Basic Methods of Linear Functional Analysis

Considered the cutting edge of microeconomic theory in the 1970s, natural monopoly research remains an active and fertile field. Policy makers and regulators have begun to implement entry and pricing policies that are based on theoretical and empirical analyses. This book develops a comprehensive framework for analyzing natural monopoly. The authors first present a historical overview of regulatory economics, followed by analyses of optimal pricing and investment for single- and multiproduct natural monopolies. Topics covered include cost and demand structures, efficiency impacts of linear and multipart pricing, peak-load pricing, capacity determination, and the sustainability of natural monopolies. After a survey and analysis of natural monopoly regulation in practice, the links between technological change and regulation are identified. The book concludes with a discussion of the alternatives to traditional regulation, including public ownership, franchise schemes, quality regulation

Holographic and speckle interferometry are optical techniques which use lasers to make non-contracting field view measurements at a sensitivity of the wavelength of light on optically rough (i.e. non-mirrored) surfaces. They may be used to measure static or dynamic displacements, the shape of objects, and refractive index variations of transparent media. As such, these techniques have been applied to the solution of a wide range of problems in strain and vibrational analysis, non-destructive testing (NDT), component inspection and design analysis and fluid flow visualisation. This book provides a self-contained, unified, theoretical analysis of the basic principles and associated opto-electronic techniques (for example Electronic Speckle Pattern Interferometry). In addition, a detailed discussion of experimental design and practical application to the solution of physical problems is presented. In this new edition, the authors have taken the opportunity to include a much more coherent

The Fourth Edition of the best-selling text on the basic concepts, theory, methods, and applications of ordinary differential equations retains the clear, detailed style of the first three editions. I

Here is the most comprehensive treatment available on practical temperature measurement methods using radiation thermometry. All aspects of measurement technology are covered: basic principles, types

This book, which grew out of Steven Bleiler's lecture notes from a course given by Andrew Casson at the University of Texas, is designed to serve as an introduction to the applications of hyperbolic geometry to low dimensional topology. In particular it provides a concise exposition of the work of Neilsen and Thurston on the automorphisms of surfaces. The reader requires only an understanding of basic topology and linear algebra, while the early chapters on hyperbolic geometry and geometric structures on surfaces can profitably be read by anyone with a knowledge of standard Euclidean geometry desiring to learn more abour other 'geometric structures'.

This book contains a modern treatment of production economics from a dual perspective, with special emphasis on recent developments. Results that were scattered throughout professional journals and monographs are now gathered into an integrated approach using a common notation. The book prepares the reader to apply the tools of the dual approach to real world problems and data sets. Particular care has been devoted to choosing topics for discussion that achieve this goal. Throughout the book there are worked examples and exercises, which are geared toward developing the reader's facility in using modern developments in production economics. Separate chapters are devoted to production, cost, and profit functions. Other topics include flexible functional forms, aggregation across inputs and outputs using the theory of separable structures, aggregation over economic optimizing firms, the representation of multioutput technologies, and the analysis and measurement of technical change from

How do I decide I am ill; how do I decide that my children are ill? How do I learn effective ways of conveying to others that I am ill? This book discusses the languages of illness which we use to present our discomforts to others through an exploration of the child's world of illness. It looks at how illness concepts are introduced to children, how the causes of illness and 'germ' rationales are incorporated into the socialisation of children, and how a particular morality about health and illness is expressed. Besides the analysis of the social context within which the children's views are developing, the book presents the children's own views from three years old up to thirteen. How we talk about illness can have as important consequences as the methods we use to cure it. This book persuades the reader to look more closely at the language of illness, allowing a reappraisal to medical practice, school health programmes and class teaching, health education and even the differences in

In this book, Professor David Starrett organizes within a single framework the major theoretical foundations of modern public sector economics. He presents a unified treatment of market failure that encompasses externalities, pure public goods, local public goods and natural monopolies. Professor Starrett then develops and assesses the efficacy of the various planning procedures - including representative voting, benefit cost analysis, incentive compatible design mechanisms and the free market. He devotes attention to both national and local issues, with the aim of identifying those methods that are best suited to each arena separately. Special attention is paid to financial arrangements, techniques for eliciting necessary information that is not readily available, and identification of biases that will result from incorrect procedures. This study will be useful to graduate students and economists who are interested in public finance or welfare economics.

