Basic Methods of Linear Functional Analysis

This volume reflects the progress made in many branches of recent research in Banach space theory. It is based on a conference attended by most of the leading figures in the area, and is intended to illustrate the interplay of Banach space theory with harmonic analysis, probability, complex function theory and finite dimensional convexity theory. The papers consist of a selection of surveys and original research papers. Research workers in functional and complex analysis will find much here to interest them.

There are few industries in modern market economies that do not manufacture differentiated products. This book provides a systematic explanation and analysis of the widespread prevalence of this important category of products. The authors concentrate on models in which product selection is endogenous. In the first four chapters they consider models that try to predict the level of product differentiation that would emerge in situations of market equilibrium. These market equilibria with differentiated products are characterised and then compared with social welfare optima. Particular attention is paid to the distinction between horizontal and vertical differentiation as well as to the related issues of product quality and durability. This book brings together the most important theoretical contributions to these topics in a succinct and coherent manner. One of its major strengths is the way in which it carefully sets out the basic intuition behind the formal results. It will be useful

There are few industries in modern market economies that do not manufacture differentiated products. This book provides a systematic explanation and analysis of the widespread prevalence of this important category of products. The authors concentrate on models in which product selection is endogenous. In the first four chapters they consider models that try to predict the level of product differentiation that would emerge in situations of market equilibrium. These market equilibria with differentiated products are characterised and then compared with social welfare optima. Particular attention is paid to the distinction between horizontal and vertical differentiation as well as to the related issues of product quality and durability. This book brings together the most important theoretical contributions to these topics in a succinct and coherent manner. One of its major strengths is the way in which it carefully sets out the basic intuition behind the formal results. It will be useful

This is the completely revised and updated version of the popular and highly regarded textbook, Applied Geophysics. It describes the physical methods involved in exploration for hydrocarbons and minerals, which include gravity, magnetic, seismic, electrical, electromagnetic, radioactivity, and well-logging methods. All aspects of these methods are described, including basic theory, field equipment, techniques of data acquisition, data processing and interpretation, with the objective of locating commercial deposits of minerals, oil, and gas and determining their extent. In the fourteen years or so since the first edition of Applied Geophysics, many changes have taken place in this field, mainly as the result of new techniques, better instrumentation, and increased use of computers in the field and in the interpretation of data. The authors describe these changes in considerable detail, including improved methods of solving the inverse problem, specialized seismic methods, magnetotellur

This book examines the economic reasons why people choose to live where they live and develops, through analysis of the bid rent function, a unified theory of urban land use and city size. The first part of the book explicates the basic theory of urban land use and optimal city size. Residential location behavior of households is examined in a microeconomic framework and equilibrium and optimal patterns of residential land use are discussed. The corresponding equilibrium and optimal city sizes are studied in a variety of contexts. Part Two extends the classical theories of von Thunen and Alonso with the addition of externality factors such as local public goods, crowding and congestion, and racial prejudice. The rigorous mathematical approach and theoretical treatment of the material make Urban Economic Theory of interest to researchers in urban economics, location theory, urban geography, and urban planning.

Contents: I. Mechanics of Continuous Media - Basic Concepts. 1. State of Strain. 2. State of Stress. 3. Thermodynamics of Continuous Media. II. Mechanism of Material Strain. 4. Linear Elasticity. Gene

Eugene Narmour formulates a comprehensive theory of melodic syntax to explain cognitive relations between melodic tones at their most basic level. Expanding on the theories of Leonard B. Meyer, the a

This third edition of The Stages of Economic Growth, first published in 1991, has a new preface and appendix, Professor Rostow extends his analysis to include economic and political developments as well as the advances in theory concerning nonlinear and chaotic phenomena. For those coming to his work for the first time, the original text and the introductions and appendices from earlier editions are included. This volume will not only be of interest to those concerned with the theory of economic growth, but also to students of policy since the 1960s. In the text Professor Rostow gives an account of economic growth based on a dynamic theory of production and interpreted in terms of actual societies. Five basic stages of economic growth are distinguished with detailed discussions of each stage including illustrative examples. He also applies the concept of stages of growth to an examination of the problems of military aggression and the nuclear arms race. The final chapter includes a com

