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Elsevier

Libros en Matemáticas

  • Group Representations

    • 1 Edición
    • Volumen 3
    • Inglés
    This third volume can be roughly divided into two parts. The first part is devoted to the investigation of various properties of projective characters. Special attention is drawn to spin representations and their character tables and to various correspondences for projective characters. Among other topics, projective Schur index and projective representations of abelian groups are covered. The last topic is investigated by introducing a symplectic geometry on finite abelian groups.The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theory for group algebras. The volume ends with a detailed investigation of the Schur index for ordinary representations. A prominant role is played in the discussion by Brauer groups together with cyclotomic algebras and cyclic algebras.

  • Computability, Complexity, and Languages

    Fundamentals of Theoretical Computer Science
    • 2 Edición
    • Martin Davis + 2 más
    • Inglés
    Computability, Complexity, and Languages is an introductory text that covers the key areas of computer science, including recursive function theory, formal languages, and automata. It assumes a minimal background in formal mathematics. The book is divided into five parts: Computability, Grammars and Automata, Logic, Complexity, and Unsolvability.

  • Composition Operators on Function Spaces

    • 1 Edición
    • Volumen 179
    • R.K. Singh + 1 más
    • Inglés
    This volume of the Mathematics Studies presents work done on composition operators during the last 25 years. Composition operators form a simple but interesting class of operators having interactions with different branches of mathematics and mathematical physics.After an introduction, the book deals with these operators on Lp-spaces. This study is useful in measurable dynamics, ergodic theory, classical mechanics and Markov process. The composition operators on functional Banach spaces (including Hardy spaces) are studied in chapter III. This chapter makes contact with the theory of analytic functions of complex variables. Chapter IV presents a study of these operators on locally convex spaces of continuous functions making contact with topological dynamics. In the last chapter of the book some applications of composition operators in isometries, ergodic theory and dynamical systems are presented. An interesting interplay of algebra, topology, and analysis is displayed.This comprehensive and up-to-date study of composition operators on different function spaces should appeal to research workers in functional analysis and operator theory, post-graduate students of mathematics and statistics, as well as to physicists and engineers.

  • Algebraic Groups and Number Theory

    • 1 Edición
    • Volumen 139
    • Vladimir Platonov + 2 más
    • Inglés
    This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.

  • Handbook of Convex Geometry

    • 1 Edición
    • Bozzano G Luisa
    • Inglés
    Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. The text then examines finite packing and covering and tilings, including plane tilings, monohedral tilings, bin packing, and sausage problems. The manuscript takes a look at valuations and dissections, geometric crystallography, convexity and differential geometry, and convex functions. Topics include differentiability, inequalities, uniqueness theorems for convex hypersurfaces, mixed discriminants and mixed volumes, differential geometric characterization of convexity, reduction of quadratic forms, and finite groups of symmetry operations. The selection is a dependable source of data for mathematicians and researchers interested in convex geometry.

  • Combinatorial Problems and Exercises

    • 2 Edición
    • L. Lovász
    • Inglés
    The aim of this book is to introduce a range of combinatorial methods for those who want to apply these methods in the solution of practical and theoretical problems. Various tricks and techniques are taught by means of exercises. Hints are given in a separate section and a third section contains all solutions in detail. A dictionary section gives definitions of the combinatorial notions occurring in the book.Combinatorial Problems and Exercises was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises on random walks on graphs and their relations to eigenvalues, expansion properties and electrical resistance. In various chapters the author found lines of thought that have been extended in a natural and significant way in recent years. About 60 new exercises (more counting sub-problems) have been added and several solutions have been simplified.

  • Theory of Convex Structures

    • 1 Edición
    • Volumen 50
    • M.L.J. van de Vel
    • Inglés
    Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging for instance from the area of partition calculus to that of continuous selection). The tools involved are borrowed from areas ranging from discrete mathematics to infinite-dimensional topology.Although addressed primarily to the researcher, parts of this monograph can be used as a basis for a well-balanced, one-semester graduate course.

