Boolean Functions

This book explains, in lay terms, the surprisingly simple system of mathematical logic used in digital computer circuitry. Anecdotal in its style and often funny, it follows the development of this lo

The most comprehensive overview of signal detection available. This is a thorough, up-to-date introduction to optimizing detection algorithms for implementation on digital computers. It focuses extensively on real-world signal processing applications, including state-of-the-art speech and communications technology as well as traditional sonar/radar systems. Start with a quick review of the fundamental issues associated with mathematical detection, as well as the most important probability density functions and their properties. Next, review Gaussian, Chi-Squared, F, Rayleigh, and Rician PDFs, quadratic forms of Gaussian random variables, asymptotic Gaussian PDFs, and Monte Carlo Performance Evaluations. Three chapters introduce the basics of detection based on simple hypothesis testing, including the Neyman-Pearson Theorem, handling irrelevant data, Bayes Risk, multiple hypothesis testing, and both deterministic and random signals. The author then presents exceptionally detailed covera

This book is about the ways in which many animals form groups; for instance, schools of fish, flocks of birds, and swarms of insects. Covering both invertebrate and vertebrate species, the authors investigate three-dimensional animal aggregations from a variety of disciplines, from physics to mathematics to biology. The first section is devoted to the various methods, mainly optical and acoustic, used to collect three-dimensional data over time. The second section focuses on analytical methods used to quantify pattern, group kinetics, and interindividual interactions within the group. The section on behavioural ecology and evolution deals with the functions of aggregative behaviour from the point of view of an inherently selfish individual member. The final section uses models to elucidate how group dynamics at the individual level creates emergent pattern at the level of the group.

Victorian women were exhilarated by the authoritative voice and the professional opportunity that, uniquely, the theatre offered them. Victorian men, anxious to preserve their dominance in this as in every other sphere of life, sought to limit the theatre as being distinctively, irrevocably masculine. Actresses were represented as inhuman monstrosities, not women at all. Furthermore, the executive functions of theatre-manager and playwright were carefully defined as requiring supposedly masculine qualities of mind and personality. A woman playwright came to be seen as an impossibility, although their number actually increased towards the close of the nineteenth century. In this book, Kerry Powell chronicles the development of women's participation in the theatre as playwrights, actresses and managers and explores the making of the Victorian actress, gender and playwriting of the period, and the contributions these made to developments in the following century.

Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential f

This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a discussion of some of its applications. The author then develops the notions of transfinite induction and descriptive set theory, with applications to the theory of real functions. The final part of the book presents the tools of 'modern' set theory: Martin's Axiom, the Diamond Principle, and elements of forcing. Written primarily as a text for beginning graduate or advanced level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields.

This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a discussion of some of its applications. The author then develops the notions of transfinite induction and descriptive set theory, with applications to the theory of real functions. The final part of the book presents the tools of 'modern' set theory: Martin's Axiom, the Diamond Principle, and elements of forcing. Written primarily as a text for beginning graduate or advanced level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields.

Recruitment to legislative office is one of the core functions of political systems, yet we know little about how the process varies from one country to another. Passages to Power provides a comparative account of legislative recruitment which applies a common analytical framework and new survey data to nineteen advanced democracies. Legislative recruitment refers to the critical step as people move from lower levels of politics into parliamentary careers. Who succeeds in becoming a politician? Who fails? And why? Based on original research which adopts a 'new institutionalist' perspective, this 1997 book compares these issues in a wide range of countries. This important study brings together an outstanding group of international scholars to look at recruitment around the world. The countries examined in depth include Australia, Canada, Finland, Germany, Japan, the Netherlands, New Zealand, the United Kingdom, and the United States, along with a comparison of all member states in the E

Recruitment to legislative office is one of the core functions of political systems, yet we know little about how the process varies from one country to another. Passages to Power provides a comparative account of legislative recruitment which applies a common analytical framework and new survey data to nineteen advanced democracies. Legislative recruitment refers to the critical step as people move from lower levels of politics into parliamentary careers. Who succeeds in becoming a politician? Who fails? And why? Based on original research which adopts a 'new institutionalist' perspective, this 1997 book compares these issues in a wide range of countries. This important study brings together an outstanding group of international scholars to look at recruitment around the world. The countries examined in depth include Australia, Canada, Finland, Germany, Japan, the Netherlands, New Zealand, the United Kingdom, and the United States, along with a comparison of all member states in the E

