Functional Analysis Methods for Reliability Models

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

This book reviews one-dimensional reactions, dynamics, diffusion and adsorption. In studies of complex systems in biology, chemistry and physics, understanding can be gained by analytical and numerical analyses of simple models. This book presents review articles at an advanced research level, describing results for one-dimensional models of dynamical processes such as chemical reactions and catalysis, kinetic ising models, phase separation and cluster growth, monolayer and multilayer adsorption with added relaxation, surface and hard-core particle dynamics, diffusional transport, random systems and experimental results. It also covers experimental results for systems ranging from chemical reactions to adsorption and reactions on polymer chains, steps on crystalline surfaces, and DNA. All chapters are written by leading scientists in the field. They present a self-contained review of this subject that will guide a reader from basic concepts, ideas, methods and models to the forefront o

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

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

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

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

Economists have developed models in which individuals form expectations of key variables in a 'rational' manner such that these expectations are consistent with actual economic environments. Professor Sheffrin first explores the logical foundation of the concept and the case for employing it in economic analysis. Subsequent chapters investigate its use in macroeconomics, financial markets, and microeconomics. A final chapter assesses its impact on theoretical and empirical work in economics and policy arenas. The author argues that while rational expectations are still central to macroeconomic policy debates, fully workable models have not yet been devised, and offers reasons for the lack of practical and conceptual progress. All chapters of the second edition have been revised or expanded. New sections inter alia include material on learning, the rationality of reported expectations, alternative recent developments explicitly or implicitly using rational expectations, new tests of the

Many phenomena in physics, chemistry, and biology can be modelled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modelled is made up of individual events that overlap, for example, the way individual raindrops eventually make the ground evenly wet. This is a systematic rigorous account of continuum percolation. Two models, the Boolean model and the random connection model, are treated in detail, and related continuum models are discussed. All important techniques and methods are explained and applied to obtain results on the existence of phase transitions, equality and continuity of critical densities, compressions, rarefaction, and other aspects of continuum models. This self-contained treatment, assuming only familiarity with measure theory and basic probability theory, will appeal to students and researchers in probability and stochastic geometry.

Economists have developed models in which individuals form expectations of key variables in a 'rational' manner such that these expectations are consistent with actual economic environments. Professor Sheffrin first explores the logical foundation of the concept and the case for employing it in economic analysis. Subsequent chapters investigate its use in macroeconomics, financial markets, and microeconomics. A final chapter assesses its impact on theoretical and empirical work in economics and policy arenas. The author argues that while rational expectations are still central to macroeconomic policy debates, fully workable models have not yet been devised, and offers reasons for the lack of practical and conceptual progress. All chapters of the second edition have been revised or expanded. New sections inter alia include material on learning, the rationality of reported expectations, alternative recent developments explicitly or implicitly using rational expectations, new tests of the

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

This book provides a distinctive and rich conception of methodology within international studies. From a rereading of the works of leading Western thinkers about international studies, Hayward Alker rediscovers a 'neo-Classical' conception of international relations which is both humanistic and scientific. He draws on the work of classical authors such as Aristotle and Thucydides; modern writers like Machiavelli, Vico, Marx, Weber, Deutsch and Bull; and post-modern writers like Havel, Connolly and Toulmin. The central challenge addressed is how to integrate 'positivist' or 'falsificationist' research styles within humanistic or interpretive ones. The author argues that appropriate, philosophically informed reformulations of conventional statistical and game-theoretic analyses are possible, and describes a number of humanistic methodologies for international relations, including argumentation analysis, narrative modeling, computational models of political understanding and reconstructiv

This book provides a distinctive and rich conception of methodology within international studies. From a rereading of the works of leading Western thinkers about international studies, Hayward Alker rediscovers a 'neo-Classical' conception of international relations which is both humanistic and scientific. He draws on the work of classical authors such as Aristotle and Thucydides; modern writers like Machiavelli, Vico, Marx, Weber, Deutsch and Bull; and post-modern writers like Havel, Connolly and Toulmin. The central challenge addressed is how to integrate 'positivist' or 'falsificationist' research styles within humanistic or interpretive ones. The author argues that appropriate, philosophically informed reformulations of conventional statistical and game-theoretic analyses are possible, and describes a number of humanistic methodologies for international relations, including argumentation analysis, narrative modeling, computational models of political understanding and reconstructiv

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

In this book the author examines and ultimately rejects the conventional economic view that workers who have more dangerous jobs accept their risks voluntarily and are compensated through higher wages. In doing so, he attacks widely used techniques for assigning a monetary value to human life for cost-benefit analysis and other purposes. Arguments are drawn from the history of occupational safety and health, econometric analysis of wage and risk data, and formal models of the labour market. In place of the conventional view, Peter Dorman proposes a view based on new work in decision theory (thick rationality) and the theory of repeated games. These insights are combined with comparative policy analysis to support an approach to risk that promotes both regulatory effectiveness and democratic values. Despite its technical content, the book is written in highly accessible style, and is concerned with matters of general interest in the development of critical social science.