The human brain contains billions of nerve cells whose activity plays a critical role in the way we behave, feel, perceive, and think. This two-volume set explains the basic properties of a neuron - an electrically active nerve cell - and develops mathematical theories for the way neurons respond to the various stimuli they receive. Volume 1 contains descriptions and analyses of the principal mathematical models that have been developed for neurons in the past thirty years. It provides a brief review of the basic neuroanatomical and neurophysiological facts that will form the focus of the mathematical treatment. Tuckwell discusses the mathematical theories, beginning with the theory of membrane potentials. He then goes on to treat the Lapicque model, linear cable theory, and time-dependent solutions of the cable equations. He concludes with a description of Rall's model nerve cell. Because the level of mathematics increases steadily upward from Chapter Two, some familiarity with differ

The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and non-space-clamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex in this volume than in the first volume and involves numerical methods of solution of partial differential equations and the statistical analysis of point processes.

This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.

Originally published in 1987, this book is devoted to the approximation of real functions by real rational functions. These are, in many ways, a more convenient tool than polynomials, and interest in them was growing, especially since D. Newman's work in the mid-sixties. The authors aim at presenting the basic achievements of the subject and, for completeness, also discuss some topics from complex rational approximation. Certain classical and modern results from linear approximation theory and spline approximation are also included for comparative purposes. This book will be of value to anyone with an interest in approximation theory and numerical analysis.

The study of sets of uniqueness for trigonometric series has a long history, originating in the work of Riemann, Heine, and Cantor in the mid-nineteenth century. Since then it has been a fertile ground for numerous investigations involving real analysis, classical and abstract harmonic analysis, measure theory, functional analysis and number theory. In this book are developed the intriguing and surprising connections that the subject has with descriptive set theory. These have only been discovered recently and the authors present here this novel theory which leads to many new results concerning the structure of sets of uniqueness and include solutions to some of the classical problems in this area. In order to make the material accessible to logicians, set theorists and analysts, the authors have covered in some detail large parts of the classical and modern theory of sets of uniqueness as well as the relevant parts of descriptive set theory. Thus the book is essentially self-contained

This book presents the basic theory of the current comparator, methods of construction leading to high ratio accuracies and the operating principles of the various applications.

In this book, Professors Baumol and Oates provide a rigorous and comprehensive analysis of the economic theory of environmental policy. They present a formal, theoretical treatment of those factors influencing the quality of life. By covering both the theory of externalities and its application to environmental policy, the authors have retained the basic structure and organization of the first edition, which has become a standard reference in the field. In this edition, however, they have updated their analysis to incorporate recent research in environmental economics.

In this book, Professors Baumol and Oates provide a rigorous and comprehensive analysis of the economic theory of environmental policy. They present a formal, theoretical treatment of those factors influencing the quality of life. By covering both the theory of externalities and its application to environmental policy, the authors have retained the basic structure and organization of the first edition, which has become a standard reference in the field. In this edition, however, they have updated their analysis to incorporate recent research in environmental economics.

Metric space topology, as the generalization to abstract spaces of the theory of sets of points on a line or in a plane, unifies many branches of classical analysis and is necessary introduction to functional analysis. Professor Copson's book, which is based on lectures given to third-year undergraduates at the University of St Andrews, provides a more leisurely treatment of metric spaces than is found in books on functional analysis, which are usually written at graduate student level. His presentation is aimed at the applications of the theory to classical algebra and analysis; in particular, the chapter on contraction mappings shows how it provides proof of many of the existence theorems in classical analysis.

In many problems of applied mathematics, science, engineering or economics, an energy expenditure or its analogue can be approximated by upper and lower bounds. This book provides a unified account of the theory required to establish such bounds, by expressing the governing conditions of the problem, and the bounds, in terms of a saddle functional and its gradients. There are several features, including a chapter on the Legendre dual transformation and some of its singularities. Many substantial examples and exercises are included, especially from the mechanics of fluids, elastic and plastic solids and from optimisation theory. The saddle functional viewpoint gives the book a wide scope. The treatment is straightforward, the only prerequisite being a basic knowledge of the calculus of variations. Part of the book is based on final-year undergraduate courses. This is developed into an account which will interest a wide range of students and professionals in applied mathematics, engineer

Forcing is a powerful tool from logic which is used to prove that certain propositions of mathematics are independent of the basic axioms of set theory, ZFC. This book explains clearly, to non-logicians, the technique of forcing and its connection with independence, and gives a full proof that a naturally arising and deep question of analysis is independent of ZFC. It provides an accessible account of this result, and it includes a discussion, of Martin's Axiom and of the independence of CH.

