Classical Recursion Theory

This collection of primary source readings covers the history of evolutionary theory from its roots in Classical Greece to the present. Beginning with excerpts from Plato and Aristotle, the volume pro

The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools le

This book deals with a careful presentation of the principles on which the physical problems are based and the mathematical treatment of the problems. The fundamental solution is used as in classical potential theory to construct solutions to initial and certain boundary value problems for the linear Stokes equations.

Mr Dobb examines the history of economic thought in the light of the modern controversy over capital theory and, more particularly, the appearance of Sraffa's book The Production of Commodities by Means of Commodities, which was a watershed in the critical discussions constituted a crucial turning-point in the history of economics: an estimate not unconnected with his reinterpretation of nineteenth-century economic thought as consisting of two streams or traditions commonly confused under the generic title of 'the classical tradition' against which Jevons so strongly reacted.

The embrace of reception theory has been one of the hallmarks of classical studies over the last 30 years. This volume builds on the critical insights thereby gained to consider reception within Greek antiquity itself. Reception, like 'intertextuality', places the emphasis on the creative agency of the later 'receiver' rather than the unilateral influence of the 'transmitter'. It additionally shines the spotlight on transitions into new cultural contexts, on materiality, on intermediality and on the body. Essays range chronologically from the archaic to the Byzantine periods and address literature (prose and verse; Greek, Roman and Greco-Jewish), philosophy, papyri, inscriptions and dance. Whereas the conventional image of ancient Greek classicism is one of quiet reverence, this book, by contrast, demonstrates how rumbustious, heterogeneous and combative it could be.

Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.

Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.

Modern republicanism - distinguished from its classical counterpart by its commercial character and jealous distrust of those in power, by its use of representative institutions, and by its employment of a separation of powers and a system of checks and balances - owes an immense debt to the republican experiment conducted in England between 1649, when Charles I was executed, and 1660, when Charles II was crowned. Though abortive, this experiment left a legacy in the political science articulated both by its champions, John Milton, Marchamont Nedham, and James Harrington, and by its sometime opponent and ultimate supporter, Thomas Hobbes. This volume examines these four thinkers, situates them with regard to the novel species of republicanism first championed in the early 1500s by Niccolò Machiavelli, and examines the debt that he and they owed the Epicurean tradition in philosophy and the political science crafted by the Arab philosophers Alfarabi, Avicenna, and Averroës.

Modern republicanism - distinguished from its classical counterpart by its commercial character and jealous distrust of those in power, by its use of representative institutions, and by its employment of a separation of powers and a system of checks and balances - owes an immense debt to the republican experiment conducted in England between 1649, when Charles I was executed, and 1660, when Charles II was crowned. Though abortive, this experiment left a legacy in the political science articulated both by its champions, John Milton, Marchamont Nedham, and James Harrington, and by its sometime opponent and ultimate supporter, Thomas Hobbes. This volume examines these four thinkers, situates them with regard to the novel species of republicanism first championed in the early 1500s by Niccolò Machiavelli, and examines the debt that he and they owed the Epicurean tradition in philosophy and the political science crafted by the Arab philosophers Alfarabi, Avicenna, and Averroës.

The Unfinished Revolution compares the post-Second World War histories of the American and British gay and lesbian movements with an eye toward understanding how distinct political institutional environments affect the development, strategies, goals, and outcomes of a social movement. Stephen M. Engel utilizes an electic mix of source materials ranging from the theories of Mancur Olson and Michel Foucault to Supreme Court rulings and film and television dialogue. The two case study chapters function as brief historical sketches to elucidate further the conclusions on theory and whilst being politically-oriented, they also examine gay influence and expansion into mainstream popular culture. The book also includes an appendix that surveys and assesses the analytical potential of five critical understandings of social movements: the classical approach, rational choice, resource mobilization, new social movement theories, and political opportunity structures. It will be of value to academi

