Basic Methods of Linear Functional Analysis

This book describes the various methods currently used to deposit highly ordered organic films, and the physical techniques employed in characterising their properties. Such films are the subject of a great deal of research, motivated by their potential application in micro-electronics. Beginning with a discussion of the necessary basic physics and chemistry, the book proceeds to a description of the main topics of current research in this field. The Langmuir–Blodgett technique, self-assembly, and methods of film deposition exploiting the ordered structure of mesophases are described in detail. Liquid crystals, films at the air/water interface and biomembranes are also discussed. The book is aimed at those graduate students and established research workers with an interest in the physics and chemistry of these fascinating structures.

This graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples of newer mathematical contributions. Relevant problems appear throughout the text. 1983 edition.

This is a substantial revision of a much-quoted monograph, first published in 1974. The structure is unchanged, but the text has been clarified and the notation brought into line with current practice. A large number of 'Additional Results' are included at the end of each chapter, thereby covering most of the major advances in the last twenty years. Professor Biggs' basic aim remains to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first part, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth. There follows an extensive account of the theory of chromatic polynomials, a subject which has strong links with the 'interaction models' studied in theoretical physics, and the theory of knots. The last part deals with symmetry and regularity properties. Here there are important connections with

"This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is r

Rational choice approaches to the study of politics are of great and growing prominence in political science. There are an increasing number of collections devoted to the methods of rational choice theory and specialised monographs applying it to individual topics. The present volume is a collection of substantive applications of rational choice theory in three of the main fields of political inquiry: comparative politics, international relations and political theory. The essays gathered here represent work by many of the most outstanding scholars in the discipline, showing how rational choice theory may be employed in the analysis of fundamental political questions.

Rational choice approaches to the study of politics are of great and growing prominence in political science. There are an increasing number of collections devoted to the methods of rational choice theory and specialised monographs applying it to individual topics. The present volume is a collection of substantive applications of rational choice theory in three of the main fields of political inquiry: comparative politics, international relations and political theory. The essays gathered here represent work by many of the most outstanding scholars in the discipline, showing how rational choice theory may be employed in the analysis of fundamental political questions.

Comparative research is exploding with alternative methodological and theoretical approaches. In this book, experts in each one of these methods provide a comprehensive explanation and application of time-series, pooled, event history and Boolean methods to substantive problems of the welfare state. Each section of the book focuses on a different method with a general introduction to the methods and then two papers using the method to deal with analysis concerning welfare state problems in a political economy perspective. Scholars concerned with methodology in this area cannot afford to overlook this book because it will help them keep up on proliferating methodologies. Graduate students in political science and sociology will find this book extremely useful in their careers.

This book provides a brief but thorough account of the basic principles of good pump design. The first three chapters present the basic hydraulic equations, including cavitation, and discuss the principles that underlie the correct performance of the impeller and casing of centrifugal pumps and the blading of axial machines. The fourth chapter outlines analytical methods for flow calculations, including special techniques used in computer aided design. The following two chapters work through two examples: the impeller and casing of a simple volute type centrifugal pump; and an axial flow pump impeller. Shafts, bearings, seals and drives are discussed in a separate chapter. The last two chapters deal with design for difficult fluids, and codes and practices.

The Schur algebra is an algebraic system providing a link between the representation theory of the symmetric and general linear groups (both finite and infinite). In the text Dr Martin gives a full, self-contained account of this algebra and these links, covering both the basic theory of Schur algebras and related areas. He discusses the usual representation-theoretic topics such as constructions of irreducible modules, the blocks containing them, their modular characters and the problem of computing decomposition numbers; moreover deeper properties such as the quasi-hereditariness of the Schur algebra are discussed. The opportunity is taken to give an account of quantum versions of Schur algebras and their relations with certain q-deformations of the coordinate rings of the general linear group. The approach is combinatorial where possible, making the presentation accessible to graduate students. This is the first comprehensive text in this important and active area of research; it wi

This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory. which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specialising in category theory.

This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory. which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specialising in category theory.

