Functional Analysis Methods for Reliability Models

Using the neo-classical theory of production economics as the analytical framework, this book, first published in 2004, provides a unified and easily comprehensible, yet fairly rigorous, exposition of the core literature on data envelopment analysis (DEA) for readers based in different disciplines. The various DEA models are developed as nonparametric alternatives to the econometric models. Apart from the standard fare consisting of the basic input- and output-oriented DEA models formulated by Charnes, Cooper, and Rhodes, and Banker, Charnes, and Cooper, the book covers developments such as the directional distance function, free disposal hull (FDH) analysis, non-radial measures of efficiency, multiplier bounds, mergers and break-up of firms, and measurement of productivity change through the Malmquist total factor productivity index. The chapter on efficiency measurement using market prices provides the critical link between DEA and the neo-classical theory of a competitive firm. The

The problem of evaluating integrals is well known to every student who has had a year of calculus. It was an especially important subject in 19th century analysis and it has now been revived with the appearance of symbolic languages. In this book, the authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics. The questions discussed in this book, first published in 2004, are as old as calculus itself. In presenting the combination of methods required for the evaluation of most integrals, the authors take the most interesting, rather than the shortest, path to the results. Along the way, they illuminate connections with many subjects, including analysis, number theory, algebra and combinatorics. This will be a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.

This book illustrates a set of tools - story grammars, relational data models, and network models - that can be profitably used for the collection, organization, and analysis of narrative data in socio-historical research. A story grammar, or Subject-Action-Object and their modifiers, is the linguistic tool the author uses to structure narrative for the purpose of collecting event data. Relational database models make such complex data collection schemes practically feasible in a computer environment. Finally, network models are a statistical tool best suited to analyze this type of data. Driven by the metaphors of the journal (from … to) and the alchemy (words into numbers), the book leads the reader throughout a number of paths, from substantive to methodological issues, across time and disciplines: sociology, linguistics, literary criticism, history, statistics, computer science, philosophy, cognitive psychology, political science.

This book illustrates a set of tools - story grammars, relational data models, and network models - that can be profitably used for the collection, organization, and analysis of narrative data in socio-historical research. A story grammar, or Subject-Action-Object and their modifiers, is the linguistic tool the author uses to structure narrative for the purpose of collecting event data. Relational database models make such complex data collection schemes practically feasible in a computer environment. Finally, network models are a statistical tool best suited to analyze this type of data. Driven by the metaphors of the journal (from … to) and the alchemy (words into numbers), the book leads the reader throughout a number of paths, from substantive to methodological issues, across time and disciplines: sociology, linguistics, literary criticism, history, statistics, computer science, philosophy, cognitive psychology, political science.

Shaping Primate Evolution is an edited collection of papers about how biological form is described in primate biology, and the consequences of form for function and behavior. The contributors are highly regarded internationally recognized scholars in the field of quantitative primate evolutionary morphology. Each chapter elaborates upon the analysis of the form-function-behavior triad in a unique and compelling way. This book is distinctive not only in the diversity of the topics discussed, but also in the range of levels of biological organization that are addressed from cellular morphometrics to the evolution of primate ecology. The book is dedicated to Charles E. Oxnard, whose influential pioneering work on innovative metric and analytic techniques has gone hand-in-hand with meticulous comparative functional analyses of primate anatomy. Through the marriage of theory with analytical applications, this volume will be an important reference work for all those interested in primate fun

A practical guide to methods of survival analysis for medical researchers with limited statistical experience. Methods and techniques described range from descriptive and exploratory analysis to multi

The statistical bootstrap is one of the methods that can be used to calculate estimates of a certain number of unknown parameters of a random process or a signal observed in noise, based on a random sample. Such situations are common in signal processing and the bootstrap is especially useful when only a small sample is available or an analytical analysis is too cumbersome or even impossible. This book covers the foundations of the bootstrap, its properties, its strengths and its limitations. The authors focus on bootstrap signal detection in Gaussian and non-Gaussian interference as well as bootstrap model selection. The theory developed in the book is supported by a number of useful practical examples written in MATLAB. The book is aimed at graduate students and engineers, and includes applications to real-world problems in areas such as radar and sonar, biomedical engineering and automotive engineering.