The great three-volume Principia Mathematica is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premisses and primitive ideas, and so to prove that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part 1 (in which the logical properties of propositions, propositional functions, classes and relations are established); section 6 of Part 2 (dealing with unit classes and couples); and Appendices A and B (which give further developments of the argument on the theory of deduction an

The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the develo

Historically, enterprises were an important delivery vehicle for the administration and financing of many programmes of social protection in the economies of Central and Eastern Europe and the former Soviet Union. In most cases this was through systems mandated by the state. When the Central and East European countries (CEECs) began their reforms many expected enterprises to quickly eliminate the benefits they had provided to workers once freed from the encumbrance of state control. This volume, originally published in 1997, investigates the size of these benefits and the forces producing changes in them. Each chapter covers a specific country, exploring the scope, scale and change of benefits in the respective countries,and investigates their determinants. Surprisingly, they find only modest declines and even some increases in aggregate benefits, rather than rapid change. Change is more visible in the details. This volume examines social functions, like early retirement, in both estab

A two-semester graduate textbook providing a comprehensive introduction to two topics of classical analysis. Presumes a good grounding in advanced calculus and complex-variable theory; previous knowle

This 1997 work explores the role of probabilistic methods for solving combinatorial problems. These methods not only provide the means of efficiently using such notions as characteristic and generating functions, the moment method and so on but also let us use the powerful technique of limit theorems. The basic objects under investigation are nonnegative matrices, partitions and mappings of finite sets, with special emphasis on permutations and graphs, and equivalence classes specified on sequences of finite length consisting of elements of partially ordered sets; these specify the probabilistic setting of Sachkov's general combinatorial scheme. The author pays special attention to using probabilistic methods to obtain asymptotic formulae that are difficult to derive using combinatorial methods. This was an important book, describing many ideas not previously available in English; the author has taken the chance to rewrite parts of the text and refresh the references where appropriate.

Semiotics is the science of signs: graphical, such as pictures; verbal (writing or sounds); or others such as body gestures and clothes. Computer semiotics studies the special nature of computer-based signs and how they function in use. This 1991 book is based on ten years of empirical research on computer usage in work situations and contains material from a course taught by the author. It introduces basic traditional semiotic concepts and adapts them so that they become useful for analysing and designing computer systems in their symbolic context of work. It presents a novel approach to the subject, rich in examples, in that it is both theoretically systematic and practical. The author refers to and reinterprets techniques already used so that readers can deepen their understanding. In addition, it offers new techniques and a consistent perspective on computer systems that is particularly appropriate for new hardware and software (e.g. hypermedia) whose main functions are presentatio

This book provides an introduction to the general principles of nuclear magnetic resonance and relaxation, concentrating on simple models and their application. The concepts of relaxation and the time domain are particularly emphasised. Some relatively advanced topics are treated, but the approach is graduated and all points of potential difficulty are carefully explained. An introductory classical discussion of relaxation is followed by a quantum-mechanical treatment. Only when the the principles of relaxation are firmly established is the density operator approach introduced; and then its power becomes apparent. A selection of case studies is considered in depth, providing applications of the ideas developed in the text. There are a number of appendices, including one on random functions. This treatment of one of the most important experimental techniques in modern science will be of great value to final-year undergraduates, graduate students and researchers using nuclear magnetic re

This book provides a comprehensive guide to Spain's major political and economic institutions, analysing their role, structure and functions, as well as their relationship to each other. Set against the background of Spain's consolidation as a young democratic nation and increasingly important contribution to EU affairs, the book examines the 1978 Constitution; the monarchy of Juan Carlos I; the Parliament; central, regional and local government; political parties; trade unions; public sector enterprises; business and professional organisations; financial institutions; and the judiciary. While most chapters reflect Spain's now well-advanced adaptation to life within the European Union, Chapter 15 also looks in detail at the country's representation in EU institutions, as well as the activities of EU-oriented institutions within Spain itself. This is a new expanded, revised and updated edition of the authors' Spain: a Guide to Political and Economic Institutions, first published in 1987

