Boolean Functions

The rational expectations revolution and other developments in economics (notably game theory) have fundamentally altered the application of optimal control theory to economic forecasting and planning. In particular, they have shown that economic systems cannot be modelled simplistically on physical systems. However, as the authors of this volume show, these developments have greatly enhanced our understanding of how an economy functions, and now make it possible for optimal control theory to be applied much more effectively to economic modelling and planning. This book is divided into two parts. The first presents the orthodox framework but extends it to allow for multiplicative uncertainty, risk and non-linearities in the econometric model. The second part looks explicitly at the question of expectations. It provides methods by which forward-looking expectations can be treated jointly with the determination of economic policy. It also examines game-theoretic considerations - where, f

How does mood affect non-verbal communication, the gazes, gestures and facial expressions which accompany dialogue? This important monograph, based on a longitudinal study of five hundred interviews with depressed patients and normal subjects, systematically examines the ways in which mental illness may affect non-verbal interaction patterns. A number of specific patterns of non-verbal behaviour are identified which relate directly to psychological state and also depend on the interaction of the participants in a dialogue. Non-verbal Communication in Depression is not only rich in much-needed empirical data, but it also offers a fresh theoretical and methodological perspective on communicative behaviour in general. Most importantly, perhaps, it represents a real advance in our understanding of the functions of various non-verbal mechanisms and thus provides the clinical psychologist and psychiatrist with an important diagnostic tool.

This incisive text, directed to advanced undergraduate and graduate students in mathematics, physics and engineering, deftly combines both theory and practical example to introduce and explore Fourie

This book is concerned with the ionosphere and the magnetosphere, and the theory of their effect on radio waves. It includes accounts of some mathematical topics now widely used in this study, particularly W. K. B. approximations, Airy integral functions and integration by steepest descents. The subject is divided into ray theory and full wave theory. Ray theory is useful for high frequencies when the ionosphere is treated as a horizonally stratified medium. The discussion of the magnetosphere, whose structure is more complicated, includes an account of whistlers and ion cyclotron whistlers. The book has been planned both for final year undergraduates and as a reference book for research. It is suitable as a course book on radio propagation for students of physics or electrical engineering or mathematics. Some of the topics are presented from an elementary viewpoint so as to help undergraduates new to the subject. The later parts are more advanced. Because the subject is so large and h

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

In this book the authors reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher order logic, and cartesian closed categories are essentially the same. In Part II, it is demonstrated that another formulation of higher order logic (intuitionistic type theories) is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludes with a set of exercises. Thus it is well-suited for graduate courses and research in mathematics and logic. Researchers in theoretical computer science, artificia

This monograph develops an approach to statistical inference that is both comprehensive in its treatment of statistical principles and sufficiently powerful to be applicable to a variety of important

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.

This short textbook provides a succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. It will be suitable for all mathematics undergraduates coming to the subject for the first time. The book is based on lectures given at the University of Cambridge and covers the basic concepts of logic: first order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. There are also chapters on recursive functions, the axiom of choice, ordinal and cardinal arithmetic and the incompleteness theorems. Dr Johnstone has included numerous exercises designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics. Consequently the book, while making an attractive first textbook for those who plan to specialise in logic, will be particularly valuable for mathematics and computer sc

A brilliant investigation into musical structure and experience through a systematic exploration of tonality, melody, harmony, texture and rhythm, and their important interpretations. These are illumi

The place of money capital in the theory of the firm has remained a relatively neglected question in traditions of economic analysis. In this highly integrative work, issues in production, pricing, capital investment and financial theory are brought to new levels of interdependence. Developing a three-part argument, Money Capital in the Theory of the Firm deals successively with the theoretical issues and analytic motivation, the neoclassical tradition and postclassical perspectives. In doing so, it presents a self-contained foundation in the basic structures of microeconomic analysis relating to optimize decision making in the firm and in the accounting concepts and statistical apparatus of probability theory relevant to the neoclassical aspects of the argument. Additionally, the book provides the essential mathematical development of such advanced topics as utility functions defined over stochastic arguments, the equilibrium theory of financial asset prices and yields, the cost of mo

