Classical Recursion Theory

Employing contemporary literary theory, eight members of the "Chicago school" of Arabic and Persian literature reorient the critical approach to classical Middle Eastern literature. The authors analyz

This book gives a detailed study of the development and the interpretation given to Niels Bohr's Principle of Correspondence. It also describes the role that this principle played in guiding Bohr's research over the critical period from 1920 to 1927. Quantum mechanics, developed in the 1920s and 1930s by Bohr, Heisenberg, Born, Schrödinger and Dirac, represents one of the most profound turning points in science. This theory required a wholly new kind of physics in which many of the principles, concepts and models representing reality, that had formed the basis of classical physics since Galileo and Newton, had to be abandoned. This book re-examines the birth of quantum mechanics, in particular examining the development of crucial and original insights of Niels Bohr.

Stoic work on ambiguity represents one of the most innovative, sophisticated and rigorous contributions to philosophy and the study of language in western antiquity. This book is both a comprehensive survey of the often difficult and scattered sources, and an attempt to locate Stoic material in the rich array of contexts, ancient and modern, which alone can guarantee full appreciation of its subtlety, scope and complexity. The comparisons and contrasts which this book constructs will intrigue not just classical scholars, and philosophers, but also logicians, theoretical linguists, communication theorists and historians of grammar and of literary theory. The Stoics on Ambiguity is designed to be intelligible to readers with no Greek or Latin.

Many classical and modern results and quadratic forms are brought together in this book. The treatment is self-contained and of a totally elementary nature requiring only a basic knowledge of rings, fields, polynomials, and matrices, such that the works of Pfister, Hilbert, Hurwitz and others are easily accessible to non-experts and undergraduates alike. The author deals with many different approaches to the study of squares; from the classical works of the late 19th century, to areas of current research. Anyone with an interest in algebra or number theory will find this a most fascinating volume.

Anybody who is not shocked by quantum theory has not understood it. Niels Bohr's dictum bears witness to the bewildering impact of quantum theory, flying in the face of classical physics and dramatically transforming scientists' outlook on our relationship with the material world. While the theory has been supremely successful in its explanation of some of the major problems in twentieth-century physics, its meaning (presenting a number of basic philosophical contradictions) is nevertheless the subject of unprecedented controversy amongst scientists. In this book, which has its origin in a series of radio broadcasts, Paul Davies interviews eight physicists involved in debating and testing the theory, with radically different views of its significance.

These notes are based on a series of lectures given at the Advanced Research Institute of Discrete Applied Mathematics held at Rutgers University. Their aim is to link together algorithmic problems arising in knot theory, statistical physics and classical combinatorics. Apart from the theory of computational complexity concerned with enumeration problems, introductions are given to several of the topics treated, such as combinatorial knot theory, randomised approximation algorithms, percolation and random cluster models. To researchers in discrete mathematics, computer science and statistical physics, this book will be of great interest, but any non-expert should find it an appealing guide to a very active area of research.

First published in 1993, this book provides an overview of issues and debates in contemporary urban sociology. It reviews critically each of the major theoretical orientations in the field, providing a brief historical introduction to each approach but emphasising the current theoretical debate. Flanagan juxtaposes the approaches of classical urbanism and urban community theory, the urban ecology approach and the postmodern approach and explains their lasting contribution to the field. Adherents of each of these methodologies contribute to debates within the field, making an overview volume all the more necessary.

This book is about one of the most baffling of all paradoxes – the famous Liar paradox. Suppose we say: 'We are lying now'. Then if we are lying, we are telling the truth; and if we are telling the truth we are lying. This paradox is more than an intriguing puzzle, since it involves the concept of truth. Thus any coherent theory of truth must deal with the Liar. Keith Simmons discusses the solutions proposed by medieval philosophers and offers his own solutions and in the process assesses other attempts to solve the paradox. Unlike such attempts, Simmons' 'singularity' solution does not abandon classical semantics and does not appeal to the kind of hierarchical view found in Barwise's and Etchemendy's The Liar. Moreover, Simmons' solution resolves the vexing problem of semantic universality – the problem of whether there are semantic concepts beyond the expressive reach of a natural language such as English.

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.