This book describes an array of power tools for data analysis that are based on nonparametric regression and smoothing techniques. These methods relax the linear assumption of many standard models and

Introductory treatment explores existence theorems for first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. "A rigoro

Profusely illustrated description and analysis of actual building practices: quarrying methods, dressing and laying blocks of stone, brickwork, pyramid construction, Egyptian mathematics, tools, much

This unique book develops the classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, in rather a novel way to provide a unifying framework in which they can be studied. The author focuses on factorisation properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to investigate non-trivial factors. The study of these properties is the central theme of the book. Basic facts about integral geometry and random point process theory are developed in a simple geometric way, so that the whole approach is suitable for a non-specialist audience. Even in the later chapters, where the factorisation principles are applied to geometrical processes, the prerequisites are only standard courses on probability and analysis. The main ideas presented here have application to such areas as stereology and tomography, geometrical statistics, pattern and texture analysis. This book will b

Building on a base of simple economic theory and elementary linear algebra and calculus, this broad treatment of static and dynamic optimization methods discusses the importance of shadow prices, and

This new manual is an indispensable working lab guide and reference for water/wastewater quality analysis. Based on procedures from "Standard Methods" and "Methods for Chemical Analysis of Water and W

This book analyzes, with unprecedented breadth and coverage, the development, maturation, growth, and sudden decline of a distinctive, regional urban economic system that developed along the upper Mississippi River north of St. Louis during the middle third of the nineteenth century. Between 1820 and the Civil War the upper Mississippi River valley was at the center of national and international attention. At the edge of the northern frontier, this area, known as 'The Great West,' was the destination of hundreds of thousands of immigrants from the East and from northern Europe. To many, its rich lands, temperate climate, and vast rivers offered an opportunity to establish a better life, as well as a chance to enter, if desired, the mainstream of American life. Drawing from a variety of methods used in historical geography, economic history, systems analysis, and social and urban history, Timothy Mahoney analyzes how early settlement patterns were affected by experience, climate, and ge

This volume explores four basic theoretical issues in public policy analysis: conceptual theory, theory of knowing, casual theory, and normative analysis; the final section addresses future aspects of

Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, b

This defense of the concept of bourgeois revolution reasserts the importance of basic historical materialist precepts to an understanding of the rise of European capitalism. In a wide-ranging analysis

Configural Frequency Analysis (CFA) is a method for analysis of groups of individuals in cross-classifications. Individuals belong to a type if their particular pattern of characteristics occurs more often than expected, and to an antityte if their particular pattern of characteristics occurs less often than expected. The author's original contribution is his linking of CFA to log-linear modeling and the General Linear Model, enabling the reader to relate CFA to a well-known statistical background. It is shown that CFA and log-linear modeling are methods that complement each other. Introduction to Configural Frequency Analysis covers the latest developments in CFA, and it will be easy to read even for those with only an elementary statistics course as a background.

This attractively illustrated book reviews the effects of agricultural development on bird populations in Britain. Examining modern farmland as a bird habitat, it explains the changes, both in habitat structure and in available resources, that have occurred as a result of mechanisation and use of agrochemicals. Farmland bird communities are described, and their composition related to farm structure and land use. Based extensively on empirical data extracted from the British Trust for Ornithology's Common Bird Census and from nest histories recorded in the BTO'S Nest Record Scheme, the book presents an important analysis of the position of agricultural bird populations under modern farming systems. Particular examination has been made of the impact of changing methods, rotations and crops, which have been underestimated in the past. Resulting from the co-operation between a professional ornithologist and a working cereal farmer, this book provides an objective and informed view of the i