What are 'emotions'? Drawing together the threads of current research on the nature and funactions of emotional expression, of physiological reactions, and of emotional experience, this book offers a balanced survey of facts and theory. Nico Frijda discusses the motivational and neurophysiological preconditions for emotions, and the ways in which emotions are regulated by the individual. Considering the kinds of events that elicit emotions, he argues that emotions arise because events are appraised by people as favorable or harmful to their own interests. he takes an information-processing perspective: Emotions are viewed as outcomes of the process of assessing the world in terms of one's own concerns, which, in turn, modify action readiness. This analysis leads him to address such fundamental issues as the place of emotion in motivation generally and the discrepancy between the functions of the emotions and their often irrational and disruptive character. An important contribution to

Marsupials differ from most other mammals in their method of reproduction, in that they have chosen, in an evolutionary sense, to develop lactation rather than placentation for the nurture of their young. The neonate is therefore born with a mixture of advanced and embryonic characters, and yet is readily accessible within the pouch, providing a unique system for the study of the ontogeny of various physiological and endocrinological parameters. Marsupials are therefore ideal animals for research into mammalian reproductive physiology. The results of this exciting new research are summarized in this book by two of the foremost workers in the field. Individual chapters analyse the genetic and hormonal control of sexual differentiation, male and female reproductive structures and their functions, the role of the corpus luteum in the oestrous cycle and pregnancy, the hormonal control of embryonic diapause and the role of the marsupial placenta in the development of the embryo. This book i

This book may be used as a self-contained manual for BBC-BASIC, the main language of the BBC Microcomputer and Master Series Computers. Information is presented in a form handy for reference. Page 163, for example, tabulates all characters in the ASCII range; pages 124-5 summarize all information needed when composing screens of MODE 7 graphics. A quick reference to all functions and operators is given on page 179; the syntax of every statement and command of BBC-Basic is summarized on pages 180-1. But there is more to this book. How do you make a computer sort names into alphabetical order? Not as obvious as it might seem. Three different sorting techniques are explained by example in this book: bubble sort, monkey puzzle (more formally the 'binary tree') and Quicksort relies on 'recursion' - an important programming concept which is explained and demonstrated. Making coloured objects rebound around the walls of a squash court is another technique demonstrated; so is making voices sin

The prevailing view of scientific popularization, both within academic circles and beyond, affirms that its objectives and procedures are unrelated to tasks of cognitive development and that its perti

It is generally recognized that larger animals eat more, live longer, have larger offspring, and so on; but it is unusual to see these commonplace observations as a basis for scientific biology. A large number of empirically based relationships describe biological rates as simple functions of body size; and other such relations predict the intrinsic rate of population growth, animal speed, animal density, territory size, prey size, physiology, and morphology. Such equations almost always exist for mammals and birds, often for other vertebrates and invertebrates, sometimes for protozoa, algae, and bacteria, and occasionally even for plants. There are too many organisms to measure all aspects of the biology of every species of population, so scientists must depend on generalizations. Body size relations represent our most extensive and powerful assemblage of generalizations, but they have never been organized for use in ecology. This book represents the largest single compilation of inte

From birth, the urge to eat is the most common everyday experience. Eating to be nourished is the most basic behaviour of human life, and is one of the main functions in all living organisms. Clear answers to a number of important questions have only recently begun to emerge. Why are animals hungry? How are they driven to seek and eat selected foods? How do they become satiated so that they ingest the exact amount of food they need for growth and to maintain stable body weight in adulthood? This book is the first synthesis, by one hand, of the new knowledge on feeding behaviour. It describes the roles of body depletion and repletion of energy and of specific nutrients, of the orosensory qualities of food and of the brain in integrating and interpreting internal and external signals. This volume complements that of B.J. & E.T. Rolls, Thirst, in the same series.

