Methods of Nonlinear Analysis

Morphometrics is the statistical study of biological shape and shape change. Its richest data are landmarks, points such as 'the bridge of the nose' that have biological names as well as geometric locations. This book is the first systematic survey of morphometric methods for landmark data. The methods presented here combine conventional multivariate statistical analysis with themes from plane and solid geometry and from biomathematics to support biological insights into the features of many different organs and organisms. This book will be of value to applied statisticians and geometers, as well as to all biological and biomedical researchers who need quantitative analyses of information from biomedical images.

This book introduces the use of Lie algebra and differential geometry methods to study nonlinear integrable systems of Toda type. Many challenging problems in theoretical physics are related to the solution of nonlinear systems of partial differential equations. One of the most fruitful approaches in recent years has resulted from a merging of group algebraic and geometric techniques. The book gives a comprehensive introduction to this exciting branch of science. Chapters 1 and 2 review basic notions of Lie algebras and differential geometry with an emphasis on further applications to integrable nonlinear systems. Chapter 3 contains a derivation of Toda type systems and their general solutions based on Lie algebra and differential geometry methods. The last chapter examines explicit solutions of the corresponding equations. The book is written in an accessible 'lecture note' style with many examples and exercises to illustrate key points and to reinforce understanding.

This is an advanced 1997 text for first-year graduate students in physics and engineering taking a standard classical mechanics course. It was the first book to describe the subject in the context of the language and methods of modern nonlinear dynamics. The organising principle of the text is integrability vs. nonintegrability. Flows in phase space and transformations are introduced early and systematically and are applied throughout the text. The standard integrable problems of elementary physics are analysed from the standpoint of flows, transformations, and integrability. This approach then allows the author to introduce most of the interesting ideas of modern nonlinear dynamics via the most elementary nonintegrable problems of Newtonian mechanics. This text will be of value to physicists and engineers taking graduate courses in classical mechanics. It will also interest specialists in nonlinear dynamics, mathematicians, engineers and system theorists.

This is an advanced 1997 text for first-year graduate students in physics and engineering taking a standard classical mechanics course. It was the first book to describe the subject in the context of the language and methods of modern nonlinear dynamics. The organising principle of the text is integrability vs. nonintegrability. Flows in phase space and transformations are introduced early and systematically and are applied throughout the text. The standard integrable problems of elementary physics are analysed from the standpoint of flows, transformations, and integrability. This approach then allows the author to introduce most of the interesting ideas of modern nonlinear dynamics via the most elementary nonintegrable problems of Newtonian mechanics. This text will be of value to physicists and engineers taking graduate courses in classical mechanics. It will also interest specialists in nonlinear dynamics, mathematicians, engineers and system theorists.

This book challenges standard accounts of early Christian exegesis of the Bible. Professor Young sets the interpretation of the Bible in the context of the Graeco-Roman world - the dissemination of books and learning, the way texts were received and read, the function of literature in shaping not only a culture but a moral universe. For the earliest Christians, the adoption of the Jewish scriptures constituted a supersessionary claim in relation to Hellenism as well as Judaism. Yet the debt owed to the practice of exegesis in the grammatical and rhetorical schools is of overriding significance. Methods were philological and deductive, and the usual analysis according to 'literal', 'typological' and 'allegorical' is inadequate to describe questions of reference and issues of religious language. The biblical texts shaped a 'totalizing discourse' which by the fifth century was giving identity, morality and meaning to a new Christian culture.

Acquaints graduate students with basic ideas and methods of modern differential geometry and their applications in physics. Half of the chapters focus on local analysis, useful for graduate students o

State-space methods form the basis of modern control theory. This graduate text is devoted to a description of these methods in the analysis of linear multi-input, multi-output dynamic systems. Following a chapter which sets out the basic concepts and definitions, state equations of finite dimensional systems, and their solution, are discussed in detail. The principles of time-domain and frequency-domain analysis are then presented, as are the properties and applications of the Z-transformation. Separate chapters deal with the controllability, observability, and stability of linear systems. A useful tutorial review of the key results from matrix theory and linear algebra is given in the appendix. The book includes several worked examples, and there are problems at the end of each chapter. It will be of great use to advanced undergraduate and graduate students of electrical or mechanical engineering taking courses in linear systems or control systems.

