Classical Recursion Theory

This is a textbook about classical elementary number theory and elliptic curves. The first part discusses elementary topics such as primes, factorization, continued fractions, and quadratic forms, in

This book demonstrates the empirical gains and integrative potentials of social systems theory for the sociology of law. Against a backdrop of classical and contemporary sociological debates about law

Rationality within Modern Psychological Theory examines the rational and irrational dimensions of human nature and of the psyche and logos through the lenses of classical philosophy and modern psychol

Nyana is the most rational and logical of all the classical Indian philosophical systems. In the study of Nyana philosophy, Karikavali with its commentary Muktavali, both by Visvanatha Nyayapancanana,

This monograph presents a general equilibrium methodology for microeconomic policy analysis. It is intended to serve as an alternative to the now classical, axiomatic general equilibrium theory as exp

Since the classical Freudian and ego psychology paradigms lost their position of dominance in the late 1950s, psychoanalysis became a multi-paradigm science with those working in the different framewo

Since the classical Freudian and ego psychology paradigms lost their position of dominance in the late 1950s, psychoanalysis became a multi-paradigm science with those working in the different framewo

The 18th-century rediscovery of the three archaic Greek-Doric temples in Paestum in southern Italy turned existing ideas on classical architecture upside down. The porous limestone temples with rough,

The Social Lens: An Invitation to Social and Sociological Theory, Third Edition is an upper division undergraduate social theory textbook that introduces the student to the major classical and contemp

Classical number theory and elliptic curves are examined in this textbook, which moves on from elementary topics such as primes, continued fractions, and quadratic forms, to elliptic curves and their

The main objective of this book is to present the basic theoretical principles and practical applications for the classical interferometric techniques and the most advanced methods in the field of mod

This book introduces a theory of music analysis that one can use to explore aspects of segmentation and associative organization in a wide range of repertoire including Western classical music from th

This book covers the theory and applications of continuum solvation models. The main focus is on the quantum-mechanical version of these models, but classical approaches and combined or hyb

This work deals with an extension of the classical Littlewood-Paley theory in the context of symmetric diffusion semigroups. In this general setting there are applications to a variety of problems, su

The main object of this book is to reorient and revitalize classical geometry in a way that will bring it closer to the mainstream of contemporary mathematics. The postulational basis of the subject w

Classical social choice theory relies heavily on the assumption that all individuals have fixed preference orderings. This highly original book presents a new theory of social preferences that explicitly accounts for important social phenomena such as coordination, compromise, negotiation and altruism. Drawing on cybernetics and network theory, it extends classical social choice theory by constructing a framework that allows for dynamic preferences that are modulated by the situation-dependent social influence that they exert on each other. In this way the book shows how members of a social network may modulate their preferences to account for social context. This important expansion of social choice theory will be of interest to readers in a wide variety of disciplines, including economists and political scientists concerned with choice theory as well as computer scientists and engineers working on network theory.

This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Bäcklund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory. It is with these transformations and the links they afford between the classical differential geometry of surfaces and the nonlinear equations of soliton theory that the present text is concerned. In this geometric context, solitonic equations arise out of the Gauß-Mainardi-Codazzi equations for various types of surfaces that admit invariance under Bäcklund-Darboux transformations. This text is appropriate for us

This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Bäcklund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory. It is with these transformations and the links they afford between the classical differential geometry of surfaces and the nonlinear equations of soliton theory that the present text is concerned. In this geometric context, solitonic equations arise out of the Gauß-Mainardi-Codazzi equations for various types of surfaces that admit invariance under Bäcklund-Darboux transformations. This text is appropriate for us

Classical algebraic geometry, inseparably connected with the names of Abel, Riemann, Weierstrass, Poincaré, Clebsch, Jacobi and other outstanding mathematicians of the last century, was mainly an analytical theory. In our century it has been enriched by the methods and ideas of topology, commutative algebra and Grothendieck's schemes seemed to have replaced once and forever the somewhat naive language of classical algebraic geometry. This book contains more than its modest title suggests. Written in 1897, its scope was as broad as it could possibly be, namely to cover the whole of algebraic geometry, and associated theories. The subject is discussed by Baker in terms of transcendental functions, and in particular theta functions. Many of the ideas put forward are of continuing relevance today, and some of the most exciting ideas from theoretical physics draw on work presented here.

