Classical Recursion Theory

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.

This book presents a theory motivated by the spaces LP, 0 ≤ p

This exposition of research on the martingale and analytic inequalities associated with Hardy spaces and functions of bounded mean oscillation (BMO) introduces the subject by concentrating on the connection between the probabilistic and analytic approaches. Short surveys of classical results on the maximal, square and Littlewood-Paley functions and the theory of Brownian motion introduce a detailed discussion of the Burkholder-Gundy-Silverstein characterization of HP in terms of maximal functions. The book examines the basis of the abstract martingale definitions of HP and BMO, makes generally available for the first time work of Gundy et al. on characterizations of BMO, and includes a probabilistic proof of the Fefferman-Stein Theorem on the duality of H11 and BMO.

Spiral Bound explores the potential for yoga as a healing modality by examining the body's anatomical structure as it has evolved embryonically. With a light touch approach, Karen weaves together threads of development to see how our morphological constraints arise in the earliest moments of life and how this rotation lays the spiral groundwork for rotational kinematics that encompass all tissue. This book sets out to link theory with practice, all at a conversational level richly illustrated with full-color photographs and drawings that bring the biomotion to life for practitioners and teachers of yoga. This book for anyone seeking to simplify the parts-list pedagogy of classical anatomy with contemporary research in fascia literature for an integrated approach especially suitable to postural yoga.

Wigner's theorem is a fundamental part of the mathematical formulation of quantum mechanics. The theorem characterizes unitary and anti-unitary operators as symmetries of quantum mechanical systems, and is a key result when relating preserver problems to quantum mechanics. At the heart of this book is a geometric approach to Wigner-type theorems, unifying both classical and more recent results. Readers are initiated in a wide range of topics from geometric transformations of Grassmannians to lattices of closed subspaces, before moving on to a discussion of applications. An introduction to all the key aspects of the basic theory is included as are plenty of examples, making this book a useful resource for beginning graduate students and non-experts, as well as a helpful reference for specialist researchers.

Regular polytopes and their symmetry have a long history stretching back two and a half millennia, to the classical regular polygons and polyhedra. Much of modern research focuses on abstract regular polytopes, but significant recent developments have been made on the geometric side, including the exploration of new topics such as realizations and rigidity, which offer a different way of understanding the geometric and combinatorial symmetry of polytopes. This is the first comprehensive account of the modern geometric theory, and includes a wide range of applications, along with new techniques. While the author explores the subject in depth, his elementary approach to traditional areas such as finite reflexion groups makes this book suitable for beginning graduate students as well as more experienced researchers.

This introduction to the theory of Diophantine approximation pays special regard to Schmidt's subspace theorem and to its applications to Diophantine equations and related topics. The geometric viewpoint on Diophantine equations has been adopted throughout the book. It includes a number of results, some published here for the first time in book form, and some new, as well as classical material presented in an accessible way. Graduate students and experts alike will find the book's broad approach useful for their work, and will discover new techniques and open questions to guide their research. It contains concrete examples and many exercises (ranging from the relatively simple to the much more complex), making it ideal for self-study and enabling readers to quickly grasp the essential concepts.

This book reconstructs how a group of nineteenth-century labor reformers appropriated and radicalized the republican tradition. These 'labor republicans' derived their definition of freedom from a long tradition of political theory dating back to the classical republics. In this tradition, to be free is to be independent of anyone else's will - to be dependent is to be a slave. Borrowing these ideas, labor republicans argued that wage laborers were unfree because of their abject dependence on their employers. Workers in a cooperative, on the other hand, were considered free because they equally and collectively controlled their work. Although these labor republicans are relatively unknown, this book details their unique, contemporary, and valuable perspective on both American history and the organization of the economy.

This book reconstructs how a group of nineteenth-century labor reformers appropriated and radicalized the republican tradition. These 'labor republicans' derived their definition of freedom from a long tradition of political theory dating back to the classical republics. In this tradition, to be free is to be independent of anyone else's will - to be dependent is to be a slave. Borrowing these ideas, labor republicans argued that wage laborers were unfree because of their abject dependence on their employers. Workers in a cooperative, on the other hand, were considered free because they equally and collectively controlled their work. Although these labor republicans are relatively unknown, this book details their unique, contemporary, and valuable perspective on both American history and the organization of the economy.