The Unfinished Revolution compares the post-Second World War histories of the American and British gay and lesbian movements with an eye toward understanding how distinct political institutional environments affect the development, strategies, goals, and outcomes of a social movement. Stephen M. Engel utilizes an electic mix of source materials ranging from the theories of Mancur Olson and Michel Foucault to Supreme Court rulings and film and television dialogue. The two case study chapters function as brief historical sketches to elucidate further the conclusions on theory and whilst being politically-oriented, they also examine gay influence and expansion into mainstream popular culture. The book also includes an appendix that surveys and assesses the analytical potential of five critical understandings of social movements: the classical approach, rational choice, resource mobilization, new social movement theories, and political opportunity structures. It will be of value to academi

Social influence network theory presents a mathematical formalization of the social process of attitude changes that unfolds in a social network of interpersonal influences. This book brings the theory to bear on lines of research in the domain of small group dynamics concerned with changes of group members' positions on an issue, including the formation of consensus and of settled disagreement, via endogenous interpersonal influences, in which group members are responding to the displayed positions of the members of the group. Social influence network theory advances a dynamic social cognition mechanism, in which individuals are weighing and combining their own and others' positions on an issue in the revision of their own positions. The influence network construct of the theory is the social structure of the endogenous interpersonal influences that are involved in this mechanism. With this theory, the authors seek to lay the foundation for a better formal integration of classical and

The theory of Schur–Weyl duality has had a profound influence over many areas of algebra and combinatorics. This text is original in two respects: it discusses affine q-Schur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum Schur–Weyl theory. To begin, various algebraic structures are discussed, including double Ringel–Hall algebras of cyclic quivers and their quantum loop algebra interpretation. The rest of the book investigates the affine quantum Schur–Weyl duality on three levels. This includes the affine quantum Schur–Weyl reciprocity, the bridging role of affine q-Schur algebras between representations of the quantum loop algebras and those of the corresponding affine Hecke algebras, presentation of affine quantum Schur algebras and the realisation conjecture for the double Ringel–Hall algebra with a proof of the classical case. This text is ideal for researchers in algebra and graduate students who want to master Ringel–Hall algebras and Sch

Social influence network theory presents a mathematical formalization of the social process of attitude changes that unfolds in a social network of interpersonal influences. This book brings the theory to bear on lines of research in the domain of small group dynamics concerned with changes of group members' positions on an issue, including the formation of consensus and of settled disagreement, via endogenous interpersonal influences, in which group members are responding to the displayed positions of the members of the group. Social influence network theory advances a dynamic social cognition mechanism, in which individuals are weighing and combining their own and others' positions on an issue in the revision of their own positions. The influence network construct of the theory is the social structure of the endogenous interpersonal influences that are involved in this mechanism. With this theory, the authors seek to lay the foundation for a better formal integration of classical and

The three-volume major reference “Photons in Fock Space and Beyond” undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum

This book presents the foundations for irreversible thermodynamics for nonlinear transport processes in gases and liquids and for generalized hydrodynamics as developed from the classical hydrodynamic

This book studies recent music in the western classical tradition, offering a critique of current analytical/theoretical approaches and proposing alternatives. The critique addresses the present fring

John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mech

This book presents in a systematic and almost self-contained way the striking analogy between classical function theory, in particular the value distribution theory of holomorphic curves in projective

This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical r

This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on pr

This book examines how epistemology was reinvented by Ibn Sina, an influential philosopher-scientist of the classical Islamic world who was known to the West by the Latinised name Avicenna. It ex

This book is unique among contemporary approaches - although it is true to the spirit of classical writers like Hobbes and Kant - in seeking a theory that applies to psychological issues of free agenc

In this innovative treatment of the ethics of war, Ryan P. Cumming brings classical sources of just war theory into conversation with African American voices. Drawing on the Black press of the early t

In this lively and provocative book, two feminist public sociologists turn to classical social thinkers—W. E. B. Du Bois, Max Weber, Karl Marx, and ?mile Durkheim—to understand a series of

The classical theory of dynamical systems has tended to concentrate on Z-actions or R-actions. However in recent years there has been considerable progress in the study of higher dimensional actions (i.e. Zd or Rd with d>1). This book represents the proceedings of the 1993–4 Warwick Symposium on Zd actions. It comprises a mixture of surveys and original articles that span many of the diverse facets of the subject, including important connections with statistical mechanics, number theory and algebra. Researchers in ergodic theory and related fields will find that this book is an invaluable resource.