This text puts together "folklore results" touching weak Asplund spaces. It presents a thorough examination of weak Asplund cases. Nonseparable Banach spaces, renorming, and differentiability are stre

The aim of this book is to develop the combinatorics of Young tableaux and to show them in action in the algebra of symmetric functions, representations of the symmetric and general linear groups, and the geometry of flag varieties. The first part of the book is a self-contained presentation of the basic combinatorics of Young tableaux, including the remarkable constructions of 'bumping' and 'sliding', and several interesting correspondences. In Part II these results are used to study representations with geometry on Grassmannians and flag manifolds, including their Schubert subvarieties, and the related Schubert polynomials. Much of this material has never appeared in book form.There are numerous exercises throughout, with hints or answers provided. Researchers in representation theory and algebraic geometry as well as in combinatorics will find Young Tableaux interesting and useful; students will find the intuitive presentation easy to follow.

In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its application, the book also illustrates a way of thinking mathematically: historical background is woven into the narrative, variant proofs illustrate obstructions, false steps and the development of insight, in a manner reminiscent of Euler. It is shown how to formulate theorems as well as how to construct their proofs. Elementary notions from functional analysis, Fourier analysis, functional equations and stability in mechanics are controlled by a geometric view and synthesized to provide an arithmetical analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions until now beyond reach. Connections with other branches of analysis are illustrated by over 250 exercises, st

This book provides a comprehensive guide to Spain's major political and economic institutions, analysing their role, structure and functions, as well as their relationship to each other. Set against the background of Spain's consolidation as a young democratic nation and increasingly important contribution to EU affairs, the book examines the 1978 Constitution; the monarchy of Juan Carlos I; the Parliament; central, regional and local government; political parties; trade unions; public sector enterprises; business and professional organisations; financial institutions; and the judiciary. While most chapters reflect Spain's now well-advanced adaptation to life within the European Union, Chapter 15 also looks in detail at the country's representation in EU institutions, as well as the activities of EU-oriented institutions within Spain itself. This is a new expanded, revised and updated edition of the authors' Spain: a Guide to Political and Economic Institutions, first published in 1987

This new edition, like the first, presents a thorough introduction to differential and integral calculus, including the integration of differential forms on manifolds. However, an additional chapter o

This new text develops an integrated management model that will prepare health information management students to become effective information managers. The focus on decision making, team building, an

This book provides an alternative foundation for the measurement of the production of nations, and applies it to the US economy for the postwar period. The patterns which result are significantly different from those derived within conventional systems of national accounts. Conventional national accounts seriously distort basic economic aggregates, because they classify military, bureaucratic and financial activities as creation of new wealth, when in fact they should be classified as forms of social consumption which, like personal consumption, actually use up social wealth in the performance of their functions. The difference between the two approaches has an impact not only on basic aggregate economic measures, but also on the very understanding of the observed patterns of growth and stagnation. In a world of burgeoning militaries, bureaucracies, and sales forces, such matters can assume great importance at the levels of both theory and policy.

This book places the plays of Aristophanes in their contemporary context, asking what aspects of Greek, and especially Athenian, culture these comedies brought into play for their original audiences. It makes particular use of the structural analysis of Greek rituals and myths to demonstrate how their meanings and functions can be used to interpret the plays. This information is then used to suggest ways in which twentieth-century audiences may read the plays in terms of contemporary literary theories and concerns. This is the first book to apply the techniques of structural anthropology systematically to all the comedies. It does not impose a single interpretative structure on the plays but argues that each play operates with a range of different structures, and that groups of plays use similar structures in different ways. All Greek is translated.

The new edition of this successful and established textbook retains its two original intentions of explaining how to program in the ML language, and teaching the fundamentals of functional programming. The major change is the early and prominent coverage of modules, which are extensively used throughout. In addition, the first chapter has been totally rewritten to make the book more accessible to those without experience of programming languages. The main features of new Standard Library for the revised version of ML are described and many new examples are given, while references have also been updated. Dr Paulson has extensive practical experience of ML and has stressed its use as a tool for software engineering; the book contains many useful pieces of code, which are freely available (via the Internet) from the author. He shows how to use lists, trees, higher-order functions and infinite data structures. Many illustrative and practical examples are included.. Efficient functional imp

