Methods of Nonlinear Analysis

Independent Component Analysis (ICA) has recently become an important tool for modelling and understanding empirical datasets. It is a method of separating out independent sources from linearly mixed data, and belongs to the class of general linear models. ICA provides a better decomposition than other well-known models such as principal component analysis. This self-contained book contains a structured series of edited papers by leading researchers in the field, including an extensive introduction to ICA. The major theoretical bases are reviewed from a modern perspective, current developments are surveyed and many case studies of applications are described in detail. The latter include biomedical examples, signal and image denoising and mobile communications. ICA is discussed in the framework of general linear models, but also in comparison with other paradigms such as neural network and graphical modelling methods. The book is ideal for researchers and graduate students in the field.

Combinatorial data analysis (CDA) refers to a wide class of methods for the study of relevant data sets in which the arrangement of a collection of objects is absolutely central. The focus of this mon

Written for mathematicians working in nonlinear analysis, calculus of variations, Hamiltonian systems, and symplectic geometry, this study explores existence and multiplicity questions for periodic so

Materials science has emerged as one of the central pillars of the modern physical sciences and engineering, and is now even beginning to claim a role in the biological sciences. A central tenet in the analysis of materials is the structure-property paradigm, which proposes a direct connection between the geometric structures within a material and its properties. The increasing power of high-speed computation has had a major impact on theoretical materials science and has permitted the systematic examination of this connection between structure and properties. In this graduate textbook, Rob Phillips examines the various methods that have been used in the study of crystals, defects and microstructures and that have made such computations possible. A second key theme is the presentation of recent efforts that have been developed to treat problems involving either multiple spatial or temporal scales simultaneously.

Materials science has emerged as one of the central pillars of the modern physical sciences and engineering, and is now even beginning to claim a role in the biological sciences. A central tenet in the analysis of materials is the structure-property paradigm, which proposes a direct connection between the geometric structures within a material and its properties. The increasing power of high-speed computation has had a major impact on theoretical materials science and has permitted the systematic examination of this connection between structure and properties. In this graduate textbook, Rob Phillips examines the various methods that have been used in the study of crystals, defects and microstructures and that have made such computations possible. A second key theme is the presentation of recent efforts that have been developed to treat problems involving either multiple spatial or temporal scales simultaneously.

The middle-class condition, seen during the twentieth century as both the symbol of progress and order and the means to achieve it, has largely evaded historical analysis. Blending historical methods

* What do we mean by discourse?* What are the different conceptions of discourse and methods of discourse analysis in the contemporary social sciences?* How can this concept help to clarify key theore

Natural Language Semantics discusses fundamental concepts for linguistic semantics. This book combines theoretical explanations of several methods of inquiry with detailed semantic analysis and emphas

Natural Language Semantics discusses fundamental concepts for linguistic semantics. This book combines theoretical explanations of several methods of inquiry with detailed semantic analysis and emphas

Optimal Reliability Design, first published in 2000, provides a detailed introduction to systems reliability and reliability optimization. Techniques for maximizing system reliability are described, focusing on component reliability enhancement and redundancy arrangement. The authors present several case studies and show how optimization techniques are applied in practice. They also pay particular attention to finding methods that give the optimal trade-off between reliability and cost. The book begins with a review of key background material, and a discussion of a range of optimization models. The authors go on to cover optimization tools, such as heuristics, discrete optimization, nonlinear programming, mixed integer programming, optimal arrangement, and metaheuristic algorithms. They also describe the computational implementation of these tools. Many numerical examples are included, and the book contains over 180 homework exercises. It is suitable as a textbook for graduate-level co

This pioneering book is based upon very extensive analysis of the famous 1851 Census of Religious Worship and earlier sources such as the 1676 Compton Census. The authors stress contextual and regional understanding of religion. Among the subjects covered for all of England and Wales are the geography of the Church of England, Roman Catholicism, the old and new dissenting denominations, the spatial complementarity of denominations, and their importance for political history. A range of further questions are then analysed, such as regional continuities in religion, the growth of religious pluralism, Sunday schools and child labour during industrialisation, free and appropriated church sittings, landownership and religion, and urbanisation and regional 'secularisation'. This book's advanced methods and findings will have far-reaching influence within the disciplines of history, historical and cultural geography, religious sociology and in the social science community general.

This book demonstrates that the state-contingent approach provides the best way to think about all problems in the economics of uncertainty, including problems of consumer choice, the theory of the firm, and principal agent relationships. The authors demonstrate that dual methods apply under uncertainty and that the dual representations can be developed for stochastic technologies. Moreover, proper exploitation of the properties of alternative primal and dual representations of preferences allows analysts to generalize and extend the results of the existing literature on preferences under uncertainty, thus making expected-utility theory largely superfluous for many decisions. These insights open the way for developments in the basic theory of production under uncertainty, the theory of hedging behavior, the analysis of agency problems and the theory of production insurance.