The attention of philosophers. linguists and literary theorists has been converging on the diverse and intriguing phenomena of analogy of meaning:the different though related meanings of the same word, running from simple equivocation to paronymy, metaphor and figurative language. So far, however, their attempts at explanation have been piecemeal and inconclusive and no new and comprehensive theory of analogy has emerged. This is what James Ross offers here. In the first full treatment of the subject since the fifteenth century, he argues that analogy is a systematic and universal feature of natural languages, with identifiable and law-like characteristics which explain how the meanings of words in a sentence are interdependent. Throughout he contrasts his with classical and medieval views.

There is a growing conflict between modern and postmodern social theorists. The latter reject modern approaches as economistic, essentialist and often leading to authoritarian policies. Modernists criticize postmodern approaches for their rejection of holistic conceptual frameworks which facilitate an overall picture of how social wholes (organizations, communities, nation-states, etc.) are constituted, reproduced and transformed. They believe the rejection of holistic methodologies leads to social myopia - a refusal to explore critically the type of broad problems that classical sociology deals with. This book attempts to bridge the divide between these two conflicting perspectives and proposes a novel holistic framework which is neither reductionist/economistic nor essentialist. Modern and Postmodern Social Theorizing will appeal to scholars and students of social theory and of social sciences in general.

There is a growing conflict between modern and postmodern social theorists. The latter reject modern approaches as economistic, essentialist and often leading to authoritarian policies. Modernists criticize postmodern approaches for their rejection of holistic conceptual frameworks which facilitate an overall picture of how social wholes (organizations, communities, nation-states, etc.) are constituted, reproduced and transformed. They believe the rejection of holistic methodologies leads to social myopia - a refusal to explore critically the type of broad problems that classical sociology deals with. This book attempts to bridge the divide between these two conflicting perspectives and proposes a novel holistic framework which is neither reductionist/economistic nor essentialist. Modern and Postmodern Social Theorizing will appeal to scholars and students of social theory and of social sciences in general.

In the first comprehensive and full-length study of the English historical economists, Gerard Koot traces their revolt against the theory, policy recommendations and academic dominance of classical and neoclassical economics in Britain between 1870 and 1926. English Historical Economics, 1870–1926 shows how these historical critics challenged the deductive method and mechanistic assumptions of the economic orthodoxy, developing an historical and inductive method for economic studies and laying the foundation for the professional study of economic history. The author examines the effect of this new methodology upon English politics, discussing the intellectual framework that the historical economists provided for the conservative attack on laissez-faire philosophy in links between such larger social, economic, political and intellectual controversies and the origin and growth of English historical economics.

This is a self-contained and systematic account of affine differential geometry from a contemporary view, not only covering the classical theory, but also introducing more modern developments. In order both to cover as much as possible and to keep the text of a reasonable size, the authors have concentrated on the significant features of the subject and their relationship and application to such areas as Riemannian, Euclidean, Lorentzian and projective differential geometry. In so doing, they also provide a modern introduction to the last. Some of the important geometric surfaces considered are illustrated by computer graphics, making this a physically and mathematically attractive book for all researchers in differential geometry, and for mathematical physicists seeking a quick entry to the subject.

What is the nature of law? Does our obligation to obey the law extend to unjust laws? From what source do lawmakers derive legitimate authority? What principles should guide us in the design of political institutions? The essays in this collection, written by prominent contemporary philosophers, explore how these questions were addressed by ancient political thinkers, including the Pre-Socratics, Plato, Aristotle, and the Stoics and Epicureans. Classical theories of human nature and their implications for political theory are examined, as is the meaning of freedom and coercion in Plato's thought. Plato's idea that philosophers should be political rulers receives scrutiny, too. Other essays ask what we can learn from ancient thinkers like Aristotle about the principles of constitutional design or the limits of political obligation.

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.

Realism is commonly portrayed as theory that reduces international relations to pure power politics. Michael Williams provides an important reexamination of the Realist tradition and its relevance for contemporary international relations. Examining three thinkers commonly invoked as Realism's foremost proponents - Hobbes, Rousseau, and Morgenthau - the book shows that, far from advocating a crude realpolitik, Realism's most famous classical proponents actually stressed the need for a restrained exercise of power and a politics with ethics at its core. These ideas are more relevant than ever at a time when the nature of responsible responses to international problems are at the centre of contemporary political debate. This original interpretation of major thinkers will interest scholars of international relations and the history of ideas.

Realism is commonly portrayed as theory that reduces international relations to pure power politics. Michael Williams provides an important reexamination of the Realist tradition and its relevance for contemporary international relations. Examining three thinkers commonly invoked as Realism's foremost proponents - Hobbes, Rousseau, and Morgenthau - the book shows that, far from advocating a crude realpolitik, Realism's most famous classical proponents actually stressed the need for a restrained exercise of power and a politics with ethics at its core. These ideas are more relevant than ever at a time when the nature of responsible responses to international problems are at the centre of contemporary political debate. This original interpretation of major thinkers will interest scholars of international relations and the history of ideas.

