Methods of Nonlinear Analysis

The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course. The authors begin by describing the wide array of scientific and mathematical questions that dynamics can address. They then use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the leve

The focus of this book is on algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions, also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon, and Camassa-Holm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The formalism presented includes trace formulas, Dubrovin-type initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces). The presentation is rigorous, detailed, and self-contained, with ample background material provided in various appendices. Detailed notes for each chapter together with an exh

An important problem that arises in many scientific and engineering applications is that of approximating limits of infinite sequences which in most instances converge very slowly. Thus, to approximate limits with reasonable accuracy, it is necessary to compute a large number of terms, and this is in general costly. These limits can be approximated economically and with high accuracy by applying suitable extrapolation (or convergence acceleration) methods to a small number of terms. This state-of-the art reference for mathematicians, scientists and engineers is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. The methods discussed are geared toward common problems in scientific and engineering disciplines. It differs from existing books by concentrateing on the most powerful nonlinear methods, presenting in-depth treatments of them, and showing which methods are most effective for different classe

Software engineering is becoming more procedural and controlled, but the estimation of IT projects is still regarded as a 'black art'. IT Project Estimation shows why it doesn't have to be. In this concise, easy-to-read guide, author Paul Coombs provides practical, detailed advice on IT project estimation. He shows why accurate estimates are needed, what different estimating methods can be used, and how to analyse the risks in order to make appropriate contingency allowances. He also covers pricing and billing strategies, and how experience of previous projects can be leveraged. Central to the book is a template for a cost model that incorporates task estimates, schedules, staff roles and costs, risk analysis, fixed costs, billing, and cashflow. Template Excel spreadsheets are included on the accompanying CD-ROM. Putting everything into practice, the end of the book is a complete case study, showing exactly how a simple example can be scaled up to a real-life problem. If you are an IT

Drawing on the theoretical methods of such writers as Caroline Walker Bynum and others who apply feminist and gender approaches to their analysis of the Middle Ages, Heng provides a thought-provoking

Space-time coding is a technique that promises greatly improved performance in wireless networks by using multiple antennas at the transmitter and receiver. Space-Time Block Coding for Wireless Communications, first published in 2003, is an introduction to the theory of this technology. The authors develop the topic using a unified framework and cover a variety of topics ranging from information theory to performance analysis and space-time coding methods for both flat and frequency-selective fading multiple-antenna channels. The authors concentrate on key principles rather than specific practical applications, and present the material in a concise and accessible manner. Their treatment reviews the fundamental aspects of multiple-input, multiple-output communication theory, and guides the reader through a number of topics at the forefront of research and development. The book includes homework exercises and is aimed at graduate students and researchers working on wireless communication

In this book, first published in 2003, the reader is provided with a tour of the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, together with some of their main applications. The author assumes only that the reader has a basic background in functional analysis, and the presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will also want this book for their library since the author illustrates the power of methods he has developed with new and simpler proofs of some of the major results in the area, many of which have not appeared earlier in the literature. An indispensable introduction to the theory of operator spaces for all who want to know more.

Spatial Data Analysis: Theory and Practice, first published in 2003, provides a broad ranging treatment of the field of spatial data analysis. It begins with an overview of spatial data analysis and the importance of location (place, context and space) in scientific and policy related research. Covering fundamental problems concerning how attributes in geographical space are represented to the latest methods of exploratory spatial data analysis and spatial modeling, it is designed to take the reader through the key areas that underpin the analysis of spatial data, providing a platform from which to view and critically appreciate many of the key areas of the field. Parts of the text are accessible to undergraduate and master's level students, but it also contains sufficient challenging material that it will be of interest to geographers, social and economic scientists, environmental scientists and statisticians, whose research takes them into the area of spatial analysis.

The volume describes analytical methods used in the analysis of macromolecular materials and elucidation of their structure. The techniques described reflect some of the recent advances which have bee

This book analyzes, with unprecedented breadth and coverage, the development, maturation, growth, and sudden decline of a distinctive, regional urban economic system that developed along the upper Mississippi River north of St. Louis during the middle third of the nineteenth century. Between 1820 and the Civil War the upper Mississippi River valley was at the center of national and international attention. At the edge of the northern frontier, this area, known as 'The Great West,' was the destination of hundreds of thousands of immigrants from the East and from northern Europe. To many, its rich lands, temperate climate, and vast rivers offered an opportunity to establish a better life, as well as a chance to enter, if desired, the mainstream of American life. Drawing from a variety of methods used in historical geography, economic history, systems analysis, and social and urban history, Timothy Mahoney analyzes how early settlement patterns were affected by experience, climate, and ge

"This book will let you see the little-known but effective trading tactics and methods of today's top market makers."--Technical Analysis of Stocks and CommoditiesActive traders must get inside the he

Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of con

Offers a current analysis of mathematical methods used in the identification of models for hydrologic forecasting, design, and water resources management. The volume's 24 contributions address calibra

Microanalysis of Parchment presents sampling techniques and non-destructive, microanalytical and semi-microanalytical methods for the analysis and testing of historic parchment based on visual, micros