This is a comprehensive analysis of J. A. Hobson's writings on international relations. Hobson is most famous for developing the neo-Marxist theory of imperialism, but in this book David Long argues that Hobson was also a key figure in the history of liberalism. He shifted liberal international theory away from its laissez-faire origins towards a focus on international organization, making him a forerunner of the functional approach in international relations. The book outlines the philosophical outlook and political economy which informed Hobson's theory, and challenges the narrow interpretation of imperialism which has dominated international relations. Setting out the sources of and contradictions within Hobson's proposals for international government, this book is a contribution not only to the study of international relations, but also to the history of political thought and British liberalism.

This is the second volume in the 4-volume set Analysis and Control Methods in the Food Industy, edited by J-L. Multon. The book describes all the main analytical techniques used in the food industry.

This book presents the newly developed theory of non-harmonic Fourier series and its applications to the control of distributed parameter systems. The authors extend the theory to include vector exponential series. The first part of the book presents the modern theory of exponentials, using an operator theory approach. The second part of the book extends and upgrades the method of moments - one of the most powerful tools in the flourishing theory of the control of distributed parameter systems. The book then goes on to discuss the controllability of systems described by parabolic and hyperbolic PDEs for internal, boundary, initial, and pointwise control. Typical applications to optimal control problems are also considered. Researchers in control theory, operator theory, functional analysis and partial differential equations will find much to interest them in this treatise.

This 1996 book defends the prospects for a science of society. It argues that behind the diverse methods of the natural sciences lies a common core of scientific rationality that the social sciences can and sometimes do achieve. It also argues that good social science must be in part about large-scale social structures and processes and thus that methodological individualism is misguided. These theses are supported by a detailed discussion of actual social research, including theories of agrarian revolution, organizational ecology, social theories of depression, and supply-demand explanations in economics. Professor Kincaid provides a general picture of explanation and confirmation in the social sciences and discusses the nature of scientific rationality, functional explanation, optimality arguments, meaning and interpretation, the place of microfoundations in social explanation, the status of neo-classical economics, the role of idealizations and non-experimental evidence, and other s

This 1996 book defends the prospects for a science of society. It argues that behind the diverse methods of the natural sciences lies a common core of scientific rationality that the social sciences can and sometimes do achieve. It also argues that good social science must be in part about large-scale social structures and processes and thus that methodological individualism is misguided. These theses are supported by a detailed discussion of actual social research, including theories of agrarian revolution, organizational ecology, social theories of depression, and supply-demand explanations in economics. Professor Kincaid provides a general picture of explanation and confirmation in the social sciences and discusses the nature of scientific rationality, functional explanation, optimality arguments, meaning and interpretation, the place of microfoundations in social explanation, the status of neo-classical economics, the role of idealizations and non-experimental evidence, and other s

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

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

Provides unified coverage of the principles and methods of various disciplines' approaches to prediction and control of processes expressed by discrete-time models, especially adaptive prediction, for

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

This book is a self-contained introduction to the theory of distributions, sometimes called generalized functions. Most books on this subject are either intuitive or else rigorous but technically demanding. Here, by concentrating on the essential results, the authors have introduced the subject in a way that will most appeal to non-specialists, yet is still mathematically correct. Topics covered include: the Dirac delta function, generalized functions, dipoles, quadrupoles, pseudofunctions and Fourier transforms. The self-contained treatment does not require any knowledge of functional analysis or topological vector spaces; even measure theory is not needed for most of the book. The book, which can be used either to accompany a course or for self-study, is liberally supplied with exercises. It will be a valuable introduction to the theory of distributions and their applications for students or professionals in statistics, physics, engineering and economics.