State-space methods form the basis of modern control theory. This graduate text is devoted to a description of these methods in the analysis of linear multi-input, multi-output dynamic systems. Following a chapter which sets out the basic concepts and definitions, state equations of finite dimensional systems, and their solution, are discussed in detail. The principles of time-domain and frequency-domain analysis are then presented, as are the properties and applications of the Z-transformation. Separate chapters deal with the controllability, observability, and stability of linear systems. A useful tutorial review of the key results from matrix theory and linear algebra is given in the appendix. The book includes several worked examples, and there are problems at the end of each chapter. It will be of great use to advanced undergraduate and graduate students of electrical or mechanical engineering taking courses in linear systems or control systems.

This 1997 book is an introduction to the application of computer simulation and theory in the study of the interaction of energetic particles (

In this book Christian Gourieroux and Alain Monfort provide an up-to-date and comprehensive analysis of modern time series econometrics. They have succeeded in synthesising in an organised and integrated way a broad and diverse literature. While the book does not assume a deep knowledge of economics, one of its most attractive features is the close attention it pays to economic models and phenomena throughout. The coverage represents a major reference tool for graduate students, researchers and applied economists. The book is divided into four sections. Section one gives a detailed treatment of classical seasonal adjustment or smoothing methods. Section two provides a thorough coverage of various mathematical tools. Section three is the heart of the book, and is devoted to a range of important topics including causality, exogeneity shocks, multipliers, cointegration and fractionally integrated models. The final section describes the main contribution of filtering and smoothing theory t

In this book Christian Gourieroux and Alain Monfort provide an up-to-date and comprehensive analysis of modern time series econometrics. They have succeeded in synthesising in an organised and integrated way a broad and diverse literature. While the book does not assume a deep knowledge of economics, one of its most attractive features is the close attention it pays to economic models and phenomena throughout. The coverage represents a major reference tool for graduate students, researchers and applied economists. The book is divided into four sections. Section one gives a detailed treatment of classical seasonal adjustment or smoothing methods. Section two provides a thorough coverage of various mathematical tools. Section three is the heart of the book, and is devoted to a range of important topics including causality, exogeneity shocks, multipliers, cointegration and fractionally integrated models. The final section describes the main contribution of filtering and smoothing theory t

This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all lev

This text bridges the gap between the classic texts on potential theory and modern books on applied geophysics. It opens with an introduction to potential theory, emphasising those aspects particularly important to earth scientists, such as Laplace's equation, Newtonian potential, magnetic and electrostatic fields, and conduction of heat. The theory is then applied to the interpretation of gravity and magnetic anomalies, drawing on examples from modern geophysical literature. Topics explored include regional and global fields, forward modeling, inverse methods, depth-to-source estimation, ideal bodies, analytical continuation, and spectral analysis. The book includes numerous exercises and a variety of computer subroutines written in FORTRAN. Graduate students and researchers in geophysics will find this book essential.

This book is an introduction to the theory of partial differential operators. It assumes that the reader has a knowledge of introductory functional analysis, up to the spectral theorem for bounded linear operators on Banach spaces. However, it describes the theory of Fourier transforms and distributions as far as is needed to analyse the spectrum of any constant coefficient partial differential operator. A completely new proof of the spectral theorem for unbounded self-adjoint operators is followed by its application to a variety of second-order elliptic differential operators, from those with discrete spectrum to Schrödinger operators acting on L2(RN). The book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques. This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on the subjec

This book describes the full range of mass spectrometry techniques and applications. This versatile technique is in ubiquitous use in universities and industry laboratories because of its ability to identify and quantify materials quickly and, if necessary, in minute amounts, and solve analytical problems in a huge variety of fields. The authors adopt an instructional approach and make use of recent examples to illustrate important points. This second edition includes new methods and applications that have developed in the last ten years. Powerful methods combining mass spectrometry with newer separation techniques, the increased use of computers, and analysis of once difficult polar and large-mass compounds such as proteins using new ionisation methods are all discussed. Requiring no previous knowledge of mass spectrometry, this is an ideal teaching text at both undergraduate and postgraduate level, and will also be of considerable interest to research workers.