First published in 2004, this is a rigorous but user-friendly book on the application of stochastic control theory to economics. A distinctive feature of the book is that mathematical concepts are introduced in a language and terminology familiar to graduate students of economics. The standard topics of many mathematics, economics and finance books are illustrated with real examples documented in the economic literature. Moreover, the book emphasises the dos and don'ts of stochastic calculus, cautioning the reader that certain results and intuitions cherished by many economists do not extend to stochastic models. A special chapter (Chapter 5) is devoted to exploring various methods of finding a closed-form representation of the value function of a stochastic control problem, which is essential for ascertaining the optimal policy functions. The book also includes many practice exercises for the reader. Notes and suggested readings are provided at the end of each chapter for more referen

This is a step-by-step introduction to object-oriented software development. It is suitable for teaching and for self study by practising software engineers seeking to add rigour to their techniques. Seven complete case studies are included along with several smaller examples derived from small software projects developed for and delivered to real users. These examples make use of a bridge process, which presents a systematic approach for developing analysis models and unfolding these incrementally and iteratively through to design models and implementation. The process could be viewed as one example of unified software development and has the potential of being scalable to large software problems. It also provides a model for organising deliverables obtained throughout different phases of the software life cycle. These case studies provide a medium for experimental use and act as templates that can be tailored by readers to fit their specific needs and circumstances.

Event History Modeling, first published in 2004, provides an accessible guide to event history analysis for researchers and advanced students in the social sciences. The substantive focus of many social science research problems leads directly to the consideration of duration models, and many problems would be better analyzed by using these longitudinal methods to take into account not only whether the event happened, but when. The foundational principles of event history analysis are discussed and ample examples are estimated and interpreted using standard statistical packages, such as STATA and S-Plus. Critical innovations in diagnostics are discussed, including testing the proportional hazards assumption, identifying outliers, and assessing model fit. The treatment of complicated events includes coverage of unobserved heterogeneity, repeated events, and competing risks models. The authors point out common problems in the analysis of time-to-event data in the social sciences and make

Spectral theory for linear operators has become an important part of functional analysis and operator theory. This text seeks to define a spectrum for nonlinear operators that preserves the useful pro

The study of algorithmic graph theory and structured families of graphs is an important branch of discrete mathematics. It finds numerous applications, from data transmission through networks to efficiently scheduling aircraft and crews, as well as contributing to breakthroughs in genetic analysis and studies of the brain. Especially important have been the theory and applications of new intersection graph models such as generalizations of permutation graphs and interval graphs. One of these is the study of tolerance graphs and tolerance orders. This book contains the first thorough study of tolerance graphs and related topics, indeed the authors have included proofs of major results previously unpublished in book form. It will act as a springboard for researchers, and especially graduate students, to pursue new directions of investigation. With many examples and exercises it is also suitable for use as the text for a graduate course in graph theory.

Axiomatic categorical domain theory is crucial for understanding the meaning of programs and reasoning about them. This book is the first systematic account of the subject and studies mathematical structures suitable for modelling functional programming languages in an axiomatic (i.e. abstract) setting. In particular, the author develops theories of partiality and recursive types and applies them to the study of the metalanguage FPC; for example, enriched categorical models of the FPC are defined. Furthermore, FPC is considered as a programming language with a call-by-value operational semantics and a denotational semantics defined on top of a categorical model. To conclude, for an axiomatisation of absolute non-trivial domain-theoretic models of FPC, operational and denotational semantics are related by means of computational soundness and adequacy results. To make the book reasonably self-contained, the author includes an introduction to enriched category theory.

Linear systems can be regarded as a causal shift-invariant operator on a Hilbert space of signals, and by doing so this book presents an introduction to the common ground between operator theory and linear systems theory. The book therefore includes material on pure mathematical topics such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be entirely suitable for a course in functional analysis; at the same time, the book includes applications to partial differential equations, to the stability and stabilization of linear systems, to power signal spaces (including some recent material not previously available in books), and to delay systems, treated from an input/output point of view. Suitable for students of analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engin

Linear systems can be regarded as a causal shift-invariant operator on a Hilbert space of signals, and by doing so this book presents an introduction to the common ground between operator theory and linear systems theory. The book therefore includes material on pure mathematical topics such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be entirely suitable for a course in functional analysis; at the same time, the book includes applications to partial differential equations, to the stability and stabilization of linear systems, to power signal spaces (including some recent material not previously available in books), and to delay systems, treated from an input/output point of view. Suitable for students of analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engin

This book presents an easy-to-read discussion of domain decomposition algorithms, their implementation and analysis. The relationship between domain decomposition and multigrid methods is carefully explained at an elementary level, and discussions of the implementation of domain decomposition methods on massively parallel super computers are also included. All algorithms are fully described and explained, and a mathematical framework for the analysis and complete understanding of the methods is also carefully developed. In addition, numerous numerical examples are included to demonstrate the behaviour of this important class of numerical methods. This book is ideal for graduate students about to embark on a career in computational science. It will also be a valuable resource for all those interested in parallel computing and numerical computational methods.

