Classical Recursion Theory

Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, proba

This book presents a systematic account of optical coherence theory within the framework of classical optics, as applied to such topics as radiation from sources of different states of coherence, foundations of radiometry, effects of source coherence on the spectra of radiated fields, coherence theory of laser modes, and scattering of partially coherent light by random media. The book starts with a full mathematical introduction to the subject area and each chapter concludes with a set of exercises. The authors are renowned scientists and have made substantial contributions to many of the topics treated in the book. Much of the book is based on courses given by them at universities, scientific meetings and laboratories throughout the world. This book will undoubtedly become an indispensable aid to scientists and engineers concerned with modern optics, as well as to teachers and graduate students of physics and engineering.

When we talk about a jazz "standard" we usually mean one of the many songs that jazz musicians repeatedly play as part of their core repertoire. But unlike musical works in the tradition of so-called classical music, standards--whether plucked from the "Great American Songbook" or from recordings by other jazz musicians--are always being transformed in performance. They are rearranged and improvised upon, given new chords and altered melodies. These transformations might be small and seemingly unimportant, or they might be radical revisions. Which raises the question: across all of these various performances, what gives a standard its identity? In Hearing Double author Brian Kane answers that question by offering a new theory of musical works that can account for the unique challenges presented by standards. Building from the bottom up--from the actual practices of jazz musicians toward their philosophical implications--he gives a comprehensive theory of how a standard can undergo radi

This book focuses on current theoretical and empirical research into countability in the nominal domain, and to a lesser extent in the verbal domain. The presented state-of-the-art studies are situated within compositional semantics combined with the theory of mereology, and draw on a wealth of data, some of which have hitherto been unknown, from a number of typologically distinct languages. Some contributions propose enrichments of classical extensional mereology with topological and temporal notions as well as with type theory and probabilistic models. The book also presents analyses that rely on cutting-edge empirical research (experimental, corpus-based) into meaning in language. It is suitable as a point of departure for original research or material for seminars in semantics, philosophy of language, psycholinguistics and other fields of cognitive science. It is of interest not only to a semanticist, but also to anybody who wishes to gain insights into the contemporary research in

The Woods Hole trace formula is a Lefschetz fixed-point theorem for coherent cohomology on algebraic varieties. It leads to a version of the sheaves-functions dictionary of Deligne, relating characteristic-p-valued functions on the rational points of varieties over finite fields to coherent modules equipped with a Frobenius structure. This book begins with a short introduction to the homological theory of crystals of Böckle and Pink with the aim of introducing the sheaves-functions dictionary as quickly as possible, illustrated with elementary examples and classical applications. Subsequently, the theory and results are expanded to include infinite coefficients, L-functions, and applications to special values of Goss L-functions and zeta functions. Based on lectures given at the Morningside Center in Beijing in 2013, this book serves as both an introduction to the Woods Hole trace formula and the sheaves-functions dictionary, and to some advanced applications on characteristic p zeta v

This book was originally published in 1975. In Einstein's General Theory of Relativity the effects of gravitation are represented by the curvature of space-time. Physical processes occurring in the presence of gravitation must then be treated mathematically in terms of their behaviour in a curved space-time. One of the most basic of these processes is wave propagation, and this book gives a rigourous discussion of the local effects of curvature on the behaviour of waves. In the course of this discussion many techniques are developed which are also needed for a study of more general problems, in which the gravitational field itself plays a dynamical role. Although much of the book deals with four-dimensional space-time, the n-dimensional case is also treated, more briefly. The subject-matter is also of interest in other branches of mathematical physics and, as a fresh account of the classical work of Hadamard and M. Riesz, in the theory of partial differential equations.

In recent years there has developed a satisfactory and coherent theory of orthogonal polynomials in several variables, attached to root systems, and depending on two or more parameters. These polynomials include as special cases: symmetric functions; zonal spherical functions on real and p-adic reductive Lie groups; the Jacobi polynomials of Heckman and Opdam; and the Askey–Wilson polynomials, which themselves include as special or limiting cases all the classical families of orthogonal polynomials in one variable. This book, first published in 2003, is a comprehensive and organised account of the subject aims to provide a unified foundation for this theory, to which the author has been a principal contributor. It is an essentially self-contained treatment, accessible to graduate students familiar with root systems and Weyl groups. The first four chapters are preparatory to Chapter V, which is the heart of the book and contains all the main results in full generality.