The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups, and the methods used are analytical but have little to do with what is described these days as real analysis. Most of the results described in this book have a dual formulation; they have a 'discrete version' related to a finitely generated discrete group, and a continuous version related to a Lie group. The authors chose to centre this book around Lie groups but could quite easily have pushed it in several other directions as it interacts with opetators, and probability theory, as well as with group theory. This book will serve as an excellent basis for graduate courses in Lie groups, Markov chains or potential theory.

The classical music of India, its history, instruments, musicians, and theory are thoroughly discussed in this copiously illustrated reference.

This 1994 book constitutes a sustained, comprehensive, and rigorous critique of contemporary Hobbesian contractarianism as expounded in the work of Jean Hampton, Gregory Kavka, and David Gauthier. Professor Kraus argues that the attempts by these three philosophers to use Hobbes to answer current political and moral questions fail. The reasons why they fail are related to fundamental problems intrinsic to Hobbesian contractarianism: first, the problem of collective action arising out of the tension in Hobbes's theory between individual and collective rationality; second, the classical problem of explaining the normative force of hypothetical action, a problem that can be traced to the conflicting strategies of hypothetical justification found in Rawls's and Hobbes's theories. Given the deep interest in Hobbesian contractarianism among philosophers, political theorists, game theorists in economics and political science, and legal theorists, this book is likely to attract wide attention

This is a book that has long needed to be written. In the period since the Second World War, a number of writers ... have drawn attention to the strong role played by a classical and medieval theory o

This book examines the love elegies of the Roman poets Tibullus, Propertius and Ovid from the point of view of the way the meanings attributed to the poems arise out of the interests and preoccupations of the cultural situation in which they are read. Each study is centred around a reading of a poem or poems together with a discussion of a variety of sophisticated theoretical approaches. All Latin texts and terms are translated or closely paraphrased. Although the book concentrates on the work of the Roman elegists, the challenging insights it offers into the processes involved in the reading and appropriation of the texts of the past are relevant to scholars and students of classical literature in general, and its discussion of such key issues as history, textuality, representation, discourse, gender, ideology and metaphor will be of concern to those interested in literary theory and cultural studies.

Many of the fundamental questions in social science entail an examination of the role played by social institutions. Why do we have so many social institutions? Why do they take one form in one society and quite different ones in others? In what ways do these institutions develop? When and why do they change? Institutions and Social Conflict addresses these questions in two ways. First it offers a thorough critique of a wide range of theories of institutional change, from the classical accounts of Smith, Hume, Marx and Weber to the contemporary approaches of evolutionary theory, the theory of social conventions and the new institutionalism. Secondly, it develops a new theory of institutional change that emphasises the distributional consequences of social institutions. The emergence of institutions is explained as a by-product of distributional conflict in which asymmetries of power in a society generate institutional solutions to conflicts.

This book focuses on the relationship between the process of production of commodities and the process of social reproduction of the labouring population, and seeks to restore that problematic relationship to the central place it had in the analysis of Smith, Ricardo, and Marx. The argument is directly opposed to that of the wages-fund theorists, who rejected the classical view of labour as a very special type of commodity whose price was determined exogenously by material, historical and institutional factors. By substituting a strict supply-and-demand mechanism they and their followers effectively removed the whole question of social reproduction from economic theory. This rendered marginal or analytically invisible certain fundamental aspects of the system. In this investigation the author draws on the history of economic thought, social history, and applied economics, using the surplus definition of profit. The resulting perspective, centred on the relation between production and

The notion of 'stopping times' is a useful one in probability theory; it can be applied to both classical problems and fresh ones. This book presents this technique in the context of the directed set, stochastic processes indexed by directed sets, and many applications in probability, analysis and ergodic theory. Martingales and related processes are considered from several points of view. The book opens with a discussion of pointwise and stochastic convergence of processes, with concise proofs arising from the method of stochastic convergence. Later, the rewording of Vitali covering conditions in terms of stopping times clarifies connections with the theory of stochastic processes. Solutions are presented here for nearly all the open problems in the Krickeberg convergence theory for martingales and submartingales indexed by directed set. Another theme of the book is the unification of martingale and ergodic theorems.

