Functional Analysis Methods for Reliability Models

This book presents a theory motivated by the spaces LP, 0 ≤ p

Computing is an exact science and the systematic study of any aspect necessarily involves the use of mathematical models. Moreover, the rate at which the subject is evolving demands a facility for developing new mathematical systems to keep pace with new computing systems and this requires an appreciation of how mathematics works. An understanding of the underlying mathematical structure facilitates the construction of suitable computer programs to perform computations. Assuming no specific knowledge of mathematics, the authors describe all the basic concepts required and progress from sets (rather than numbers) through a variety of algebraic structures that permit the precise description, specification and subsequent analysis of many problems in computing. The material included provides the essential mathematical foundations for core topics of computer science and extends into the areas of language theory, abstract machine theory and computer geometry. Computer Mathematics will be of

The Handbook is a definitive reference source and teaching aid for econometricians. It examines models, estimation theory, data analysis and field applications in econometrics. Comprehensive surveys,

This guide to playreading for students and practitioners of both theater and literature complements, rather then contradicts or repeats, traditional methods of literary analysis of scripts.Ball devel

Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained. The author gives direct and concise proofs of all results yet avoids the heavy machinery of functional analysis. Moreover, representative examples are treated in some detail.

In these notes the abstract theory of analytic one-parameter semigroups in Banach algebras is discussed, with the Gaussian, Poisson and fractional integral semigroups in convolution Banach algebras serving as motivating examples. Such semigroups are constructed in a Banach algebra with a bounded approximate identity. Growth restrictions on the semigroup are linked to the structure of the underlying Banach algebra. The Hille-Yosida Theorem and a result of J. Esterle's on the nilpotency of semigroups are proved in detail. The lecture notes are an expanded version of lectures given by the author at the University of Edinburgh in 1980 and can be used as a text for a graduate course in functional analysis.

The division of the world into rich and poor nations, and the division within poor nations between a minority of rich people and a majority of poor people living at a minimum subsistence level, has been obvious to careful observers for a long time. This book gives an overview of the problems of underdevelopment confronting third-world countries, making use of both Marxist and neo-Keynesian methods of analysis. It makes clear the historical origins of these contemporary problems, particularly with reference to the major countries of Asia and Latin America, and discusses the ways in which inequalities, both within and between countries, are propaged and perpetuated. Other problems analysed are the typical patterns of fluctuating growth faced by third-world countries; the social structures in both rural and urban areas and their influence on the behaviour of governments and private investors in these countries; and environmental control and population planning issues faced by these countr

How are different cultures to be described and compared? This book provides a clear and concise discussion of the theoretical issues involved in ethnographic description and comparative study. Taking up the classic problems in the study of of social organisation, Professor Goodenough describes the major issues in the cross-cultural study of kinship and the family, revealing the kinds of constants, both formal and functional, on which such study must be based. The result is new definitions of marriage, family and parenthood for use in cross-cultural analysis and a greater understanding of this form of analysis itself. The statement on the interdependence of description and comparison in cultural anthropology and its implications for a science of culture, provides fresh insights into cross-cultural analysis for both the theoretical and the practical anthropologist.

Originally published in Italian in 1976, this book describes the methods scientists use to investigate the physical world. It is ideal for students and teachers of science and the philosophy of science. It is both a high-level popularization and a critical appraisal of these methods, describing important advances in physics and analyzing the historical development, value, reliability and philosophical implications of the way physicists approach the problems confronting them. The introductory chapter on the meaning of physical theories and the mathematical tools used to develop them is followed by a general discussion on the foundations of physics under four major headings: the physics of the reversible, the physics of the irreversible, microphysics, and cosmology. Throughout, the subject matter of physical theories is linked to discussion of the attendant philosophical and epistemological implications, such as the validity of the theories, inductive inference, causal explanation, proba

The use of modelling techniques in the analysis and solution of problems in science and other fields of knowledge is widespread and has often come under intensive scrutiny. This 1978 book concerns the use of models in learning, understanding, and practising chemistry. It will therefore be of interest to chemists, biochemists and chemical engineers in research and industry, and to many students of chemical science. The chemist uses models in his work not only in the material sense, for example molecular models, but also in his patterns of thought, coming to grips with chemistry and its applications through the manipulation of models. The present work outlines the scope of modelling and, from a discussion of the general principles involved, develops themes relevant to both academic and industrial scientists.

The basis of this graduate-level textbook is a careful survey of a wide range of problems affecting the solution of linear partial differential equations. The book begins with a fairly elementary introduction to the theory of Fourier series of continuous functions and goes on to describe the fundamental theory of linear partial differential equations of elliptic and hyperbolic types, equations of evolution, semi-linear hyperbolic equations and selected topics on Green's functions and spectra of some special operators. The book is intended for use by pure mathematicians in functional analysis. The selection of material is interesting and differs from existing literature in European languages. This paperback edition will make it particularly attractive to graduate students in pure and applied mathematics.

This is a sequel to Dr Weir's undergraduate textbook on Lebesgue Integration and Measure (CUP. 1973) in which he provided a concrete approach to the Lebesgue integral in terms of step functions and went on from there to deduce the abstract concept of Lebesgue measure. In this second volume, the treatment of the Lebesgue integral is generalised to give the Daniell integral and the related general theory of measure. This approach via integration of elementary functions is particularly well adapted to the proof of Riesz's famous theorems about linear functionals on the classical spaces C (X) and LP and also to the study of topological notions such as Borel measure. This book will be used for final year honours courses in pure mathematics and for graduate courses in functional analysis and measure theory.