What is a promise? What are the consequences of the act of promising? In this bold yet subtle meditation, the author contemplates the seductive promise of speech and the seductive promise of love. Imagining an encounter between Molière’s Don Juan and J. L. Austin, between a mythical figure of the French classical theater and a twentieth-century philosopher, she explores the relation between speech and the erotic, using a literary text as the ground for a telling encounter between philosophy, linguistics, and Lacanian psychoanalytic theory. In the years since the publication of this book (which the author today calls “the boldest, the most provocative, but also the most playful” she has written), speech act theory has continued to play a central and defining role in the theories of sexuality, gender, performance studies, post-colonial studies, and cultural studies. This book remains topical as readers increasingly discover how multiply relevant the speaking body is.Moving beyond the dom

The theory of natural dualities, as presented in this text, is broad enough to encompass many known dualities through a rich assortment of substantive theorems, yet concrete enough to be used to generate an array of previously undiscovered dualities. This text will serve as a user manual for algebraists, for category theorists and for those who use algebra in their work, particularly mathematicians and computer scientists interested in non-classical logics. It will also give the specialist a complete account of the foundations, leading to the research frontier of this rapidly developing field. As the first text devoted to the theory of Natural Dualities, it provides an efficient path through a large body of results, examples and applications in this subject which is otherwise available only in scattered research papers. To enable the book to be used in courses, each chapter ends with an extensive exercise set. Several fundamental unsolved problems are included.

In Psyche and Eros, first published in 1994, Gisela Labouvie-Vief describes historical and current concepts of mind and development, drawing from disciplines as diverse as philosophy, mythology, religion, literature, and psychology. She then presents a powerful theory of the maturing of mind, which brings together her empirical work and her exploration into mythology. The classical Greek myth of the gods Psyche and Eros serves as an evocative illustration of the author's theory. Psyche and Eros asserts that the core experience of development differs along gender lines. Rationality is regarded as masculine, while imagination is viewed as feminine. Competition between 'masculine' and 'feminine' parts of the mind has limited our ability to describe the mind and its development over the life course, just as it limits our experiences of development as men and women. The author suggests that we overcome the dualistic way of thinking about mind, and see how rationality and imagination can co

In Psyche and Eros, first published in 1994, Gisela Labouvie-Vief describes historical and current concepts of mind and development, drawing from disciplines as diverse as philosophy, mythology, religion, literature, and psychology. She then presents a powerful theory of the maturing of mind, which brings together her empirical work and her exploration into mythology. The classical Greek myth of the gods Psyche and Eros serves as an evocative illustration of the author's theory. Psyche and Eros asserts that the core experience of development differs along gender lines. Rationality is regarded as masculine, while imagination is viewed as feminine. Competition between 'masculine' and 'feminine' parts of the mind has limited our ability to describe the mind and its development over the life course, just as it limits our experiences of development as men and women. The author suggests that we overcome the dualistic way of thinking about mind, and see how rationality and imagination can co

Convex polytopes are the analogues in space of any dimension of convex plane polygons and of convex polyhedra in ordinary space. This book describes a fresh approach to the classification of these objects according to their symmetry properties, based on ideas of topology and transformation group theory. Although there is considerable agreement with traditional treatments, a number of new concepts emerge that present classical ideas in a quite new way. For example, the family of regular convex polytopes is extended to the family of 'perfect polytopes'. Thus the familiar set of five Platonic polyhedra is replaced by the less familiar set of nine perfect polyhedra. Among the many unsolved problems that arise, that of finding all perfect polytopes, and more generally all perfect convex bodies, is perhaps the most attractive. This book will be of value to specialists and graduate students in pure mathematics, especially those studying symmetry theory, convex bodies, and polytopes.

