Basic Methods of Linear Functional Analysis

This 1997 book is an introduction to the application of computer simulation and theory in the study of the interaction of energetic particles (

In this book Christian Gourieroux and Alain Monfort provide an up-to-date and comprehensive analysis of modern time series econometrics. They have succeeded in synthesising in an organised and integrated way a broad and diverse literature. While the book does not assume a deep knowledge of economics, one of its most attractive features is the close attention it pays to economic models and phenomena throughout. The coverage represents a major reference tool for graduate students, researchers and applied economists. The book is divided into four sections. Section one gives a detailed treatment of classical seasonal adjustment or smoothing methods. Section two provides a thorough coverage of various mathematical tools. Section three is the heart of the book, and is devoted to a range of important topics including causality, exogeneity shocks, multipliers, cointegration and fractionally integrated models. The final section describes the main contribution of filtering and smoothing theory t

In this book Christian Gourieroux and Alain Monfort provide an up-to-date and comprehensive analysis of modern time series econometrics. They have succeeded in synthesising in an organised and integrated way a broad and diverse literature. While the book does not assume a deep knowledge of economics, one of its most attractive features is the close attention it pays to economic models and phenomena throughout. The coverage represents a major reference tool for graduate students, researchers and applied economists. The book is divided into four sections. Section one gives a detailed treatment of classical seasonal adjustment or smoothing methods. Section two provides a thorough coverage of various mathematical tools. Section three is the heart of the book, and is devoted to a range of important topics including causality, exogeneity shocks, multipliers, cointegration and fractionally integrated models. The final section describes the main contribution of filtering and smoothing theory t

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

Amniote Origins integrates modern systematic methods with studies of functional and physiological processes, and illustrates how studies of paleobiology can be illuminated by studies of neonatology. F

On the basis that only distributed hydrological models can provide an analysis of the wide-ranging data that best acquits an engineer's obligation to a client, explains the basic principles, a variety

This text bridges the gap between the classic texts on potential theory and modern books on applied geophysics. It opens with an introduction to potential theory, emphasising those aspects particularly important to earth scientists, such as Laplace's equation, Newtonian potential, magnetic and electrostatic fields, and conduction of heat. The theory is then applied to the interpretation of gravity and magnetic anomalies, drawing on examples from modern geophysical literature. Topics explored include regional and global fields, forward modeling, inverse methods, depth-to-source estimation, ideal bodies, analytical continuation, and spectral analysis. The book includes numerous exercises and a variety of computer subroutines written in FORTRAN. Graduate students and researchers in geophysics will find this book essential.

Despite the waves of re-engineering, there is still a gap between the opportunities offered by information technology and the progress of business transformation. New forms of information technology offer an increasing variety of network-based applications that range from groupware to electronic commerce, but its applications lack a sound understanding of the link between organizational processes, information and technology. This book provides a new set of concepts and methods to design new forms of business organizations around the latest network infrastructures. Professor Ciborra uses the principles of institutional economics to propose reforms of the relationships with suppliers, customers, strategic partners, and internal work organisation, based on a different mix of three basic organizational forms: teams, markets and hierarchies. Information technology can indeed be harnessed to shape businesses and markets so as to increase the transparency of markets, the agility of hierarchie

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 brings together in a single coherent framework a research programme begun by the author in the forties. The main model around which the analysis is built is Hicksian in character, having been drawn in large part from John Hicks's Value and Capital. The model is extended so as to include money and securities. In respect of the theory of the firm the model focuses on demand and supply plans, on inputs and outputs, on inventories, and on dependencies between them. The stability of temporary equilibrium is discussed for linear and non-linear cases. Because the concept of structural stability is important for understanding non-linear cases, it is defined and applied to the case of economic motion generated from the temporary equilibrium analysis. The addenda focus on developments in economic theory following the publication of the main model.

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.

The theory of sets of multiples, a subject which lies at the intersection of analytic and probabilistic number theory, has seen much development since the publication of Sequences by Halberstam and Roth nearly thirty years ago. The area is rich in problems, many of them still unsolved or arising from current work. The author sets out to give a coherent, essentially self-contained account of the existing theory and at the same time to bring the reader to the frontiers of research. One of the fascinations of the theory is the variety of methods applicable to it, which include Fourier analysis, group theory, high and ultra-low moments, probability and elementary inequalities, as well as several branches of number theory. This Tract is the first devoted to the subject, and will be of value to research workers or graduate students in number theory.