The theory of water waves has been a source of intriguing and often difficult mathematical problems for at least 150 years. Virtually every classical mathematical technique appears somewhere within its confines. Beginning with the introduction of the appropriate equations of fluid mechanics, the opening chapters of this text consider the classical problems in linear and non-linear water-wave theory. This sets the ground for a study of more modern aspects, problems that give rise to soliton-type equations. The book closes with an introduction to the effects of viscosity. All the mathematical developments are presented in the most straightforward manner, with worked examples and simple cases carefully explained. Exercises, further reading, and historical notes on some of the important characters in the field round off the book and help to make this an ideal text for a beginning graduate course on water waves.

The theory of water waves has been a source of intriguing and often difficult mathematical problems for at least 150 years. Virtually every classical mathematical technique appears somewhere within its confines. Beginning with the introduction of the appropriate equations of fluid mechanics, the opening chapters of this text consider the classical problems in linear and non-linear water-wave theory. This sets the ground for a study of more modern aspects, problems that give rise to soliton-type equations. The book closes with an introduction to the effects of viscosity. All the mathematical developments are presented in the most straightforward manner, with worked examples and simple cases carefully explained. Exercises, further reading, and historical notes on some of the important characters in the field round off the book and help to make this an ideal text for a beginning graduate course on water waves.

The topic of 'circle packing' was born of the computer age but takes its inspiration and themes from core areas of classical mathematics. A circle packing is a configuration of circles having a specified pattern of tangencies, as introduced by William Thurston in 1985. This book, first published in 2005, lays out their study, from first definitions to latest theory, computations, and applications. The topic can be enjoyed for the visual appeal of the packing images - over 200 in the book - and the elegance of circle geometry, for the clean line of theory, for the deep connections to classical topics, or for the emerging applications. Circle packing has an experimental and visual character which is unique in pure mathematics, and the book exploits that to carry the reader from the very beginnings to links with complex analysis and Riemann surfaces. There are intriguing, often very accessible, open problems throughout the book and seven Appendices on subtopics of independent interest. Th

It is a common complaint against moral philosophers that their abstract theorising bears little relation to the practical problems of everyday life. Professor Braithwaite believes that this criticism need not be inevitable. With the help of the Theory of Games he shows how arbitration is possible between two neighbours, a jazz trumpeter and a classical pianist, whose performances are a source of mutual discord. The solution of the problem in the lecture is geometrical, and is based on the formal analogy between the logic of the situation and the geometry of a parabola. But an appendix provides the alternative algebraic treatment of a general two-person collaboration situation.

In this book, Professor Thomson and Professor Lensberg extrapolate upon the Nash (1950) treatment of the bargaining problem to consider the situation where the number of bargainers may vary. The authors formulate axioms to specify how solutions should respond to such changes, and provide new characterizations of all the major solutions as well as generalizations of these solutions. The book also contains several other comparative studies of solutions in the context of a variable number of agents. Much of the theory of bargaining can be rewritten within this context. The pre-eminence of the three solutions at the core of the classical theory is confirmed. These are the solutions introducted by Nash (1950) and two solutions axiomatized in the 1970s (Kalai-Smorodinsky and egalitarian solutions).

In this book, Professor Thomson and Professor Lensberg extrapolate upon the Nash (1950) treatment of the bargaining problem to consider the situation where the number of bargainers may vary. The authors formulate axioms to specify how solutions should respond to such changes, and provide new characterizations of all the major solutions as well as generalizations of these solutions. The book also contains several other comparative studies of solutions in the context of a variable number of agents. Much of the theory of bargaining can be rewritten within this context. The pre-eminence of the three solutions at the core of the classical theory is confirmed. These are the solutions introducted by Nash (1950) and two solutions axiomatized in the 1970s (Kalai-Smorodinsky and egalitarian solutions).