  • Topological Rings

    • 1 Edición
    • Volumen 178
    • S. Warner
    • Inglés
    This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included.The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zorn's Lemma, is also expected.

  • Projective Differential Geometry of Submanifolds

    • 1 Edición
    • Volumen 49
    • M.A. Akivis + 1 más
    • Inglés
    In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are studied: submanifolds carrying a net of conjugate lines (in particular, conjugate systems), tangentially degenerate submanifolds, submanifolds with asymptotic and conjugate distributions etc. The method of moving frames and the apparatus of exterior differential forms are systematically used in the book and the results presented can be applied to the problems dealing with the linear subspaces or their generalizations.Grad... students majoring in differential geometry will find this monograph of great interest, as will researchers in differential and algebraic geometry, complex analysis and theory of several complex variables.

  • Estimation Theory in Hydrology and Water Systems

    • 1 Edición
    • Volumen 42
    • K. Nacházel
    • Inglés
    Methodological procedures of the theory of estimation of statistical parameters of time series and their application to hydrology and water engineering, particularly the sphere of reservoir-controlled runoffs, are dealt with in this volume. For estimates use is made of random sequences generated for various probability properties. This methodological approach enables examination of the properties of random and systematic errors of the parameters estimated even for the asymmetrical probability distributions, which are frequent in hydrology and water engineering. This book will be of interest to stochastic hydrologists.

  • Quo Vadis, Graph Theory?

    A Source Book for Challenges and Directions
    • 1 Edición
    • Volumen 55
    • J. Gimbel + 2 más
    • Inglés
    Graph Theory (as a recognized discipline) is a relative newcomer to Mathematics. The first formal paper is found in the work of Leonhard Euler in 1736. In recent years the subject has grown so rapidly that in today's literature, graph theory papers abound with new mathematical developments and significant applications.As with any academic field, it is good to step back occasionally and ask Where is all this activity taking us?, What are the outstanding fundamental problems?, What are the next important steps to take?. In short, Quo Vadis, Graph Theory?. The contributors to this volume have together provided a comprehensive reference source for future directions and open questions in the field.

  • Delay Differential Equations

    With Applications in Population Dynamics
    • 1 Edición
    • Volumen 191
    • Yang Kuang
    • Inglés
    Delay Differential Equations emphasizes the global analysis of full nonlinear equations or systems. The book treats both autonomous and nonautonomous systems with various delays. Key topics addressed are the possible delay influence on the dynamics of the system, such as stability switching as time delay increases, the long time coexistence of populations, and the oscillatory aspects of the dynamics. The book also includes coverage of the interplay of spatial diffusion and time delays in some diffusive delay population models. The treatment presented in this monograph will be of great value in the study of various classes of DDEs and their multidisciplinary applications.

  • Dimension and Extensions

    • 1 Edición
    • Volumen 48
    • J.M. Aarts + 1 más
    • Inglés
    Two types of seemingly unrelated extension problems are discussed in this book. Their common focus is a long-standing problem of Johannes de Groot, the main conjecture of which was recently resolved. As is true of many important conjectures, a wide range of mathematical investigations had developed, which have been grouped into the two extension problems. The first concerns the extending of spaces, the second concerns extending the theory of dimension by replacing the empty space with other spaces.The problem of de Groot concerned compactifications of spaces by means of an adjunction of a set of minimal dimension. This minimal dimension was called the compactness deficiency of a space. Early success in 1942 lead de Groot to invent a generalization of the dimension function, called the compactness degree of a space, with the hope that this function would internally characterize the compactness deficiency which is a topological invariant of a space that is externally defined by means of compact extensions of a space. From this, the two extension problems were spawned.With the classical dimension theory as a model, the inductive, covering and basic aspects of the dimension functions are investigated in this volume, resulting in extensions of the sum, subspace and decomposition theorems and theorems about mappings into spheres. Presented are examples, counterexamples, open problems and solutions of the original and modified compactification problems.