This book deals with automorphism groups of compact Riemann surfaces, of genus at least two, viewed as factor groups of Fuchsian groups. The author uses modern methods from computational group theory and representation theory, providing classifications of all automorphism groups up to genus 48. The book also classifies the ordinary characters for several groups, arising from the action of automorphisms on the space of holomorphic abelian differentials of a compact Reimann surface. This book is suitable for graduate students and researchers in group theory, representation theory, complex analysis and computer algebra.

This book demonstrates that the state-contingent approach provides the best way to think about all problems in the economics of uncertainty, including problems of consumer choice, the theory of the firm, and principal agent relationships. The authors demonstrate that dual methods apply under uncertainty and that the dual representations can be developed for stochastic technologies. Moreover, proper exploitation of the properties of alternative primal and dual representations of preferences allows analysts to generalize and extend the results of the existing literature on preferences under uncertainty, thus making expected-utility theory largely superfluous for many decisions. These insights open the way for developments in the basic theory of production under uncertainty, the theory of hedging behavior, the analysis of agency problems and the theory of production insurance.

Many man-made materials and naturally occurring substances are aggregates of crystals, or polycrystals, with a non-random distribution of orientations. In such textured polycrystals, many macroscopic physical properties are anisotropic, i.e. they depend on direction. This book is about the measurement and analysis of textures, the prediction of polycrystal properties from measured textures and known single crystal properties, and the prediction of the development of texture and the ensuing anisotropic properties during elastic and plastic deformation. It also gives an overview of observed textures in metals, ceramics and rocks. There is a balance between theoretical concepts and experimental techniques. The book addresses several issues. Part I provides tools and describes methods to obtain quantitative data on textures of polycrystals. It should be of interest to experimentalists. Part II emphasizes modeling of deformation and incorporates theoretical concepts of mechanics. Part III i

Recently molecular biology has undergone unprecedented development generating vast quantities of data needing sophisticated computational methods for analysis, processing and archiving. This requireme

Recently molecular biology has undergone unprecedented development generating vast quantities of data needing sophisticated computational methods for analysis, processing and archiving. This requirem

This book presents and analyses vortex methods as a tool for the direct numerical simulation of incompressible viscous flows. Vortex methods have matured, offering an interesting alternative to finite difference and spectral methods for high-resolution numerical solutions of the Navier–Stokes equations. Research in the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character that was the motivation for their introduction. Scientists working in the areas of numerical analysis and fluid mechanics will benefit from this book, which may serve both communities as both a reference monograph and a textbook for computational fluid dynamics courses.

Multiple regression, linear modelling, and multivariate analysis are among the most useful statistical methods for the elucidation of complicated data, and all of them are most easily explained in mat

This book provides a lucid and comprehensive introduction to the differential geometric study of partial differential equations. It was the first book to present substantial results on local solvability of general and, in particular, nonlinear PDE systems without using power series techniques. The book describes a general approach to systems of partial differential equations based on ideas developed by Lie, Cartan and Vessiot. The most basic question is that of local solvability, but the methods used also yield classifications of various families of PDE systems. The central idea is the exploitation of singular vector field systems and their first integrals. These considerations naturally lead to local Lie groups, Lie pseudogroups and the equivalence problem, all of which are covered in detail. This book will be a valuable resource for graduate students and researchers in partial differential equations, Lie groups and related fields.

Although nearly all major social science departments offer graduate students training in quantitative methods, the typical sequencing of topics generally delays training in regression analysis and oth

Safety through design is defined as the integration of hazard analysis and risk assessment methods early in the design and engineering stages and the taking of the action necessary so that the risks o

An overview of the theory and application of linear and nonlinear mixed-effects models in the analysis of grouped data, such as longitudinal data, repeated measures, and multilevel data. The authors p

When a mechanical system consists of two or more coupled vibrating components, the vibration of one of the component subsystems may destabilize the motion of the other components. This destabilization effect is called autoparametric resonance. It is a concept that has important engineering applications. For example, vibrations in a pipeline induced by high-speed gas flows must be considered in the design and operation of the pipeline. This book is the first completely devoted to the subject of autoparametric resonance in an engineering context. Using the tools of nonlinear analysis, the authors show how to carry out the first crucial step, that is, how to determine the regions of parameter space where the semi-trivial solution is unstable. They describe what happens in these regions and then discuss non-trivial solutions and their stability. The study of autoparametric systems is a lively area of current research in engineering and applied mathematics, and this book will appeal to gra

