Classical Recursion Theory

Classical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves. But the noncommutative equivalent is mainly

An Introduction to Nonlinear Analysis: Theory is an overview of some basic, important aspects of Nonlinear Analysis, with an emphasis on those not included in the classical treatment of the field. Tod

The events of the last decade have challenged the contemporary neo-classical synthesis in all branches of economics, but particularly public finance. The most notable feature of the 2nd edition of Pub

The events of the last decade have challenged the contemporary neo-classical synthesis in all branches of economics, but particularly public finance. The most notable feature of the 2nd edition of Pub

What are the aims of sociology? What are its objects of study? How relevant is the classical tradition to the practice of sociology today? This volume brings together internationally renowned and new

This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonic analysis. The four parts of the text

These notes are based on six Fermi Lectures held at the Scuola Normale Superiore in Pisa in March and April 1981. The topics treated depend on basic concepts of classical mechanics, elementary geometr

This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. Beginning with a discussion of the rudiments of set t

Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the bas

The Heat Equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it c

This book is a classical theory text aimed at teaching theorizing as a skill. After analyzing the process of theorizing into a set of simple steps, it shows how the theories of Marx, Weber, Durkheim,

Scattering theory provides a framework for understanding the scattering of waves and particles. This book presents a simple physical picture of diffractive nuclear scattering in terms of semi-classical trajectories, illustrated throughout with examples and case studies. Trajectories in a complex impact parameter plane are discussed, and it stresses the importance of the analytical properties of the phase shift function in this complex impact plane in the asymptotic limit. Several new rainbow phenomena are also discussed and illustrated. Written by Nobel Prize winner Roy J. Glauber, and Per Osland, an expert in the field of particle physics, the book illustrates the transition from quantum to classical scattering, and provides a valuable resource for researchers using scattering theory in nuclear, particle, atomic and molecular physics.

Combining the classical theories of contact mechanics and lubrication with the study of friction on the nanometer range, this multi-scale book for researchers and students alike guides the reader deftly through the mechanisms governing friction processes, based on state-of-the-art models and experimental results. The first book in the field to incorporate recent research on nanotribology with classical theories of contact mechanics, this unique text explores atomic scale scratches, non-contact friction and fishing of molecular nanowires as observed in the lab. Beginning with simple key concepts, the reader is guided through progressively more complex topics, such as contact of self-affine surfaces and nanomanipulation, in a consistent style, encompassing both macroscopic and atomistic descriptions of friction, and using unified notations to enable use by physicists and engineers across the scientific community.

Playing a prominent role in communications, quantum science and laser physics, quantum nonlinear optics is an increasingly important field. This book presents a self-contained treatment of field quantization and covers topics such as the canonical formalism for fields, phase-space representations and the encompassing problem of quantization of electrodynamics in linear and nonlinear media. Starting with a summary of classical nonlinear optics, it then explains in detail the calculation techniques for quantum nonlinear optical systems and their applications, quantum and classical noise sources in optical fibers and applications of nonlinear optics to quantum information science. Supplemented by end-of-chapter exercises and detailed examples of calculation techniques in different systems, this book is a valuable resource for graduate students and researchers in nonlinear optics, condensed matter physics, quantum information and atomic physics. A solid foundation in quantum mechanics and

Recent experimental advances in the control of quantum superconducting circuits, nano-mechanical resonators and photonic crystals has meant that quantum measurement theory is now an indispensable part of the modelling and design of experimental technologies. This book, aimed at graduate students and researchers in physics, gives a thorough introduction to the basic theory of quantum measurement and many of its important modern applications. Measurement and control is explicitly treated in superconducting circuits and optical and opto-mechanical systems, and methods for deriving the Hamiltonians of superconducting circuits are introduced in detail. Further applications covered include feedback control, metrology, open systems and thermal environments, Maxwell's demon, and the quantum-to-classical transition.

In Goodness and Justice, Joseph Mendola develops a unified moral theory that defends the hedonism of classical utilitarianism, while evading utilitarianism's familiar difficulties by adopting two modifications. His theory incorporates a developed form of consequentialism. When, as is common, someone is engaged in conflicting group acts, it requires that one perform one's role in that group act that is most beneficent. The theory also holds that overall value is distribution-sensitive, ceding maximum weight to the well-being of the worst-off sections of sentient lives. It is properly congruent with commonsense intuition and required by the true metaphysics of value, by the unconstituted natural good found in our world.