This revised and updated second edition of a highly successful book is the only text at this level to embrace a universal approach to three major developments in classical physics; namely nonlinear waves, solitons and chaos. The authors now include new material on biology and laser theory, and go on to discuss important recent developments such as soliton metamorphosis. A comprehensive treatment of basic plasma and fluid configurations and instabilities is followed by a study of the relevant nonlinear structures. Each chapter concludes with a set of problems. This text will be particularly valuable for students taking courses in nonlinear aspects of physics. In general, it will be of value to final year undergraduates and beginning graduate students studying fluid dynamics, plasma physics and applied mathematics.

This is a self-contained and systematic account of affine differential geometry from a contemporary view, not only covering the classical theory, but also introducing more modern developments. In order both to cover as much as possible and to keep the text of a reasonable size, the authors have concentrated on the significant features of the subject and their relationship and application to such areas as Riemannian, Euclidean, Lorentzian and projective differential geometry. In so doing, they also provide a modern introduction to the last. Some of the important geometric surfaces considered are illustrated by computer graphics, making this a physically and mathematically attractive book for all researchers in differential geometry, and for mathematical physicists seeking a quick entry to the subject.

In this far-ranging and innovative study Christopher Berry explores the meanings and ramifications of the idea of luxury. Insights from political theory, philosophy and intellectual history are utilised in a sophisticated conceptual analysis that is complemented by a series of specific historical investigations. Dr Berry suggests that the value attached to luxury is a crucial component in any society's self-understanding, and shows how luxury has changed from being essentially a negative term, threatening social virtue, to a guileless ploy supporting consumption. His analytic focus upon the interplay between the notions of need and desire suggests that luxuries fall into four categories - sustenance, shelter, clothing and leisure - and these are exemplified in sources as diverse as classical philosophy and contemporary advertising.

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.

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.

Adopting an innovative and theoretical approach, Greek Tragedy and the Digital is an original study of the encounter between Greek tragedy and digital media in contemporary performance. It challenges Greek tragedy conventions through the contemporary arsenal of sound masks, avatars, live code poetry, new media art and digital cognitive experimentations. These technological innovations in performances of Greek tragedy shed new light on contemporary transformations and adaptations of classical myths, while raising emerging questions about how augmented reality works within interactive and immersive environments. Drawing on cutting-edge productions and theoretical debates on performance and the digital, this collection considers issues including performativity, liveness, immersion, intermediality, aesthetics, technological fragmentation, conventions of the chorus, theatre as hypermedia and reception theory in relation to Greek tragedy. Case studies include Kzryztof Warlikowski, Jan F

This self-contained introduction to machine learning, designed from the start with engineers in mind, will equip students with everything they need to start applying machine learning principles and algorithms to real-world engineering problems. With a consistent emphasis on the connections between estimation, detection, information theory, and optimization, it includes: an accessible overview of the relationships between machine learning and signal processing, providing a solid foundation for further study; clear explanations of the differences between state-of-the-art techniques and more classical methods, equipping students with all the understanding they need to make informed technique choices; demonstration of the links between information-theoretical concepts and their practical engineering relevance; reproducible examples using Matlab, enabling hands-on student experimentation. Assuming only a basic understanding of probability and linear algebra, and accompanied by lecture slide

This book retraces the history of macroeconomics from Keynes's General Theory to the present. Central to it is the contrast between a Keynesian era and a Lucasian - or dynamic stochastic general equilibrium (DSGE) - era, each ruled by distinct methodological standards. In the Keynesian era, the book studies the following theories: Keynesian macroeconomics, monetarism, disequilibrium macroeconomics (Patinkin, Leijongufvud and Clower), non-Walrasian equilibrium models, and first-generation new Keynesian models. Three stages are identified in the DSGE era: new classical macroeconomics (Lucas), RBC modelling, and second-generation new Keynesian modeling. The book also examines a few selected works aimed at presenting alternatives to Lucasian macroeconomics. While not eschewing analytical content, Michel De Vroey focuses on substantive assessments, and the models studied are presented in a pedagogical and vivid yet critical way.

