Classical Recursion Theory

Electrodynamics is a basic area of physics, encompassing also classical and quantum physics, optics, relativity and field theory, and is of universal practical importance. The present text aims at a b

Electrodynamics is a basic area of physics, encompassing also classical and quantum physics, optics, relativity and field theory, and is of universal practical importance. The present text aims at a b

This book provides a self-contained and systematic introduction to classical electron theory and its quantization, non-relativistic quantum electrodynamics. The first half of the book covers the classical theory. It discusses the well-defined Abraham model of extended charges in interaction with the electromagnetic field, and gives a study of the effective dynamics of charges under the condition that, on the scale given by the size of the charge distribution, they are far apart and the applied potentials vary slowly. The second half covers the quantum theory, leading to a coherent presentation of non-relativistic quantum electrodynamics. Topics discussed include non-perturbative properties of the basic Hamiltonian, the structure of resonances, the relaxation to the ground state through emission of photons, the non-perturbative derivation of the g-factor of the electron and the stability of matter.

In this provocative book, Paul Glimcher argues that economic theory may provide analternative to the classical Cartesian model of the brain and behavior. Glimcher argues thatCartesian dualism operates

John Bell, FRS was one of the leading expositors and interpreters of modern quantum theory. He is particularly famous for his discovery of the crucial difference between the predictions of conventional quantum mechanics and the implications of local causality, a concept insisted on by Einstein. John Bell's work played a major role in the development of our current understanding of the profound nature of quantum concepts and of the fundamental limitations they impose on the applicability of the classical ideas of space, time and locality. This book includes all of John Bell's published and unpublished papers on the conceptual and philosophical problems of quantum mechanics, including two papers that appeared after the first edition was published. The book includes a short Preface written by the author for the first edition, and also an introduction by Alain Aspect that puts into context John Bell's enormous contribution to the quantum philosophy debate.

In this book, Tim Whitmarsh offers an innovative new introduction to ancient Greek literature. The volume integrates cutting-edge cultural theory with the latest research in classical scholarship, pro

Topological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure. Examples are monopoles and Skyrmions, Ginzburg-Landau vortices and sigma-model lumps, and Yang-Mills instantons. This book is a comprehensive survey of static topological solitons and their dynamical interactions. Particular emphasis is placed on the solitons which satisfy first-order Bogomolny equations. For these, the soliton dynamics can be investigated by finding the geodesics on the moduli space of static multi-soliton solutions. Remarkable scattering processes can be understood this way. The book starts with an introduction to classical field theory, and a survey of several mathematical techniques useful for understanding many types of topological soliton. Subsequent chapters explore key examples of solitons in one, two, three and four dimensions. The final chapter discusses the unstable sphaleron solutions which exist in several

Using the neo-classical theory of production economics as the analytical framework, this book, first published in 2004, provides a unified and easily comprehensible, yet fairly rigorous, exposition of the core literature on data envelopment analysis (DEA) for readers based in different disciplines. The various DEA models are developed as nonparametric alternatives to the econometric models. Apart from the standard fare consisting of the basic input- and output-oriented DEA models formulated by Charnes, Cooper, and Rhodes, and Banker, Charnes, and Cooper, the book covers developments such as the directional distance function, free disposal hull (FDH) analysis, non-radial measures of efficiency, multiplier bounds, mergers and break-up of firms, and measurement of productivity change through the Malmquist total factor productivity index. The chapter on efficiency measurement using market prices provides the critical link between DEA and the neo-classical theory of a competitive firm. The

John Bell, FRS was one of the leading expositors and interpreters of modern quantum theory. He is particularly famous for his discovery of the crucial difference between the predictions of conventional quantum mechanics and the implications of local causality, a concept insisted on by Einstein. John Bell's work played a major role in the development of our current understanding of the profound nature of quantum concepts and of the fundamental limitations they impose on the applicability of the classical ideas of space, time and locality. This book includes all of John Bell's published and unpublished papers on the conceptual and philosophical problems of quantum mechanics, including two papers that appeared after the first edition was published. The book includes a short Preface written by the author for the first edition, and also an introduction by Alain Aspect that puts into context John Bell's enormous contribution to the quantum philosophy debate.

