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Elsevier

Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

  • Symmetries and Laplacians

    Introduction to Harmonic Analysis, Group Representations and Applications
    • 1st Edition
    • Volume 174
    • D. Gurarie
    • English
    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.

  • Convex Functions, Partial Orderings, and Statistical Applications

    • 1st Edition
    • Josip E. Peajcariaac + 1 more
    • English
    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

    • 1st Edition
    • Volume 3
    • L. Lorentzen + 1 more
    • English
    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

    • 1st Edition
    • Volume 25
    • A.V. Babin + 1 more
    • English
    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

    • 1st Edition
    • Volume 172
    • T.V. Tonev
    • English
    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
    • 1st Edition
    • A. Stern
    • English
    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
    • 1st Edition
    • Volume 125
    • P. Odifreddi
    • English
    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

    • 2nd Edition
    • Volume 71I
    • English

  • Continuous Linear Representations

    • 1st Edition
    • Volume 168
    • Z. Magyar
    • English
    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.

  • Pure Mathematics

    • 1st Edition
    • Volume 2
    • J.L. Britton
    • English
    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.

  • Mechanical Intelligence

    • 1st Edition
    • Volume 1
    • D.C. Ince
    • English
    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.

  • Lectures on Homotopy Theory

    • 1st Edition
    • Volume 171
    • R.A. Piccinini
    • English
    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

    • 1st Edition
    • Volume 170
    • K.D. Bierstedt + 3 more
    • English
    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

    • 1st Edition
    • Volume 1
    • Charles K. Chui
    • English
    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
    • 1st Edition
    • Scott Miller + 1 more
    • English
    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.

  • Managing Data Protection

    • 2nd Edition
    • Chris Pounder + 1 more
    • English

  • Managing Data Protection

    • 2nd Edition
    • Chris Pounder + 1 more
    • English

  • Graphics Gems

    • 1st Edition
    • David Kirk
    • English

  • Newnes Z80 Pocket Book

    • 1st Edition
    • Chris Roberts
    • English

  • All-in-1

    A Technical Odyssey
    • 1st Edition
    • Tony Redmond
    • English
    All-in-1

  • Pseudo-Differential Operators on Manifolds with Singularities

    • 1st Edition
    • Volume 24
    • B.-W. Schulze
    • English
    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
    • 1st Edition
    • Daniel T. Gillespie
    • English
    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
    • 1st Edition
    • Gene H. Golub + 1 more
    • English
    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

    • 1st Edition
    • Volume 4
    • W. Hildenbrand + 1 more
    • English
    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....

  • Rings, Fields and Groups

    • 2nd Edition
    • Reg Allenby
    • English
    'Rings, Fields and Groups' gives a stimulating and unusual introduction to the results, methods and ideas now commonly studied on abstract algebra courses at undergraduate level. The author provides a mixture of informal and formal material which help to stimulate the enthusiasm of the student, whilst still providing the essential theoretical concepts necessary for serious study.Retaining the highly readable style of its predecessor, this second edition has also been thoroughly revised to include a new chapter on Galois theory plus hints and solutions to many of the 800 exercises featured.

  • Exploratory and Multivariate Data Analysis

    • 1st Edition
    • Michel Jambu
    • English
    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.

  • Truth, Possibility and Probability

    New Logical Foundations of Probability and Statistical Inference
    • 1st Edition
    • Volume 166
    • R. Chuaqui
    • English
    Anyone involved in the philosophy of science is naturally drawn into the study of the foundations of probability. Different interpretations of probability, based on competing philosophical ideas, lead to different statistical techniques, and frequently to mutually contradictory consequences.This unique book presents a new interpretation of probability, rooted in the traditional interpretation that was current in the 17th and 18th centuries. Mathematical models are constructed based on this interpretation, and statistical inference and decision theory are applied, including some examples in artificial intelligence, solving the main foundational problems. Nonstandard analysis is extensively developed for the construction of the models and in some of the proofs. Many nonstandard theorems are proved, some of them new, in particular, a representation theorem that asserts that any stochastic process can be approximated by a process defined over a space with equiprobable outcomes.