Designed for students with only a basic knowledge of linguistics, this leading textbook provides a clear and practical introduction to phonology, the study of sound patterns in language. It teaches in a step-by-step fashion the logical techniques of phonological analysis and the fundamental theories that underpin it. This thoroughly revised and updated edition teaches students how to analyze phonological data, how to think critically about data, how to formulate rules and hypotheses, and how to test them. New to this edition: • Improved examples, over 60 exercises and 14 new problem sets from a wide variety of languages encourage students to practise their own analysis of phonological processes and patterns • A new and updated reference list of phonetic symbols and an updated transcription system, making data more accessible to students • Additional online material includes pedagogical suggestions and password-protected answer keys for instructors

Comparative research is exploding with alternative methodological and theoretical approaches. In this book, experts in each one of these methods provide a comprehensive explanation and application of time-series, pooled, event history and Boolean methods to substantive problems of the welfare state. Each section of the book focuses on a different method with a general introduction to the methods and then two papers using the method to deal with analysis concerning welfare state problems in a political economy perspective. Scholars concerned with methodology in this area cannot afford to overlook this book because it will help them keep up on proliferating methodologies. Graduate students in political science and sociology will find this book extremely useful in their careers.

The ultimate objective of any controls text is to teach students how to achieve the best possible design. In this new text, Wolovich integrates classical and modern techniques, systematically develops

The study of composition operators links some of the most basic questions you can ask about linear operators with beautiful classical results from analytic-function theory. The process invests old the

This is a guide to the various frameworks, concepts, and methods available for the analysis of discourse within linguistics. It compares six dominant approaches to discourse analysis: speech act theor

An in-depth treatment of the transient stability problem, its physical description and formulation. Discusses methods for transient stability analysis, sensitivity assessment and control. Considers co

This book presents a mathematical programming approach to the analysis of production frontiers and efficiency measurement. The authors construct a variety of production frontiers, and by measuring distances to them are able to develop a model of efficient producer behaviour and a taxonomy of possible types of departure from efficiency in various environments. Linear programming is used as an analytical and computational technique in order to accomplish this. The approach developed is then applied to modelling producer behaviour. By focusing on the empirical relevance of production frontiers and distances to them, and applying linear programming techniques to artificial data to illustrate the type of information they can generate, this book provides a unique study in applied production analysis. It will be of interest to scholars and students of economics and operations research, and analysts in business and government.

As the analysis of social networks, or networks of interpersonal and social relationships among social groups, has become an increasingly important method of research in several of the social and behavioural sciences, the gathering of network data has outpaced the development of new methods for its analysis. Addressing the need for analytical tools, Philippa Pattison presents a number of algebraic models for the analysis of network data, explaining in the process the rationale for an algebraic approach. Models are developed for both complete networks, meaning those representing the social ties between all pairs of members in a given group, and local networks, meaning those structured around the social ties of one particular group member. Many applications are presented and the ways that these methods can address a number of important issues confronting network analysis are explained.

An understanding of the origins of earnings distributions is of central importance for any public policy which has the aim of combating economic inequality. The aim of this book is to provide a satisfactory theoretical foundation which could serve as the rational basis for such policies. The approach, strongly influenced by human capital theory, is especially novel in that it permits individual analyses at three interconnecting levels of aggregation using the same basic microeconomic model: the level of earnings distribution within age groups; the level of the overall earnings distribution across all age groups; and the distribution of lifetime earnings. The analysis demonstrates the interdependence between age composition, inequality, and public distribution policy. It also addresses the question of how differences between individuals are transformed into income differences.

Numbers are part of our everyday experience and their properties have fascinated mankind since ancient times. Deciding whether a number is prime and if not, what its factors are, are both fundamental problems. In recent years analysis and solution of these problems have assumed commercial significance since large primes are an essential feature of secure methods of information transmission. The purely mathematical fascination that led to the development of methods for primality testing has been supplemented by the need to test within reasonable timescales, and computational methods have entered at all levels of number theory. In this book, Peter Giblin describes, in the context of an introduction to the theory of numbers, some of the more elementary methods for factorization and primality testing; that is, methods independent of a knowledge of other areas of mathematics. Indeed everything is developed from scratch so the mathematical prerequisites are minimal. An essential feature of t

This book introduces the theory of the structural loading on ships and offshore structures caused by wind, waves and currents, and goes on to describe the applications of this theory in terms of real structures. The main topics described are linear-wave induced motions, loads on floating structures, numerical methods for ascertaining wave induced motions and loads, viscous wave loads and damping, station-keeping and water impact and entry. The applications of the theoretical principles are introduced with extensive use of exercises and examples. Applications covered include conventional ships, barges, high speed marine vehicles, semisubmersibles, tension leg platforms, moored or dynamic positioned ships, risers, buoys, fishing nets, jacket structures and gravity platforms.