What are the best ways to do research on the psychology of women and gender? Within feminist psychology, there is a great deal of methodological creativity and diversity. This volume, first published in 2000, highlights how familiar methods such as focus groups can be brought to bear on feminist issues. It demonstrates less common methods, such as Q-sort, phenomenological analysis, concept mapping, and discourse analysis. Moreover, it explores the role of personal values, interpersonal dynamics, and sociopolitical influences on the research process. Over 60 international contributors share insights into adolescent girls' and adult women's sexuality, violence and its prevention, life patterns and narratives, the teaching-research nexus, gender and race in clinical practice, and more. Included is a comprehensive resource guide for research, publication and teaching on methodological diversity.

Scientists tend to take the thought processes that drive their research for granted, often learning them indirectly by observing first their supervisors and then their colleagues. This book emphasises the advantages of being explicit about these thought processes and aims to help those undertaking ecological research to develop a critical attitude to approaching a scientific problem and constructing a procedure for assessment. The outcome is a text which provides a framework for understanding methodological issues and which assists with the effective definition and planning of research. As such it represents a unique resource for anyone embarking on their research career. It also provides a valuable source of information for those more experienced researchers who are seeking to strengthen the methodology underlying their studies or who have an interest in the analysis of research methods in ecology.

Lets you target the specific information you need quickly and easily, so you can stay in the lab and out of the library. This invaluable database also available on CD-ROM gives you fast, hands-on acc

Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provid

This introductory text covers basic electronics and the behavior of passive components, circuit analysis and systematic troubleshooting. The analytical methods used are strongly based on Ohm's and Ki

Contrasts are statistical procedures for asking focused questions of data. Compared to diffuse or omnibus questions, focused questions are characterized by greater conceptual clarity and greater statistical power when examining those focused questions. If an effect truly exists, we are more likely to discover it and to believe it to be real when asking focused questions rather than omnibus ones. Researchers, teachers of research methods and graduate students will be familiar with the principles and procedures of contrast analysis, but will also be introduced to a series of newly developed concepts, measures, and indices that permit a wider and more useful application of contrast analysis. This volume takes on this new approach by introducing a family of correlational effect size estimates.

Contrasts are statistical procedures for asking focused questions of data. Compared to diffuse or omnibus questions, focused questions are characterized by greater conceptual clarity and greater statistical power when examining those focused questions. If an effect truly exists, we are more likely to discover it and to believe it to be real when asking focused questions rather than omnibus ones. Researchers, teachers of research methods and graduate students will be familiar with the principles and procedures of contrast analysis, but will also be introduced to a series of newly developed concepts, measures, and indices that permit a wider and more useful application of contrast analysis. This volume takes on this new approach by introducing a family of correlational effect size estimates.

Computer vision aims to detect and reconstruct features of surfaces from the images produced by cameras, in some way mimicking the way in which humans reconstruct features of the world around them by using their eyes. In this book the authors describe research in computer vision aimed at recovering the 3D shape of surfaces from image sequences of their 'outlines'. They provide all the necessary background in differential geometry (assuming knowledge of elementary algebra and calculus) and in the analysis of visual motion, emphasising intuitive visual understanding of the geometric techniques with computer-generated illustrations. They also give a thorough introduction to the mathematical techniques and the details of the implementations and apply the methods to data from real images using the most current techniques.

This book concerns the use of concepts from statistical physics in the description of financial systems. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully developed turbulent fluids. These concepts are then applied to financial time series. The authors also present a stochastic model that displays several of the statistical properties observed in empirical data. Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling permit an understanding of the global behaviour of economic systems without first having to work out a detailed microscopic description of the system. Physicists will find the application of statistical physics concepts to economic systems interesting. Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number o

Lets you target the specific information you need quickly and easily-so you can stay in the lab and out of the library.This invaluable database-also available on CD-ROM-gives you fast, hands-on access

Lets you target the specific information youneed quickly and easily-so you can stay inthe lab and out of the libraryThis invaluable database-also available on CD-ROM-gives you fast, hands-on access to

An exploration of the features and methods of Imami exegesis. Principally, it offers a description and analysis of the major tenets of Imami doctrine, as reflected in the earliest Imami works of exege

Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be

For graduate students looking for an introduction to this area of nonlinear analysis, Liu (mathematics, Stanford U.) offers a self-contained study of shock waves explaining the new wave interactions f

This concise guide covers the fundamental aspects of the numerical analysis, basing upon it the construction of its routines for solving nonlinear equations, linear and nonlinear systems of equations,

Proven statistical reliability analysis methods-available for the first time to engineers in the West While probabilistic methods of system reliability analysis have reached an unparalleled degree of