These lecture notes are devoted to an area of current research interest that bridges functional analysis and function theory. The unifying theme is the notion of subharmonicity with respect to a uniform algebra. The topics covered include the rudiments of Choquet theory, various classes of representing measures, the duality between abstract sub-harmonic functions and Jensen measures, applications to problems of approximation of plurisubharmonic functions of several complex variables, and Cole's theory of estimates for conjugate functions. Many of the results are published here for the first time in monograph form.

Vector analysis provides the language that is needed for a precise quantitative statement of the general laws and relationships governing such branches of physics as electromagnetism and fluid dynamics. The account of the subject is aimed principally at physicists but the presentation is equally appropriate for engineers. The justification for adding to the available textbooks on vector analysis stems from Professor Kemmer's novel presentation of the subject developed through many years of teaching, and in relating the mathematics to physical models. While maintaining mathematical precision, the methodology of presentation relies greatly on the visual, geometric aspects of the subject and is supported throughout the text by many beautiful illustrations that are more than just schematic. A unification of the whole body of results developed in the book - from the simple ideas of differentiation and integration of vector fields to the theory of orthogonal curvilinear coordinates and to th

Demography is the study by statistical methods of human populants involving the measurement of their size, growth and diminution, the proportions living within some areas, being born, marrying, having children or dying and the related functions of fertility, nuptially and morality. This book begins by defining a number of concepts which are useful for demographic analysis, including the significant events in life and types of statistical data which are collected, published and used. It then describes the various kinds of change which can occur and the underlying causes - social, economic and political. The central section provides an account of the history of population growth and development, and of the situation on an international and national scale. Resources available for the support of mankind and their relationship with living standards are explored. The politics of population and the prospects for the future are also described.

In this book, Professor Copson gives a rigorous account of the theory of partial differential equations of the first order and of linear partial differential equations of the second order, using the methods of classical analysis. In spite of the advent of computers and the applications of the methods of functional analysis to the theory of partial differential equations, the classical theory retains its relevance in several important respects. Many branches of classical analysing have their origins in the rigourous discussion of problems in applies mathematics and theoretical physics, and the classical treatment of the theory of partial differential equations still provides the best method of treating many physical problems. A knowledge of the classical theory is essential for pure mathematics who intend to undertake research in this field, whatever approach they ultimately adopt. The numerical analyst needs a knowledge of classical theory in order to decide whether a problem has a uni

This paperback, which comprises the first part of Introduction to Measure and Probability by J. F. C. Kingman and S. J. Taylor, gives a self-contained treatment of the theory of finite measures in general spaces at the undergraduate level. It sets the material out in a form which not only provides an introduction for intending specialists in measure theory but also meets the needs of students of probability. The theory of measure and integration is presented for general spaces, with Lebesgue measure and the Lebesgue integral considered as important examples whose special properties are obtained. The introduction to functional analysis which follows covers the material to probability theory and also the basic theory of L2-spaces, important in modern physics. A large number of examples is included; these form an essential part of the development.

Offers students with an understanding of fundamental models in macroeconomics, and introduces them to the methods of formal macroeconomic analysis. This book focuses on macroeconomics for the long run

Suitable for a one or two semester course, this book takes a practical approach to methods of statistical modeling and data analysis that are most often used in scientific work.

Probability models, statistical methods, and the information to be gained from them is vital for work in business, engineering, sciences (including social and behavioral), and other fields. Data must

This essay is a foray into the debatable borderland between history, technology and economics. On the history of technical processes there exist several works, pre-eminent among them the great five-volumed History of Technology. But few historians of technology have shown interest in the models of the economists; and the theorists have concentrated on analysis or on problems of contemporary technology. The present work is an attempt to re-examine some of the more familiar nineteenth-century developments in technology. It originated in lectures given at Columbia University in the autumn of 1958.

Neurobiological Background of Exploration Geosciences: New Methods for Data Analysis Based on Cognitive Criteria examines the neurobiological background of earth science disciplines. It presents the f

Nanomaterials Characterization Techniques, Volume Two, part of an ongoing series, offers a detailed analysis of the different types of spectroscopic methods currently being used in nanocharacterizatio

As Non-Life Insurance models are strictly connected with stochastic processes, the main aim of this book is to show how classical and recent advanced stochastic models can be used to improve the stoch

Stochastic modeling facilitates an understanding of natural phenomena depicted in medical anatomical and functional (dynamic) MRI and CT images. This textbook details efficient stochastic modeling tec

Simulation modeling is increasingly integrated into research and policy analysis of complex sociotechnical systems in a variety of domains. Model-based analysis and policy design inform a range of app

Blending theoretical results with practical applications, this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications. The Stieltjes transform method, free probability theory, combinatoric approaches, deterministic equivalents and spectral analysis methods for statistical inference are all covered from a unique engineering perspective. Detailed mathematical derivations are presented throughout, with thorough explanation of the key results and all fundamental lemmas required for the reader to derive similar calculus on their own. These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, including performance analysis of CDMA, MIMO and multi-cell networks, as well as signal detection and estimation in cognitive radio networks. The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose

The book unifies classical continuum mechanics and turbulence modeling, i.e. the same fundamental concepts are used to derive model equations for material behaviour and turbulence closure and compleme

Ott and Longnecker's AN INTRODUCTION TO STATISTICAL METHODS AND DATA ANALYSIS, Sixth Edition, provides a broad overview of statistical methods for advanced undergraduate and graduate students from a v

There are many excellent computational biology resources now available for learning about methods that have been developed to address specific biological systems, but comparatively little attention h

Intersecting two large research areas--numerical analysis and applied probability/quering theory--this book is a self -contained introduction to the numerical solution of structured Markov chains, whi

Third Edition brings the text up to date with new material and updated references.New content includes an introduction to left and interval censored data; the log-logistic distribution; estimation pro