  • Differential Manifolds

    • 1 Edición
    • Volumen 138
    • Antoni A. Kosinski
    • Inglés
    Differential Manifolds is a modern graduate-level introduction to the important field of differential topology. The concepts of differential topology lie at the heart of many mathematical disciplines such as differential geometry and the theory of lie groups. The book introduces both the h-cobordism theorem and the classification of differential structures on spheres. The presentation of a number of topics in a clear and simple fashion make this book an outstanding choice for a graduate course in differential topology as well as for individual study.

  • Morphogenesis

    • 1 Edición
    • Volumen 3
    • P.T. Saunders
    • Inglés
    The collected works of Turing, including a substantial amount of unpublished material, will comprise four volumes: Mechanical Intelligence, Pure Mathematics, Morphogenesis and Mathematical Logic. Alan Mathison Turing (1912-1954) was a brilliant man who made major contributions in several areas of science. Today his name is mentioned frequently in philosophical discussions about the nature of Artificial Intelligence. Actually, he was a pioneer researcher in computer architecture and software engineering; his work in pure mathematics and mathematical logic extended considerably further and his last work, on morphogenesis in plants, is also acknowledged as being of the greatest originality and of permanent importance. He was one of the leading figures in Twentieth-century science, a fact which would have been known to the general public sooner but for the British Official Secrets Act, which prevented discussion of his wartime work. What is maybe surprising about these papers is that although they were written decades ago, they address major issues which concern researchers today.

  • Recent Progress in General Topology

    • 1 Edición
    • M. Husek + 1 más
    • Inglés
    These papers survey the developments in General Topology and the applications of it which have taken place since the mid 1980s. The book may be regarded as an update of some of the papers in the Handbook of Set-Theoretic Topology (eds. Kunen/Vaughan, North-Holland, 1984), which gives an almost complete picture of the state of the art of Set Theoretic Topology before 1984. In the present volume several important developments are surveyed that surfaced in the period 1984-1991.This volume may also be regarded as a partial update of Open Problems in Topology (eds. van Mill/Reed, North-Holland, 1990). Solutions to some of the original 1100 open problems are discussed and new problems are posed.

  • Handbook of Game Theory with Economic Applications

    • 1 Edición
    • Volumen 1
    • R.J. Aumann + 1 más
    • Inglés
    This is the first volume of the Handbook of Game Theory with Economic Applications, to be followed by two additional volumes. Game Theory has developed greatly in the last decade, and today it is an essential tool in much of economic theory. The three volumes will cover the fundamental theoretical aspects, a wide range of applications to economics, several chapters on applications to political science, and individual chapters on relations with other disciplines.The topics covered in the present volume include chess-playing computers, an introduction to the non-cooperative theory, repeated games, bargaining theory, auctions, location, entry deterrence, patents, the cooperative theory and its applications, and the relation between Game Theory and ethics.For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier....

  • Explorations with Texas Instruments TI-85

    • 1 Edición
    • John W. Kenelly + 1 más
    • Inglés
    The TI-85 is the latest and most powerful graphing calculator produced by Texas Instruments. This book describes the use of the TI-85 in courses in precalculus, calculus, linear algebra, differential equations, business mathematics, probability, statistics and advanced engineering mathematics. The book features in-depth coverage of the calculator's use in specific course areas by distinguished experts in each field.

  • Tensor Norms and Operator Ideals

    • 1 Edición
    • Volumen 176
    • A. Defant + 1 más
    • Inglés
    The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exercises.

  • Applied Chaos Theory

    A Paradigm for Complexity
    • 1 Edición
    • Ali Bulent Cambel
    • Inglés
    This book differs from others on Chaos Theory in that it focuses on its applications for understanding complex phenomena. The emphasis is on the interpretation of the equations rather than on the details of the mathematical derivations. The presentation is interdisciplinary in its approach to real-life problems: it integrates nonlinear dynamics, nonequilibrium thermodynamics, information theory, and fractal geometry. An effort has been made to present the material ina reader-friendly manner, and examples are chosen from real life situations. Recent findings on the diagnostics and control of chaos are presented, and suggestions are made for setting up a simple laboratory. Included is a list of topics for further discussion that may serve not only for personal practice or homework, but also as themes for theses, dissertations, and research proposals.