Dr Burkill gives a straightforward introduction to Lebesgue's theory of integration. His approach is the classical one, making use of the concept of measure, and deriving the principal results required for applications of the theory.

Originally published as a French edition in 1991, and first translated into English for this Cambridge edition in 2004, in this exhaustive study Christian Bidard develops a theory of prices of production. This theory breaks down the symmetry between producers and consumers and gives more importance to reproduction rather than scarcity. In his analysis of multiple-product systems, Bidard focuses on the notion of an all-engaging system which elucidates the link with von Neumann's theory; examines the notions of sector and vertical integration which make possible an elegant treatment of fixed capital; clarifies the status of the internal rate of return; proposes a general theory of rent. In the discussion of capital theory and marginal equalities or, more specifically, the treatment of exhaustible resources, Bidard compares different readings of Sraffa's work and revisits the question of relationships between classical theory (Smith, Ricardo, Marx) and the general equilibrium theory (Walr

The most basic algebraic varieties are the projective spaces, and rational varieties are their closest relatives. In many applications where algebraic varieties appear in mathematics and the sciences, we see rational ones emerging as the most interesting examples. The authors have given an elementary treatment of rationality questions using a mix of classical and modern methods. Arising from a summer school course taught by János Kollár, this book develops the modern theory of rational and nearly rational varieties at a level that will particularly suit graduate students. There are numerous examples and exercises, all of which are accompanied by fully worked out solutions, that will make this book ideal as the basis of a graduate course. It will act as a valuable reference for researchers whilst helping graduate students to reach the point where they can begin to tackle contemporary research problems.

The most comprehensive study of ideology and utopia since Karl Mannheim's work of the 1930s, Utopia and Revolution can be understood as turning classical political theory on its head or, perhaps, insi

Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of m

This is a book for those who want to understand the main ideas in the theory of optimal problems. It provides a good introduction to classical topics (under the heading of "the calculus of variations"

Acclaimed as one of the pioneering texts to introduce narratology (the theory that deals with the general principles underlying narrative texts) to classical scholarship, Irene de Jong's work explains

First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide a stock of examples to foster a clear understanding of the theory. Once these ideas are established, the author goes on to show that the scope of harmonic analysis extends far beyond the setting of the circle group, and he opens the door to other contexts by considering Fourier transforms on the real line as well as a brief look at Fourier analysis on locally compact abelian groups. This new edition has been revised by the author, to include several new sections and a new appendix.

A practical guide for today's wireless engineerHigh Frequency Techniques: An Introduction to RF and Microwave Engineering is a clearly written classical circuit and field theory text illustrated with

This timely volume provides a broad survey of (2+1)-dimensional quantum gravity. It emphasises the 'quantum cosmology' of closed universes and the quantum mechanics of the (2+1)-dimensional black hole. It compares and contrasts a variety of approaches, and examines what they imply for a realistic theory of quantum gravity. General relativity in three spacetime dimensions has become a popular arena in which to explore the ramifications of quantum gravity. As a diffeomorphism-invariant theory of spacetime structure, this model shares many of the conceptual problems of realistic quantum gravity. But it is also simple enough that many programs of quantization can be carried out explicitly. After analysing the space of classical solutions, this book introduces some fifteen approaches to quantum gravity - from canonical quantization in York's 'extrinsic time' to Chern-Simons quantization, from the loop representation to covariant path integration to lattice methods. Relationships among quant

This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.