Philosophers are increasingly coming to recognize the importance of Freudian theory for the understanding of the mind. The picture Freud presents of the mind's growth and organization holds implications not just for such perennial questions as the relation of mind and body, the nature of memory and personal identity, the interplay of cognitive and affective processes in reasoning and acting, but also for the very way in which these questions are conceived and an interpretation of the mind is sought. This volume of essays, by some of today's leading philosophers, explores all these topics, as well as the methods, results and status of the theory itself, while two 'classical' discussions by Wittgenstein and Sartre are also included. A number of the contributions – those by Donald Davidson, W. D. Hart, Jim Hopkins, Adam Morton, David Pears and Richard Wollheim – have not been published before, and a very useful bibliography is provided. It is an anthology that will be vital to anyone inte

This book embarks on a thorough review of Eastern and Western philosophies of propriety over the past 2,500 years, followed by an investigation of the ideas of propriety found in five key schools of economics: classical, neoclassical, institutional, behavioral, and cultural economics. The author then outlines the core principles and recommended practices for the study and implementation of propriety economics in the future. With its unique mixture of theory, literature reviews, methods, and case studies, this book will be useful not only to economic scholars, but also historians, policy makers, and any reader with an interest in making the economy work better for the benefit of all humankind.

This volume compiles notes from four mini courses given at the summer school on asymptotic analysis in general relativity, held at the Institut Fourier in Grenoble, France. It contains an up-to-date panorama of modern techniques in the asymptotic analysis of classical and quantum fields in general relativity. Accessible to graduate students, these notes gather results that were not previously available in textbooks or monographs and will be of wider interest to researchers in general relativity. The topics of these mini courses are: the geometry of black hole spacetimes; an introduction to quantum field theory on curved spacetimes; conformal geometry and tractor calculus; and microlocal analysis for wave propagation.

Raymond Arthur Lyttleton (1911–95) was a British astronomer who won the Royal Society Royal Medal in 1965 for significant contributions to his field. In this book, which was first published in 1953, Lyttleton presents an account of advances in relation to a classical problem of mathematical astronomy. The text is mainly concerned with those parts of the theory most directly involved in determining the evolution of gravitating liquid masses. The important conclusion is reached that the dynamical evidence is against the so-called 'fission process' of binary system formation. This book will be of value to anyone with an interest in astronomy and the history of science.

This 1989 monograph deals with parametric minimal surfaces in Euclidean space. The author presents a broad survey which extends from the classical beginnings to the current situation whilst highlighting many of the subject's main features and interspersing the mathematical development with pertinent historical remarks. The presentation is complete and is complemented by a bibliography of nearly 1600 references. The careful expository style and emphasis on geometric aspects are extremely valuable. Moreover, in the years leading up to the publication of this book, the theory of minimal surfaces was finding increasing application to other areas of mathematics and the physical sciences ensuring that this account will appeal to non-specialists as well.

First published in 1997, Reinventing Allegory asks how and why allegory has survived as a literary mode from the late Renaissance to the postmodern present. Three chapters on Romanticism, including one on the painter J. M. W. Turner, present this era as the pivotal moment in allegory's modern survival. Other chapters describe larger historical and philosophical contexts, including classical rhetoric and Spenser, Milton and seventeenth-century rhetoric, Neoclassical distrust of allegory, and recent theory and metafiction. By using a series of key historical moments to define the special character of modern allegory, this study offers an important framework for assessing allegory's role in contemporary literary culture.

This first volume takes the story from its beginnings in Ionian philosophy as far as the formation of the Atomic Theory and the first criticisms of it by Plato and Aristotle. The second volume will describe the cosmology of Plato and Aristotle, the attempt by Epicurean opponents to revive Atomism and later developments of the debate in classical philosophy and science up to the sixth century of our era. Both are accessible to anyone interested in the history of science and philosophy, even if they have no specialized knowledge of Greek philosophy and no Greek; but professional scholars too will find much of importance to them.

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.

First published in 1997, Reinventing Allegory asks how and why allegory has survived as a literary mode from the late Renaissance to the postmodern present. Three chapters on Romanticism, including one on the painter J. M. W. Turner, present this era as the pivotal moment in allegory's modern survival. Other chapters describe larger historical and philosophical contexts, including classical rhetoric and Spenser, Milton and seventeenth-century rhetoric, Neoclassical distrust of allegory, and recent theory and metafiction. By using a series of key historical moments to define the special character of modern allegory, this study offers an important framework for assessing allegory's role in contemporary literary culture.