  • Mathematical Problems in Elasticity and Homogenization

    • 1 Edición
    • Volumen 26
    • O.A. Oleinik + 2 más
    • Inglés
    This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional analysis and the theory of partial differential equations, all results in this book are given detailed mathematical proof.It is expected that the results and methods presented in this book will promote further investigation of mathematical models for processes in composite and perforated media, heat-transfer, energy transfer by radiation, processes of diffusion and filtration in porous media, and that they will stimulate research in other problems of mathematical physics and the theory of partial differential equations.

  • Differential Topology and Quantum Field Theory

    • 1 Edición
    • Charles Nash
    • Inglés
    The remarkable developments in differential topology and how these recent advances have been applied as a primary research tool in quantum field theory are presented here in a style reflecting the genuinely two-sided interaction between mathematical physics and applied mathematics. The author, following his previous work (Nash/Sen: Differential Topology for Physicists, Academic Press, 1983), covers elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory. The explanatory approach serves to illuminate and clarify these theories for graduate students and research workers entering the field for the first time.

  • The Steiner Tree Problem

    • 1 Edición
    • Volumen 53
    • F.K. Hwang + 2 más
    • Inglés
    The Steiner problem asks for a shortest network which spans a given set of points. Minimum spanning networks have been well-studied when all connections are required to be between the given points. The novelty of the Steiner tree problem is that new auxiliary points can be introduced between the original points so that a spanning network of all the points will be shorter than otherwise possible. These new points are called Steiner points - locating them has proved problematic and research has diverged along many different avenues.This volume is devoted to the assimilation of the rich field of intriguing analyses and the consolidation of the fragments. A section has been given to each of the three major areas of interest which have emerged. The first concerns the Euclidean Steiner Problem, historically the original Steiner tree problem proposed by Jarník and Kössler in 1934. The second deals with the Steiner Problem in Networks, which was propounded independently by Hakimi and Levin and has enjoyed the most prolific research amongst the three areas. The Rectilinear Steiner Problem, introduced by Hanan in 1965, is discussed in the third part. Additionally, a forth section has been included, with chapters discussing areas where the body of results is still emerging.The collaboration of three authors with different styles and outlooks affords individual insights within a cohesive whole.

  • Regenerative Stochastic Simulation

    • 1 Edición
    • Gerald S. Shedler
    • Inglés
    Simulation is a controlled statistical sampling technique that can be used to study complex stochastic systems when analytic and/or numerical techniques do not suffice. The focus of this book is on simulations of discrete-event stochastic systems; namely, simulations in which stochastic state transitions occur only at an increasing sequence of random times. The discussion emphasizes simulations on a finite or countably infinite state space.

  • Combinatorics '90

    Recent Trends and Applications
    • 1 Edición
    • Volumen 52
    • A. Barlotti + 3 más
    • Inglés
    This volume forms a valuable source of information on recent developments in research in combinatorics, with special regard to the geometric point of view. Topics covered include: finite geometries (arcs, caps, special varieties in a Galois space; generalized quadrangles; Benz planes; foundation of geometry), partial geometries, Buekenhout geometries, transitive permutation sets, flat-transitive geometries, design theory, finite groups, near-rings and semifields, MV-algebras, coding theory, cryptography and graph theory in its geometric and design aspects.