Almost all the results available in the literature on multivariate t-distributions published in the last 50 years are now collected together in this comprehensive reference. Because these distributions are becoming more prominent in many applications, this book is a must for any serious researcher or consultant working in multivariate analysis and statistical distributions. Much of this material has never before appeared in book form. The first part of the book emphasizes theoretical results of a probabilistic nature. In the second part of the book, these are supplemented by a variety of statistical aspects. Various generalizations and applications are dealt with in the final chapters. The material on estimation and regression models is of special value for practitioners in statistics and economics. A comprehensive bibliography of over 350 references is included.

Using multiple data sources and methods, this book involves a micro-historical analysis of the nature of change and stability in homicide situations over time. It focuses on the homicide situation as the unit of analysis, and explores similarities and differences in the context of homicide for different social groups. For example, using Qualitative Comparative Analysis, we investigate whether various social groups (e.g., men vs women, teenagers vs adults, strangers vs intimates, Blacks vs Whites) kill under qualitatively different circumstances and, if so, what are the characteristics of these unique profiles. The analysis of over 400,000 US homicides is supplemented with qualitative analysis of narrative accounts of homicide events to more fully investigate the structure and process underlying these lethal situations. Our findings of unique and common homicide situations across different time periods and social groups are then discussed in terms of their implications for criminologica

Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial markets. Summarising theoretical developments in the field, this 2003 second edition has been substantially expanded. Additional chapters now cover stochastic processes, Monte-Carlo methods, Black-Scholes theory, the theory of the yield curve, and Minority Game. There are discussions on aspects of data analysis, financial products, non-linear correlations, and herding, feedback and agent based models. This book has become a classic reference for graduate students and researchers working in econophysics and mathematical finance, and for quantitative analysts working on risk management, derivative pricing and quantitative trading strategies.

Using multiple data sources and methods, this book involves a micro-historical analysis of the nature of change and stability in homicide situations over time. It focuses on the homicide situation as the unit of analysis, and explores similarities and differences in the context of homicide for different social groups. For example, using Qualitative Comparative Analysis, we investigate whether various social groups (e.g., men vs women, teenagers vs adults, strangers vs intimates, Blacks vs Whites) kill under qualitatively different circumstances and, if so, what are the characteristics of these unique profiles. The analysis of over 400,000 US homicides is supplemented with qualitative analysis of narrative accounts of homicide events to more fully investigate the structure and process underlying these lethal situations. Our findings of unique and common homicide situations across different time periods and social groups are then discussed in terms of their implications for criminologica

This is a step-by-step introduction to object-oriented software development. It is suitable for teaching and for self study by practising software engineers seeking to add rigour to their techniques. Seven complete case studies are included along with several smaller examples derived from small software projects developed for and delivered to real users. These examples make use of a bridge process, which presents a systematic approach for developing analysis models and unfolding these incrementally and iteratively through to design models and implementation. The process could be viewed as one example of unified software development and has the potential of being scalable to large software problems. It also provides a model for organising deliverables obtained throughout different phases of the software life cycle. These case studies provide a medium for experimental use and act as templates that can be tailored by readers to fit their specific needs and circumstances.

Gambling in America carefully breaks ground by developing analytical tools to assess the benefits and costs of the economic and social changes introduced by casino gambling in monetary terms, linking them to individual households' utility and well-being. Since casinos are associated with unintended and often negative economic consequences, these factors are incorporated into the discussion. The book also shows how amenity benefits - for casinos, the benefit to consumers of closer proximity - enter the evaluation. Other topics include agent incentives and public decision making, conceptual clarifications about economic development, cost-benefit analysis, and net export multiplier models. Professor Grinols finds that, in considering all relevant factors, the social costs of casino gambling outweigh their social benefits.

This refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used either for 1-term or 1-semester courses. Topics such as Euler's method, difference equations, the dynamics of the logistic map, and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated. The files to produce the figures using MATLAB are all provided in an accompanying website. Numerous worked examples provide motivation for and illustration of key ideas and show how to make the transition from theory to practice. Exercises are also provided to test and extend understanding: solutions for these are available for teachers.