After several decades in which it became a prime target for critique, universalism remains one of the most important issues in social and political thought. Daniel Chernilo reassesses social theory's universalistic orientation and explains its origins in natural law theory, using an impressive array of classical and contemporary sources that include, among others, Habermas, Leo Strauss, Weber, Marx, Hegel, Rousseau and Hobbes. The Natural Law Foundations of Modern Social Theory challenges previous accounts of the rise of social theory, recovers a strong idea of humanity, and revisits conventional arguments on sociology's relationship to modernity, the enlightenment and natural law. It reconnects social theory to its scientific and philosophical roots, its descriptive and normative tasks and its historical and systematic planes. Chernilo's defense of universalism for contemporary social theory will surely engage students of sociology, political theory and moral philosophy alike.

After several decades in which it became a prime target for critique, universalism remains one of the most important issues in social and political thought. Daniel Chernilo reassesses social theory's universalistic orientation and explains its origins in natural law theory, using an impressive array of classical and contemporary sources that include, among others, Habermas, Leo Strauss, Weber, Marx, Hegel, Rousseau and Hobbes. The Natural Law Foundations of Modern Social Theory challenges previous accounts of the rise of social theory, recovers a strong idea of humanity, and revisits conventional arguments on sociology's relationship to modernity, the enlightenment and natural law. It reconnects social theory to its scientific and philosophical roots, its descriptive and normative tasks and its historical and systematic planes. Chernilo's defense of universalism for contemporary social theory will surely engage students of sociology, political theory and moral philosophy alike.

The Standard Model of particle physics is an amazingly successful theory describing the fundamental particles and forces of nature. This text, written for a two-semester graduate course on the Standard Model, develops a practical understanding of the theoretical concepts it's built upon, to prepare students to enter research. The author takes a historical approach to demonstrate to students the process of discovery which is often overlooked in other textbooks, presenting quantum field theory and symmetries as the necessary tools for describing and understanding the Standard Model. He develops these tools using a basic understanding of quantum mechanics and classical field theory, such as Maxwell's electrodynamics, before discussing the important role that Noether's theorem and conserved charges play in the theory. Worked examples feature throughout the text, while homework exercises are included for the first five parts, with solutions available online for instructors. Inspired by the

The unique features of the quantum world are explained in this book through the language of diagrams, setting out an innovative visual method for presenting complex theories. Requiring only basic mathematical literacy, this book employs a unique formalism that builds an intuitive understanding of quantum features while eliminating the need for complex calculations. This entirely diagrammatic presentation of quantum theory represents the culmination of ten years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations. Written in an entertaining and user-friendly style and including more than one hundred exercises, this book is an ideal first course in quantum theory, foundations, and computation for students from undergraduate to PhD level, as well as an opportunity for researchers from a broad range of fields, from physics to biology, linguistics, and cognitive science, to discover a new set of

This book is devoted to the systematic presentation of the Theory of Inventive Problem Solving (TRIZ) and is the most comprehensive book in the classical TRIZ and beyond. It details methods for formulating non-standard problems and various ways to solve them, etc. The book is illustrated by many examples, problems, and graphical material (approximately 300 examples and problems, and approximately 400 illustrations). It describes more than 300 concepts. Materials for independent work is provided at the end of each chapter. Some reference solutions are included. The book is intended for students of engineering disciplines who would like to have in-depth understanding of. It can also be useful for engineers and inventors, scientists, university professors, and those who solve creative problems. Professor and TRIZ Master Vladimir Petrov, is one of the most authoritative students and best friends of the Father of TRIZ, Genrich S. Altshuller. Since 1972, TRIZ Master Vladimir Petrov often con

The rigorous mathematical theory of the Navier–Stokes and Euler equations has been a focus of intense activity in recent years. This volume, the product of a workshop in Venice in 2013, consolidates, surveys and further advances the study of these canonical equations. It consists of a number of reviews and a selection of more traditional research articles on topics that include classical solutions to the 2D Euler equation, modal dependency for the 3D Navier–Stokes equation, zero viscosity Boussinesq equations, global regularity and finite-time singularities, well-posedness for the diffusive Burgers equations, and probabilistic aspects of the Navier–Stokes equation. The result is an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. The book serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.