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

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

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

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

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

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

Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods; the area is an expanding source for novel and relevant 'real-world' mathematics. In this book the authors describe the modelling of financial derivative products from an applied mathematician's viewpoint, from modelling through analysis to elementary computation. A unified approach to modelling derivative products as partial differential equations is presented, using numerical solutions where appropriate. Some mathematics is assumed, but clear explanations are provided for material beyond elementary calculus, probability, and algebra. Over 140 exercises are included. This volume will become the standard introduction to this exciting new field for advanced undergraduate students.

Stochastic partial differential equations can be used in many areas of science to model complex systems that evolve over time. Their analysis is currently an area of much research interest. This book consists of papers given at the ICMS Edinburgh meeting held in 1994 on this topic, and it brings together some of the world's best known authorities on stochastic partial differential equations. Subjects covered include the stochastic Navier–Stokes equation, critical branching systems, population models, statistical dynamics, and ergodic properties of Markov semigroups. For all workers on stochastic partial differential equations this book will have much to offer.

Observational Astrophysics provides a comprehensive and accessible introduction to the whole of modern astrophysics beyond the Solar System. It combines a critical account of observational methods (telescopes and instrumentation) with a lucid description of the Universe, including stars, galaxies and cosmology. The first half describes the techniques used by astronomers to observe the Universe: optical telescopes and instruments are discussed in detail, but observations at all wavelengths are covered, from radio to gamma-rays. After a short interlude describing the appearance of the sky at all wavelengths, the role of positional astronomy is highlighted. In the second half, a clear description is given of the contents of the Universe, including accounts of stellar evolution and cosmological models. Fully illustrated throughout, with exercises given in each chapter, this textbook provides a thorough introduction to astrophysics for all physics undergraduates, and a valuable background f

Making a substantiated choice of the most efficient statistical test is one of the basic problems of statistics. Asymptotic efficiency is an indispensable technique for comparing and ordering statistical tests in large samples. It is especially useful in nonparametric statistics where it is usually necessary to rely on heuristic tests. This monograph presents a unified treatment of the analysis and calculation of the asymptotic efficiencies of nonparametric tests. Powerful new methods are developed to evaluate explicitly different kinds of efficiencies. Of particular interest is the description of domains of the Bahadur local optimality and related characterisation problems based on recent research by the author. Other Russian results are also published here for the first time in English. Researchers, professionals and students in statistics will find this book invaluable.

Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.

Between States is the first book that assesses systematically the broad implications of interim governments in the establishment of democratic regimes and on the existence of states. Based on historical and contemporary democratisation experiences, the book presents four ideal types of interim government: opposition-led provisional governments, power-sharing interim governments, incumbent-led caretaker governments, and international interim government by the United Nations. The first part explores the theoretical problems of each of these models from a broad comparative perspective. It uses as illustrations historical and contemporary cases that present a wide spectrum of contexts for comparison. The second part provides extensive case studies that are intended to illustrate, appraise, amplify and criticise the analysis in volume one. These include Iran, East Germany, Portugal, Afghanistan, and Yugoslavia.

This book is a tool for the theoretical and numerical investigation of nonlinear dynamical systems modelled by means of ordinary differential and difference equations. The work is divided into two parts: a book, comprising a theoretical overview of the subject matter and a number of applications; and an integrated software program. Although the emphasis is laid on dynamical systems arising from economic motivation, and the applications are derived from these systems, both the text and the program will also be of use to researchers in other fields of study. The book first discusses the fundamental concepts and methods of chaos theory, and then applies these theoretical results and the facilities provided by the companion software program to models suggested by economic problems.

Markov chains are an important idea, related to random walks, which crops up widely in applied stochastic analysis. They are used, for example, in performance modelling and evaluation of computer networks, queuing networks, and telecommunication systems. The main point of the present book is to provide methods, based on the construction of Lyapunov functions, of determining when a Markov chain is ergodic, null recurrent, or transient. These methods can also be extended to the study of questions of stability. Of particular concern are reflected random walks and reflected Brownian motion. The authors provide not only a self-contained introduction to the theory but also details of how the required Lyapunov functions are constructed in various situations.

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

This book provides an account of developments and applications of social accounts. It concentrates particularly on the methods of social accounting that Richard Stone, Nobel Laureate in Economics, developed and applied during his long and distinguished career. The contributors to the volume examine applications of social accounts in economics and demography, addressing issues of new formulations and specifications at the national and regional levels. Economic structure and issues of structural change are investigated within the context of social accounts matrices, and Linear Expenditure Systems are used to model population change and household consumption. The importance of social accounts matrices (SAM) in generating Computable General Equilibrium (CGE) models and the enormous potential that both SAM and CGE models have for policy analysis are stressed.