This book discusses recent research in the theoretical foundations of several subjects of importance for the design of hardware, and for computer science in general. The physical technologies of very large scale integration (VLSI) are having major effects on the electronic industry. The potential diversity and complexity of digital systems have begun a revolution in the technologies of digital design, involving the application of concepts and methods to do with algorithms and programming. In return, the problems of VLSI design have led to new subjects becoming of importance in computer science. Topics covered in this volume include: models of VLSI complexity; complexity theory; systolic algorithm design; specification theory; verification theory; design by stepwise refinement and transformations. A thorough literature survey with an exhaustive bibliography is also included. The book has grown from a workshop held at the Centre for Theoretical Computer Science at Leeds University and or

This 2003 book provides a rigorous introduction to the theory of complex angular momenta, based on the methods of field theory. It comprises an English translation of the series of lectures given by V. N. Gribov in 1969, when the physics of high-energy hadron interactions was being created. Besides their historical significance, these lectures contain material which is highly relevant to research today. The basic physical results and the approaches Gribov developed are now being rediscovered in an alternative context: in the microscopic theory of hadrons provided by quantum chromodynamics. The ideas and calculation techniques presented in this book are useful for analysing high-energy hadron scattering phenomena, deep inelastic lepton-hadron scattering, the physics of heavy ion collisions, kinetic phenomena in phase transitions, and will be instrumental in the analysis of electroweak processes at the next-generation particle accelerators, such as LHC and TESLA.

Dynamic stochastic general equilibrium (DSGE) models have begun to dominate the field of macroeconomic theory and policy-making. These models describe the evolution of macroeconomic activity as a recursive sequence of outcomes based upon the optimal decision rules of rational households, firms and policy-makers. Whilst posing a micro-founded dynamic optimisation problem for agents under uncertainty, such models have been shown to be both analytically tractable and sufficiently rich for meaningful policy analysis in a wide class of macroeconomic problems, for example, monetary and fiscal policy, economic cycles and growth and capital flows. This volume collects specially commissioned papers from leading researchers, which pull together some of the key results in diverse areas. This book will promote research using optimising models and inform researchers, post-graduate students and economists in policy-oriented organisations of some of the key findings and policy implications.

Dynamic stochastic general equilibrium (DSGE) models have begun to dominate the field of macroeconomic theory and policy-making. These models describe the evolution of macroeconomic activity as a recursive sequence of outcomes based upon the optimal decision rules of rational households, firms and policy-makers. Whilst posing a micro-founded dynamic optimisation problem for agents under uncertainty, such models have been shown to be both analytically tractable and sufficiently rich for meaningful policy analysis in a wide class of macroeconomic problems, for example, monetary and fiscal policy, economic cycles and growth and capital flows. This volume collects specially commissioned papers from leading researchers, which pull together some of the key results in diverse areas. This book will promote research using optimising models and inform researchers, post-graduate students and economists in policy-oriented organisations of some of the key findings and policy implications.

Many phenomena in nature, engineering or society when seen at an intermediate distance, in space or time, exhibit the remarkable property of self-similarity: they reproduce themselves as scales change, subject to so-called scaling laws. It's crucial to know the details of these laws, so that mathematical models can be properly formulated and analysed, and the phenomena in question can be more deeply understood. In this 2003 book, the author describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. He demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural attributes of self-similarity and shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used for self-study by biologists, chemists, astronomers, engineers and g

Many phenomena in nature, engineering or society when seen at an intermediate distance, in space or time, exhibit the remarkable property of self-similarity: they reproduce themselves as scales change, subject to so-called scaling laws. It's crucial to know the details of these laws, so that mathematical models can be properly formulated and analysed, and the phenomena in question can be more deeply understood. In this 2003 book, the author describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. He demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural attributes of self-similarity and shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used for self-study by biologists, chemists, astronomers, engineers and g

Contention and Democracy in Europe, 1650–2000, first published in 2004, is an analysis of the relationship between democratization and contentious politics that builds upon the model set forth in the pathbreaking book, Dynamics of Contention. Using a sustained comparison of French and British histories since 1650 or so as a springboard for more general comparison within Europe Contention and Democracy goes on to demonstrate that democratization occurred as result of struggles during which (as in 19th century Britain and France) few, if any, of the participants were self-consciously trying to create democratic institutions. Consequently, circumstances for democratization vary from era to era, region to region as functions of previous history, international environments, available models of political organization, and predominant patterns of social relations.