Originally published in 1955, this textbook on electron optics was aimed both at scientists already engaged in research as well as scientists new to this field of study. The book has a threefold purpose: firstly, 'to relate the theory of electron-optical instruments and particle accelerators to classical optics and dynamics'; secondly, 'to set out general procedures which may be applied to the study of image-formation in electron-optical instruments and stability in particle accelerators'; thirdly, 'to apply these procedures to the analysis of the properties of the more important instruments and machines'. Chapters are detailed and range from 'The variational equation' to 'Uniform focusing in particle accelerators'. Diagrams are included for reference. This book will be of great value to scholars of the history of physics and electromagnetics.

During the past two decades there has been active interplay between geometric measure theory and Fourier analysis. This book describes part of that development, concentrating on the relationship between the Fourier transform and Hausdorff dimension. The main topics concern applications of the Fourier transform to geometric problems involving Hausdorff dimension, such as Marstrand type projection theorems and Falconer's distance set problem, and the role of Hausdorff dimension in modern Fourier analysis, especially in Kakeya methods and Fourier restriction phenomena. The discussion includes both classical results and recent developments in the area. The author emphasises partial results of important open problems, for example, Falconer's distance set conjecture, the Kakeya conjecture and the Fourier restriction conjecture. Essentially self-contained, this book is suitable for graduate students and researchers in mathematics.

Today's pervasive computing and communications networks have created an intense need for secure and reliable cryptographic systems. Bringing together a fascinating mixture of topics in engineering, mathematics, computer science, and informatics, this book presents the timeless mathematical theory underpinning cryptosystems both old and new. Major branches of classical and modern cryptography are discussed in detail, from basic block and stream cyphers through to systems based on elliptic and hyperelliptic curves, accompanied by concise summaries of the necessary mathematical background. Practical aspects such as implementation, authentication and protocol-sharing are also covered, as are the possible pitfalls surrounding various cryptographic methods. Written specifically with engineers in mind, and providing a solid grounding in the relevant algorithms, protocols and techniques, this insightful introduction to the foundations of modern cryptography is ideal for graduate students and r

An Introduction to the Philosophy of Art is a clear and compact survey of philosophical theories of the nature and value of art, including in its scope literature, painting, sculpture, music, dance, architecture, movies, conceptual art and performance art. This second edition incorporates significant new research on topics including pictorial depiction, musical expression, conceptual art, Hegel, and art and society. Drawing on classical and contemporary philosophy, literary theory and art criticism, Richard Eldridge explores the representational, formal and expressive dimensions of art. He argues that the aesthetic and semantic density of the work, in inviting imaginative exploration, makes works of art cognitively, morally and socially important. This importance is further elaborated in discussions of artistic beauty, originality, imagination and criticism. His accessible study will be invaluable to students of philosophy of art and aesthetics.

An Introduction to the Philosophy of Art is a clear and compact survey of philosophical theories of the nature and value of art, including in its scope literature, painting, sculpture, music, dance, architecture, movies, conceptual art and performance art. This second edition incorporates significant new research on topics including pictorial depiction, musical expression, conceptual art, Hegel, and art and society. Drawing on classical and contemporary philosophy, literary theory and art criticism, Richard Eldridge explores the representational, formal and expressive dimensions of art. He argues that the aesthetic and semantic density of the work, in inviting imaginative exploration, makes works of art cognitively, morally and socially important. This importance is further elaborated in discussions of artistic beauty, originality, imagination and criticism. His accessible study will be invaluable to students of philosophy of art and aesthetics.

This book examines the behavior of individuals at risk and insurance industry decision makers involved in selling, buying and regulation. It compares their actions to those predicted by benchmark models of choice derived from classical economic theory. Where actual choices stray from predictions, the behavior is considered to be anomalous. Howard C. Kunreuther, Mark Pauly and Stacey McMorrow attempt to understand why these anomalies occur, in many cases using insights from behavioral economics. The authors then consider if and how such behavioral anomalies could be modified to improve individual and social welfare. This book describes situations in which both public policy and the insurance industry's collective posture need to change. This may require incentives, rules and institutions to help reduce both inefficient and anomalous behavior, thereby encouraging behavior that will improve individual and social welfare.

This book examines the behavior of individuals at risk and insurance industry decision makers involved in selling, buying and regulation. It compares their actions to those predicted by benchmark models of choice derived from classical economic theory. Where actual choices stray from predictions, the behavior is considered to be anomalous. Howard C. Kunreuther, Mark Pauly and Stacey McMorrow attempt to understand why these anomalies occur, in many cases using insights from behavioral economics. The authors then consider if and how such behavioral anomalies could be modified to improve individual and social welfare. This book describes situations in which both public policy and the insurance industry's collective posture need to change. This may require incentives, rules and institutions to help reduce both inefficient and anomalous behavior, thereby encouraging behavior that will improve individual and social welfare.