The theory of sets of multiples, a subject which lies at the intersection of analytic and probabilistic number theory, has seen much development since the publication of Sequences by Halberstam and Roth nearly thirty years ago. The area is rich in problems, many of them still unsolved or arising from current work. The author sets out to give a coherent, essentially self-contained account of the existing theory and at the same time to bring the reader to the frontiers of research. One of the fascinations of the theory is the variety of methods applicable to it, which include Fourier analysis, group theory, high and ultra-low moments, probability and elementary inequalities, as well as several branches of number theory. This Tract is the first devoted to the subject, and will be of value to research workers or graduate students in number theory.

This substantial revision of the text Numerical Solution of Partial Differential Equations by the Finite Element Method by C. Johnson is a two volume introduction to the computational solution of differential equations using a unified approach organised around the adaptive finite element method. It presents a synthesis of mathematical modelling, analysis and computation. It provides the student with theoretical and practical tools useful for addressing the basic questions of computational mathematical modelling in science and engineering: How to model physical phenomena using differential equations? What are the properties of solutions of differential equations? How to compute solutions in practice? How to estimate and control the accuracy of computed solutions? The first volume begins by developing the basic issues at an elementary level in the context of a set of model problems in ordinary differential equations. The second volume extends the scope to nonlinear differential equations

As expenditure on health care has increasingly become an area of public debate and concern, public and private health care decision-makers have called for more rigorous use of cost-benefit and cost-effectiveness analysis to guide spending. Concerns have arisen, however, about the overall quality of such analyses. This book discusses and evaluates best-practice methods of conducting cost-benefit and cost-effectiveness studies of pharmaceuticals and other medical technologies. It encompasses a wide variety of topics, ranging from measuring cost and effectiveness to discounting to the use of dynamic modelling of cost-effectiveness. The book also includes conceptual and practical aspects of cost-effectiveness analysis by researchers who have conducted applied research in these areas. Rarely does the book provide a singular solution to a measurement problem; rather, the reader is directed to choices among alternative approaches and an analysis of the advantages and disadvantages of each.

This book describes the most reliable methods available for evaluating the transport properties, such as viscosity, thermal conductivity and diffusion, of pure gases and fluid mixtures. Particular emphasis is placed on recent theoretical advances in our understanding of fluid transport properties in all the different regions of temperature and pressure. In addition to the important theoretical tools, the different methods of data representation are also covered, followed by a section which demonstrates the application of selected models in a range of circumstances. Case studies of transport property analysis for real fluids are then given, and the book concludes with a discussion of various international data banks and prediction packages. Advanced students of kinetic theory, as well as engineers and scientists involved with the design of process equipment or the interpretation of measurements of fluid transport properties, will find this book indispensable.

This edited collection of essays from world-leading academic and industrial authors yields insight into all aspects of reverse engineering. Methods of reverse engineering analysis are covered, along w

Explicates the mathematical theory of regularization methods and gives an account of currently available results about regularization methods for both linear and nonlinear ill-posed problems. Overview

Irmela Hijiya-Kirschnereit brings her sophisticated literary methods and graceful method of analysis to this English translation of her book on the shishosetsu, one of the most important yet misunders

This comprehensive reference presents the latest techniques for numerical analysis of forming operations. This is the perfect tool for those who wish to investigate new analytical methods for forming.