The Swiss psychologist Jean Piaget is generally considered to be the founder of modern developmental psychology. This book, first published in 1988, provides a conceptual critique of six of Piaget's central, earlier works, including his account of the child's conception of the world, the development of morality, and the origins of intelligence in infancy. Sugarman's detailed, step-by-step analysis of some of Piaget's major arguments shows exactly where, and why, they fail. Through the same analysis she suggests the alternative lines of inquiry that might result in a clearer and more basic understanding of the child's mind and of the origins of adult thought.

FrettedThis Berklee Workshop is for bassists beyond beginning methods who now seek comprehensive knowledge of all basic and extended chords. Features exercises for developing technique and melodic sen

This book classifies methods of synthesizing a heterocyclic ring which is fused to another ring. Classification is based on the functional group or groups present in the substrate, each chapter being

First published in 1962 this book is a graduate-level introduction to the theory of electro-magnetic flow-measurement. Electromagnetic flowmeters have been in use for many years and are still one of the most widely used methods of measuring flow rates. Although the sophistication of the instrumentation has changed radically since Shercliff's book was first published, the theoretical principles expounded in the book are still relevant and sound. Students of mechanical engineering and research workers will find this reissue to be a useful and lucid exposition of the basic theory.

This 1987 book is a self-contained text on the probabilistic modelling method. It provides the reader with an understanding of the available results as well as with examples of their application. The only background assumed is a knowledge of basic calculus. The necessary fundamentals of probability are presented followed by an introduction to stochastic processes. The remainder of the book is devoted to the treatment of various single-station and their application to uni-programmed and multi-programmed systems and local and wide-area networks. Both exact and approximate solution methods are discussed, with as much emphasis on explaining the ideas and providing information, as on derivations and proofs. This book will still be of use for anyone with an interest in the history of computer science.

This book follows the same successful approach as Dr Burn's previous book on number theory. It consists of a carefully constructed sequence of questions which will enable the reader, through his or her own participation, to generate all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to the study of Möbius transformations and stereographic projection, are also included. Quaternions and their relationship to three-dimensional isometries are covered, and the climax of the book is a study of crystallographic groups, with a complete analysis of these groups in two dimensions.

Canada and Immigration is a portrait of Canadian immigration since the end of the Second World War. It is an important record and analysis of immigration policies, laws, and methods of management duri

A behind-the-scenes look at prep school life offers an incisive analysis of the complex ways in which these elite schools prepare students for success and power

This textbook is an introduction to the techniques of summing and nuclear norms. The author's aim is to present a clear and simple account of these ideas and to demonstrate the power of their application to a variety of Banach space questions. The style is expository and the only prerequisite is a beginner's course on Wormed linear spaces and a minimal knowledge of functional analysis. Thus, Dr Jameson is able to concentrate on important, central results and gives concrete and largely non-technical proofs, often supplying alternative proofs which both contribute something to the understanding. Final-year undergraduates and postgraduates in functional analysis will enjoy this introduction to the subject, and there are many examples and exercises throughout the text to help the reader and to demonstrate the range of application these techniques find. A list of references indicates the way for further reading.

This book is a rigorous introduction to the abstract theory of partial differential equations. The main prerequisite is familiarity with basic functional analysis: more advanced topics such as Fredholm operators, the Schauder fixed point theorem and Bochner integrals are introduced when needed, and the book begins by introducing the necessary material from the theory of distributions and Sobolev spaces. Using such techniques, the author presents different methods available for solving elliptic, parabolic and hyperbolic equations. He also considers the difference process for the practical solution of a partial differential equation, emphasising that it is possible to solve them numerically by simple methods. Many examples and exercises are provided throughout, and care is taken to explain difficult points. Advanced undergraduates and graduate students will appreciate this self-contained and practical introduction.