From their inception, Siegel modular forms have been studied extensively because of their significance in both automorphic functions in several complex variables and number theory. The comprehensive theory of automorphic forms to subgroups of algebraic groups and the arithmetical theory of modular forms illustrate these two aspects in an illuminating manner. The author's aim is to present a straightforward and easily accessible survey of the main ideas of the theory at an elementary level, providing a sound basis from which the reader can study advanced works and undertake original research. This book is based on lectures given by the author for a number of years and is intended for a one-semester graduate course, though it can also be used profitably for self-study. The only prerequisites are a basic knowledge of algebra, number theory and complex analysis.

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.

An introductory undergraduate text demonstrating the use of geostatistical methods in the analysis of earth science data. The fundamental concepts are developed through the use of numerical examples d

The Bending and Stretching of Plates is written by one of the world's leading authorities on plate-behaviour. Although the mathematical content is necessarily high, the aim is to give a clear physical insight into elastic plate behaviour; the style is thus appropriate to engineers and applied mathematicians. Small-deflexion theory is treated in Part 1, with a discussion of basic equations (including thermal effects and multi-layered anisotropic plates, rectangular plates, circular and other shaped plates, plates whose boundaries are amenable to conformal transformation, plates with variable thickness, and approximate methods). Large-deflexion theory is treated in Part 2 in chapters dealing with basic equations and exact solutions, approximate methods (including post-buckling behaviour), and asymptotic theories for very thin plates (including tension field theory and inextensional theory).

This book sets out a generative structuralist conception of general theoretical sociology; its philosophy, its problems, and its methods. The field is defined as a comprehensive research tradition with many intersecting subtraditions that share conceptual components. The focus is on formalization and unification as processes that can help advance the state of theory today. An integrative philosophy of the field is set out in terms of a process worldview, with a focus on generativity in explanation and a conception of the structure of theories as hierarchical meaning control systems. This philosophy is implemented in two phases. In the first phase, Professor Fararo defines the core problems of theoretical sociology in the context of setting out and illustrating the logic of a nonlinear dynamical social systems framework. A critical analysis of the outcome of this phase then leads, in the second phase, to formal treatments of action principles and structural analysis. A variety of tradit

The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently undergoing intense research. By selecting one or more of these topics to focus on, the reader can quickly approach the specialized literature and indeed the frontier of the area of interest. Each of the four basic aspects of ergodic theory - examples, convergence theorems, recurrence properties, and entropy - receives first a basic and then a more advanced, particularized treatment. At the introductory level, the book provides clear and complete discussions of the standard examples, the mean and pointwise ergodic theorems, recurrence, ergodicity, weak mixing, strong mixing, and the fundamentals of entropy. Among the advanced topics are a thoro

This work outlines the important considerations of policy that confront a democratic state in trying to combat terrorism and at the same time remain democratic. Part I of this book, provides the reader with a comprehensive introduction to the definition, history, theory, operation and effects of terrorism as an essential background to policy analysis. Part II analyses counter-terrorist policies. It begins by outlining basic policy choices and then looks at specific policy areas such as the role of intelligence agencies, the use of the armed forces, the development of anti-terrorist legislation and international treaties, and the issue of regulation of media reporting of terrorist incidents. Developments in the strategic dimension of terrorism are discussed in chapters on the importance of hostage takings to international terrorism and issues surrounding state involvement in international terrorism. In the preparation of this second edition, Grant Wardlaw has considerably expanded the s

This comprehensive textbook conveys the basic physical ideas and laws used in the study of the outer layers of a star. The stellar atmosphere emits the light which we see. The only layers of a star where we can get direct information about temperature, pressure and composition are in the atmosphere. This complete account first introduces stellar magnitudes, spectra and temperatures. This is followed by a full discussion of radiative transfer in a stellar atmosphere, which leads to descriptions of line formation, the spectrum of hydrogen, and spectral analysis. Finally the structural components that are accessible, such as the convestion zone, chromosphere, corona, and mass outflow are described. The book will interest any student with a knowledge of physics and mathematics who needs to learn about stellar atmospheres.