  • Real Reductive Groups II

    • 1 Edición
    • Volumen 132II
    • Inglés

  • Group Representations Volume 1 Part B

    Introduction to Group Representations and Characters
    • 1 Edición
    • Volumen 1
    • Inglés
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  • Fourth Czechoslovakian Symposium on Combinatorics, Graphs and Complexity

    • 1 Edición
    • Volumen 51
    • J. Nešetril + 1 más
    • Inglés
    This volume in the Annals of Discrete Mathematics brings together contributions by renowned researchers in combinatorics, graphs and complexity. The conference on which this book is based was the fourth in a series which began in 1963, which was the first time specialists from East and West were able to come together. The 1990 meeting attracted 170 mathematicians and computer scientists from around the world, so this book represents an international, detailed view of recent research.

  • Differential Topology

    • 1 Edición
    • Volumen 173
    • J. Margalef-Roig + 1 más
    • Inglés
    ...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry.Peter W. Michor

  • Symmetries and Laplacians

    Introduction to Harmonic Analysis, Group Representations and Applications
    • 1 Edición
    • Volumen 174
    • D. Gurarie
    • Inglés
    Designed as an introduction to harmonic analysis and group representations,this book covers a wide range of topics rather than delving deeply into anyparticular one. In the words of H. Weyl ...it is primarily meant forthe humble, who want to learn as new the things set forth therein, rather thanfor the proud and learned who are already familiar with the subject and merelylook for quick and exact information....The main objective is tointroduce the reader to concepts, ideas, results and techniques that evolvearound symmetry-groups, representations and Laplacians. Morespecifically, the main interest concerns geometrical objects and structures{X}, discrete or continuous, that possess sufficiently large symmetrygroup G, such as regular graphs (Platonic solids), lattices, andsymmetric Riemannian manifolds. All such objects have a natural Laplacian&Dgr;, a linear operator on functions over X, invariant underthe group action. There are many problems associated with Laplacians onX, such as continuous or discrete-time evolutions, on X,random walks, diffusion processes, and wave-propagation. This book containssufficient material for a 1 or 2-semester course.

  • Recursive Functionals

    • 1 Edición
    • Volumen 131
    • L.E. Sanchis
    • Inglés
    This work is a self-contained elementary exposition of the theory of recursive functionals, that also includes a number of advanced results. Although aiming basically at a theory of higher order computability, attention is restricted to second order functionals, where the arguments are numerical functions and the values, when defined, are natural numbers. This theory is somewhat special, for to some extent it can be reduced to first order theory, but when properly extended and relativized it requires the full machinery of higher order computations. In the theory of recursive monotonic functionals the author formulates a reasonable notion of computation which provides the right frame for what appears to be a convincing form of the extended Church's thesis. At the same time, the theory provides sufficient room to formulate the classical results that are usually derived in terms of singular functionals. Presented are complete proofs of Gandy's selector theorem, Kleene's theorem on hyperarithmetical predicates, and Grilliot's theorem on effectively discontinuous functionals.

  • Convex Functions, Partial Orderings, and Statistical Applications

    • 1 Edición
    • Josip E. Peajcariaac + 1 más
    • Inglés
    This research-level book presents up-to-date information concerning recent developments in convex functions and partial orderings and some applications in mathematics, statistics, and reliability theory. The book will serve researchers in mathematical and statistical theory and theoretical and applied reliabilists.

  • Continued Fractions with Applications

    • 1 Edición
    • Volumen 3
    • L. Lorentzen + 1 más
    • Inglés
    This book is aimed at two kinds of readers: firstly, people working in or near mathematics, who are curious about continued fractions; and secondly, senior or graduate students who would like an extensive introduction to the analytic theory of continued fractions. The book contains several recent results and new angles of approach and thus should be of interest to researchers throughout the field. The first five chapters contain an introduction to the basic theory, while the last seven chapters present a variety of applications. Finally, an appendix presents a large number of special continued fraction expansions. This very readable book also contains many valuable examples and problems.