The practice of growing two or more crops together is widespread throughout the tropics and is becoming increasingly practised in temperate agriculture. The benefits of nutrient exchange, reduced weed competition and pathogen control can generate substantial improvements in growth and yield. In this book John Vandermeer, a leading worker on the subject, shows how classical ecological principles, especially those relating to competition and population ecology, can be applied to intercropping. Despite the large amount of research activity directed towards the subject over the last 20 years, the practice of intercropping has, until now, received very little serious academic attention. The Ecology of Intercropping is unique in approaching the question of intercropping from a theoretical point of view. In addition the details of the approach will take as their starting point well-accepted ecological theory. Using this basis the author shows how the approach can be used to design and evaluat

The use of geometric methods in classical mechanics has proven to be a fruitful exercise, with the results being of wide application to physics and engineering. Here Professor Marsden concentrates on these geometric aspects, and especially on symmetry techniques. The main points he covers are: the stability of relative equilibria, which is analyzed using the block diagonalization technique; geometric phases, studied using the reduction and reconstruction technique; and bifurcation of relative equilibria and chaos in mechanical systems. A unifying theme for these points is provided by reduction theory, the associated mechanical connection and techniques from dynamical systems. These methods can be applied to many control and stabilization situations, and this is illustrated using rigid bodies with internal rotors, and the use of geometric phases in mechanical systems. To illustrate the above ideas and the power of geometric arguments, the author studies a variety of specific systems, in

In this book, Professor Nicholson outlines social scientific approaches to international relations and then describes the problems of rational decision-making in conflict situations. He shows how rationality is in many strategic situations hard to define and often leads to paradoxes such as the prisoners' dilemma. In the following part the author explores rational beliefs about the international system. He examines theories of arms races, alliances and the international problems of ecology. Here he is critical of the classical school of international relations for a lack of rigour in dealing with the problems of evidence and belief. Finally, Michael Nicholson discusses the philosophy of science, policy and ethics. This book is both an exposition and a defence of a social scientific approach to international relations. With its emphasis on social scientific approaches, theory building and testing - and above all its clarity and accessibility - it provides students with a key to understa

The Schwarz function originates in classical complex analysis and potential theory. Here the author presents the advantages favoring a mode of treatment which unites the subject with modern theory of

Screening the male re-examines the problematic status of masculinity both in Hollywood cinema and feminist film theory. Classical Hollywood cinema has been theoretically established as a vast pleasure

The dominant moral philosophy of nineteenth-century Britain was utilitarianism, beginning with Bentham and ending with Sidgwick. Though once overshadowed by his immediate predecessors in that tradition (especially John Stuart Mill), Sidgwick is now regarded as a figure of great importance in the history of moral philosophy. Indeed his masterpiece, The Methods of Ethics (1874), has been described by John Rawls as the 'most philosophically profound' of the classical utilitarian works. In this volume a distinguished group of philosophers reassesses the full range of Sidgwick's work, not simply his ethical theory, but also his contributions as a historian of philosophy, a political theorist, and a reformer.

Over 1500 problems on theory of functions of the complex variable; coverage of nearly every branch of classical function theory. Topics include conformal mappings, integrals and power series, Laurent

Johnson argues that nineteenth-century rhetoric was primarily synthetic, derived from the combination of classical elements and eighteenth-century belletristic and epistemological approaches to theory

The study of spatial processes and their applications is an important topic in statistics and finds wide application particularly in computer vision and image processing. This book is devoted to statistical inference in spatial statistics and is intended for specialists needing an introduction to the subject and to its applications. One of the themes of the book is the demonstration of how these techniques give new insights into classical procedures (including new examples in likelihood theory) and newer statistical paradigms such as Monte-Carlo inference and pseudo-likelihood. Professor Ripley also stresses the importance of edge effects and of lack of a unique asymptotic setting in spatial problems. Throughout, the author discusses the foundational issues posed and the difficulties, both computational and philosophical, which arise. The final chapters consider image restoration and segmentation methods and the averaging and summarising of images. Thus, the book will find wide appeal

The volume is an enlarged edition of a classic textbook on complex analysis. It bridges the gap between the classical material of the first edition and recent advances in half-plane Loewner theory, th