Presenting the various approaches to the study of integration, a well-known mathematics professor brings together in one volume "a blend of the particular and the general, of the concrete and the abst

This major 1984 study of South African trade unionism traces the history of the South African Trades and Labour Council (TLC) from its origins in the 1920s to its demise in the early 1950s. The book focuses on South Africa's secondary industrialisation and subsequent changes in work organization. By analysing trade union structures and strategies Dr Lewis shows how divisions within the labour movement were bound up with the development of production processes and the division of labour, rather than being the inevitable outcome of racial antagonisms. The early chapters analyse the emergence of different trade union strategies. As work processes were transformed by the rapid industrialisation of the 1940s, the traditional craftsmen lost their technical indispensability and increasingly performed supervisory functions. Faced with dilution and undercutting, and increasingly hostile to the majority of black production workers, the craft unions responded by redefining membership on the basis

This book considers convergence of adapted sequences of real and Banach space-valued integrable functions, emphasizing the use of stopping time techniques. Not only are highly specialized results given, but also elementary applications of these results. The book starts by discussing the convergence theory of martingales and sub-( or super-) martingales with values in a Banach space with or without the Radon-Nikodym property. Several inequalities which are of use in the study of the convergence of more general adapted sequence such as (uniform) amarts, mils and pramarts are proved and sub- and superpramarts are discussed and applied to the convergence of pramarts. Most of the results have a strong relationship with (or in fact are characterizations of) topological or geometrical properties of Banach spaces. The book will interest research and graduate students in probability theory, functional analysis and measure theory, as well as proving a useful textbook for specialized courses on m

The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level. This second edition includes a deep

This book is a self-contained account of the theory of classgroups of group rings. The guiding philosophy has been to describe all the basic properties of such classgroups in terms of character functions. This point of view is due to A. Frohlich and it achieves a considerable simplification and clarity over previous techniques. A main feature of the book is the introduction of the author's group logarithm, with numerous examples of its application. The main results dealt with are: Ullom's conjecture for Swan modules of p-groups; the self-duality theorem for rings of integers of tame extensions; the fixed-point theorem for determinants of group rings; the existence of Adams operations on classgroups. In addition, the author includes a number of calculations of classgroups of specific families of groups such as generalized dihedral groups, and quaternion and dihedral 2-groups. The work contained in this book should be readily accessible to any graduate student in pure mathematics who has

First published in 1983, this book summarises the principles of structure and functions of membranes at the molecular level where so much living activity occurs. The dynamic nature of the molecular activity is stressed and examples are drawn from the range of living organisms from bacteria to higher plants and to man. The descriptions and hypotheses in the text are illustrated with some electron micrographs but especially with diagrams based on space-filling atomic models to illustrate the molecular movements. The first four chapters are concerned with the molecular constituents, their packing and their movements. Two chapters deal with membranes in energy transduction, two with trans-membrane diffusion, transport, absorption and secretion and one with excited membranes and signal transmission. the membrane-bound reactions of hormones, antibodies and synthesis are outlined. Finally, membranes are discussed in relation to life's origin and evolution.

Animals may be careful in their choice of mates for a variety of reasons. The ideal mate may have to hold valuable resources as well as being highly fertile or fecund. As likely as not, it should be neither too closely related nor too distantly related, and it should be maximally attractive. All these aspects of a member of the opposite sex may influence how many descendants the pair could produce, but the importance of each will usually depend on the sex and the species of the individual making the choice. This book brings together modern thinking on the various functions of mate choice and its role in evolution. The ways in which finely tuned preferences for a particular member of the opposite sex develop are described, as is the importance of compatibility between mates in long-lived species. Finally, the book deals with the underlying mechanisms and the decision rules involved in choosing a mate. The different approaches of the authors combine to make an excellent overview of an at

First published in 1981, this book is an introduction to studies of the behaviour of a wide variety of animals including man, farm animals and pest species. The approach is ethological and much reference is made to detailed description of behaviour and to biological function, although there is extensive reference to physiology, brain mechanisms and relevant psychological research. Ideas from sociobiology, motivation and learning studies are emphasised. There is, therefore, very broad coverage of the role of behaviour in all aspects of life. Another novel feature is the extensive reference to applied aspects of behaviour, particularly its importance to the production of farm animals and the control of agricultural and medical pests. The book is intelligible to the educated layman but it deals with some complex ideas. It is an adequate text for all requirements in this area for most undergraduates.