Focusing on the period of Milton Friedman's collaboration with Anna J. Schwartz, from 1948 to 1991, this 1996 work examines the history of debates between Friedman and his critics over money's causal role in business cycles. Professor Hammond shows that critics' reactions were grounded in two distinctive features of Friedman and Schwartz's way of doing economic analysis - their National Bureau business cycle methods and Friedman's Marshallian methodology. With the post-war dominance of Cowles Commission methods and Walrasian methodology, Friedman and Schwartz's monetary economics appeared to contemporary critics to be 'measurement without theory'. Drawing extensively upon unpublished materials, Professor Hammond's treatment offers new insights on Milton Friedman's attempts to settle debates with his critics and his eventual recognition of the methodological impediments. The book will interest monetary economists and macroeconomists, as well as historians of economics and methodologists

This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded as dynamical systems controlled by synaptic matrices, and set-valued analysis that plays a natural and crucial role in qualitative analysis and simulation. This allows many examples of neural networks to be presented in a unified way. In addition, several results on the control of linear and nonlinear systems are used to obtain a 'learning algorithm' of pattern classification problems, such as the back-propagation formula, as well as learning algorithms of feedback regulation laws of solutions to control systems subject to state constraints. This book will be of value to anyone with an interest in neural networks and cognitive systems.

The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at undergraduate level. It was widely praised for the clarity of the writing and for the unique and effective way in which the authors presented the basic ideas. These same qualities characterise this revised and expanded second edition. Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. This second edition includes additional material on the analysis and characterisation of chaotic data, and applications of chaos. This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second and third year level.

Argumentation theory is a distinctly multidisciplinary field of inquiry. It draws its data, assumptions, and methods from disciplines as disparate as formal logic and discourse analysis, linguistics a

Automatic control systems have become essential features in virtually every area of technology, from machine tools to aerospace vehicles. This book is a comprehensive, clearly written introduction to automatic control engineering. The author begins with the fundamentals of modelling mechanical, electrical, and electromechanical systems in the state variable format. The emphasis is on classical feedback control theory and design, and their application to practical electromechanical and aerospace problems. Following a careful grounding in classical control theory, the author introduces modern control theory, including digital control and nonlinear system analysis. Over 230 problems help the reader apply principles discussed in the text to practical engineering situations. Engineering students and practising engineers will find all they need to know about control system analysis and design in this valuable text.

This book offers an original interpretation of the history of falling fertilities in Britain between 1860 and 1940. It integrates the approaches of the social sciences and of demographic, feminist, and labour history with intellectual, social, and political history. It exposes the conceptual and statistical inadequacies of the orthodox picture of a national, unitary class-differential fertility decline, and presents an entirely new analysis of the famous 1911 fertility census of England and Wales. Surprising and important findings emerge concerning the principal methods of birth control: births were spaced from early on in marriage; and sexual abstinence by married couples was a far more significant practice than previously imagined. The author presents a new general approach to the study of fertility change, raising central issues concerning the relationship between history and social science.

A unique guide to the application and theory of photothermal spectroscopy.This book debunks the myth that photothermal spectroscopy is too complicated for practical application to chemical analysis, a

Information systems development is not merely a technical intervention but involves social and ethical dilemmas that affect the human, social and organizational domains. To demonstrate this point, the authors conduct a thorough and substantive description and analysis of the conceptual and philosophical underpinnings of systems development. In particular they analyse a number of systems development methodologies including structured methods, prototyping, ETHICS and Soft Systems Methodology to reveal the underlying conceptual and philosophical foundations. The book provides an in-depth analysis of data modelling theory and its links with theories of language and cognition. It offers a framework to describe and analyse different systems development approaches and to explain their strengths and weaknesses. The book is aimed at graduate students taking courses in information systems and data modelling, but will also appeal to information systems managers and professionals for whom the summ

Romulus founded Rome - but why does the myth give him a twin brother Remus, who is killed at the moment of the foundation? This mysterious legend has been oddly neglected. Roman historians ignore it as irrelevant to real history; students of myth concentrate on the more glamorous mythology of Greece. In this book, Professor Wiseman provides, for the first time, a detailed analysis of all the variants of the story, and a historical explanation for its origin and development. His conclusions offer important new insights, both into the history and ideology of pre-imperial Rome and into the methods and motives of myth-creation in a non-literate society. In the richly unfamiliar Rome of Pan, Hermes and Circe the witch-goddess, where a general grows miraculous horns and prophets demand human sacrifice, Remus stands for the unequal struggle of the many against the powerful few.

