Basic Methods of Linear Functional Analysis

This text presents a general introduction to soft tissue biomechanics. One of its primary goals is to introduce basic analytical, experimental and computational methods. In doing so, it enables reader

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 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

Wittgenstein once wrote that 'The philosopher strives to find the liberating word, that is, the word that finally permits us to grasp what up until now has intangibly weighed down our consciousness'. Would Wittgenstein have been willing to describe the Tractatus as an attempt to find 'the liberating word'? This is the basic contention of this strikingly innovative study of the Tractatus. Matthew Ostrow argues that, far from seeking to offer a new theory in logic in the tradition of Frege and Russell, Wittgenstein from the very beginning viewed all such endeavors as the ensnarement of thought. Providing a lucid and systematic analysis of the Tractatus, he argues that Wittgenstein's ultimate aim is to put an end to philosophy itself. He also highlights the intrinsic obstacles to any kind of interpretation that claims to summarize Wittgenstein's thought.

Wittgenstein once wrote that 'The philosopher strives to find the liberating word, that is, the word that finally permits us to grasp what up until now has intangibly weighed down our consciousness'. Would Wittgenstein have been willing to describe the Tractatus as an attempt to find 'the liberating word'? This is the basic contention of this strikingly innovative study of the Tractatus. Matthew Ostrow argues that, far from seeking to offer a new theory in logic in the tradition of Frege and Russell, Wittgenstein from the very beginning viewed all such endeavors as the ensnarement of thought. Providing a lucid and systematic analysis of the Tractatus, he argues that Wittgenstein's ultimate aim is to put an end to philosophy itself. He also highlights the intrinsic obstacles to any kind of interpretation that claims to summarize Wittgenstein's thought.

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.

This 2002 book presents the reader with mathematical tools taken from matrix calculus and zero-one matrices and demonstrates how these tools greatly facilitate the application of classical statistical procedures to econometric models. The matrix calculus results are derived from a few basic rules that are generalizations of the rules of ordinary calculus. These results are summarized in a useful table. Well-known zero-one matrices, together with some newer ones, are defined, their mathematical roles explained, and their useful properties presented. The basic building blocks of classical statistics, namely the score vector, the information matrix, and the Cramer-Rao lower bound, are obtained for a sequence of linear econometric models of increasing statistical complexity. From these are obtained interactive interpretations of maximum likelihood estimators, linking them with efficient econometric estimators. Classical test statistics are also derived and compared for hypotheses of intere

This was the first cross-over book into the history of science written by an historian of economics. It shows how 'history of technology' can be integrated with the history of economic ideas. The analysis combines Cold War history with the history of postwar economics in America and later elsewhere, revealing that the Pax Americana had much to do with abstruse and formal doctrines such as linear programming and game theory. It links the literature on 'cyborg' to economics, an element missing in literature to date. The treatment further calls into question the idea that economics has been immune to postmodern currents, arguing that neoclassical economics has participated in the deconstruction of the integral 'self'. Finally, it argues for an alliance of computational and institutional themes, and challenges the widespread impression that there is nothing else besides American neoclassical economic theory left standing after the demise of Marxism.

This was the first cross-over book into the history of science written by an historian of economics. It shows how 'history of technology' can be integrated with the history of economic ideas. The analysis combines Cold War history with the history of postwar economics in America and later elsewhere, revealing that the Pax Americana had much to do with abstruse and formal doctrines such as linear programming and game theory. It links the literature on 'cyborg' to economics, an element missing in literature to date. The treatment further calls into question the idea that economics has been immune to postmodern currents, arguing that neoclassical economics has participated in the deconstruction of the integral 'self'. Finally, it argues for an alliance of computational and institutional themes, and challenges the widespread impression that there is nothing else besides American neoclassical economic theory left standing after the demise of Marxism.