  • Eulerian Graphs and Related Topics

    • 1st Edition
    • Volume 2
    • English

  • Lukasiewicz-Moisil Algebras

    • 1st Edition
    • Volume 49
    • V. Boicescu + 3 more
    • English
    The Lukasiewicz-Moisil algebras were created by Moisil as an algebraic counterpart for the many-valued logics of Lukasiewicz. The theory of LM-algebras has developed to a considerable extent both as an algebraic theory of intrinsic interest and in view of its applications to logic and switching theory.This book gives an overview of the theory, comprising both classical results and recent contributions, including those of the authors. N-valued and &THgr;-valued algebras are presented, as well as &THgr;-algebras with negation.Mathematici... interested in lattice theory or symbolic logic, and computer scientists, will find in this monograph stimulating material for further research.

  • Interpolation Functors and Interpolation Spaces

    • 1st Edition
    • Volume 47
    • English
    The theory of interpolation spaces has its origin in the classical work of Riesz and Marcinkiewicz but had its first flowering in the years around 1960 with the pioneering work of Aronszajn, Calderón, Gagliardo, Krein, Lions and a few others. It is interesting to note that what originally triggered off this avalanche were concrete problems in the theory of elliptic boundary value problems related to the scale of Sobolev spaces. Later on, applications were found in many other areas of mathematics: harmonic analysis, approximation theory, theoretical numerical analysis, geometry of Banach spaces, nonlinear functional analysis, etc. Besides this the theory has a considerable internal beauty and must by now be regarded as an independent branch of analysis, with its own problems and methods. Further development in the 1970s and 1980s included the solution by the authors of this book of one of the outstanding questions in the theory of the real method, the K-divisibility problem. In a way, this book harvests the results of that solution, as well as drawing heavily on a classic paper by Aronszajn and Gagliardo, which appeared in 1965 but whose real importance was not realized until a decade later. This includes a systematic use of the language, if not the theory, of categories. In this way the book also opens up many new vistas which still have to be explored. This volume is the first of three planned books. Volume II will deal with the complex method, while Volume III will deal with applications.

  • Ring Theory, 83

    Student Edition
    • 1st Edition
    • Louis H. Rowen
    • English
    This is an abridged edition of the author's previous two-volume work, Ring Theory, which concentrates on essential material for a general ring theory course while ommitting much of the material intended for ring theory specialists. It has been praised by reviewers:**"As a textbook for graduate students, Ring Theory joins the best....The experts will find several attractive and pleasant features in Ring Theory. The most noteworthy is the inclusion, usually in supplements and appendices, of many useful constructions which are hard to locate outside of the original sources....The audience of nonexperts, mathematicians whose speciality is not ring theory, will find Ring Theory ideally suited to their needs....They, as well as students, will be well served by the many examples of rings and the glossary of major results."**--NOTICES OF THE AMS

  • Topics on Domination

    • 1st Edition
    • S.T. Hedetniemi + 1 more
    • English
    The contributions in this volume are divided into three sections: theoretical, new models and algorithmic. The first section focuses on properties of the standard domination number &ggr;(G), the second section is concerned with new variations on the domination theme, and the third is primarily concerned with finding classes of graphs for which the domination number (and several other domination-related parameters) can be computed in polynomial time.

  • Submodular Functions and Optimization

    • 1st Edition
    • Volume 47
    • S. Fujishige
    • English
    The importance of submodular functions has been widely recognized in recent years in combinatorial optimization. This is the first book devoted to the exposition of the theory of submodular functions from an elementary technical level to an advanced one. A unifying view of the theory is shown by means of base polyhedra and duality for submodular and supermodular systems. Among the subjects treated are: neoflows (submodular flows, independent flows, polymatroidal flows), submodular analysis (submodular programs, duality, Lagrangian functions, principal partitions), nonlinear optimization with submodular constraints (lexicographically optimal bases, fair resource allocation). Special emphasis is placed on the constructive aspects of the theory, which lead to practical, efficient algorithms.