Mathematics has become indispensable in the modelling of economics, finance, business and management. Without expecting any particular background of the reader, this book covers the following mathematical topics, with frequent reference to applications in economics and finance: functions, graphs and equations, recurrences (difference equations), differentiation, exponentials and logarithms, optimisation, partial differentiation, optimisation in several variables, vectors and matrices, linear equations, Lagrange multipliers, integration, first-order and second-order differential equations. The stress is on the relation of maths to economics, and this is illustrated with copious examples and exercises to foster depth of understanding. Each chapter has three parts: the main text, a section of further worked examples and a summary of the chapter together with a selection of problems for the reader to attempt. For students of economics, mathematics, or both, this book provides an introducti

Originally published in 1996, this is a presentation of some complex problems of discrete mathematics in a simple and unified form using an original, general combinatorial scheme. The author's aim is not always to present the most general results, but rather to focus attention on ones that illustrate the methods described. A distinctive aspect of the book is the large number of asymptotic formulae derived. Professor Sachkov begins with a discussion of block designs and Latin squares before proceeding to treat transversals, devoting much attention to enumerative problems. The main role in these problems is played by generating functions, which are considered in Chapter 3. The general combinatorial scheme is then introduced and in the last chapter Polya's enumerative theory is discussed. This is an important book, describing many ideas not previously available in English; the author has taken the chance to update the text and references where appropriate.

Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position o

Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position o

The concept of a system as an entity in its own right has emerged with increasing force in the past few decades in, for example, the areas of electrical and control engineering, economics, ecology, ur

From the Preface:"The purpose of this book is to present and apply a language and to discuss methods which make it very convenient to exploit such analogies, and which are uniquely suited to

Calculations on lens systems are often marred by the unjustifiable use of the small-angle approximation. This book describes in detail how the ray and wave pictures of lens behaviour can be combined and developed into a theory capable of dealing with the large angles encountered in real optical systems. A distinct advantage of this approach is that Fourier optics appears naturally, in a form valid for arbitrarily large angles. The book begins with extensive reviews of geometrical optiks, eikonal functions and the theory of wave propagation. The propagation of waves through lenses is then treated by exploiting the close connection between eikonal function theory and the stationary phase approximation. Aberrations are then discussed, and the book concludes with various applications in lens design and analysis, including chapters on laser beam propagation and diffractive optical elements. Throughout, special emphasis is placed on the intrinsic limitations of lens performance. The many pra

Originally published in 1994, this was the first volume to look in depth at the way the brain responds to trauma and subsequently integrates and influences behavioural, metabolic, neurohumoral, cardiovascular and immune functions. At the time, the role of the brain in the control and integration of the responses to injury and infection was becoming increasingly clear. It had been established that some of these responses, such as fever and neuroendocrine changes, responded to the direct influence of the central nervous system. These, and other advances, provided fresh insights into this area and formed a basis for the more effective understanding and clinical management of trauma patients. In this volume, the authors, all international authorities in their fields, discuss data from experimental and clinical studies and considered the implications of these findings for the treatment of the trauma patient.

This book provides an introduction to recent developments in the theory of blow up algebras - Rees algebras, associated graded rings, Hilbert functions, and birational morphisms. The emphasis is on deriving properties of rings from their specifications in terms of generators and relations. While this limits the generality of many results, it opens the way for the application of computational methods. A highlight of the book is the chapter on advanced computational methods in algebra using Gröbner basis theory and advanced commutative algebra. The author presents the Gröbner basis algorithm and shows how it can be used to resolve computational questions in algebra. This volume is intended for advanced students in commutative algebra, algebraic geometry and computational algebra, and homological algebra. It can be used as a reference for the theory of Rees algebras and related topics.

"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

This book places the plays of Aristophanes in their contemporary context, asking what aspects of Greek, and especially Athenian, culture these comedies brought into play for their original audiences. It makes particular use of the structural analysis of Greek rituals and myths to demonstrate how their meanings and functions can be used to interpret the plays. This information is then used to suggest ways in which twentieth-century audiences may read the plays in terms of contemporary literary theories and concerns. This is the first book to apply the techniques of structural anthropology systematically to all the comedies. It does not impose a single interpretative structure on the plays but argues that each play operates with a range of different structures, and that groups of plays use similar structures in different ways. All Greek is translated.