This was the first paperback edition of a classic work of recent English historiography, first published in 1981. In analysing the population of a country over several centuries, the authors qualify, confirm or overturn traditional assumptions and marshal a mass of statistical material into a series of clear, lucid arguments about past patterns of demographic behaviour and their relationship to economic trends. The Population History of England presents basic demographic statistics - monthly totals of births, deaths and marriages - and uses them in conjunction with new methods of analysis to determine population size, gross production rates, expectation of life at birth, age structure and net migration totals. The results make it possible to construct a new model of the interplay of economic and demographic variables in England before and during the industrial picture of English population trends between 1541 and 1871 is a remarkable achievement and in a short preface, the authors cons

Combining the methods of the modern philosopher with those of the historian of ideas, Knud Haakonssen presents an interpretation of the philosophy of law which Adam Smith developed out of - and partly in response to - David Hume's theory of justice. While acknowledging that the influences on Smith were many and various, Dr Haakonssen suggests that the decisive philosophical one was Hume's analysis of justice in A Treatise of Human Nature and the second Enquiry. He therefore begins with a thorough investigation of Hume, from which he goes on to show the philosophical originality of Smith's new form of natural jurisprudence. At the same time, he provides an over all reading of Smith's social and political thought, demonstrating clearly the exact links between the moral theory of The Theory of Moral Sentiments, the Lectures on Jurisprudence, and the sociohistorical theory of The Wealth of Nations. This is the first full analysis of Adam Smith's jurisprudence; it emphasizes its normative a

This pioneering book studies the function and status of the written word in Carolingian society in France and Germany in the eighth- and ninth-centuries. It demonstrates that literacy was by no means confined to a clerical élite, but was dispersed in lay society and used for government and administration, and for ordinary legal transactions among the peoples of the Frankish kingdom. While exploiting a huge range of primary material, Professor McKitterick does not confine herself to a functional analysis of the written word in Carolingian northern Europe but goes on to assess the consequences and implications of literacy for the Franks themselves and for the subsequent development of European society after 1000. Key topics discussed include law and the use of the written word, the conduct and record of legal transactions, the economic and social status of the book in Carolingian society, the methods evolved to organize and define written knowledge, and the whole question of lay literacy

First published in 1961 this monograph deals with the analysis of unsteady lift distributions of thin oscillating wings at transonic speeds. Such distributions are needed for the prediction of flutter, which tends to occur more frequently at speeds near that of sound than in any other speed regime. This book emphasises analytical methods that treat the linearised problem for simple wing planforms such as rectangular and delta wings. There is a thorough discussion of the limitations of the validity of linearised theory as well as the proper boundary conditions to be applied for the case of flows with shocks. Although the standard approach in engineering practice is to sense transonic flow calculations with the aid of direct numerical simulations on a high-speed computer, the treatment in this classic monograph is still of value in the physical insight it provides and in the reference 'exact' solutions it supplies for simplified cases that may serve as validation cases for complicated co

This book examines the economic reasons why people choose to live where they live and develops, through analysis of the bid rent function, a unified theory of urban land use and city size. The first part of the book explicates the basic theory of urban land use and optimal city size. Residential location behavior of households is examined in a microeconomic framework and equilibrium and optimal patterns of residential land use are discussed. The corresponding equilibrium and optimal city sizes are studied in a variety of contexts. Part Two extends the classical theories of von Thunen and Alonso with the addition of externality factors such as local public goods, crowding and congestion, and racial prejudice. The rigorous mathematical approach and theoretical treatment of the material make Urban Economic Theory of interest to researchers in urban economics, location theory, urban geography, and urban planning.