  • Quasihomogeneous Distributions

    • 1st Edition
    • Volume 165
    • O. von Grudzinski
    • English
    This is a systematic exposition of the basics of the theory of quasihomogeneous (in particular, homogeneous) functions and distributions (generalized functions). A major theme is the method of taking quasihomogeneous averages. It serves as the central tool for the study of the solvability of quasihomogeneous multiplication equations and of quasihomogeneous partial differential equations with constant coefficients. Necessary and sufficient conditions for solvability are given. Several examples are treated in detail, among them the heat and the Schrödinger equation. The final chapter is devoted to quasihomogeneous wave front sets and their application to the description of singularities of quasihomogeneous distributions, in particular to quasihomogeneous fundamental solutions of the heat and of the Schrödinger equation.

  • Latin Squares

    New Developments in the Theory and Applications
    • 1st Edition
    • József Dénes + 1 more
    • English
    In 1974 the editors of the present volume published a well-received book entitled ``Latin Squares and their Applications''. It included a list of 73 unsolved problems of which about 20 have been completely solved in the intervening period and about 10 more have been partially solved. The present work comprises six contributed chapters and also six further chapters written by the editors themselves. As well as discussing the advances which have been made in the subject matter of most of the chapters of the earlier book, this new book contains one chapter which deals with a subject (r-orthogonal latin squares) which did not exist when the earlier book was written.The success of the former book is shown by the two or three hundred published papers which deal with questions raised by it.

  • Algebraic and Structural Automata Theory

    • 1st Edition
    • Volume 44
    • B. Mikolajczak
    • English
    Automata Theory is part of computability theory which covers problems in computer systems, software, activity of nervous systems (neural networks), and processes of live organisms development.The result of over ten years of research, this book presents work in the following areas of Automata Theory: automata morphisms, time-varying automata, automata realizations and relationships between automata and semigroups.Aimed at those working in discrete mathematics and computer science, parts of the book are suitable for use in graduate courses in computer science, electronics, telecommunications, and control engineering. It is assumed that the reader is familiar with the basic concepts of algebra and graph theory.

  • Digital Systems Reference Book

    • 1st Edition
    • Brian Holdsworth + 1 more
    • English

  • Windows 3 Pocket Book

    • 1st Edition
    • Ian Sinclair
    • English

  • Stochastic Models in Queuing Theory

    • 1st Edition
    • J. Medhi
    • English

  • The Mathematics of Finite Elements and Applications VII

    MAFELAP 1990
    • 1st Edition
    • J. R. Whiteman
    • English

  • Quantum Physics, Relativity, and Complex Spacetime

    • 1st Edition
    • Volume 163
    • G. Kaiser
    • English
    A new synthesis of the principles of quantum mechanics and Relativity is proposed in the context of complex differential geometry. The positivity of the energy implies that wave functions and fields can be extended to complex spacetime, and it is shown that this complexification has a solid physical interpretation as an extended phase space. The extended fields can be said to be realistic wavelet transforms of the original fields. A new, algebraic theory of wavelets is developed.

  • Classification Theory

    and the Number of Non-Isomorphic Models
    • 2nd Edition
    • Volume 92
    • S. Shelah
    • English
    In this research monograph, the author's work on classification and related topics are presented. This revised edition brings the book up to date with the addition of four new chapters as well as various corrections to the 1978 text.The additional chapters X - XIII present the solution to countable first order T of what the author sees as the main test of the theory. In Chapter X the Dimensional Order Property is introduced and it is shown to be a meaningful dividing line for superstable theories. In Chapter XI there is a proof of the decomposition theorems. Chapter XII is the crux of the matter: there is proof that the negation of the assumption used in Chapter XI implies that in models of T a relation can be defined which orders a large subset of m

  • Non-Linear Partial Differential Equations

    An Algebraic View of Generalized Solutions
    • 1st Edition
    • Volume 164
    • E.E. Rosinger
    • English
    A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomena have presented increasing difficulties in the mentioned order. In particular, the latter two phenomena necessarily lead to nonclassical or generalized solutions for nonlinear partial differential equations.