This book examines the theory of boundary value problems for elliptic systems of partial differential equations, a theory which has many applications in mathematics and the physical sciences. The aim is to 'algebraize' the index theory by means of pseudo-differential operators and methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. This book is ideal for use in graduate-level courses on partial differential equations, elliptic systems, pseudo-differential operators and matrix analysis. Since many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises.

Serious Money offers detailed analysis of the relationship between fundraising methods and contributing decisions in presidential nomination campaigns, based largely upon newly conducted surveys of contributors to both the 1988 and 1992 campaigns. Brown, Powell and Wilcox explore the fundamental differences detween direct mail solicitation and personal-solicitation networks, and how candidate resources dictate the use of unique methods of solicitation. Candidate resources analysed include home state power bases, access to national party networks and the national legislative agenda, congressional office, social identity, and ideological proximity. With respect to contributing decisions, the book focuses on the three fundamental sources of the decision to contribute: the purposive, solidary, and material motives of contributors.

This book, which is published in two volumes, studies heat transfer problems by modern numerical methods. Basic mathematical models of heat transfer are considered. The main approaches to the analysis

The aim of the book is to introduce the reader to the kinetic analysis of a wide range of biological processes at the molecular level. It is intended to show that the same approach can be used to resolve the number of steps in enzyme reactions, muscle contraction, visual perception and ligand binding receptors that trigger other physiological processes. Attention is also given to methods for characterizing these steps in chemical terms. Although the treatment is mainly theoretical, a wide range of examples and experimental techniques are also introduced and an historical approach is used to demonstrate the development of the theory and experimental techniques of kinetic analysis in biology.

The continuing development of automated production methods, combined with increasing competition from low-wage developing economies, is likely to reduce yet further the scope for the employment of low-skilled and inexperienced personnel in advanced economies. Higher standards of schooling and of vocational training are now widely recognised as essential. Based on visits by expert teams over the last ten years to matched samples of manufacturing plants, as well as to schools and vocational colleges in Britain and the European Continent, this book provides a realistic analysis of what needs to be done. The emphasis is on the need to expand, not the proportion of the workforce with university qualifications, but those with craft and vocational qualifications. The findings of this research have been influential in the development of government policies, and the author explains why these policies need to move even further, and in which directions they must next move.

The aim of the book is to introduce the reader to the kinetic analysis of a wide range of biological processes at the molecular level. It is intended to show that the same approach can be used to resolve the number of steps in enzyme reactions, muscle contraction, visual perception and ligand binding receptors that trigger other physiological processes. Attention is also given to methods for characterizing these steps in chemical terms. Although the treatment is mainly theoretical, a wide range of examples and experimental techniques are also introduced and an historical approach is used to demonstrate the development of the theory and experimental techniques of kinetic analysis in biology.

Acta Numerica has established itself as the prime forum for the presentation of definitive reviews of numerical analysis topics. The invited review papers, by leaders in their respective fields, allow researchers and graduate students alike quickly to grasp trends and developments. Highlights of the 1995 issue include articles on sequential quadratic programming, mesh adaption, free boundary problems and particle methods in continuum computations.

The second edition of this very successful and authoritative set of tables still benefits from clear typesetting, which makes the figures easy to read and use. It has, however, been improved by the addition of new tables that provide Bayesian confidence limits for the binomial and Poisson distributions, and for the square of the multiple correlation coefficient, which have not been previously available. The intervals are the shortest possible, consistent with the requirement on probability. Great care has been taken to ensure that it is clear just what is being tabulated and how the values may be used; the tables are generally capable of easy interpolation. The book contains all the tables likely to be required for elementary statistical methods in the social, business and natural sciences. It will be an essential aid for teachers, researchers and students in those subjects where statistical analysis is not wholly carried out by computers.