This self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory. The book starts with a concise introduction to statistical mechanics, proceeds to disordered lattice spin systems, and concludes with a presentation of the latest developments in the mathematical understanding of mean-field spin glass models. In particular, progress towards a rigorous understanding of the replica symmetry-breaking solutions of the Sherrington-Kirkpatrick spin glass models, due to Guerra, Aizenman-Sims-Starr and Talagrand, is reviewed in some detail.

The instability of fluid flows is a key topic in classical fluid mechanics because it has huge repercussions for applied disciplines such as chemical engineering, hydraulics, aeronautics, and geophysics. This modern introduction is written for any student, researcher, or practitioner working in the area, for whom an understanding of hydrodynamic instabilities is essential. Based on a decade's experience of teaching postgraduate students in fluid dynamics, this book brings the subject to life by emphasizing the physical mechanisms involved. The theory of dynamical systems provides the basic structure of the exposition, together with asymptotic methods. Wherever possible, Charru discusses the phenomena in terms of characteristic scales and dimensional analysis. The book includes numerous experimental studies, with references to videos and multimedia material, as well as over 150 exercises which introduce the reader to new problems.

The instability of fluid flows is a key topic in classical fluid mechanics because it has huge repercussions for applied disciplines such as chemical engineering, hydraulics, aeronautics, and geophysics. This modern introduction is written for any student, researcher, or practitioner working in the area, for whom an understanding of hydrodynamic instabilities is essential. Based on a decade's experience of teaching postgraduate students in fluid dynamics, this book brings the subject to life by emphasizing the physical mechanisms involved. The theory of dynamical systems provides the basic structure of the exposition, together with asymptotic methods. Wherever possible, Charru discusses the phenomena in terms of characteristic scales and dimensional analysis. The book includes numerous experimental studies, with references to videos and multimedia material, as well as over 150 exercises which introduce the reader to new problems.

Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics, as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the Atiyah–Singer index theorem, to provide double covers (spin groups) of the classical groups and to generalize the Hilbert transform. They also have their place in physics, setting the scene for Maxwell's equations in electromagnetic theory, for the spin of elementary particles and for the Dirac equation. This straightforward introduction to Clifford algebras makes the necessary algebraic background - including multilinear algebra, quadratic spaces and finite-dimensional real algebras - easily accessible to research students and final-year undergraduates. The author also introduces many applications in mathematics and physics, equipping the reader with Clifford algebras as a working tool in a variety of contexts.

Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics, as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the Atiyah–Singer index theorem, to provide double covers (spin groups) of the classical groups and to generalize the Hilbert transform. They also have their place in physics, setting the scene for Maxwell's equations in electromagnetic theory, for the spin of elementary particles and for the Dirac equation. This straightforward introduction to Clifford algebras makes the necessary algebraic background - including multilinear algebra, quadratic spaces and finite-dimensional real algebras - easily accessible to research students and final-year undergraduates. The author also introduces many applications in mathematics and physics, equipping the reader with Clifford algebras as a working tool in a variety of contexts.

Under what conditions is a group of scientists rational? How would rational scientists collectively agree to make their group more effective? What sorts of negotiations would occur among them and under what conditions? What effect would their final agreement have on science and society? These questions have been central to the philosophy of science for the last two decades. In this 2007 book, Husain Sarkar proposes answers to them by building on classical solutions - the skeptical view, two versions of the subjectivist view, the objectivist view, and the view of Hilary Putnam. Although he finds these solutions not completely adequate, Sarkar retrieves what is of value from them and also expropriates the arguments of John Rawls and Amartya Sen, in order to weave a richer, deeper, and more developed theory of group rationality.

This book examines the conceptual and temporal frames through which modern Western historiography has linked itself to classical antiquity. In doing so, it articulates a genealogical problematic of what history is and a more strictly focused reappraisal of Greek and Roman historical thought. Ancient ideas of history have played a key role in modern debates about history writing, from Kant through Hegel to Nietzsche and Heidegger, and from Friedrich Creuzer through George Grote and Theodor Mommsen to Momigliano and Moses Finley; yet scholarship has paid little attention to the theoretical implications of the reception of these ideas. The essays in this collection cover a wide range of relevant topics and approaches and boast distinguished authors from across Europe in the fields of classics, ancient and modern history and the theory of historiography.