This introduction to recent work in p-adic analysis and number theory will make accessible to a relatively general audience the efforts of a number of mathematicians over the last five years. After reviewing the basics (the construction of p-adic numbers and the p-adic analog of the complex number field, power series and Newton polygons), the author develops the properties of p-adic Dirichlet L-series using p-adic measures and integration. p-adic gamma functions are introduced, and their relationship to L-series is explored. Analogies with the corresponding complex analytic case are stressed. Then a formula for Gauss sums in terms of the p-adic gamma function is proved using the cohomology of Fermat and Artin-Schreier curves. Graduate students and research workers in number theory, algebraic geometry and parts of algebra and analysis will welcome this account of current research.

What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). Dr Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory, including a full discussion of non-computability and undecidability, and the theory of recursive and recursively enumerable sets. The later chapters provide an introduction to more advanced topics such as Gödel's incompleteness theorem, degrees of uns

"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

The first systematic exposition of all the central topics in the philosophy of logic, Susan Haack's book has established an international reputation (translated into five languages) for its accessibility, clarity, conciseness, orderliness, and range as well as for its thorough scholarship and careful analyses. Haack discusses the scope and purpose of logic, validity, truth-functions, quantification and ontology, names, descriptions, truth, truth-bearers, the set-theoretical and semantic paradoxes, and modality. She also explores the motivations for a whole range of non-classical systems of logic, including many-valued logics, fuzzy logic, moddal and tense logics, and relevance logics. Persupposing only an elementary knowledge of formal logic, this book includes many useful summary tables and diagrams, as well as a helpful glossary of technical terms. Wide-ranging, informative, and eminently readable, this book has proven a valuable resource for generations of students and scholars in

This book is based on a set of lectures given to a mixed audience of physicists and mathematicians. The desire to be intelligible to both groups is the underlying preoccupation of the author. Physicists nowadays are particularly interested in phase transitions. The typical situation is that a system of interacting particles exhibits an abrupt change of behaviour at a certain temperature, although the local forces between the particles are thought to be smooth functions of temperature. This account discusses the theory behind a simple model of such phenomena. An important tool is the mathematical discipline known as the Theory of Graphs. There are five chapters, each subdivided into sections. The first chapter is intended as a broad introduction to the subject, and it is written in a more informal manner than the rest. Notes and references for each chapter are given at the end of the chapter.

This is a book about the history of family life in several senses. The author puts forward a thesis about the European family in relation to the conspicuous differences between European economic and social development and that of the rest of the world. He discusses the numbers and functions of servants, the numbers and situation of orphans and the aged, and the difficult question of whether American slaves lived in families at all. There is an extended analysis of the extraordinary turnover in population in England and in Europe in pre-industrial times, and a full discussion of the figures for English illegitimacy since Shakespeare's day. There is also a consideration of the elusive topic of the age of sexual maturity and its variations over time. The book represents some of the results of the first fifteen years of work in the newly instituted subject of historical sociology with particular reference to the family.

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

First published in 1973, Dr Clemmow's Introduction to Electromagnetic Theory provides a crisp and selective account of the subject. It concentrates on field theory (with the early development of Maxwell's equations) and omits extended descriptions of experimental phenomena and technical applications, though without losing sight of the practical nature of the subject. Rationalized mks units are used and an awareness of orders of magnitude is fostered. Fields in media are discussed from both the macroscopic and microscopic points of view. As befits a mainly theoretical treatment, a knowledge of vector algebra and vector calculus is assumed, the standard results required being summarized in an appendix. Other comparatively advanced mathematical techniques, such as tensors anf those involving Legendre or Bessel functions, are avoided. Problems for solution, some 180 in all, are given at the end of each chapter.

Lebesgue integration is a technique of great power and elegance which can be applied in situations where other methods of integration fail. It is now one of the standard tools of modern mathematics, and forms part of many undergraduate courses in pure mathematics. Dr Weir's book is aimed at the student who is meeting the Lebesgue integral for the first time. Defining the integral in terms of step functions provides an immediate link to elementary integration theory as taught in calculus courses. The more abstract concept of Lebesgue measure, which generalises the primitive notions of length, area and volume, is deduced later. The explanations are simple and detailed with particular stress on motivation. Over 250 exercises accompany the text and are grouped at the ends of the sections to which they relate; notes on the solutions are given.