This book focuses on the role of education in relation to music and gender. Invoking a concept of musical patriarchy and a theory of the social construction musical meanings, Lucy Green shows how women's musical practices and gendered musical meanings have been reproduced, hand in hand, through history. Covering a wide range of music, including classical, jazz and popular styles, Dr Green uses ethnographic methods to convey the everyday interactions and experiences of girls, boys, and their teachers. She views the contemporary school music classroom as a microcosm of the wider society, and reveals the participation of music education in the continued production and reproduction of gendered musical practices and meanings.

Developed over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. In this book Professor Beauville gives a lucid and concise account of the subject, following the strategy of F. Enriques, but expressed simply in the language of modern topology and sheaf theory, so as to be accessible to any budding geometer. This volume is self contained and the exercises succeed both in giving the flavour of the extraordinary wealth of examples in the classical subject, and in equipping the reader with most of the techniques needed for research.

Developed over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. In this book Professor Beauville gives a lucid and concise account of the subject, following the strategy of F. Enriques, but expressed simply in the language of modern topology and sheaf theory, so as to be accessible to any budding geometer. This volume is self contained and the exercises succeed both in giving the flavour of the extraordinary wealth of examples in the classical subject, and in equipping the reader with most of the techniques needed for research.

The concept of sovereignty is central to international relations theory and theories of state formation, and provides the foundation of the conventional separation of modern politics into domestic and international spheres. In this book Jens Bartelson provides a critical analysis and conceptual history of sovereignty, dealing with this separation as reflected in philosophical and political texts during three periods: the Renaissance, the Classical Age, and Modernity. He argues that the concept of sovereignty and its place within political discourse are conditioned by philosophical and historiographical discontinuities between the periods, and that sovereignty should be regarded as a concept contingent upon, rather than fundamental to, political science and its history.

This short introduction to microlocal analysis is presented, in the spirit of Hörmander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjöstrand emphasise the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions. The contents of the book correspond to a graduate course given many times by the authors. It should prove to be useful to mathematicians and theoretical physicists, either to enrich their general knowledge of this area, or as preparation for the current research literature.

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.

This first volume takes the story from its beginnings in Ionian philosophy as far as the formation of the Atomic Theory and the first criticisms of it by Plato and Aristotle. The second volume will describe the cosmology of Plato and Aristotle, the attempt by Epicurean opponents to revive Atomism and later developments of the debate in classical philosophy and science up to the sixth century of our era. Both are accessible to anyone interested in the history of science and philosophy, even if they have no specialized knowledge of Greek philosophy and no Greek; but professional scholars too will find much of importance to them.

What is the nature of truth? Blake E. Hestir offers an investigation into Plato's developing metaphysical views, and examines Plato's conception of being, meaning, and truth in the Sophist, as well as passages from several other later dialogues including the Cratylus, Parmenides, and Theaetetus, where Plato begins to focus more directly on semantics rather than only on metaphysical and epistemological puzzles. Hestir's interpretation challenges both classical and contemporary interpretations of Plato's metaphysics and conception of truth, and highlights new parallels between Plato and Aristotle, as well as clarifying issues surrounding Plato's approach to semantics and thought. This book will be of interest to scholars and students of ancient Greek philosophy, metaphysics, contemporary truth theory, linguistics, and philosophy of language.

Understand the theory, design and applications of the two principal candidates for the next mainstream semiconductor-industry device with this concise and clear guide to FD/UTB transistors. • Describes FD/SOI MOSFETs and 3-D FinFETs in detail • Covers short-channel effects, quantum-mechanical effects, applications of UTB devices to floating-body DRAM and conventional SRAM • Provides design criteria for nanoscale FinFET and nanoscale thin- and thick-BOX planar FD/SOI MOSFET to help reduce technology development time • Projects potential nanoscale UTB CMOS performances • Contains end-of-chapter exercises. For professional engineers in the CMOS IC field who need to know about optimal non-classical device design and integration, this is a must-have resource.