  • Attractors of Evolution Equations

    • 1 Edición
    • Volumen 25
    • A.V. Babin + 1 más
    • Inglés
    Problems, ideas and notions from the theory of finite-dimensional dynamical systems have penetrated deeply into the theory of infinite-dimensional systems and partial differential equations. From the standpoint of the theory of the dynamical systems, many scientists have investigated the evolutionary equations of mathematical physics. Such equations include the Navier-Stokes system, magneto-hydrodynamic... equations, reaction-diffusion equations, and damped semilinear wave equations. Due to the recent efforts of many mathematicians, it has been established that the attractor of the Navier-Stokes system, which attracts (in an appropriate functional space) as t - ∞ all trajectories of this system, is a compact finite-dimensional (in the sense of Hausdorff) set. Upper and lower bounds (in terms of the Reynolds number) for the dimension of the attractor were found. These results for the Navier-Stokes system have stimulated investigations of attractors of other equations of mathematical physics. For certain problems, in particular for reaction-diffusion systems and nonlinear damped wave equations, mathematicians have established the existence of the attractors and their basic properties; furthermore, they proved that, as t - +∞, an infinite-dimensional dynamics described by these equations and systems uniformly approaches a finite-dimensional dynamics on the attractor U, which, in the case being considered, is the union of smooth manifolds. This book is devoted to these and several other topics related to the behaviour as t - ∞ of solutions for evolutionary equations.

  • Big-Planes, Boundaries and Function Algebras

    • 1 Edición
    • Volumen 172
    • T.V. Tonev
    • Inglés
    Treated in this volume are selected topics in analytic &Ggr;-almost-per... functions and their representations as &Ggr;-analytic functions in the big-plane; n-tuple Shilov boundaries of function spaces, minimal norm principle for vector-valued functions and their applications in the study of vector-valued functions and n-tuple polynomial and rational hulls. Applications to the problem of existence of n-dimensional complex analytic structures, analytic &Ggr;-almost-per... structures and structures of &Ggr;-analytic big-manifolds respectively in commutative Banach algebra spectra are also discussed.

  • Matrix Logic and Mind

    A Probe into a Unified Theory of Mind and Matter
    • 1 Edición
    • A. Stern
    • Inglés
    In this revolutionary work, the author sets the stage for the science ofthe 21st Century, pursuing an unprecedented synthesis of fields previouslyconsidered unrelated. Beginning with simple classical concepts, he endswith a complex multidisciplinary theory requiring a high level ofabstraction. The work progresses across the sciences in severalmultidiscipli... directions: Mathematical logic, fundamental physics,computer science and the theory of intelligence. Extraordinarily enough,the author breaks new ground in all these fields.In the field offundamental physics the author reaches the revolutionary conclusion thatphysics can be viewed and studied as logic in a fundamental sense, ascompared with Einstein's view of physics as space-time geometry. This opensnew, exciting prospects for the study of fundamental interactions. Aformulation of logic in terms of matrix operators and logic vector spacesallows the author to tackle for the first time the intractable problem ofcognition in a scientific manner. In the same way as the findings ofHeisenberg and Dirac in the 1930s provided a conceptual and mathematicalfoundati... for quantum physics, matrix operator logic supports an importantbreakthroug... in the study of the physics of the mind, which is interpretedas a fractal of quantum mechanics. Introducing a concept of logic quantumnumbers, the author concludes that the problem of logic and theintelligence code in general can be effectively formulated as eigenvalueproblems similar to those of theoretical physics. With this important leapforward in the study of the mechanism of mind, the author concludes thatthe latter cannot be fully understood either within classical or quantumnotions. A higher-order covariant theory is required to accommodate thefundamental effect of high-level intelligence. The landmark resultsobtained by the author will have implications and repercussions for thevery foundations of science as a whole. Moreover, Stern's Matrix Logic issuitable for a broad spectrum of practical applications in contemporarytechnolo...

  • Classical Recursion Theory

    The Theory of Functions and Sets of Natural Numbers
    • 1 Edición
    • Volumen 125
    • P. Odifreddi
    • Inglés
    1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles.Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.