This is a book about Aristotle's philosophy of language, interpreted in a framework that provides a comprehensive interpretation of Aristotle's metaphysics, philosophy of mind, epistemology and science. The aim of the book is to explicate the description of meaning contained in De Interpretatione and to show the relevance of that theory of meaning to much of the rest of Aristotle's philosophy. In the process Deborah Modrak reveals how that theory of meaning has been much maligned. This is a major reassessment of an underestimated aspect of Aristotle that will be of particular interest to classical philosophers, classicists and historians of psychology and cognitive science.

In Goodness and Justice, Joseph Mendola develops a unified moral theory that defends the hedonism of classical utilitarianism, while evading utilitarianism's familiar difficulties by adopting two modifications. His theory incorporates a developed form of consequentialism. When, as is common, someone is engaged in conflicting group acts, it requires that one perform one's role in that group act that is most beneficent. The theory also holds that overall value is distribution-sensitive, ceding maximum weight to the well-being of the worst-off sections of sentient lives. It is properly congruent with commonsense intuition and required by the true metaphysics of value, by the unconstituted natural good found in our world.

This is a book about Aristotle's philosophy of language, interpreted in a framework that provides a comprehensive interpretation of Aristotle's metaphysics, philosophy of mind, epistemology and science. The aim of the book is to explicate the description of meaning contained in De Interpretatione and to show the relevance of that theory of meaning to much of the rest of Aristotle's philosophy. In the process Deborah Modrak reveals how that theory of meaning has been much maligned. This is a major reassessment of an underestimated aspect of Aristotle that will be of particular interest to classical philosophers, classicists and historians of psychology and cognitive science.

In this innovative introduction, Robert Layton reviews the ideas that have inspired anthropologists in their studies of societies around the world. An Introduction to Theory in Anthropology provides a clear and concise analysis of the theories, and traces the way in which they have been translated into anthropological debates. The opening chapter sets out the classical theoretical issues formulated by Hobbes, Rousseau, Marx and Durkheim. Successive chapters discuss Functionalism, Structuralism, Interactionist theories, and Marxist anthropology, while the final chapters address the competing paradigms of Socioecology and Postmodernism. Using detailed case studies, Professor Layton illustrates the way in which various theoretical perspectives have shaped competing, or complementary, accounts of specific human societies.

Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context. The authors then present examples and applications, showing how Heisenberg manifolds (step 2 sub-Riemannian manifolds) might in the future play a role in quantum mechanics similar to the role played by the Riemannian manifolds in classical mechanics. Sub-Riemannian Geometry: General Theory and Examples is the perfect resource for graduate students and researchers in pure and applied mathematics, theoretical physics, control theory, and thermodynamics interested in the most recent developments in sub-Riemannian geometry.

Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.

Discover a fresh take on classical screw theory and understand the geometry embedded within robots and mechanisms with this essential text. The book begins with a geometrical study of points, lines, and planes and slowly takes the reader toward a mastery of screw theory with some cutting-edge results, all while using only basic linear algebra and ordinary vectors. It features a discussion of the geometry of parallel and serial robot manipulators, in addition to the reciprocity of screws and a singularity study. All 41 essential screw systems are unveiled, establishing the possible freedom twists and constraint wrenches for a kinematic joint. Familiarizing the reader with screw geometry in order to study the statics and kinematics of robots and mechanisms, this is a perfect resource for engineers and graduate students.

This book is a collection about cultural-historical activity theory as it has been developed and applied by Yrjö Engeström. The work of Engeström is both rooted in the legacy of Vygotsky and Leont'ev and focuses on current research concerns that are related to learning and development in work practices. His publications cross various disciplines and develop intermediate theoretical tools to deal with empirical questions. In this volume, Engeström's work is used as a springboard to reflect on the question of the use, appropriation, and further development of the classic heritage within activity theory. The book is structured as a discussion among senior scholars, including Y. Engeström himself. The work of the authors pushes on classical activity theory to address pressing issues and critical contradictions in local practices and larger social systems.