The volume is an enlarged edition of a classic textbook on complex analysis. It bridges the gap between the classical material of the first edition and recent advances in half-plane Loewner theory, th

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 well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, s

Noel Burch's singularly perceptive view of film and its origins will interest all who care about film theory and history. Life to Those Shadows presents a critique of "classical" approaches to film: t

An introduction to classical water wave theory for college seniors or first-year graduate students. Almost all the necessary mathematical and engineering concepts are either presented or derived in th

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

This introduction to the theory of Hamiltonian chaos outlines the main results in the field, and goes on to consider implications for quantum mechanics. The study of nonlinear dynamics, and in particular of chaotic systems, is one of the fastest growing and most productive areas in physics and applied mathematics. In its first six chapters, this timely book introduces the theory of classical Hamiltonian systems. The aim is not to be comprehensive but, rather, to provide a mathematical trunk from which the reader will be able to branch out. The main focus is on periodic orbits and their neighbourhood, as this approach is especially suitable as an introduction to the implications of the theory of chaos in quantum mechanics, which are discussed in the last three chapters.

An important research programme has developed in economics that extends neo-classical economic theory in order to examine the effects of institutions on economic behaviour. The body of work emerging from this line of inquiry includes contributions from various branches of economic theory, such as the economics of property rights, the theory of the firm, cliometrics and law and economics. This book is a comprehensive survey of this research programme which the author terms 'neoinstitutional economics'. The author proposes a unified approach to this research, integrating the work of various contributors and emphasising the common principles of inquiry that tie the work together. The theoretical discussion is accompanied by empirical studies dealing with a range of institutions and economic systems. This book will serve as the primary resource for economists and students who want to learn about this important branch of economic theory.

Paul Adrien Maurice Dirac was undoubtedly one of the most brilliant and influential physicists of the twentieth century. Between 1925 and 1934, this Nobel Laureate revolutionized physics with his contributions to quantum theory. This book, the first full length biography of Dirac, offers a comprehensive account of his life and presents his physics in its historical context, including known areas such as cosmology and classical electron theory. The author examines Dirac's successes and failures, and pays particular attention to Dirac's opposition to modern quantum electrodynamics - an opposition based on aesthetic objections. This book, which draws extensively from unpublished sources, including Dirac's correspondence with Bohr, Heisenberg, Pauli, Schrödinger, Gamow, and other physicists, is a history of modern physics as seen through one scientist's career.

A text/reference on analysis of structures that deform in use. Presents a new, integrated approach to analytical dynamics, structural dynamics and control theory and goes beyond classical dynamics of

With the rise of naturalism in the art of the late Middle Ages and the Renaissance there developed an extensive and diverse literature about art which helped to explain, justify and shape its new aims. In this book, David Summers provides an investigation of the philosophical and psychological notions invoked in this new theory and criticism. From a thorough examination of the sources, he shows how the medieval language of mental discourse derived from an understanding of classical thought.

This book is a quantitative study of relocation costs among European soldiers in the tropics between about 1815 and 1914. This study, however, has broader implications. For Europe itself, this was the crucial century of the 'mortality revolution', with its profound influence on European and world demographic history. For the history of medicine, this was the transitional century between the kind of medicine that had been practiced in Europe since classical times and the kind of scientific medicine that would be spawned by the germ theory of disease. For Europe's global, political and military relations, this was the final period for the European conquest. For all these reasons, the relocation costs of this period have great bearing on human history.

This commentary fulfils the need for a student edition of Horace's literary epistles, which have recently been the subject of renewed scholarly interest. Professor Rudd provides a clear introduction to each of the three poems: the Epistles to Augustus, to Florus, and to the Pisones (the so-called 'Ars Poetica'). He sketches the historical context in which the poems were written, and comments on their structure and purpose. Attention is paid to the literary preoccupations of the individual epistles: the relations of poet and patron, and the role of poetry in the state (Augustus), the problems of a (professedly) tiring poet (Florus), and the presentation of classical poetic theory in the 'Ars Poetica'. Horace's influence on later criticism is noted, and there is a brief section on one of Alexander Pope's Imitations. In his commentary on the text Professor Rudd addresses problems of grammar and style, focusing on linguistic difficulties and on the subtle movement of the poet's thought.