  • A First Course in Rational Continuum Mechanics V1

    • 2 Edición
    • Volumen 71I
    • Inglés

  • Mechanical Intelligence

    • 1 Edición
    • Volumen 1
    • D.C. Ince
    • Inglés
    The collected works of Turing, including a substantial amount of unpublished material, will comprise four volumes: Mechanical Intelligence, Pure Mathematics, Morphogenesis and Mathematical Logic. Alan Mathison Turing (1912-1954) was a brilliant man who made major contributions in several areas of science. Today his name is mentioned frequently in philosophical discussions about the nature of Artificial Intelligence. Actually, he was a pioneer researcher in computer architecture and software engineering; his work in pure mathematics and mathematical logic extended considerably further and his last work, on morphogenesis in plants, is also acknowledged as being of the greatest originality and of permanent importance. He was one of the leading figures in Twentieth-century science, a fact which would have been known to the general public sooner but for the British Official Secrets Act, which prevented discussion of his wartime work. What is maybe surprising about these papers is that although they were written decades ago, they address major issues which concern researchers today.

  • Pure Mathematics

    • 1 Edición
    • Volumen 2
    • J.L. Britton
    • Inglés
    The collected works of Turing, including a substantial amount of unpublished material, will comprise four volumes: Mechanical Intelligence, Pure Mathematics, Morphogenesis and Mathematical Logic. Alan Mathison Turing (1912-1954) was a brilliant man who made major contributions in several areas of science. Today his name is mentioned frequently in philosophical discussions about the nature of Artificial Intelligence. Actually, he was a pioneer researcher in computer architecture and software engineering; his work in pure mathematics and mathematical logic extended considerably further and his last work, on morphogenesis in plants, is also acknowledged as being of the greatest originality and of permanent importance. He was one of the leading figures in Twentieth-century science, a fact which would have been known to the general public sooner but for the British Official Secrets Act, which prevented discussion of his wartime work. What is maybe surprising about these papers is that although they were written decades ago, they address major issues which concern researchers today.

  • Continuous Linear Representations

    • 1 Edición
    • Volumen 168
    • Z. Magyar
    • Inglés
    This monograph gives access to the theory of continuous linear representations of general real Lie groups to readers who are already familiar with the rudiments of functional analysis and Lie groups. The first half of the book is centered around the relation between a continuous linear representation (of a Lie group over a Banach space or even a more general space) and its tangent; the latter is a Lie algebra representation in a sense. Starting with the Hille-Yosida theory, quite recent results are reached. The second half is more standard unitary theory with applications concerning the Galilean and Poincaré groups. Appendices help readers with diverse backgrounds to find the precise descriptions of the concepts needed from earlier literature.Each chapter includes exercises.

  • Lectures on Homotopy Theory

    • 1 Edición
    • Volumen 171
    • R.A. Piccinini
    • Inglés
    The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the nth homotopy group of the sphere Sn, for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of Sn are trivial and that the third homotopy group of S2 is also isomorphic to the group of the integers. All this was achieved by discussing H-spaces and CoH-spaces, fibrations and cofibrations (rather thoroughly), simplicial structures and the homotopy groups of maps.Later, the book was expanded to introduce CW-complexes and their homotopy groups, to construct a special class of CW-complexes (the Eilenberg-Mac Lane spaces) and to include a chapter devoted to the study of the action of the fundamental group on the higher homotopy groups and the study of fibrations in the context of a category in which the fibres are forced to live; the final material of that chapter is a comparison of various kinds of universal fibrations. Completing the book are two appendices on compactly generated spaces and the theory of colimits. The book does not require any prior knowledge of Algebraic Topology and only rudimentary concepts of Category Theory are necessary; however, the student is supposed to be well at ease with the main general theorems of Topology and have a reasonable mathematical maturity.