This volume collects seven of Marc Nerlove's previously published, classic essays on panel data econometrics written over the past thirty-five years, together with a cogent essay on the history of the subject, which began with George Biddell Airey's monograph published in 1861. Since Professor Nerlove's 1966 Econometrica paper with Pietro Balestra, panel data and methods of econometric analysis appropriate to such data have become increasingly important in the discipline. The principal factors in the research environment affecting the future course of panel data econometrics are the phenomenal growth in the computational power available to the individual researcher at his or her desktop and the ready availability of data sets, both large and small, via the Internet. The best way to formulate statistical models for inference is motivated and shaped by substantive problems and understanding of the processes generating the data at hand to resolve them. The essays illustrate both the role

Cylindrical arrays lie at the heart of the antenna systems of most major radio communication systems, including broadcasting networks, cellular 'phone systems and radar. In this book, the authors present practical theoretical methods for determining current distributions, input admittances and field patterns of a wide variety of cylindrical antennas, including the isolated antenna, the two-element array, the circular array, curtain arrays, Yagi and log-periodic arrays, planar arrays and three-dimensional arrays. Coverage includes analysis of horizontal antennas over, on and in the earth and sea, large resonant arrays of electrically short dipoles and a chapter on the theory and techniques of experimental measurement. Written by three of the leading engineers in the field, and based on world-class research carried out at Harvard over the last forty years, Cylindrical Antennas and Arrays is destined to become established as the basic reference for practising engineers and advanced studen

This thoughtful and beautifully written book demonstrates compellingly that emotions are central to personality development across the lifespan. Carol Magai and Jeannette Haviland-Jones draw on a wealth of textual and film material to forge an original empirical and theoretical analysis of the dynamics of emotion in human development. For its content, the work examines the lives of three mid-century psychologists, Carl Rogers, Albert Ellis, and Fritz Perls. Each man adopted a unique stance on the question of emotion in personality and in therapeutic interventions and, tellingly, the therapeutic methods they developed necessarily reflected their own emotional dynamics. Drawing on the most important research in clinical, social, and personality psychology, the authors reveal the pervasive influence of emotional organization in the lives of these individuals. Having presented a new approach to personology, autobiography, autobiography, narrative studies, psychotherapy and the theory of em

Coming at a time of profound change in the global conditions under which American organized labor exists, The Future of the American Labor Movement, first published in 2002, describes and analyzes labor's strategic alternatives. The analysis is broadly cast, taking into account ideas that range from the current European Social Dialogue to the methods of the nineteenth-century American Knights of Labor. There are a number of intriguing strategies that have potential for reviving the labor movement in the United States, of which worker ownership and labor capital strategies are examples. This book demonstrates the necessity for a number of diverse strategies to be pursued simultaneously. For this to work, one has to think in terms of a broad movement of labor, consisting of diverse parts, held together by a clear idea of its purpose and a new structure.

In a comprehensive analysis of rivers, this text scrutinizes select methods underlining both theory and engineering applications, emphasizing the mechanics of flood wave propagation and sediment trans

Covers all aspects of astrology, including interpretation and analysis of all the signs and planets along with information on applying psychological methods to astrology.

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.

This title is part of a series that aims to present timely, scholarly work on multiple levels of analysis, multi-level theory, research, and methods. The focus is on 'critical essays', theoretical wor

This book provides a thorough introduction to one of the most efficient approximation methods for the analysis and solution of problems in theoretical physics and applied mathematics. It is written with practical needs in mind and contains a discussion of 50 problems with solutions, of varying degrees of difficulty. The problems are taken from quantum mechanics, but the method has important applications in any field of science involving second order ordinary differential equations. The power of the asymptotic solution of second order differential equations is demonstrated, and in each case the authors clearly indicate which concepts and results of the general theory are needed to solve a particular problem. This book will be ideal as a manual for users of the phase-integral method, as well as a valuable reference text for experienced research workers and graduate students.

Much of ancient history can only be written thanks to evidence supplied by Plutarch. His historical methods and qualities were for long subjected to little systematic analysis. However, in recent deca

The only method of circuit analysis known to most engineers and students is nodal or loop analysis. Although this works well for obtaining numerical solutions, it is almost useless for obtaining analytical solutions in all but the simplest cases. In this unusual 2002 book, Vorpérian describes remarkable alternative techniques to solve, almost by inspection, complicated linear circuits in symbolic form and obtain meaningful analytical answers for any transfer function or impedance. Although not intended to replace traditional computer-based methods, these techniques provide engineers with a powerful set of tools for tackling circuit design problems. They also have great value in enhancing students' understanding of circuit operation, making this an ideal course book, and numerous problems and worked examples are included. Originally developed by Professor David Middlebrook and others at Caltech (California Institute of Technology), the techniques described here are now widely taught at

This definitive handbook uniquely documents the 2001 UK Census from both theoretical and practical perspectives. Collating a wide range of indicators, classification and analysis methods based on the

The concept of modelling using graph theory has its origin in several scientific areas, notably statistics, physics, genetics, and engineering. The use of graphical models in applied statistics has in

Contain s current methods of analysis for new formulations of cosmetics, perfumes, creams, and lotions!With contributions from world-renowned experts in the field, Topical Absorption of Dermatological