This book is a collection about cultural-historical activity theory as it has been developed and applied by Yrjö Engeström. The work of Engeström is both rooted in the legacy of Vygotsky and Leont'ev and focuses on current research concerns that are related to learning and development in work practices. His publications cross various disciplines and develop intermediate theoretical tools to deal with empirical questions. In this volume, Engeström's work is used as a springboard to reflect on the question of the use, appropriation, and further development of the classic heritage within activity theory. The book is structured as a discussion among senior scholars, including Y. Engeström himself. The work of the authors pushes on classical activity theory to address pressing issues and critical contradictions in local practices and larger social systems.

The study of hydrodynamic stability is fundamental to many subjects, ranging from geophysics and meteorology through to engineering design. This treatise covers both classical and modern aspects of the subject, systematically developing it from the simplest physical problems, then progressing to the most complex, considering linear and nonlinear situations, and analyzing temporal and spatial stability. The authors examine each problem both analytically and numerically. Many relevant fluid flows are treated, including those where the fluid may be compressible, or those from geophysics, or those that require salient geometries for description. Details of initial-value problems are explored equally with those of stability. The text includes copious illustrations and an extensive bibliography, making it suitable for courses on hydrodynamic stability or as an authoritative reference for researchers. In this second edition the opportunity has been taken to update the text and, most important

The study of hydrodynamic stability is fundamental to many subjects, ranging from geophysics and meteorology through to engineering design. This treatise covers both classical and modern aspects of the subject, systematically developing it from the simplest physical problems, then progressing to the most complex, considering linear and nonlinear situations, and analyzing temporal and spatial stability. The authors examine each problem both analytically and numerically. Many relevant fluid flows are treated, including those where the fluid may be compressible, or those from geophysics, or those that require salient geometries for description. Details of initial-value problems are explored equally with those of stability. The text includes copious illustrations and an extensive bibliography, making it suitable for courses on hydrodynamic stability or as an authoritative reference for researchers. In this second edition the opportunity has been taken to update the text and, most important

An H(b) space is defined as a collection of analytic functions which are in the image of an operator. The theory of H(b) spaces bridges two classical subjects: complex analysis and operator theory, which makes it both appealing and demanding. The first volume of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators, and Clark measures. The second volume focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.

An H(b) space is defined as a collection of analytic functions which are in the image of an operator. The theory of H(b) spaces bridges two classical subjects: complex analysis and operator theory, which makes it both appealing and demanding. The first volume of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators, and Clark measures. The second volume focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.

This book lays the foundations for an exciting new area of research in descriptive set theory. It develops a robust connection between two active topics: forcing and analytic equivalence relations. This in turn allows the authors to develop a generalization of classical Ramsey theory. Given an analytic equivalence relation on a Polish space, can one find a large subset of the space on which it has a simple form? The book provides many positive and negative general answers to this question. The proofs feature proper forcing and Gandy–Harrington forcing, as well as partition arguments. The results include strong canonization theorems for many classes of equivalence relations and sigma-ideals, as well as ergodicity results in cases where canonization theorems are impossible to achieve. Ideal for graduate students and researchers in set theory, the book provides a useful springboard for further research.

Developed from the author's popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy–Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studies.

Developed from the author's popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy–Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studies.

'Keeping time', along with artistic accentuation and intelligent phrasing, is essential to successful musical performance. Rhythm alone had rarely been the subject of specialised study until the late nineteenth century, when several books on this topic by Rudolf Westphal were published in Leipzig. Westphal's work inspired Charles Francis Abdy Williams's 1911 book which is reissued here. Williams re-examines the classical and romantic repertoire from Handel to Tchaikovsky in the light of ancient Greek musical theory, focusing particularly on the earliest writings by Artistoxenus of Tarentum (fourth century BCE). In Williams's view, the rhythmic forms used by the Greeks are universally intelligible, and appear in all ages and cultures, unlike melodies or scales, which vary hugely. He provides insights into the microstructure of works including Bach's oratorios, Beethoven's sonatas and Schubert's songs, which will continue to intrigue musicians, classicists and mathematicians today.