The American Novel series provides students of American literature with introductory critical guides to the great works of American fiction by giving details of the novel's composition, publication history and contemporary reception. The group of essays, each specially commissioned from a leading scholar in the field, examines the interpretative methods and prominent ideas on the text. There are also helpful guides to further reading. Specifically designed for undergraduates, the series will be a powerful resource for anyone engaged in the critical analysis of major American novels. This collection of essays on Moby-Dick reconnects Melville's great work with concerns that are central to readers in critical studies. Richard Brodhead introduces the volume with a discussion of the book's unique place in the canon of American literature. He then recounts the novel's history from its mixed reception in the mid-nineteenth century to its prevalent status as a classic. The five essays that fol

This book gives a new interpretation of the reception of the new world by the old. It is the first in-depth study of the pre-Enlightenment methods by which Europeans attempted to describe and classify the American Indian and his society. Between 1512 and 1724 a simple determinist view of human society was replaced by a more sophisticated relativist approach. Anthony Pagden uses new methods of technical analysis, already developed in philosophy and anthropology, to examine four groups of writers who analysed Indian culture: the sixteenth-century theologian, Francisco de Vitoria, and his followers; the 'champion of the Indians' Bartolomé de Las Casas; and the Jesuit historians José de Acosta and Joseph François Lafitau. Dr Pagden explains the sources for their theories and how these conditioned their observations. He also examines for the first time the key terms in each writer's vocabulary - words such as 'barbarian' and 'civil' - and the assumptions that lay beneath them.

Totally revised, this 2nd Edition includes a new chapter on decision analysis, and additional material on computer solutions of linear programming problems, LP applications, the use of sensitivity ana

This book provides the basic technical knowledge necessary to complete the first half of a City and Guilds Course in Carpentry and Joinery. The text covers the skills, tools, materials and methods li

Multiple Comparisons demonstrates the most important methods of investigating differences between levels of an independent variable within an experimental design. The authors review the analysis of va

In an increasingly leisure-orientated society, a proper understanding of ecological factors is necessary to reduce the scale of environmental damage associated with recreational and tourist activities. Ecology, Recreation and Tourism presents a comprehensive analysis of such effects on the environment. Using the framework of basic ecological principles, which are introduced and explained in the first chapter, the planning and design for recreation and tourism is considered from 3 major standpoints: the impact of recreational damage; the constraints imposed by biological agents, and finally the design of resorts and associated support facilities. The authors have been involved with the application of ecology to land use planning for many years, both in this country and overseas. With a wide geographical and environmental scope, this text shows clearly the crucial role that ecology has to play in maintaining the balance between recreation and the environment.

Over the last 45 years, Boolean theorem has been generalized and extended in several different directions and its applications have reached into almost every area of modern mathematics; but since it lies on the frontiers of algebra, geometry, general topology and functional analysis, the corpus of mathematics which has arisen in this way is seldom seen as a whole. In order to give a unified treatment of this rather diverse body of material, Dr Johnstone begins by developing the theory of locales (a lattice-theoretic approach to 'general topology without points' which has achieved some notable results in the past ten years but which has not previously been treated in book form). This development culminates in the proof of Stone's Representation Theorem.

This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods.

Comprehensive, classic introduction to space-flight engineering for advanced undergraduate and graduate students. Provides basic tools for quantitative analysis of the motions of satellites and other

This is an introductory text in several complex variables, using methods of integral representations. It begins with elementary local results, discusses basic new concepts of the multi-dimensional the

This study examines the history of the sugar economy and the peculiar development of plantation society over a three hundred year period in Bahia, a major sugar plantation zone and an important terminus of the Atlantic slave trade. Drawing on little-used archival sources, plantations accounts, and notarial records, Professor Schwartz has examined through both quantitative and qualitative methods the various groups that made up plantation society. While he devotes much attention to masters and slaves, he views slavery ultimately as part of a larger structure of social and economic relations. The peculiarities of sugar-making and the nature of plantation labour are used throughout the book as keys to an understanding of roles and relationships in plantation society. A comparative perspective is also employed, so that studies of slavery elsewhere in the Americas inform the analysis, while at many points direct comparisons of the Bahian case with other plantation societies are also made.