This substantial revision of the text Numerical Solution of Partial Differential Equations by the Finite Element Method by C. Johnson is a two volume introduction to the computational solution of differential equations using a unified approach organised around the adaptive finite element method. It presents a synthesis of mathematical modelling, analysis and computation. It provides the student with theoretical and practical tools useful for addressing the basic questions of computational mathematical modelling in science and engineering: How to model physical phenomena using differential equations? What are the properties of solutions of differential equations? How to compute solutions in practice? How to estimate and control the accuracy of computed solutions? The first volume begins by developing the basic issues at an elementary level in the context of a set of model problems in ordinary differential equations. The second volume extends the scope to nonlinear differential equations

Numerical Recipes in Fortran 90 starts with a detailed introduction to the Fortran 90 language and then presents the basic concepts of parallel programming. All 350+ routines from the second edition of Numerical Recipes are presented in Fortran 90. Many are completely reworked algorithmically so as to be 'parallel-ready' and to utilise Fortran 90's advanced language features. Numerical Recipes in Fortran 90 emphasises general principles, but throughout there are also numerous hints and tips. This volume is intended for use with the original Numerical Recipes in Fortran, 2nd Edition (now called Numerical Recipes in Fortran 77) and does not discuss how the individual programs are used, or how the mathematical methods are used. An excellent guide for Fortran programmers interested in moving to Fortran 90, or C/C++ programmers interested in parallel programming.

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.

This is an introduction to modern Banach space theory, in which applications to other areas such as harmonic analysis function theory, orthogonal series and approximation theory are also given prominence. The author begins with a discussion of weak topologies, weak compactness and isomorphisms of Banach spaces before proceeding to the more detailed study of particular spaces. The book is intended to be used with graduate courses in Banach space theory, so the prerequisites are a background in functional, complex and real analysis. As the only introduction to the modern theory it will be an essential companion for professional mathematicians working in the subject, or interested in applying it to other areas of analysis.

This book describes various approaches to the Inverse Galois Problem, a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory, algebraic geometry and number theory, topology, and analysis. Assuming only elementary algebra and complex analysis, the author develops the necessary background from topology, Riemann surface theory and number theory. The first part of the book is quite elementary, and leads up to the basic rigidity criteria for the realisation of groups as Galois groups. The second part presents more advanced topics, such as braid group action and moduli spaces for covers of the Riemann sphere, GAR- and GAL- realizations, and patching over complete valued fields. Graduate students and mathematicians from other areas (especially group theory) will find this an excellent introduction to a fascinating field.

Minkowski geometry is a type of non-Euclidean geometry in a finite number of dimensions in which distance is not 'uniform' in all directions. This book presents the first comprehensive treatment of Minkowski geometry since the 1940s. The author begins by describing the fundamental metric properties and the topological properties of existence of Minkowski space. This is followed by a treatment of two-dimensional spaces and characterisations of Euclidean space among normed spaces. The central three chapters present the theory of area and volume in normed spaces, a fascinating geometrical interplay among the various roles of the ball in Euclidean space. Later chapters deal with trigonometry and differential geometry in Minkowski spaces. The book ends with a brief look at J. J. Schaffer's ideas on the intrinsic geometry of the unit sphere. Minkowski Geometry will appeal to students and researchers interested in geometry, convexity theory and functional analysis.

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.

A good grasp of the theory of structures - the theoretical basis by which the strength, stiffness and stability of a building can be understood - is fundamental to structural engineers and architects. Yet most modern structural analysis and design is carried out by computer, with the user isolated from the processes in action. This book provides a broad introduction to the mathematics behind a range of structural processes. The basic structural equations have been known for at least 150 years, but modern plastic theory has opened up a fundamentally new way of advancing structural theory. Paradoxically, the powerful plastic theorems can be used to examine 'classic' elastic design activity, and strong mathematical relationships exist between these two approaches. Some of the techniques used in this book may be familiar to the reader, and some may not, but each of the topics examined will give the structural engineer valuable insight into the basis of the subject. This lucid volume provid

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.

The leading Thomas Paine expert in the U.S. presents both a biography of the controversial Founding Father and an analysis of his works. Known as "the Voice of the Revolution, " Paine was a truly ori

This edited collection of essays from world-leading academic and industrial authors yields insight into all aspects of reverse engineering. Methods of reverse engineering analysis are covered, along w

Explicates the mathematical theory of regularization methods and gives an account of currently available results about regularization methods for both linear and nonlinear ill-posed problems. Overview

In this introduction to commutative algebra, the author leads the beginning student through the essential ideas, without getting embroiled in technicalities. The route chosen takes the reader quickly to the fundamental concepts for understanding complex projective geometry, the only prerequisites being a basic knowledge of linear and multilinear algebra and some elementary group theory. In the first part, the general theory of Noetherian rings and modules is developed. A certain amount of homological algebra is included, and rings and modules of fractions are emphasised, as preparation for working with sheaves. In the second part, the central objects are polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalisation lemma and Hilbert's Nullstellensatz, affine complex schemes and their morphisms are introduced; Zariski's main theorem and Chevalley's semi-continuity theorem are then proved. Finally, a detailed study of Weil and Cart

This book concisely examines the use of elasticity in solving geotechnical engineering problems. In a highly illustrated and user-friendly format, it provides a thorough grounding in the linear theory of elasticity and an understanding of the applications, for upper level students in civil engineering and engineering geology. The first two chapters present a basic framework of the theory of elasticity and describe test procedures for the determination of elastic parameters for soils. Chapters 3 and 4 present the fundamental solutions of Boussinesque, Kelvin and Mindlin and use these to formulate solutions to problems of practical interest in geotechnical engineering. The book concludes with a sequence of appendices designed to provide the interested student with details of elasticity theory which are peripheral to the main text. Each chapter includes a set of questions for the student to answer.