One of the basic premises of the theory of syntax is that clause structures can be minimally identified as containing a verb phrase, playing the role of predicate, and a noun phrase, playing the role of subject. In this study Andrea Moro identifies a new category of copular sentences, namely inverse copular sentences, where the noun phrase which co-occurs with the verb phrase plays the role of predicate, occupying the position which is canonically reserved for subjects, and the subject is embedded in the verb phrase. The consequences of such a discovery are pervasive. Four distinct areas of syntax are unified into a unique natural class. Along with inverse copular sentences, existential sentences, sentences with seem and unaccusative constructions are analysed as involving the raising of a predicative noun phrase to the most prominent position in the clause structure. In addition, new light is shed on some classical issues such as the distribution and nature of expletives, locality the

This book offers an elementary and unified introduction to the non-perturbative results obtained in relativistic quantum field theory based on classical soliton and instanton solutions. Such solution

This book offers an explicitly covariant canonical formalism that is devised in the usual mathematical language of standard textbooks on classical dynamics. It elaborates on important questions: How d

Combining three books into a single volume, this text comprises Multicolor Problems, dealing with several of the classical map-coloring problems; Problems in the Theory of Numbers, an elementary intro

The Green function can be viewed as a propagator or as a response function and is equally meaningful all the way from classical physics to ordinary quantum mechanics to the most intricate manybody qua

Quantum gravity is among the most fascinating problems in physics. It modifies our understanding of time, space and matter. The recent development of the loop approach has allowed us to explore domains ranging from black hole thermodynamics to the early Universe. This book provides readers with a simple introduction to loop quantum gravity, centred on its covariant approach. It focuses on the physical and conceptual aspects of the problem and includes the background material needed to enter this lively domain of research, making it ideal for researchers and graduate students. Topics covered include quanta of space; classical and quantum physics without time; tetrad formalism; Holst action; lattice QCD; Regge calculus; ADM and Ashtekar variables; Ponzano-Regge and Turaev-Viro amplitudes; kinematics and dynamics of 4D Lorentzian quantum gravity; spectrum of area and volume; coherent states; classical limit; matter couplings; graviton propagator; spinfoam cosmology and black hole thermody

This 2006 textbook provides a concise introduction to the key concepts and tools of statistical mechanics. It also covers advanced topics such as non-relativistic quantum field theory and numerical methods. After introducing classical analytical techniques, such as cluster expansion and Landau theory, the authors present important numerical methods with applications to magnetic systems, Lennard-Jones fluids and biophysics. Quantum statistical mechanics is discussed in detail and applied to Bose-Einstein condensation and topics in astrophysics and cosmology. In order to describe emergent phenomena in interacting quantum systems, canonical non-relativistic quantum field theory is introduced and then reformulated in terms of Feynman integrals. Combining the authors' many years' experience of teaching courses in this area, this textbook is ideal for advanced undergraduate and graduate students in physics, chemistry and mathematics.

This 2006 textbook provides a concise introduction to the key concepts and tools of statistical mechanics. It also covers advanced topics such as non-relativistic quantum field theory and numerical methods. After introducing classical analytical techniques, such as cluster expansion and Landau theory, the authors present important numerical methods with applications to magnetic systems, Lennard-Jones fluids and biophysics. Quantum statistical mechanics is discussed in detail and applied to Bose-Einstein condensation and topics in astrophysics and cosmology. In order to describe emergent phenomena in interacting quantum systems, canonical non-relativistic quantum field theory is introduced and then reformulated in terms of Feynman integrals. Combining the authors' many years' experience of teaching courses in this area, this textbook is ideal for advanced undergraduate and graduate students in physics, chemistry and mathematics.