The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics. Readers familiar with the very basic notions of category theory will learn about the main tools that are used in modern categorical mathematics but are not readily available in the literature. Hence, in eight rather independent chapters the reader will encounter various ways of how to study 'spaces': order-theoretically via their open-set lattices, as objects of a fairly abstract category merely via their interaction with other objects, or via their topoi of set-valued sheaves. Likewise, 'algebras' are treated both as models for Lawvere's algebraic theories and as Eilenberg-Moore algebras for monads, but they appear also as the objects of an abstract category with various levels of 'exactness' conditions. The abstract methods are illustrated by applications which, in many cases, lead to results not yet found in more tradi

Contention and Democracy in Europe, 1650–2000, first published in 2004, is an analysis of the relationship between democratization and contentious politics that builds upon the model set forth in the pathbreaking book, Dynamics of Contention. Using a sustained comparison of French and British histories since 1650 or so as a springboard for more general comparison within Europe Contention and Democracy goes on to demonstrate that democratization occurred as result of struggles during which (as in 19th century Britain and France) few, if any, of the participants were self-consciously trying to create democratic institutions. Consequently, circumstances for democratization vary from era to era, region to region as functions of previous history, international environments, available models of political organization, and predominant patterns of social relations.

This book presents an approach to introductory graduate courses on atomic structure. The author's approach utilizes conceptually powerful semiclassical modeling methods, and demonstrates the degree to which the Maslov-indexed EBK quantization elucidates the quantum mechanical formulation of level energies and lifetimes. It merges this with an update and extension of semiempirical data systematizations developed by Bengt Edlén to describe complex atoms, and adapts them to include the specification of lifetimes. The text emphasizes the historical basis of the nomenclature and methodologies of spectroscopy. However, interaction mechanisms are presented deductively, based on quantum mechanical and field theoretical models, rather than tracing their indirect paths of discovery. Many worked examples provide applications to areas such as astrophysics, hyperfine structure, and coherent anisotropic excitation. The book presents a firm foundation for specialists in atomic physics, as well as a c

This book presents an approach to introductory graduate courses on atomic structure. The author's approach utilizes conceptually powerful semiclassical modeling methods, and demonstrates the degree to which the Maslov-indexed EBK quantization elucidates the quantum mechanical formulation of level energies and lifetimes. It merges this with an update and extension of semiempirical data systematizations developed by Bengt Edlén to describe complex atoms, and adapts them to include the specification of lifetimes. The text emphasizes the historical basis of the nomenclature and methodologies of spectroscopy. However, interaction mechanisms are presented deductively, based on quantum mechanical and field theoretical models, rather than tracing their indirect paths of discovery. Many worked examples provide applications to areas such as astrophysics, hyperfine structure, and coherent anisotropic excitation. The book presents a firm foundation for specialists in atomic physics, as well as a c

This book discusses in detail all the relevant numerical methods for the classical N-body problem. It demonstrates how to develop clear and elegant algorithms for models of gravitational systems, and explains the fundamental mathematical tools needed to describe the dynamics of a large number of mutually attractive particles. Particular attention is given to the techniques needed to model astrophysical phenomena such as close encounters and the dynamics of black hole binaries. The author reviews relevant work in the field and covers applications to the problems of planetary formation and star cluster dynamics, both of Pleiades type and globular clusters. Self-contained and pedagogical, this book is suitable for graduate students and researchers in theoretical physics, astronomy and cosmology.

The methods by which a student becomes a speech and language therapist have developed since the 1970s and have been influenced by different models of higher and professional education. Although it is

Originally published in 2003, The Cultures within Ancient Greek Culture challenges the conventional perception of ancient Greece as the paradigm for unified models of culture. It offers an alternative view of archaic and classical Greece, one in which the contact, conflict and collaboration of a variety of 'sub-cultures' combine to comprise what we understand as 'Greekness'. This volume argues for the recognition and analysis of cultural contact within Greece, focussing on the micromechanics of cultural exchange, the permeability of cultural boundaries, and the significance of Delphi's geographically marginal, yet symbolically central location as an 'internal contact zone'. Through attention to everyday practices and professions, the essays reveal important ways of conceiving of diversity within Greek culture, ranging from the non-elite culture of athletic trainers to the competing musical cultures at work in fifth-century Athens.

Olof Dahlback's book breaks new ground for the analysis of crime from a rationality perspective by presenting models and methods that go far beyond those with which researchers have hitherto been equi

This is the second volume of a set of two devoted to the operator approach to linear problems in hydrodynamics. It presents functional analytical methods applied to the study of small movements and no

Significant advances in the field of microflora of aquatic animals, including fish and invertebrates, demands a practical laboratory text with the current methods for the bacteriological analysis of h