Sir Horace Lamb (1849–1934) the British mathematician, wrote a number of influential works in classical physics. A pupil of Stokes and Clerk Maxwell, he taught for ten years as the first professor of mathematics at the University of Adelaide before returning to Britain to take up the post of professor of physics at the Victoria University of Manchester (where he had first studied mathematics at Owens College). As a teacher and writer his stated aim was clarity: 'somehow to make these dry bones live'. His Statics was first published in 1912, and the third edition, offered here, in 1928. It was intended as a textbook for students with some knowledge of mechanics, and deals mainly with two-dimensional problems: examples are provided at the end of each section.

Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi–Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi–Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses wi

Introducing graduate students and researchers to mathematical physics, this book discusses two recent developments: the demonstration that causality can be defined on discrete space-times; and Sewell's measurement theory, in which the wave packet is reduced without recourse to the observer's conscious ego, nonlinearities or interaction with the rest of the universe. The definition of causality on a discrete space-time assumes that space-time is made up of geometrical points. Using Sewell's measurement theory, the author concludes that the notion of geometrical points is as meaningful in quantum mechanics as it is in classical mechanics, and that it is impossible to tell whether the differential calculus is a discovery or an invention. Providing a mathematical discourse on the relation between theoretical and experimental physics, the book gives detailed accounts of the mathematically difficult measurement theories of von Neumann and Sewell.

The fast multipole method is one of the most important algorithms in computing developed in the 20th century. Along with the fast multipole method, the boundary element method (BEM) has also emerged as a powerful method for modeling large-scale problems. BEM models with millions of unknowns on the boundary can now be solved on desktop computers using the fast multipole BEM. This is the first book on the fast multipole BEM, which brings together the classical theories in BEM formulations and the recent development of the fast multipole method. Two- and three-dimensional potential, elastostatic, Stokes flow, and acoustic wave problems are covered, supplemented with exercise problems and computer source codes. Applications in modeling nanocomposite materials, bio-materials, fuel cells, acoustic waves, and image-based simulations are demonstrated to show the potential of the fast multipole BEM. Enables students, researchers, and engineers to learn the BEM and fast multipole method from a s

Child fostering in West Africa connects classical and new kinship theory and offers ethnographic studies on a mobile and creative kinship practice.

The Psychology of Learning and Motivation series publishes empirical and theoretical contributions in cognitive and experimental psychology, ranging from classical and instrumental conditioning to com

The Psychology of Learning and Motivation series publishes empirical and theoretical contributions in cognitive and experimental psychology, ranging from classical and instrumental conditioning to com

The Psychology of Learning and Motivation series publishes empirical and theoretical contributions in cognitive and experimental psychology, ranging from classical and instrumental conditioning to com

The Psychology of Learning and Motivation publishes empirical and theoretical contributions in cognitive and experimental psychology, ranging from classical and instrumental conditioning to complex le

"The Politics of Hollywood Cinema radically transforms our understanding of cinema's potential to be politically engaging and challenging. Examining several films from Hollywood's classical era, inclu

Offering an integrated presentation of classical and statistical array processing, this book develops synthesis techniques for linear and planet arrays; it also provides a statistical characterization

Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact

The study of phase transitions is among the most fascinating fields in physics. Originally limited to transition phenomena in equilibrium systems, this field has outgrown its classical confines during

This book contains theory and applications of gravity both for physical geodesy and geophysics. It identifies classical and modern topics for studying the Earth. Worked-out examples illustrate basic b

This major new text provides systematic coverage of classical and more recent theoretical approaches to inequality and poverty, as well as a thorough assessment of development in the twentieth century