This book is a comprehensive account of the theory and applications of regular variation. It is concerned with the asymptotic behaviour of a real function of a real variable x which is 'close' to a power of x. Such functions are much more than a convenient extension of powers. In many limit theorems regular variation is intrinsic to the result, and exactly characterises the limit behaviour. The book emphasises such characterisations, and gives a comprehensive treatment of those applications where regular variation plays an essential (rather then merely convenient) role. The authors rigorously develop the basic ideas of Karamata theory and de Haan theory including many new results and 'second-order' theorems. They go on to discuss the role of regular variation in Abelian, Tauberian, and Mercerian theorems. These results are then applied in analytic number theory, complex analysis, and probability, with the aim above all of setting the theory in context. A widely scattered literature is

This textbook, covering the basic mathematics taught to first-year students of science and engineering, reflects the growing awareness that ancillary mathematics should not be taught in isolation from its applications. Topics covered include calculus, ordinary and partial differential equations and statistics. Each chapter starts with two or three examples setting the new techniques to be studied in the context of the scientific world; the mathematics is then presented, along with worked examples. Numerical methods are integrated with analytical techniques where appropriate. The resulting textbook provides the teacher with a rich and varied source of applications for classroom use and students with a textbook for self-learning, giving insight into the significance and role of mathematics in science and engineering.

This is the third edition of a successful textbook, now with material added to illustrate the potential of computers for biologists. It is a lucid introduction to the principles and more elementary techniques of statistical reasoning, particularly as they are relevant to the biologist. Special attention is paid to the validity and use of statistical procedures, the interpretation of results, and the meanings of the conclusions which can then be drawn. The understanding of statistical methods is aided by full explanations of how calculations are built up. A particular feature of this edition is the inclusion, of new material to demonstrate the potential usefulness of computers in biological statistical analysis and to this end computer analyses of a selection of the examples are presented, using several different statistical languages. The examples are designed to guide and encourage the biologist to pursue the use of these languages further. The book assumes no mathematical training an

Analysis of Ordinal Categorical Data Alan Agresti Statistical Science Now has its first coordinated manual of methods for analyzing ordered categorical data. This book discusses specialized models tha

In studying the dynamics of populations, whether of animals, plants or cells, it is crucial to allow for intrinsic delays, due to such things as gestation, maturation or transport. This book is concerned with one of the fundamental questions in the analysis of the effect of delays, namely determining whether they effect the stability of steady states. The analysis is presented for one or two such delays treated both as discrete, where an event which occurred at a precise time in the past has an effect now, and distributed, where the delay is averaged over the population's history. Both of these types occur in biological contexts. The method used to tackle these questions is linear stability analysis which leads to an understanding of the local stability. By avoiding global questions, the author has kept the mathematical prerequisites to a minimum, essentially advanced calculus and ordinary differential equations.

Hankel operators are of wide application in mathematics (functional analysis, operator theory, approximation theory) and engineering (control theory, systems analysis) and this account of them is both elementary and rigorous. The book is based on graduate lectures given to an audience of mathematicians and control engineers, but to make it reasonably self-contained, the author has included several appendices on mathematical topics unlikely to be met by undergraduate engineers. The main prerequisites are basic complex analysis and some functional analysis, but the presentation is kept straightforward, avoiding unnecessary technicalities so that the fundamental results and their applications are evident. Some 45 exercises are included.

One of the key issues in the analysis of the capitalist state is its relationship with democracy. To what extent can a capitalist state be democratised? Where and how do democratic institutions intervene in the management and control of capitalism? Has the emergence of democracy changed the composition of the state? These questions lead inevitably to the basic issue of the interconnections between economics and politics, economy and polity, with which this volume is concerned. This wide-ranging and eclectic collection, combining theoretical and empirical material, and containing contributions from several leading authorities on the modern state, will be of value for teachers and students of political science, sociology and political economy, as well as appealing to historians and philosophers interested in the nature of the state.