov-Arnold-Moser theory and to conjugacy problems.After more than 20 years, this book continues to be an excellent

Nanomaterials possess special mechanical, electrical, and electronic properties. As a result, nanomaterials play a significant role in various nanoelectromechanical systems. Some of these materials include nanoparticles, nanowires, nanotubes, nanotube resonators, and nanoactuators. These structures are broadly utilized in civil, mechanical, and aerospace engineering. The dynamic analysis of nanostructures is important, because one must have knowledge about the mechanical behaviours to get an accurate prediction of dynamic characteristics. Conducting experiments at the nanoscale size is both complicated and expensive. Therefore, the development of appropriate mathematical models for the study of the dynamic behaviour of nanostructures is important. These models/problems are governed by linear/nonlinear differential equations which are not always possible to solve analytically. This deficiency compels us to search for numerical and computational methods. This book provides a detailed exp

Introduction to Intelligence: Institutions, Operations, and Analysis offers you a strategic, international, and comparative approach to covering intelligence organizations and domestic security issues. Written by multiple authors, each chapter draws on the author's professional and scholarly expertise in the subject matter. As a core text for an introductory survey course in intelligence, this text provides you with a comprehensive introduction to intelligence, including institutions and processes, collection, communications, and common analytic methods.

This book is a compendium of fundamental mathematical concepts, methods, models, and their wide range of applications in diverse fields of engineering. It comprises essentially a comprehensive and con

This detailed volume introduces the reader to current methods in glaucoma research, in particular those that make use of animal disease models. Given that the retinal ganglion cells damaged and destro

This book gives an introduction to quantum mechanics with the matrix method. Heisenberg's matrix mechanics is described in detail. The fundamental equations are derived by algebraic methods using matr