  • Categories, Allegories

    • 1st Edition
    • Volume 39
    • P.J. Freyd + 1 more
    • English
    General concepts and methods that occur throughout mathematics – and now also in theoretical computer science – are the subject of this book. It is a thorough introduction to Categories, emphasizing the geometric nature of the subject and explaining its connections to mathematical logic. The book should appeal to the inquisitive reader who has seen some basic topology and algebra and would like to learn and explore further.The first part contains a detailed treatment of the fundamentals of Geometric Logic, which combines four central ideas: natural transformations, sheaves, adjoint functors, and topoi. A special feature of the work is a general calculus of relations presented in the second part. This calculus offers another, often more amenable framework for concepts and methods discussed in part one. Some aspects of this approach find their origin in the relational calculi of Peirce and Schroeder from the last century, and in the 1940's in the work of Tarski and others on relational algebras. The representation theorems discussed are an original feature of this approach.

  • Statistical Methods in Longitudinal Research

    Time Series and Categorical Longitudinal Data
    • 1st Edition
    • Volume 2
    • Alexander von Eye
    • English
    These edited volumes present new statistical methods in a way that bridges the gap between theoretical and applied statistics. The volumes cover general problems and issues and more specific topics concerning the structuring of change, the analysis of time series, and the analysis of categorical longitudinal data. The book targets students of development and change in a variety of fields - psychology, sociology, anthropology, education, medicine, psychiatry, economics, behavioural sciences, developmental psychology, ecology, plant physiology, and biometry - with basic training in statistics and computing.

  • Statistical Methods in Longitudinal Research

    Principles and Structuring Change
    • 1st Edition
    • Volume 1
    • Alexander von Eye
    • English
    These edited volumes present new statistical methods in a way that bridges the gap between theoretical and applied statistics. The volumes cover general problems and issues and more specific topics concerning the structuring of change, the analysis of time series, and the analysis of categorical longitudinal data. The book targets students of development and change in a variety of fields - psychology, sociology, anthropology, education, medicine, psychiatry, economics, behavioural sciences, developmental psychology, ecology, plant physiology, and biometry - with basic training in statistics and computing.

  • Handbook of Convex Geometry

    • 1st Edition
    • Bozzano G Luisa
    • English
    Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.

  • Functional Analysis

    An Introduction for Physicists
    • 1st Edition
    • Nino Boccara
    • English
    Based on a third-year course for French students of physics, this book is a graduate text in functional analysis emphasizing applications to physics. It introduces Lebesgue integration, Fourier and Laplace transforms, Hilbert space theory, theory of distribution a la Laurent Schwartz, linear operators, and spectral theory. It contains numerous examples and completely worked out exercises.

  • Probability, Statistics, and Queueing Theory

    • 2nd Edition
    • Arnold O. Allen
    • English
    This is a textbook on applied probability and statistics with computer science applications for students at the upper undergraduate level. It may also be used as a self study book for the practicing computer science professional. The successful first edition of this book proved extremely useful to students who need to use probability, statistics and queueing theory to solve problems in other fields, such as engineering, physics, operations research, and management science. The book has also been successfully used for courses in queueing theory for operations research students. This second edition includes a new chapter on regression as well as more than twice as many exercises at the end of each chapter. While the emphasis is the same as in the first edition, this new book makes more extensive use of available personal computer software, such as Minitab and Mathematica.

  • C*-Algebras and Operator Theory

    • 1st Edition
    • Gerald J. Murphy
    • English
    This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.

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