This book presents a collection of analog electronic circuits based on the op-amp, supported by a wealth of practical detail which will enable the reader to speedily select, build and test a desired circuit. The book is primarily intended to be a practical reference volume rather than a teaching text. Readers will discover an extensive and invaluable source of functional and established analog circuits, from integrators and differentiators to logarithmic amplifiers, from filters to instrumentation amplifiers. The circuits are grouped according to function, and the approach is to build up slowly from the basic textbook examples towards a series of practical, workable circuits. Students who need to build and test particular types of analog circuitry as part of an assignment or project based activities will find this book invaluable. Professional engineers will also find the book useful for design and development work. The coverage is extensive and up-to-date, and provides a wealth of tec

Numerical Mathematics is a unique textbook which presents rudimentary numerical mathematics in conjunction with computational laboratory assignments. No previous knowledge of calculus or linear algebra is presupposed, and thus the book is tailor-made for undergraduate students, as well as prospective mathematics teachers. The material in the book emphasises algorithmic aspects of mathematics, which are made viable through numerical assignments, in which the traditional 'chalk-and-talk' lecturer turns, in part, into a laboratory instructor. The book is not a numerical methods book, containing ready-made computational recipes. Rather, it guides the student to create the algorithm required for any given assignment - expressed in whichever programming language is used - on the basis of the underlying mathematics. The computational assignments cover iterative processes, area approximations, solution of linear systems, acceleration of series summation, interpolative approximations, and const

This is a fully revised and updated version of Hans van der Doel's Democracy and Welfare Economics. It presents the economic theory of political decision-making (otherwise knownn as new political economy, or public choice), providing students with an accessible and clear introduction to this important subject. The authors identify four different methods of decision-making by which the political process transforms the demands of individual citizens into government policy and public goods and services: negotiation, majority decision, representations and bureaucratic implementation. These are analysed, in turn, as independent decision-making models whose effectiveness is examined with reference to economic theory. A final chapter draws conclusions from this analysis, arguing that the size of the public sector is a result of forces that work in different directions at different stages of the political process.

This is an advanced text for higher degree materials science students and researchers concerned with the strength of highly brittle covalent–ionic solids, principally ceramics. It is a reconstructed and greatly expanded edition of a book first published in 1975. The book presents a unified continuum, microstructural and atomistic treatment of modern day fracture mechanics from a materials perspective. Particular attention is directed to the basic elements of bonding and microstructure that govern the intrinsic toughness of ceramics. These elements hold the key to the future of ceramics as high-technology materials - to make brittle solids strong, we must first understand what makes them weak. The underlying theme of the book is the fundamental Griffith energy-balance concept of crack propagation. The early chapters develop fracture mechanics from the traditional continuum perspective, with attention to linear and nonlinear crack-tip fields, equilibrium and non-equilibrium crack states.

This procedure offers complete methodologies for sampling and measuring particle streams and summarizes methods of particle size analysis. It also lists operating variables to be considered and measur

This is a new and revised edition of a book which has already established itself as a basic text in social theory. The first section of the work provides a concise critical analysis of some leading

This book describes the research done on the problems of Bénard convection, as well as its modern offspring the Rayleigh–Bénard problem, and Taylor vortices. Bénard convection differs from Rayleigh–Bénard convection by the presence of surface tension, whilst Bénard convection is characterized by parallel rolls. Toroidal vortices characterize Taylor vortex flow. Convection and Taylor vortex flow deal with the consequences of the presence of infinitesimal disturbances in a fluid layer. Both problems are classical examples in the theory of hydrodynamic stability and share many features. Linear theory describing the onset of instability for both problems is practically completed; nonlinear problems have been at the forefront of research during the last 30 years. The impressive progress that has been made in the theoretical and experimental investigation of the nonlinear problems is described and the remaining basic problems are outlined.