This book examines qualitative and quantitative methods for nonlinear differential equations and treats integrability and nonintegrability theory. Starting from the idea of a constant of motion for si

This book presents the general theory and basic methods of linear and nonlinear stochastic systems (StS). It outlines StS structural theory, including direct numerical methods, methods of normalizatio

This book provides a clear and detailed survey of basic neural network architectures and learning rules. In it, the authors emphasize mathematical analysis of networks, methods for training netw

This survey of recent work on Herodotus, Thucydides, and Polybius focuses on new developments in the study of Greek historiography and synthesises some of the most important research from the last thirty years. There is a detailed treatment of each writer, with an emphasis on analysis of the historians' sources, their narrative methods, and their use of speeches. Also examined are the structure and themes of each man's work, together with consideration of the way each historian employs characterisation. The book provides a full bibliography of recent work done mainly (but not exclusively) in English, and suggests future directions that the study of these historians may take. It will be of interest to upper-level students and scholars who would like an overview of recent trends in the study both of the historians themselves and of ancient Greek historiography in general.

Designed to provide an up-to-date broad coverage of pertinent topics concerning water resource engineering. This book focuses on modern computer-based modeling and analysis methods, illustrating recen

Almost every artifact in archaeological analysis originates in or on the ground. While there are elaborate methods for extracting and analyzing artifacts, treatment of the matrix within which they are

This book presents a study of co-offering relations among youths under twenty-one suspected of criminal offences in Stockholm during 1991–5. In total, the study includes just over 22,000 individuals suspected of around 29,000 offences. Jerzy Sarnecki employs the methods of network analysis which makes it possible to study the ties, social bonds, interactions, differential associations and connections that are central to many of the sociologically oriented theories on the aetiology of crime. Up to now, network analysis has been used only rarely in the criminological context. The book discusses many aspects of Stockholm's delinquent networks such as the existence of delinquent gangs and a criminal underworld, the durability of delinquent relations, and the choice of co-offenders with respect to sex, age, residential location, ethnic background and earlier delinquent experience. It also considers the effects of societal intervention on criminal networks. This unique study will appeal to a

In the clinical neurosciences, decision-making becomes ever more complicated because of rapidly emerging new diagnostic tests and treatments and increasing demands from patients to participate in their management. This concise but wide-ranging handbook reviews the epidemiology of neurological disease and the treatment and prognosis of all major diseases of the nervous system. Part one offers essential guidance for clinicians to quantitative methods in research, including genetic epidemiology, decision analysis, meta-analysis, outcomes research and survival analysis, and thus provides a good understanding of the evidence underlying clinical management. The second part is devoted to individual neurological diseases, covering etiology, diagnosis, prognosis, interventions, and implications for clinical practice. With contributions from leading international authorities, this book is an invaluable guide to clinical decision-making for neurologists and others involved in the management of ne

The control of vibrating systems is a significant issue in the design of aircraft, spacecraft, bridges and high-rise buildings. This 2001 book discusses the control of vibrating systems, integrating structural dynamics, vibration analysis, modern control and system identification. Integrating these subjects is an important feature in that engineers will need only one book, rather than several texts or courses, to solve vibration control problems. The book begins with a review of basic mathematics needed to understand subsequent material. Chapters then cover more recent and valuable developments in aerospace control and identification theory, including virtual passive control, observer and state-space identification, and data-based controller synthesis. Many practical issues and applications are addressed, with examples showing how various methods are applied to real systems. Some methods show the close integration of system identification and control theory from the state-space perspec

A concise survey of compliant mechanisms-from fundamentals to state-of-the-art applicationsThis volume presents the newest and most effective methods for the analysis and design of compliant mechanism

What do variables really tell us? When exactly do inventions occur? Why do we always miss turning points as they transpire? When does what doesn't happen mean as much, if not more, than what does? Andrew Abbott considers these fascinating questions in Time Matters, a diverse series of essays that constitutes the most extensive analysis of temporality in social science today. Ranging from abstract theoretical reflection to pointed methodological critique, Abbott demonstrates the inevitably theoretical character of any methodology.Time Matters focuses particularly on questions of time, events, and causality. Abbott grounds each essay in straightforward examinations of actual social scientific analyses. Throughout, he demonstrates the crucial assumptions we make about causes and events, about actors and interaction and about time and meaning every time we employ methods of social analysis, whether in academic disciplines, market research, public opinion polling, or even evaluation researc

Mechanisms are fundamental components of machines. They are used to transmit forces and moments and to manipulate objects in industrial machinery, robots, automobiles, aircraft, mechatronics devices and biomechanical systems. A knowledge of the kinematic and dynamic properties of mechanisms is essential for their design and control. This book describes methods and algorithms for the analysis of kinematic systems. Beginning with basic concepts, the book then discusses a variety of problem-solving approaches and computational techniques. Its distinctive feature is its focus on the contour equation as a powerful, computationally efficient tool that will help the reader to design complex spatial mechanisms. This handy text will be useful for senior or graduate students, researchers and practising engineers working in robotics, vehicle dynamics, mechatronics and machine design.