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

Presents data to challenge the idea that racism is in decline, argues that prejudice is inherent in how the human mind works and in how people respond to each other, and recommends methods of reconcil

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 offers a major reassessment of Leibniz's metaphysics. Christia Mercer has exposed the underlying doctrines of Leibniz's philosophy. By analysing Leibniz's early works she demonstrates that the metaphysics of pre-established harmony developed many years earlier than previously believed and for reasons which have not been understood. As a result of this analysis she has unearthed a philosophical school that Leibniz scholars have not recognized. A much deeper understanding of some of Leibniz's key doctrines emerges. Moreover, since the Leibniz that is revealed here does not fit neatly into the standard accounts of the history of philosophy and science, Christia Mercer's study will prompt scholars to reconsider their basic assumptions about early modern philosophy and science.

Mathematical modeling and computer simulation are useful tools for improving materials processing. While courses in materials processing have covered modeling, they have traditionally been devoted to one particular class of materials, that is, polymers, metals, or ceramics. This text offers a different approach, presenting an integrated treatment of metallic and non-metallic materials. The authors show that a common base of knowledge - specifically, the fundamentals of heat transfer and fluid mechanics - provides a unifying theme for these seemingly disparate areas. Emphasis is placed on understanding basic physical phenomena and knowing how to include them in a model. The book also treats selected numerical methods, showing the relationship between the physical system, analytical solution, and the numerical scheme. A wealth of practical, realistic examples are provided, as well as homework exercises. Students, and practising engineers who must deal with a wide variety of materials a

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

A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a measure-theoretical point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selecte

A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a measure-theoretical point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selecte

This 2001 book charts the evolution of clientelist practices in several western European countries. Through the historical and comparative analysis of countries as diverse as Sweden and Greece, England and Spain, France and Italy, Iceland and the Netherlands, the authors study both the 'supply-side' - the institutional context in which party leaders devise and implement their political strategies - and the 'demand-side' - the degree of 'empowerment' of civil society - of clientelism. This approach contends that clientelism is a particular mix of particularism and universalism, in which interests are aggregated at the level of the individual and his family 'particularism', but in which all interests can potentially find expression and accommodation 'universalism'. In contrast, 'consociationalism' and 'corporatism' are systems of interest representation in which interests are aggregated at the level of 'social pillar' or the functional association 'universalism', but in which not all in

This 2001 book charts the evolution of clientelist practices in several western European countries. Through the historical and comparative analysis of countries as diverse as Sweden and Greece, England and Spain, France and Italy, Iceland and the Netherlands, the authors study both the 'supply-side' - the institutional context in which party leaders devise and implement their political strategies - and the 'demand-side' - the degree of 'empowerment' of civil society - of clientelism. This approach contends that clientelism is a particular mix of particularism and universalism, in which interests are aggregated at the level of the individual and his family 'particularism', but in which all interests can potentially find expression and accommodation 'universalism'. In contrast, 'consociationalism' and 'corporatism' are systems of interest representation in which interests are aggregated at the level of 'social pillar' or the functional association 'universalism', but in which not all in

In this volume, the authors present theoretical explanations for a few basic problems connected with the propagation of extra wide band, short impulses in linear media, and with the propagation of

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

Traditional textbook analysis of international trade and labour movements typically ignores basic features of the welfare state. Similarly, the theory of finance and capital structure seldom treats international capital flows and their implications for central macroeconomic variables such as saving and investment. Under such circumstances, barriers to capital flows are undesirable. Despite the volumes that have been written on the markets and the desirability of regulating capital flows, there has been little work on the magnitude of distortions in these flows. This book fills a gap by combining elements from these disjointed parts of economics and presents them in an analytical framework. It lays the groundwork for the integration of capital, labour, and finance into a unified treatment of globalisation. The book is intended as a compact textbook for advanced undergraduate and graduate courses in international economics and public economics. It also serves as a reference for researche

Traditional textbook analysis of international trade and labour movements typically ignores basic features of the welfare state. Similarly, the theory of finance and capital structure seldom treats international capital flows and their implications for central macroeconomic variables such as saving and investment. Under such circumstances, barriers to capital flows are undesirable. Despite the volumes that have been written on the markets and the desirability of regulating capital flows, there has been little work on the magnitude of distortions in these flows. This book fills a gap by combining elements from these disjointed parts of economics and presents them in an analytical framework. It lays the groundwork for the integration of capital, labour, and finance into a unified treatment of globalisation. The book is intended as a compact textbook for advanced undergraduate and graduate courses in international economics and public economics. It also serves as a reference for researche

This book aims to bridge the gap between practising mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The book is the result of many years of research by the authors to analyse turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier–Stokes equations what had been arrived at earlier by phenomenological arguments. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience. Each chapter is accompanied by appendices giving full details of the mathematical proofs and subtleties. This unique presentation should ensure a volume of interest to mathematicians, engineers and physicists.