Flow cytometry is now well established in research laboratories and is gaining increasing use in clinical medicine and pathology. The technique enables multiple simultaneous light scatter and fluorescence measurements to be made at the individual cell level at very rapid rates and results in very large quantities of data being collected. Data, however, is just a series of numbers which have to be converted to information which, in turn, must be shown to have meaning. This is the most important single aspect of flow cytometry but it has received relatively little attention. One of the frequently voiced advantages of the technology is that it produces 'good statistics' because large numbers of cells have been analysed. However, it is not very often that confidence limits are placed on results, hence the reader has little or no feel for the inherent variability in the information produced. This book covers very basic number handling techniques, regression analysis, probability functions,

Motor development is an integral part of the developmental process. Understanding the organization of the sensory-motor system and its adaptations in response to environmental factors is a vital part of understanding individual development as a whole. This volume describes and discusses human motor development using longitudinal study methods, and from an interdisciplinary perspective. Researchers from a variety of different backgrounds and disciplines provide a broad-ranging analysis of human motor development, from both the practical and theoretical standpoint, in a book which will be of great interest to paediatricians, psychologists, developmental biologists, developmental psychiatrists and neurologists as well as to research scientists in these fields.

The theory of p-adic and classic modular forms, and the study of arithmetic and p-adic L-functions has proved to be a fruitful area of mathematics over the last decade. Professor Hida has given courses on these topics in the USA, Japan, and in France, and in this book provides the reader with an elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise, and the subject is approached using only basic tools from complex analysis and cohomology theory. Graduate students wishing to know more about L-functions will find that this book offers a unique introduction to this fascinating branch of mathematics.

The theory of p-adic and classic modular forms, and the study of arithmetic and p-adic L-functions has proved to be a fruitful area of mathematics over the last decade. Professor Hida has given courses on these topics in the USA, Japan, and in France, and in this book provides the reader with an elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise, and the subject is approached using only basic tools from complex analysis and cohomology theory. Graduate students wishing to know more about L-functions will find that this book offers a unique introduction to this fascinating branch of mathematics.

Pesin theory consists of the study of the theory of non-uniformly hyperbolic diffeomorphisms. The aim of this book is to provide the reader with a straightforward account of this theory, following the approaches of Katok and Newhouse. The notes are divided into two parts. The first develops the basic theory, starting with general ergodic theory and introducing Liapunov exponents. Part Two deals with the applications of Pesin theory and contains an account of the existence (and distribution) of periodic points. It closes with a look at stable manifolds, and gives some results on absolute continuity. These lecture notes provide a unique introduction to Pesin theory and its applications. The author assumes that the reader has only a good background of undergraduate analysis and nothing further, so making the book accessible to complete newcomers to the field.

The first half deals with the motion of a single particle under the influence of electronic and magnetic fields. The basic language of linear and circular accelerators is developed. The principle of p

Piranesi builds a shopping mall, Giotto supervises a training analysis, Milton directs a film. In Postmodernism Across the Ages the traditional notion of change in history, the linear analogy of human

This book of edited contributions provides a wide-ranging survey of the use of probability models for ranking data and it introduces new methods for the statistical analysis of ranking data. The contr

Fluid flow turbulence is a phenomenon of great importance in many fields of engineering and science. Turbulence and related areas have continued to be subjects of intensive research over the last century. In this second edition of their successful textbook Professors Landahl and Mollo-Christensen have taken the opportunity to include recent developments in the field of chaos and its applications to turbulent flow. This timely update continues the original theme of the book: presenting the fundamental concepts and basic methods of fluid flow turbulence which enable the reader to follow the literature and understand current research. The emphasis upon the dynamic processes that create and maintain turbulent flows gives this book an original approach. This book should be useful to graduate students and researchers in fluid dynamics and, in particular, turbulence and related fields.

This book outlines the basic science underlying the prediction of stress and velocity distributions in granular materials. It takes the form of a textbook suitable for postgraduate courses, research workers and for use in design offices. The nature of a rigid-plastic material is discussed and a comparison is made between the Coulomb and conical (extended Von Mises) models. The methods of measuring material properties are described and an interpretation of the experimental results is considered in the context of the Critical State Theory. The book will be an invaluable text for all those working with or doing research into granular materials. Exercises and solutions are provided which will be particularly useful for the student.

Developed fifty years ago by the National Bureau of Economic Research, the analytic methods of business cycles and economic indicators enable economists to forecast economic trends by examining the repetitive sequences that occur in business cycles. The methodology has proven to be an inexpensive and useful tool that is now used extensively throughout the world. In recent years, however, significant new developments have emerged in the field of business cycles and economic indicators. This volume contains twenty-two articles by international experts who are working with new and innovative approaches to indicator research. They cover advances in three broad areas of research: the use of new developments in economic theory and time-series analysis to rationalise existing systems of indicators; more appropriate methods to evaluate the forecasting records of leading indicators, particularly of turning point probability; and the development of new indicators.