This is a systematic presentation of quantum field theory from first principles, emphasizing both theoretical concepts and experimental applications. Starting from introductory quantum and classical mechanics, this book develops the quantum field theories that make up the 'Standard Model' of elementary processes. It derives the basic techniques and theorems that underly theory and experiment, including those that are the subject of theoretical development. Special attention is also given to the derivations of cross sections relevant to current high-energy experiments and to perturbative quantum chromodynamics, with examples drawn from electron-positron annihilation, deeply inelastic scattering and hadron-hadron scattering. The first half of the book introduces the basic ideas of field theory. The discussion of mathematical issues is everywhere pedagogical and self contained. Topics include the role of internal symmetry and relativistic invariance, the path integral, gauge theories and

This collection of essays is concerned with philosophy, politics and society. The first group examines what philosophers such as Hegel, Wittgenstein and Chomsky have said or implied about the nature of society in general. A second group examines the cognitive predicament, questions concerning the nature of the possibility of knowledge, as handled by a thinker such as Descartes, or the Pragmatist tradition. The third group handles the political predicament and deals specifically with problems such as nationalism, the nature of the liberalisation process, the future of the welfare and consumer state and the option facing underdeveloped societies. The essays deal not only with classical theories concerning these problems but also with various recent discussions. The volume will interest many individual philosophers and social theorists and those with a more general interest in our culture and political discussions.

Why should anyone be a Zionist, a supporter of a Jewish state in the land of Israel? Why should there be a Jewish state in the land of Israel? This book seeks to provide a philosophical answer to these questions. Although a Zionist need not be Jewish, nonetheless this book argues that Zionism is only a coherent political stance when it is intelligently rooted in Judaism, especially in the classical Jewish doctrine of God's election of the people of Israel and the commandment to them to settle the land of Israel. The religious Zionism advocated here is contrasted with secular versions of Zionism that take Zionism to be a replacement of Judaism. It is also contrasted with versions of religious Zionism that ascribe messianic significance to the State of Israel, or which see the main task of religious Zionism to be the establishment of an Israeli theocracy.

Why should anyone be a Zionist, a supporter of a Jewish state in the land of Israel? Why should there be a Jewish state in the land of Israel? This book seeks to provide a philosophical answer to these questions. Although a Zionist need not be Jewish, nonetheless this book argues that Zionism is only a coherent political stance when it is intelligently rooted in Judaism, especially in the classical Jewish doctrine of God's election of the people of Israel and the commandment to them to settle the land of Israel. The religious Zionism advocated here is contrasted with secular versions of Zionism that take Zionism to be a replacement of Judaism. It is also contrasted with versions of religious Zionism that ascribe messianic significance to the State of Israel, or which see the main task of religious Zionism to be the establishment of an Israeli theocracy.

In this volume, Richard Ned Lebow introduces his own constructivist theory of political order and international relations based on theories of motives and identity formation drawn from the ancient Greeks. His theory stresses the human need for self-esteem, and shows how it influences political behavior at every level of social aggregation. Lebow develops ideal-type worlds associated with four motives: appetite, spirit, reason and fear, and demonstrates how each generates a different logic concerning cooperation, conflict and risk-taking. Expanding and documenting the utility of his theory in a series of historical case studies, ranging from classical Greece to the war in Iraq, he presents a novel explanation for the rise of the state and the causes of war, and offers a reformulation of prospect theory. This is a novel theory of politics by one of the world's leading scholars of international relations.

In this volume, Richard Ned Lebow introduces his own constructivist theory of political order and international relations based on theories of motives and identity formation drawn from the ancient Greeks. His theory stresses the human need for self-esteem, and shows how it influences political behavior at every level of social aggregation. Lebow develops ideal-type worlds associated with four motives: appetite, spirit, reason and fear, and demonstrates how each generates a different logic concerning cooperation, conflict and risk-taking. Expanding and documenting the utility of his theory in a series of historical case studies, ranging from classical Greece to the war in Iraq, he presents a novel explanation for the rise of the state and the causes of war, and offers a reformulation of prospect theory. This is a novel theory of politics by one of the world's leading scholars of international relations.

This 2006 work began with the author's exploration of the applicability of the finite deformation theory of elasticity when various standard assumptions such as convexity of various energies or ellipticity of the field equations of equilibrium are relinquished. The finite deformation theory of elasticity turns out to be a natural vehicle for the study of phase transitions in solids where thermal effects can be neglected. This text will be of interest to those interested in the development and application of continuum-mechanical models that describe the macroscopic response of materials capable of undergoing stress- or temperature-induced transitions between two solid phases. The focus is on the evolution of phase transitions which may be either dynamic or quasi-static, controlled by a kinetic relation which in the framework of classical thermomechanics represents information that is supplementary to the usual balance principles and constitutive laws of conventional theory.