The statistical theory of unimolecular reactions is now universally known as RRKM theory. This textbook covers the basics necessary for the understanding of RRKM theory in its original and variational, phase-space and angular momentum-conserved incarnations. After a review of the Kassel quantum model and the theory of Slater, the specific-energy RRKM rate constant k(E) is derived. The argument is then extended to the angular momentum-dependent rate constant k(E,J), to non-classical effects (tunneling and non-adiabatic transition), and the general problem of angular momentum conservation. A long chapter is devoted to the counting of quantum states. The chapter on thermal systems discusses both analytical and numerical solutions and is later extended to include the variational approach and discussion of exit channel effects. Containing many problem sets and solutions, the book is targeted at graduate and advanced undergraduate students studying chemical dynamics, chemical kinetics and th

The statistical theory of unimolecular reactions is now universally known as RRKM theory. This textbook covers the basics necessary for the understanding of RRKM theory in its original and variational, phase-space and angular momentum-conserved incarnations. After a review of the Kassel quantum model and the theory of Slater, the specific-energy RRKM rate constant k(E) is derived. The argument is then extended to the angular momentum-dependent rate constant k(E,J), to non-classical effects (tunneling and non-adiabatic transition), and the general problem of angular momentum conservation. A long chapter is devoted to the counting of quantum states. The chapter on thermal systems discusses both analytical and numerical solutions and is later extended to include the variational approach and discussion of exit channel effects. Containing many problem sets and solutions, the book is targeted at graduate and advanced undergraduate students studying chemical dynamics, chemical kinetics and th

Corings and comodules are fundamental algebraic structures, which can be thought of as both dualisations and generalisations of rings and modules. Introduced by Sweedler in 1975, only recently they have been shown to have far reaching applications ranging from the category theory including differential graded categories through classical and Hopf-type module theory to non-commutative geometry and mathematical physics. This is the first extensive treatment of the theory of corings and their comodules. In the first part, the module-theoretic aspects of coalgebras over commutative rings are described. Corings are then defined as coalgebras over non-commutative rings. Topics covered include module-theoretic aspects of corings, such as the relation of comodules to special subcategories of the category of modules (sigma-type categories), connections between corings and extensions of rings, properties of new examples of corings associated to entwining structures, generalisations of bialgebras

Incorporated in this 2003 volume are the first two books in Mukai's series on moduli theory. The notion of a moduli space is central to geometry. However, its influence is not confined there; for example, the theory of moduli spaces is a crucial ingredient in the proof of Fermat's last theorem. Researchers and graduate students working in areas ranging from Donaldson or Seiberg-Witten invariants to more concrete problems such as vector bundles on curves will find this to be a valuable resource. Amongst other things this volume includes an improved presentation of the classical foundations of invarant theory that, in addition to geometers, would be useful to those studying representation theory. This translation gives an accurate account of Mukai's influential Japanese texts.

This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere. Various models for Möbius geometry are presented: the classical projective model, the quaternionic approach, and an approach that uses the Clifford algebra of the space of homogeneous coordinates of the classical model; the use of 2-by-2 matrices in this context is elaborated. For each model in turn applications are discussed. Topics comprise conformally flat hypersurfaces, isothermic surfaces and their transformation theory, Willmore surfaces, orthogonal systems and the Ribaucour transformation, as well as analogous discrete theories for isothermic surfaces and orthogonal systems. Certain relations with curved flats, a particular type of integrable system, are revealed. Thus this book will serve both as an introduction to newcomers (with background in Riemannian geometry and elementary differential geometry) and as a reference work for researchers.

Formerly The Longman Dictionary of Poetic Terms, this newly updated version contains over 1,600 entries on the devices, techniques, history, theory, and terminology of poetry from the Classical perio

When do countries democratize? What facilitates the survival of authoritarian regimes? What determines the occurrence of revolutions, often leading to left-wing dictatorships, such as the Soviet regime? Although a large literature has developed since Aristotle through contemporary political science to answer these questions, we still lack a convincing understanding of the process of political development. Employing analytical tools borrowed from game theory, Carles Boix offers a complete theory of political transitions, in which political regimes ultimately hinge on the nature of economic assets, their distribution among individuals, and the balance of power among different social groups. Backed up by detailed historical work and extensive statistical analysis that goes back to the mid-nineteenth century, this 2003 book explains why democracy emerged in classical Athens. It also discusses the early triumph of democracy in both nineteenth-century agrarian Norway, Switzerland and northea