Human Goodness presents an original, pragmatic moral theory that successfully revives and revitalizes the classical Greek concept of happiness. It also includes in-depth discussions of our freedoms, our obligations, and our virtues, as well as adroit comparisons with the moral theories of Kant and Hume. Paul Schollmeier explains that the Greeks define happiness as an activity that we may perform for its own sake. Obvious examples might include telling stories, making music, or dancing. He then demonstrates that we may use the pragmatic method to discover and to define innumerable activities of this kind. Schollmeier's demonstration rests on the modest assumption that our happiness takes not one ideal form, but many empirical forms.

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.

Human Goodness presents an original, pragmatic moral theory that successfully revives and revitalizes the classical Greek concept of happiness. It also includes in-depth discussions of our freedoms, our obligations, and our virtues, as well as adroit comparisons with the moral theories of Kant and Hume. Paul Schollmeier explains that the Greeks define happiness as an activity that we may perform for its own sake. Obvious examples might include telling stories, making music, or dancing. He then demonstrates that we may use the pragmatic method to discover and to define innumerable activities of this kind. Schollmeier's demonstration rests on the modest assumption that our happiness takes not one ideal form, but many empirical forms.

Asymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in other standard references on asymptotics.

This book helps explain one of the most intriguing and politically salient puzzles in comparative political economy: why some countries have much higher unemployment rates than others. Contrary to new classical economics the focus is on explaining distribution and equilibrium unemployment, and contrary to neo-corporatist theory the role of monetary policy and rational expectation is integral to the analysis. The book makes two central arguments. The first is that monetary policies affect equilibrium employment whenever wages are set above the firm level. The second argument focuses on the distributive effects of different institutions, and models institutional design as a strategic game between partisan governments and cross-class alliances of unions and employers.

This book helps explain one of the most intriguing and politically salient puzzles in comparative political economy: why some countries have much higher unemployment rates than others. Contrary to new classical economics the focus is on explaining distribution and equilibrium unemployment, and contrary to neo-corporatist theory the role of monetary policy and rational expectation is integral to the analysis. The book makes two central arguments. The first is that monetary policies affect equilibrium employment whenever wages are set above the firm level. The second argument focuses on the distributive effects of different institutions, and models institutional design as a strategic game between partisan governments and cross-class alliances of unions and employers.

Adam Ferguson's Essay on the History of Civil Society (first published in 1767) is a classic of the Scottish - and European - Enlightenment. Drawing on such diverse sources as classical authors and contemporary travel literature, Ferguson offers a complex model of historical advance which challenges both Hume's and Smith's embrace of modernity and the primitivism of Rousseau. Ferguson combines a subtle analysis of the emergence of modern commercial society with a critique of its abandonment of civic and communal virtues. Central to Ferguson's theory of citizenship are the themes of conflict, play, political participation and military valour. The Essay is a bold and novel attempt to reclaim the tradition of active, virtuous citizenship and apply it to the modern state.

Adam Ferguson's Essay on the History of Civil Society (first published in 1767) is a classic of the Scottish - and European - Enlightenment. Drawing on such diverse sources as classical authors and contemporary travel literature, Ferguson offers a complex model of historical advance which challenges both Hume's and Smith's embrace of modernity and the primitivism of Rousseau. Ferguson combines a subtle analysis of the emergence of modern commercial society with a critique of its abandonment of civic and communal virtues. Central to Ferguson's theory of citizenship are the themes of conflict, play, political participation and military valour. The Essay is a bold and novel attempt to reclaim the tradition of active, virtuous citizenship and apply it to the modern state.

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.

This book covers a broad range of topics in the history of economics that have relevance to economic theories. The author believes that one of the tasks for a historian of economics is to analyze and interpret theories currently outside the mainstream of economic theory, in this case non-Walrasian economics. By doing so, he argues, new directions and new areas for research can be developed that will extend the current theories. Familiar topics covered include: the division of labor, economies of scale, wages, profit, international trade, market mechanisms, and money. These are considered in the light of the well-known non-Walrasian schools of thought: the classical, Marxian, Austrian, and Cambridge schools.