Irmela Hijiya-Kirschnereit brings her sophisticated literary methods and graceful method of analysis to this English translation of her book on the shishosetsu, one of the most important yet misunders

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.

The distinguished mathematician offers meditations on mind, creativity, artificial intelligence, and other tops, fusing humor, hard thought, and analysis and ranging from Rubik's cube to the genetic c

This book is a modern pedagogic introduction to the ideas and techniques of quantum field theory. After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian methods, the quantum theory of scalar and spinor fields, and then of gauge fields, is developed. The emphasis throughout is on functional methods, which have played a large part in modern field theory. The book concludes with a brief survey of 'topological' objects in field theory and, new to this edition, a chapter devoted to supersymmetry.

Focusing on the period of Milton Friedman's collaboration with Anna J. Schwartz, from 1948 to 1991, this 1996 work examines the history of debates between Friedman and his critics over money's causal role in business cycles. Professor Hammond shows that critics' reactions were grounded in two distinctive features of Friedman and Schwartz's way of doing economic analysis - their National Bureau business cycle methods and Friedman's Marshallian methodology. With the post-war dominance of Cowles Commission methods and Walrasian methodology, Friedman and Schwartz's monetary economics appeared to contemporary critics to be 'measurement without theory'. Drawing extensively upon unpublished materials, Professor Hammond's treatment offers new insights on Milton Friedman's attempts to settle debates with his critics and his eventual recognition of the methodological impediments. The book will interest monetary economists and macroeconomists, as well as historians of economics and methodologists

This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded as dynamical systems controlled by synaptic matrices, and set-valued analysis that plays a natural and crucial role in qualitative analysis and simulation. This allows many examples of neural networks to be presented in a unified way. In addition, several results on the control of linear and nonlinear systems are used to obtain a 'learning algorithm' of pattern classification problems, such as the back-propagation formula, as well as learning algorithms of feedback regulation laws of solutions to control systems subject to state constraints. This book will be of value to anyone with an interest in neural networks and cognitive systems.

The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at undergraduate level. It was widely praised for the clarity of the writing and for the unique and effective way in which the authors presented the basic ideas. These same qualities characterise this revised and expanded second edition. Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. This second edition includes additional material on the analysis and characterisation of chaotic data, and applications of chaos. This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second and third year level.

Argumentation theory is a distinctly multidisciplinary field of inquiry. It draws its data, assumptions, and methods from disciplines as disparate as formal logic and discourse analysis, linguistics a

The authors present a basic and accessible introduction to the world of microbiology. In three sections, this book provides both a foundation and overview of the subject. In the first section, 'Microbial Structure and Mode of Life', the structure and functioning of fungi, bacteria and viruses are discussed (with particular attention being paid to their description and discussion of their reproduction and nutrition). The second section, 'Handling Microbes' introduces the methods used to culture, control and study these organisms in the laboratory. The final section covers the 'Isolation, Classification and Identification of Microbes'. This book is essential reading for anyone becoming interested in this subject, whether it be 6th form students, their teachers, or undergraduates.

Abraham Edel fashions a sound comparative way of using current analysis to deepen our understanding of Aristotle rather than argue with or simply appropriate him. Edel examines how Aristotle's basic i

This book concisely examines the use of elasticity in solving geotechnical engineering problems. In a highly illustrated and user-friendly format, it provides a thorough grounding in the linear theory of elasticity and an understanding of the applications, for upper level students in civil engineering and engineering geology. The first two chapters present a basic framework of the theory of elasticity and describe test procedures for the determination of elastic parameters for soils. Chapters 3 and 4 present the fundamental solutions of Boussinesque, Kelvin and Mindlin and use these to formulate solutions to problems of practical interest in geotechnical engineering. The book concludes with a sequence of appendices designed to provide the interested student with details of elasticity theory which are peripheral to the main text. Each chapter includes a set of questions for the student to answer.

Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and a lar

This book offers an original interpretation of the history of falling fertilities in Britain between 1860 and 1940. It integrates the approaches of the social sciences and of demographic, feminist, and labour history with intellectual, social, and political history. It exposes the conceptual and statistical inadequacies of the orthodox picture of a national, unitary class-differential fertility decline, and presents an entirely new analysis of the famous 1911 fertility census of England and Wales. Surprising and important findings emerge concerning the principal methods of birth control: births were spaced from early on in marriage; and sexual abstinence by married couples was a far more significant practice than previously imagined. The author presents a new general approach to the study of fertility change, raising central issues concerning the relationship between history and social science.

A unique guide to the application and theory of photothermal spectroscopy.This book debunks the myth that photothermal spectroscopy is too complicated for practical application to chemical analysis, a