  • Progress in Functional Analysis

    • 1 Edición
    • Volumen 170
    • K.D. Bierstedt + 3 más
    • Inglés
    This volume includes a collection of research articles inFunctional Analysis, celebrating the occasion of Manuel Valdivia'ssixtieth birthday. The papers included in the volume are basedon the main lectures presented during the internationalfunctio... analysis meeting held in Peñíscola(Valencia, Spain) in October 1990.During his career, Valdiviahas made contributions to a wide variety of areas of FunctionalAnalysis and his work has had a profound impact. A thoroughappreciation of Valdivia's work is presented in J.Horváth's article. In honor of Valdivia's achievements, this volume presents more than twenty-five papers on topics related to his research(Banach spaces, operator ideals, tensor products, Fréchet,(DF) and (LF) spaces, distribution theory, infinite holomorphyetc.). While the majority of papers are research articles, survey articles are also included. The book covers a broad spectrum of interests in today's Functional Analysis and presents new results by leading specialists in the field.

  • An Introduction to Wavelets

    • 1 Edición
    • Volumen 1
    • Charles K. Chui
    • Inglés
    An Introduction to Wavelets is the first volume in a new series, WAVELET ANALYSIS AND ITS APPLICATIONS. This is an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and time-frequency analysis. Among the basic topics covered in this book are time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents a unified treatment of nonorthogonal, semiorthogonal, and orthogonal wavelets. This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis. It is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject. Specialists may use this volume as a valuable supplementary reading to the vast literature that has already emerged in this field.

  • Probability and Random Processes

    With Applications to Signal Processing and Communications
    • 1 Edición
    • Scott Miller + 1 más
    • Inglés
    Probability and Random Processes provides a clear presentation of foundational concepts with specific applications to signal processing and communications, clearly the two areas of most interest to students and instructors in this course. It includes unique chapters on narrowband random processes and simulation techniques. It also includes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and other fields. The appendices provide a refresher in such areas as linear algebra, set theory, random variables, and more. Exceptional exposition and numerous worked out problems make the book extremely readable and accessible. It is meant for practicing engineers as well as graduate students.

  • Pseudo-Differential Operators on Manifolds with Singularities

    • 1 Edición
    • Volumen 24
    • B.-W. Schulze
    • Inglés
    The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics.The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.

  • Markov Processes

    An Introduction for Physical Scientists
    • 1 Edición
    • Daniel T. Gillespie
    • Inglés
    Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level.

  • Scientific Computing and Differential Equations

    An Introduction to Numerical Methods
    • 1 Edición
    • Gene H. Golub + 1 más
    • Inglés
    Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context.This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also well-suited to serve as a textbook for numerical differential equations courses at the graduate level.

  • Handbook of Mathematical Economics

    • 1 Edición
    • Volumen 4
    • W. Hildenbrand + 1 más
    • Inglés
    The Handbook of Mathematical Economics aims to provide a definitive source, reference, and teaching supplement for the field of mathematical economics. It surveys, as of the late 1970's the state of the art of mathematical economics. This is a constantly developing field and all authors were invited to review and to appraise the current status and recent developments in their presentations. In addition to its use as a reference, it is intended that this Handbook will assist researchers and students working in one branch of mathematical economics to become acquainted with other branches of this field.The emphasis of this fourth volume of the Handbook of Mathematical Economics is on choice under uncertainty, general equilibrium analysis under conditions of uncertainty, economies with an infinite number of consumers or commodities, and dynamical systems. The book thus reflects some of the ideas that have been most influential in mathematical economics since the appearance of the first three volumes of the Handbook.Researchers... students, economists and mathematicians will all find this Handbook to be an indispensable reference source. It surveys the entire field of mathematical economics, critically reviewing recent developments. The chapters (which can be read independently) are written at an advanced level suitable for professional, teaching and graduate-level use. For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier....

  • Exploratory and Multivariate Data Analysis

    • 1 Edición
    • Michel Jambu
    • Inglés
    With a useful index of notations at the beginning, this book explains and illustrates the theory and application of data analysis methods from univariate to multidimensional and how to learn and use them efficiently. This book is well illustrated and is a useful and well-documented review of the most important data analysis techniques.

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