Advances in data collection and data storage techniques have enabled marketing researchers to study the individual characteristics of a large range of transactions and purchases, in particular the effects of household-specific characteristics. This 2001 book presents important and practically relevant quantitative models for marketing research. Each model is presented in detail with a self-contained discussion, which includes: a demonstration of the mechanics of the model, empirical analysis, real world examples, and interpretation of results and findings. The reader of the book will learn how to apply the techniques, as well as understand the methodological developments in the academic literature. Pathways are offered in the book for students and practitioners with differing numerical skill levels; a basic knowledge of elementary numerical techniques is assumed.

Coping with uncertainty is a necessary part of ordinary life and is crucial to an understanding of how the mind works. For example, it is a vital element in developing artificial intelligence that will not be undermined by its own rigidities. There have been many approaches to the problem of uncertain inference, ranging from probability to inductive logic to nonmonotonic logic. Thisbook seeks to provide a clear exposition of these approaches within a unified framework. The principal market for the book will be students and professionals in philosophy, computer science, and AI. Among the special features of the book are a chapter on evidential probability, which has not received a basic exposition before; chapters on nonmonotonic reasoning and theory replacement, matters rarely addressed in standard philosophical texts; and chapters on Mill's methods and statistical inference that cover material sorely lacking in the usual treatments of AI and computer science.

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

Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces mathematics students of the intrinsic interest of statistics and probability, and statistics students that the language of mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, e.g., genetics, filtering, the Black–Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUG

Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces mathematics students of the intrinsic interest of statistics and probability, and statistics students that the language of mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, e.g., genetics, filtering, the Black–Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUG

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

This book has evolved from the lecture course on Functional Analysis I had given several times at the ETH. The text has a strict logical order, in the style of “Definition - Theorem - Proof - Example

This general introduction to the ideas and techniques required for the mathematical modelling of diseases begins with an outline of some disease statistics dating from Daniel Bernoulli's 1760 smallpox data. The authors then describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (non-homogeneous) populations. Several techniques for constructing and analysing models are provided, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumours and vector-borne diseases like malaria. Questions of fitting data to models, and their use in understanding methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text, which will be useful for students taking courses in mathematical biology who have some basic knowledge of probability and statistics.

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.

This book develops the theory of global attractors for a class of parabolic PDEs which includes reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated in detail. A lengthy chapter on Sobolev spaces provides the framework that allows a rigorous treatment of existence and uniqueness of solutions for both linear time-independent problems (Poisson's equation) and the nonlinear evolution equations which generate the infinite-dimensional dynamical systems of the title. Attention then switches to the global attractor, a finite-dimensional subset of the infinite-dimensional phase space which determines the asymptotic dynamics. In particular, the concluding chapters investigate in what sense the dynamics restricted to the attractor are themselves 'finite-dimensional'. The book is intended as a didactic text for first year graduates, and assumes only a basic knowledge of Banach and Hilbert spaces, and a working understanding of the Lebesgue integral.

This book develops the theory of global attractors for a class of parabolic PDEs which includes reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated in detail. A lengthy chapter on Sobolev spaces provides the framework that allows a rigorous treatment of existence and uniqueness of solutions for both linear time-independent problems (Poisson's equation) and the nonlinear evolution equations which generate the infinite-dimensional dynamical systems of the title. Attention then switches to the global attractor, a finite-dimensional subset of the infinite-dimensional phase space which determines the asymptotic dynamics. In particular, the concluding chapters investigate in what sense the dynamics restricted to the attractor are themselves 'finite-dimensional'. The book is intended as a didactic text for first year graduates, and assumes only a basic knowledge of Banach and Hilbert spaces, and a working understanding of the Lebesgue integral.

This book discusses convex analysis, the basic underlying structure of argumentation in economic theory. Convex analysis is also common to the optimization of problems encountered in many applications

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

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.