When do countries democratize? What facilitates the survival of authoritarian regimes? What determines the occurrence of revolutions, often leading to left-wing dictatorships, such as the Soviet regime? Although a large literature has developed since Aristotle through contemporary political science to answer these questions, we still lack a convincing understanding of the process of political development. Employing analytical tools borrowed from game theory, Carles Boix offers a complete theory of political transitions, in which political regimes ultimately hinge on the nature of economic assets, their distribution among individuals, and the balance of power among different social groups. Backed up by detailed historical work and extensive statistical analysis that goes back to the mid-nineteenth century, this 2003 book explains why democracy emerged in classical Athens. It also discusses the early triumph of democracy in both nineteenth-century agrarian Norway, Switzerland and northea

This book contains eight expository articles by well-known authors of the theory of Galois groups and fundamental groups. They focus on presenting developments, avoiding classical aspects which have already been described at length in the standard literature. The volume grew from the special semester held at the MSRI in Berkeley in 1999 and many of the results are due to work accomplished during that program. Among the subjects covered are elliptic surfaces, Grothendieck's anabelian conjecture, fundamental groups of curves and differential Galois theory in positive characteristic. Although the articles contain fresh results, the authors have striven to make them as introductory as possible, making them accessible to graduate students as well as researchers in algebraic geometry and number theory. The volume also contains a lengthy overview by Leila Schneps that sets the individual articles into the broader context of contemporary research in Galois groups.

The focus of this book is on algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions, also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon, and Camassa-Holm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The formalism presented includes trace formulas, Dubrovin-type initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces). The presentation is rigorous, detailed, and self-contained, with ample background material provided in various appendices. Detailed notes for each chapter together with an exh

This volume is easily accessible to young people and mathematicians unfamiliar with logic. It gives a terse historical picture of Model Theory and introduces the latest developments in the area. It fu

Offering an excellent overview of approximately 400 years of social theory with a concentration on sociological thought, this book reflects the convergence of social science, natural science, philosop

At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.

At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.

The aim of this book is to present a modern treatment of the theory of theta functions in the context of algebraic geometry. The novelty of its approach lies in the systematic use of the Fourier-Mukai transform. The author starts by discussing the classical theory of theta functions from the point of view of the representation theory of the Heisenberg group (in which the usual Fourier transform plays the prominent role). He then shows that in the algebraic approach to this theory, the Fourier–Mukai transform can often be used to simplify the existing proofs or to provide completely new proofs of many important theorems. Graduate students and researchers with strong interest in algebraic geometry will find much of interest in this volume.

Polynomial equations have been long studied, both theoretically and with a view to solving them. Until recently, manual computation was the only solution method and the theory was developed to accommodate it. With the advent of computers, the situation changed dramatically. Many classical results can be more usefully recast within a different framework which in turn lends itself to further theoretical development tuned to computation. This first book in a trilogy is devoted to the new approach. It is a handbook covering the classical theory of finding roots of a univariate polynomial, emphasising computational aspects, especially the representation and manipulation of algebraic numbers, enlarged by more recent representations like the Duval Model and the Thom Codification. Mora aims to show that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate

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.

The 78 letters in this Anthology (41 Greek, 36 Latin and 1 bilingual, with facing English translation) are selected both for their intrinsic interest, and to illustrate the range of functions letters performed in the ancient world. Dating from between c. 500 BC and c. 400 AD, they include naive and high-style, 'real' and 'fictitious', and classical and patristic items: Cicero, Horace, Ovid, Seneca, Pliny, Julian, Basil and Augustine are juxtaposed with Phalaris, Diogenes, Chion, and the authors of letters on lead, wood, papyrus and stone. Four final items exemplify ancient epistolary theory. The Commentary, besides providing contextual and linguistic assistance, draws attention to specifically epistolary features and to different stylistic levels of Greek and Latin represented. Epistolary topics and formulae are discussed in the Introduction, which also provides biographical and bibliographical information on all texts and authors included, and a history of letter-writing and letter-re

aiming at a more conceptual understanding of classical and qu- tum ?eld theory from a novel mathematical point of view.

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing.