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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.

  • Axiomatics of Classical Statistical Mechanics

    • 1st Edition
    • Volume 11
    • Rudolf Kurth
    • I. N. Sneddon + 2 more
    • English
    Axiomatics of Classical Statistical Mechanics provides an understanding of classical statistical mechanics as a deductive system. This book presents the mechanical systems of a finite number of degrees of freedom. Organized into seven chapters, this book begins with an overview of the average behavior of mechanical systems. This text then examines the concept of a mechanical system and explains the equations of motion of the system. Other chapters consider an ensemble of mechanical systems wherein a Hamiltonian function and a truncated canonical probability density corresponds to each system. This book discusses as well the necessary and sufficient conditions that are given for the existence of statistically stationary states and for the approach of mechanical systems towards these states. The final chapter deals with the fundamental laws of thermodynamics. This book is a valuable resource for mathematicians.

  • Capital Theory and the Distribution of Income

    • 1st Edition
    • Volume 4
    • C. J. Bliss
    • C. J. Bliss
    • English
    Advanced Textbooks in Economics, Volume 4: Capital Theory and the Distribution of Income focuses on the interconnection of capital theory and the distribution of income, including marginal products, capital, interest rates, and price systems. The book first takes a look at production without capital, equilibrium, prices, and time, and semi-stationary growth, as well as the existence of constant-rate-of-int... price systems. The manuscript then discusses marginal products and capital and the Cambridge model. The text examines the aggregation of miscellaneous objects, production function, linear production model, and efficiency, production prices, and rates of return, as well as prices and efficiency for infinite developments. The manuscript also ponders on investment, structure of interest rates, and disputations. Discussions focus on sets and convex sets, concave functions, and linear and non-linear programming. The publication is a dependable source of data for economists and researchers interested in capital theory and the distribution of income.

  • The Theory of Jets in an Ideal Fluid

    • 1st Edition
    • Volume 93
    • M. I. Gurevich
    • J. P. Kahane + 2 more
    • English
    Pure and Applied Mathematics, Volume 39: The Theory of Jets in an Ideal Fluid provides a general idea of the theory of jets. This book serves as an introduction to the classical problems in the theory and provides some knowledge of the fundamentals of hydromechanics. Organized into 12 chapters, this volume begins with an overview of the theory of plane, steady flow of an ideal, incompressible fluid. This text then examines the jet flow of an unbounded current about a flat plate, placed perpendicular to the flow. Other chapters consider a number of problems involving the plane flow of fluid out of vessels. This book discusses as well the physical importance of Brillouin's condition and also the problem of cavitational flow. The final chapter deals with the flows of weightless fluid in order to know the effect of surface tension forces. This book is a valuable resource for marine and hydraulic engineers.

  • Theory of Approximation of Functions of a Real Variable

    • 1st Edition
    • Volume 34
    • A. F. Timan
    • I. N. Sneddon + 2 more
    • English
    Theory of Approximation of Functions of a Real Variable discusses a number of fundamental parts of the modern theory of approximation of functions of a real variable. The material is grouped around the problem of the connection between the best approximation of functions to their structural properties. This text is composed of eight chapters that highlight the relationship between the various structural properties of real functions and the character of possible approximations to them by polynomials and other functions of simple construction. Each chapter concludes with a section containing various problems and theorems, which supplement the main text. The first chapters tackle the Weierstrass's theorem, the best approximation by polynomials on a finite segment, and some compact classes of functions and their structural properties. The subsequent chapters describe some properties of algebraic polynomials and transcendental integral functions of exponential type, as well as the direct theorems of the constructive theory of functions. These topics are followed by discussions of differential and constructive characteristics of converse theorems. The final chapters explore other theorems connecting the best approximations functions with their structural properties. These chapters also deal with the linear processes of approximation of functions by polynomials. The book is intended for post-graduate students and for mathematical students taking advanced courses, as well as to workers in the field of the theory of functions.

  • Investment

    The Study of an Economic Aggregate
    • 1st Edition
    • Volume 13
    • Philip J. Lund
    • C. J. Bliss + 1 more
    • English
    Advanced Textbooks in Economics: Investment: The Study of an Economic Aggregate focuses on the principles, methodologies, and approaches involved in the determination of investments. The book first offers information on the theories of aggregate investment and statistical and questionnaire studies. Discussions focus on statistical studies, tax incentives and disincentives to investment, capital stock adjustment models, acceleration principle, replacement investment, level of aggregation, sources of funds, neoclassical theory of capital accumulation, and tax incentives and disincentives to investment. The text then examines the estimation of lag distributions, including geometrically declining lag distributions, Pascal and rational distributions, variable lag distributions, and the first-in first-out method. The publication ponders on econometric studies, as well as United Kingdom and United States studies, two-stage studies of investment, and guidelines for future research. The text is a dependable source of information for economists and researchers interested in economic aggregates.

  • Foundations of Econometrics

    • 1st Edition
    • Volume 7
    • Albert Madansky
    • C. J. Bliss + 1 more
    • English
    Advanced Textbooks in Economics, Volume 7: Foundations of Econometrics focuses on the principles, processes, methodologies, and approaches involved in the study of econometrics. The publication examines matrix theory and multivariate statistical analysis. Discussions focus on the maximum likelihood estimation of multivariate normal distribution parameters, point estimation theory, multivariate normal distribution, multivariate probability distributions, Euclidean spaces and linear transformations, orthogonal transformations and symmetric matrices, and determinants. The manuscript then ponders on linear expected value models and simultaneous equation estimation. Topics include random exogenous variables, maximum likelihood estimation of a single equation, identification of a single equation, linear stochastic difference equations, and errors-in-variables models. The book takes a look at a prolegomenon to econometric model building, tests of hypotheses in econometric models, multivariate statistical analysis, and simultaneous equation estimation. Concerns include maximum likelihood estimation of a single equation, tests of linear hypotheses, testing for independence, and causality in economic models. The publication is a valuable source of data for economists and researchers interested in the foundations of econometrics.

  • Integral Equations

    And Their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology
    • 1st Edition
    • Volume 4
    • S. G. Mikhlin
    • I. N. Sneddon + 2 more
    • English
    Integral Equations: And their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology, Second Revised Edition contains an account of the general theory of Fredholm and Hilbert-Schmidt. This edition discusses methods of approximate solution of Fredholm's equation and, in particular, their application to the solution of basic problems in mathematical physics, including certain problems in hydrodynamics and the theory of elasticity. Other topics include the equations of Volterra type, determination of the first eigenvalue by Ritz's method, and systems of singular integral equations. The generalized method of Schwarz, convergence of successive approximations, stability of a rod in compression, and mixed problem of the theory of elasticity are also elaborated. This publication is recommended for mathematicians, students, and researchers concerned with singular integral equations.

  • Variational Methods in Economics

    • 1st Edition
    • Volume 1
    • G. Hadley + 1 more
    • C. J. Bliss
    • English
    Advanced Textbooks in Economics, Volume 1: Variational Methods in Economics focuses on the application of variational methods in economics, including autonomous system, dynamic programming, and phase spaces and diagrams. The manuscript first elaborates on growth models in economics and calculus of variations. Discussions focus on connection with dynamic programming, variable end points-free boundaries, transversality at infinity, sensitivity analysis-end point changes, Weierstrass and Legendre necessary conditions, and phase diagrams and phase spaces. The text then ponders on the constraints of classical theory, including unbounded intervals of integration, free boundary conditions, comparison functions, normality, and the problem of Bolza. The publication explains two-sector models of optimal economic growth, optimal control theory, and connections with the classical theory. Topics include capital good immobile between industries, constrained state variables, linear control problems, conversion of a control problem into a problem of Lagrange, and the conversion of a nonautonomous system into an autonomous system. The book is a valuable source of information for economists and researchers interested in the variational methods in economics.

  • Representations of Lie Groups, Kyoto, Hiroshima, 1986

    • 1st Edition
    • K. Okamoto + 1 more
    • English
    Representations of Lie Groups, Kyoto, Hiroshima, 1986 contains the proceedings of a symposium on "Analysis on Homogeneous Spaces and Representations of Lie Groups" held on September 1-6, 1986 in Japan. The symposium provided a forum for discussing Lie groups and covered topics ranging from geometric constructions of representations to the irreducibility of discrete series representations for semisimple symmetric spaces. A classification theory of prehomogeneous vector spaces is also described. Comprised of 22 chapters, this volume first considers the characteristic varieties of certain modules over the enveloping algebra of a semisimple Lie algebra, such as highest weight modules and primitive quotients. The reader is then introduced to multiplicity one theorems for generalized Gelfand-Graev representations of semisimple Lie groups and Whittaker models for the discrete series. Subsequent chapters focus on Lie algebra cohomology and holomorphic continuation of generalized Jacquet integrals; the generalized Geroch conjecture; algebraic structures on virtual characters of a semisimple Lie group; and fundamental groups of semisimple symmetric spaces. The book concludes with an analysis of the boundedness of certain unitarizable Harish-Chandra modules. This monograph will appeal to students, specialists, and researchers in the field of pure mathematics.

  • Applied Methods of the Theory of Random Functions

    • 1st Edition
    • Volume 89
    • A. A. Sveshnikov
    • I. N. Sneddon + 1 more
    • English
    International Series of Monographs in Pure and Applied Mathematics, Volume 89: Applied Methods of the Theory of Random Functions presents methods of random functions analysis with their applications in various branches of technology, such as in the theory of ships, automatic regulation and control, and radio engineering. This book discusses the general properties of random functions, spectral theory of stationary random functions, and determination of optimal dynamical systems. The experimental methods for the determination of characteristics of random functions, method of envelopes, and some supplementary problems of the theory of random functions are also deliberated. This publication is intended for engineers and scientists who use the methods of the theory of probability in various branches of technology.

  • Algebra

    • 1st Edition
    • Volume 91
    • L. Rédei
    • I. N. Sneddon + 1 more
    • English
    Compared with the original German edition this volume contains the results of more recent research which have to some extent originated from problems raised in the previous German edition. Moreover, many minor and some important modifications have been carried out. For example paragraphs 2 — 5 were amended and their order changed. On the advice of G. Pickert, paragraph 7 has been thoroughly revised. Many improvements originate from H. J. Weinert who, by enlisting the services of a working team of the Teachers' Training College of Potsdam, has subjected large parts of this book to an exact and constructive review. This applies particularly to paragraphs 9, 50, 51, 60, 63, 66, 79, 92, 94, 97 and 100 and to the exercises. In this connection paragraphs 64 and 79 have had to be partly rewritten in consequence of the correction

  • Vector Measures

    • 1st Edition
    • Volume 95
    • N. Dinculeanu
    • I. N. Sneddon + 1 more
    • English
    International Series of Monographs in Pure and Applied Mathematics, Volume 95: Vector Measures focuses on the study of measures with values in a Banach space, including positive measures with finite or infinite values. This book is organized into three chapters. Chapter I covers classes of sets, set functions, variation and semi-variation of set functions, and extension of set functions from a certain class to a wider one. The integration of vector functions with respect to vector measures is reviewed in Chapter II. In Chapter III, the regular measures on a locally compact space and integral representation of the dominated operations on the space of continuous functions with compact carrier are described. This volume is intended for specialists, researchers, and students interested in vector measures.

  • Nomography

    • 1st Edition
    • Volume 42
    • Edward Otto
    • English
    Nomography deals with geometrical transformations, particularly projective transformations of a plane. The book reviews projective plane and collineation transformations in geometrical and algebraical terms. The geometrical approach aims at permitting the use of elementary geometrical methods in drawing collineation nomograms consisting of three rectilinear scales. The algebraical treatment concerns nomograms containing curvilinear scales. The text explains functional scales that include the graph of a function and a logarithmic scale. The book explores equations which can be represented by elementary methods without the use of a system of coordinates, some equations that require algebraic calculations, as well as nomograms with a binary field (lattice nomograms). The text investigates collineation monograms of many variables, elementary geometrical methods of joining nomograms, and also of nomograms consisting of two parts to be superimposed on each other. In addition to the Massau method and the criterion of Saint Robert, the book also applies the criteria of nomogrammability of a function to address mathematical problems related to the analysis of the methods in constructing nomograms. The book can be useful for mathematicians, geometricians, engineers, and researchers working in the physical sciences who use graphical calculations in their work.

  • Barsotti Symposium in Algebraic Geometry

    • 1st Edition
    • Volume 15
    • Valentino Cristante + 1 more
    • English
    Barsotti Symposium in Algebraic Geometry contains papers corresponding to the lectures given at the 1991 memorial meeting held in Abano Terme in honor of Iacopo Barsotti. This text reflects Barsotti’s significant contributions in the field. This book is composed of 10 chapters and begins with a review of the centers of three-dimensional skylanin algebras. The succeeding chapters deal with the theoretical aspects of the Abelian varieties, Witt realization of p-Adic Barsotti-Tate Groups, and hypergeometric series and functions. These topics are followed by discussions of logarithmic spaces and the estimates for and inequalities among A-numbers. The closing chapter describes the moduli of Abelian varieties in positive characteristic. This book will be of value to mathematicians.

  • Introduction to Higher Algebra

    • 1st Edition
    • Volume 37
    • A. Mostowski + 1 more
    • I. N. Sneddon + 2 more
    • English
    Introduction to Higher Algebra is an 11-chapter text that covers some mathematical investigations concerning higher algebra. After an introduction to sets of functions, mathematical induction, and arbitrary numbers, this book goes on considering some combinatorial problems, complex numbers, determinants, vector spaces, and linear equations. These topics are followed by discussions of the determination of polynomials in ne variable, rings of real and complex polynomials, and algebraic and transcendental numbers. The final chapters deal with the polynomials in several variables, symmetric functions, the theory of elimination, and the quadratic and Hermitian forms. This book will be of value to mathematicians and students.

  • Mathematical Techniques of Operational Research

    • 1st Edition
    • Volume 38
    • L. S. Goddard
    • I. N. Sneddon + 2 more
    • English
    Mathematical Techniques of Operational Research is a seven-chapter text that covers the principles and applications of various mathematical tools and models to for operational research. Chapter I provides the basic mathematical ideas used in later chapters. Chapters II and III deal with linear programming, including the special cases of transportation and assignment, as well as their applications such as the Trim Problem. Chapters IV and V discuss the theory of queues and describe the general stationary properties of the single-channel queue, and of simple queues in series and in parallel. These chapters also examine some transient properties of queues. Chapter VI focuses on machine interference, which is an aspect of queueing theory, while Chapter VII deals with the important and mathematically subject of Stock Control or Inventory Theory. This book is intended primarily to graduate mathematicians, business manages, and industrial leaders.

  • Generalized Analytic Functions

    • 1st Edition
    • Volume 25
    • I. N. Vekua
    • I. N. Sneddon + 2 more
    • English
    Generalized Analytic Functions is concerned with foundations of the general theory of generalized analytic functions and some applications to problems of differential geometry and theory of shells. Some classes of functions and operators are discussed, along with the reduction of a positive differential quadratic form to the canonical form. Boundary value problems and infinitesimal bendings of surfaces are also considered. Comprised of six chapters, this volume begins with a detailed treatment of various problems of the general theory of generalized analytic functions as as well as boundary value problems. The reader is introduced to some classes of functions and functional spaces, with emphasis on functions of two independent variables. Subsequent chapters focus on the problem of reducing a positive differential quadratic form to the canonical form; basic properties of solutions of elliptic systems of partial differential equations of the first order, in a two-dimensional domain; and some boundary value problems for an elliptic system of equations of the first order and for an elliptic equation of the second order, in a two-dimensional domain. The final part of the book deals with problems of the theory of surfaces and the membrane theory of shells. This book is intended for students of advanced courses of the mechanico-mathematic... faculties, postgraduates, and research workers.

  • Some Topics in Complex Analysis

    • 1st Edition
    • Volume 86
    • E. G. Phillips
    • I. N. Sneddon + 2 more
    • English
    International Series of Monographs in Pure and Applied Mathematics, Volume 86, Some Topics in Complex Analysis deals with a variety of topics related to complex analysis. This book discusses the method of comparison, periods of an integral, generalized Joukowski transformations, and Koebe's distortion theorems. The deductions from the maximum-modulus principle, canonical products and genus of an I.F., and Weierstrass's primary factors are also reviewed. This text likewise considers Mittag-Leffler's theorem, summation of series by the calculus of residues, definition of regular functions by integrals, and Riemann zeta function. This publication is a good reference for students and specialists researching in the field of applied and pure mathematics.

  • Mathematical Analysis

    Functions, Limits, Series, Continued Fractions
    • 1st Edition
    • Volume 69
    • L. A. Lyusternik + 1 more
    • English
    Mathematical Analysis: Functions, Limits, Series, Continued Fractions provides an introduction to the differential and integral calculus. This book presents the general problems of the theory of continuous functions of one and several variables, as well as the theory of limiting values for sequences of numbers and vectors. Organized into six chapters, this book begins with an overview of real numbers, the arithmetic linear continuum, limiting values, and functions of one variable. This text then presents the theory of series and practical methods of summation. Other chapters consider the theory of numerical series and series of functions and other analogous processes, particularly infinite continued fractions. This book discusses as well the general problems of the reduction of functions to orthogonal series. The final chapter deals with constants and the most important systems of numbers, including Bernoulli and Euler numbers. This book is a valuable resource for mathematicians, engineers, and research workers.

  • Linear Representations of the Lorentz Group

    • 1st Edition
    • Volume 63
    • M. A. Naimark
    • H. K. Farahat
    • English
    Linear Representations of the Lorentz Group is a systematic exposition of the theory of linear representations of the proper Lorentz group and the complete Lorentz group. This book consists of four chapters. The first two chapters deal with the basic material on the three-dimensional rotation group, on the complete Lorentz group and the proper Lorentz group, as well as the theory of representations of the three-dimensional rotation group. These chapters also provide the necessary basic information from the general theory of group representations. The third chapter is devoted to the representations of the proper Lorentz group and the complete Lorentz group, while the fourth chapter examines the theory of invariant equations. This book will prove useful to mathematicians and students.

  • Foundation of Euclidean and Non-Euclidean Geometries according to F. Klein

    • 1st Edition
    • Volume 97
    • L. Redei
    • I. N. Sneddon + 1 more
    • English
    Foundation of Euclidean and Non-Euclidean Geometries according to F. Klein aims to remedy the deficiency in geometry so that the ideas of F. Klein obtain the place they merit in the literature of mathematics. This book discusses the axioms of betweenness, lattice of linear subspaces, generalization of the notion of space, and coplanar Desargues configurations. The central collineations of the plane, fundamental theorem of projective geometry, and lines perpendicular to a proper plane are also elaborated. This text likewise covers the axioms of motion, basic projective configurations, properties of triangles, and theorem of duality in projective space. Other topics include the point-coordinates in an affine space and consistency of the three geometries. This publication is beneficial to mathematicians and students learning geometry.

  • Abelian Groups

    • 3rd Edition
    • Volume 12
    • L. Fuchs
    • J. P. Kahane + 2 more
    • English
    Abelian Groups deals with the theory of abelian or commutative groups, with special emphasis on results concerning structure problems. More than 500 exercises of varying degrees of difficulty, with and without hints, are included. Some of the exercises illuminate the theorems cited in the text by providing alternative developments, proofs or counterexamples of generalizations. Comprised of 16 chapters, this volume begins with an overview of the basic facts on group theory such as factor group or homomorphism. The discussion then turns to direct sums of cyclic groups, divisible groups, and direct summands and pure subgroups, as well as Kulikov's basic subgroups. Subsequent chapters focus on the structure theory of the three main classes of abelian groups: the primary groups, the torsion-free groups, and the mixed groups. Applications of the theory are also considered, along with other topics such as homomorphism groups and endomorphism rings; the Schreier extension theory with a discussion of the group of extensions and the structure of the tensor product. In addition, the book examines the theory of the additive group of rings and the multiplicative group of fields, along with Baer's theory of the lattice of subgroups. This book is intended for young research workers and students who intend to familiarize themselves with abelian groups.

  • Fundamental Concepts of Mathematics

    • 2nd Edition
    • R. L. Goodstein
    • I. N. Sneddon
    • English
    Fundamental Concepts of Mathematics, 2nd Edition provides an account of some basic concepts in modern mathematics. The book is primarily intended for mathematics teachers and lay people who wants to improve their skills in mathematics. Among the concepts and problems presented in the book include the determination of which integral polynomials have integral solutions; sentence logic and informal set theory; and why four colors is enough to color a map. Unlike in the first edition, the second edition provides detailed solutions to exercises contained in the text. Mathematics teachers and people who want to gain a thorough understanding of the fundamental concepts of mathematics will find this book a good reference.

  • Elements of Linear Space

    • 1st Edition
    • Volume 26
    • A. R. Amir-Moez + 1 more
    • I. N. Sneddon + 2 more
    • English
    Elements of Linear Space is a detailed treatment of the elements of linear spaces, including real spaces with no more than three dimensions and complex n-dimensional spaces. The geometry of conic sections and quadric surfaces is considered, along with algebraic structures, especially vector spaces and transformations. Problems drawn from various branches of geometry are given. Comprised of 12 chapters, this volume begins with an introduction to real Euclidean space, followed by a discussion on linear transformations and matrices. The addition and multiplication of transformations and matrices are given emphasis. Subsequent chapters focus on some properties of determinants and systems of linear equations; special transformations and their matrices; unitary spaces; and some algebraic structures. Quadratic forms and their applications to geometry are also examined, together with linear transformations in general vector spaces. The book concludes with an evaluation of singular values and estimates of proper values of matrices, paying particular attention to linear transformations always on a unitary space of dimension n over the complex field. This book will be of interest to both undergraduate and more advanced students of mathematics.

  • Introduction to Calculus

    • 2nd Edition
    • Volume 17
    • Kazimierz Kuratowski
    • A. J. Lohwater
    • English
    The English edition does not differ essentially from the Polish one. Among the more important supplements I should mention § 6.5 containing elementary information on the notation of mathematical logic. To this supplement I was inclined by the experience of many years. For many students (not for all, perhaps) the notation of definitions of certain notions by means of the logical symbols makes it easier to understand these notions (e.g. the notions of uniform continuity or uniform convergence). Besides that, this supplement is included in the book in such a manner that it can be omitted in reading the whole book. Among other changes introduced in the English text, I should mention the addition of a number of exercises and problems; in the second English edition, many of them have been collected in the Supplement. I am glad also to mention the simplification of certain proofs, and finally the removal of mistakes which were found in the primary text

  • The Theory of Lebesgue Measure and Integration

    • 1st Edition
    • Volume 15
    • S. Hartman + 1 more
    • I. N. Sneddon + 2 more
    • English
    The Theory of Lebesgue Measure and Integration deals with the theory of Lebesgue measure and integration and introduces the reader to the theory of real functions. The subject matter comprises concepts and theorems that are now considered classical, including the Yegorov, Vitali, and Fubini theorems. The Lebesgue measure of linear sets is discussed, along with measurable functions and the definite Lebesgue integral. Comprised of 13 chapters, this volume begins with an overview of basic concepts such as set theory, the denumerability and non-denumerability of sets, and open sets and closed sets on the real line. The discussion then turns to the theory of Lebesgue measure of linear sets based on the method of M. Riesz, together with the fundamental properties of measurable functions. The Lebesgue integral is considered for both bounded functions — upper and lower integrals — and unbounded functions. Later chapters cover such topics as the Yegorov, Vitali, and Fubini theorems; convergence in measure and equi-integrability; integration and differentiation; and absolutely continuous functions. Multiple integrals and the Stieltjes integral are also examined. This book will be of interest to mathematicians and students taking pure and applied mathematics.

  • Tables and Formulae for the Spherical Functions Pm – ½ + i t (Z)

    Mathematical Tables Series
    • 1st Edition
    • M. I. Zhurina + 1 more
    • English
    Tables and Formulae for the Spherical Functions Pm – ½ + i t (Z)

  • A Collection of Problems on a Course of Mathematical Analysis

    • 1st Edition
    • G. N. Berman
    • I. N. Sneddon + 2 more
    • English
    Collection of Problems on a Course of Mathematical Analysis contains selected problems and exercises on the main branches of a Technical College course of mathematical analysis. This book covers the topics of functions, limits, derivatives, differential calculus, curves, definite integral, integral calculus, methods of evaluating definite integrals, and their applications. Other topics explored include numerical problems related to series and the functions of several variables in differential calculus, as well as their applications. The remaining chapters examine the principles of multiple, line, and surface integrals, the trigonometric series, and the elements of the theory of fields. This book is intended for students studying mathematical analysis within the framework of a technical college course.

  • Analytic Properties of Automorphic L-Functions

    • 1st Edition
    • Volume 6
    • Stephen Gelbart + 1 more
    • J. Coates + 1 more
    • English
    Analytic Properties of Automorphic L-Functions is a three-chapter text that covers considerable research works on the automorphic L-functions attached by Langlands to reductive algebraic groups. Chapter I focuses on the analysis of Jacquet-Langlands methods and the Einstein series and Langlands’ so-called “Euler products”. This chapter explains how local and global zeta-integrals are used to prove the analytic continuation and functional equations of the automorphic L-functions attached to GL(2). Chapter II deals with the developments and refinements of the zeta-inetgrals for GL(n). Chapter III describes the results for the L-functions L (s, ?, r), which are considered in the constant terms of Einstein series for some quasisplit reductive group. This book will be of value to undergraduate and graduate mathematics students.

  • Automorphic Forms and Geometry of Arithmetic Varieties

    • 1st Edition
    • K. Hashimoto + 1 more
    • English
    Automorphic Forms and Geometry of Arithmetic Varieties deals with the dimension formulas of various automorphic forms and the geometry of arithmetic varieties. The relation between two fundamental methods of obtaining dimension formulas (for cusp forms), the Selberg trace formula and the index theorem (Riemann-Roch's theorem and the Lefschetz fixed point formula), is examined. Comprised of 18 sections, this volume begins by discussing zeta functions associated with cones and their special values, followed by an analysis of cusps on Hilbert modular varieties and values of L-functions. The reader is then introduced to the dimension formula of Siegel modular forms; the graded rings of modular forms in several variables; and Selberg-Ihara's zeta function for p-adic discrete groups. Subsequent chapters focus on zeta functions of finite graphs and representations of p-adic groups; invariants and Hodge cycles; T-complexes and Ogata's zeta zero values; and the structure of the icosahedral modular group. This book will be a useful resource for mathematicians and students of mathematics.

  • Huygens' Principle and Hyperbolic Equations

    • 1st Edition
    • Volume 5
    • Gunther Paul
    • J. Coates + 1 more
    • English
    Huygens' Principle and Hyperbolic Equations is devoted to certain mathematical aspects of wave propagation in curved space-times. The book aims to present special nontrivial Huygens' operators and to describe their individual properties and to characterize these examples of Huygens' operators within certain more or less comprehensive classes of general hyperbolic operators. The materials covered in the book include a treatment of the wave equation for p-forms over a space of constant sectional curvature, the Riesz distributions, the Euler-Poisson-Darbou... over a Riemannian manifold, and plane wave manifolds. Physicists will find the book invaluable.

  • Recent Topics in Differential and Analytic Geometry

    • 1st Edition
    • Volume 18
    • T. Ochiai
    • English
    Advanced Studies in Pure Mathematics, Volume 18-I: Recent Topics in Differential and Analytic Geometry presents the developments in the field of analytical and differential geometry. This book provides some generalities about bounded symmetric domains. Organized into two parts encompassing 12 chapters, this volume begins with an overview of harmonic mappings and holomorphic foliations. This text then discusses the global structures of a compact Kähler manifold that is locally decomposable as an isometric product of Ricci-positive, Ricci-negative, and Ricci-flat parts. Other chapters consider the most recognized non-standard examples of compact homogeneous Einstein manifolds constructed via Riemannian submersions. This book discusses as well the natural compactification of the moduli space of polarized Einstein–Kähler orbitfold with a given Hilbert polynomials. The final chapter deals with solving a degenerate Monge–Ampère equation by constructing a family of Einstein–Kähler metrics on the smooth part of minimal varieties of general kind. This book is a valuable resource for graduate students and pure mathematicians.

  • Non-Linear Differential Equations

    • 1st Edition
    • Volume 67
    • G. Sansone + 1 more
    • I. N. Sneddon + 2 more
    • English
    Non-Linear Differential Equations covers the general theorems, principles, solutions, and applications of non-linear differential equations. This book is divided into nine chapters. The first chapters contain detailed analysis of the phase portrait of two-dimensional autonomous systems. The succeeding chapters deal with the qualitative methods for the discovery of periodic solutions in periodic systems. The remaining chapters describe a synthetical approach to the study of asymptotic properties, especially stability properties, of the solutions of general n-dimensional systems. This book will be of great value to mathematicians, researchers, and students.

  • The Boundary Element Method for Plate Analysis

    • 1st Edition
    • John T. Katsikadelis
    • English
    Boundary Element Method for Plate Analysis offers one of the first systematic and detailed treatments of the application of BEM to plate analysis and design. Aiming to fill in the knowledge gaps left by contributed volumes on the topic and increase the accessibility of the extensive journal literature covering BEM applied to plates, author John T. Katsikadelis draws heavily on his pioneering work in the field to provide a complete introduction to theory and application. Beginning with a chapter of preliminary mathematical background to make the book a self-contained resource, Katsikadelis moves on to cover the application of BEM to basic thin plate problems and more advanced problems. Each chapter contains several examples described in detail and closes with problems to solve. Presenting the BEM as an efficient computational method for practical plate analysis and design, Boundary Element Method for Plate Analysis is a valuable reference for researchers, students and engineers working with BEM and plate challenges within mechanical, civil, aerospace and marine engineering.

  • Interpretation of Visual Motion

    A Computational Study
    • 1st Edition
    • Muralidhara Subbarao
    • English
    Interpretation of Visual Motion: A Computational Study provides an information processing point of view to the phenomenon of visual motion. This book discusses the computational theory formulated for recovering the scene from monocular visual motion, determining the local geometry and rigid body motion of surfaces from spatio-temporal parameters of visual motion. This compilation also provides a theoretical and computational framework for future research on visual motion, both in human vision and machine vision areas. Other topics include the computation of image flow from intensity derivatives, instantaneous image flow due to rigid motion, time and space-time derivatives of image flow, and estimation of maximum absolute error. This publication is recommended for professionals and non-specialists intending to acquire knowledge of visual motion.

  • Design Problem Solving

    Knowledge Structures and Control Strategies
    • 1st Edition
    • David C. Brown + 1 more
    • English
    Design Problem Solving: Knowledge Structures and Control Strategies describes the application of the generic task methodology to the problem of routine design. This book discusses the generic task methodology and what constitutes the essence of the Al approach to problem solving, including the analysis of design as an information processing activity. The basic design problem solving framework, DSPL language, and AIR-CYL Air cylinder design system are also elaborated. Other topics include the high level languages based on generic tasks, structure of a Class 3 design problem solver, and failure handling in routine design. The conceptual structure for the air cylinder and improvements to DSPL system support are likewise covered in this text. This publication is beneficial to students and specialists concerned with solving design problems.

  • Calculus of Variations

    • 1st Edition
    • Volume 19
    • L. E. Elsgolc
    • I. N. Sneddon + 2 more
    • English
    Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter is illustrated by a large number of problems some of which are taken from existing textbooks. The solutions to the problems in each chapter are provided at the end of the book.

  • A Course of Higher Mathematics

    International Series of Monographs in Pure and Applied Mathematics, Volume 62: A Course of Higher Mathematics, V: Integration and Functional Analysis
    • 1st Edition
    • V. I. Smirnov
    • I. N. Sneddon + 2 more
    • English
    International Series of Monographs in Pure and Applied Mathematics, Volume 62: A Course of Higher Mathematics, V: Integration and Functional Analysis focuses on the theory of functions. The book first discusses the Stieltjes integral. Concerns include sets and their powers, Darboux sums, improper Stieltjes integral, jump functions, Helly’s theorem, and selection principles. The text then takes a look at set functions and the Lebesgue integral. Operations on sets, measurable sets, properties of closed and open sets, criteria for measurability, and exterior measure and its properties are discussed. The text also examines set functions, absolute continuity, and generalization of the integral. Absolutely continuous set functions; absolutely continuous functions of several variables; supplementary propositions; and the properties of the Hellinger integral are presented. The text also focuses on metric and normed spaces. Separability, compactness, linear functionals, conjugate spaces, and operators in normed spaces are underscored. The book also discusses Hilbert space. Linear functionals, projections, axioms of the space, sequences of operators, and weak convergence are described. The text is a valuable source of information for students and mathematicians interested in studying the theory of functions.

  • Integration of Equations of Parabolic Type by the Method of Nets

    • 1st Edition
    • V. K. Saul'Yev
    • I. N. Sneddon + 2 more
    • English
    International Series of Monographs in Pure and Applied Mathematics, Volume 54: Integration of Equations of Parabolic Type by the Method of Nets deals with solving parabolic partial differential equations using the method of nets. The first part of this volume focuses on the construction of net equations, with emphasis on the stability and accuracy of the approximating net equations. The method of nets or method of finite differences (used to define the corresponding numerical method in ordinary differential equations) is one of many different approximate methods of integration of partial differential equations. The other methods, and some based on newer equations, are described. By analyzing these newer methods, older and existing methods are evaluated. For example, the asymmetric net equations; the alternating method of using certain equations; and the method of mean arithmetic and multi-nodal symmetric method point out that when the accuracy needs to be high, the requirements for stability become more defined. The methods discussed are very theoretical and methodological. The second part of the book concerns the practical numerical solution of the equations posed in Part I. Emphasis is on the commonly used iterative methods that are programmable on computers. This book is suitable for statisticians and numerical analysts and is also recommended for scientists and engineers with general mathematical knowledge.

  • Homology Theory on Algebraic Varieties

    • 1st Edition
    • Andrew H. Wallace
    • I. N. Sneddon
    • English
    Homology Theory on Algebraic Varieties, Volume 6 deals with the principles of homology theory in algebraic geometry and includes the main theorems first formulated by Lefschetz, one of which is interpreted in terms of relative homology and another concerns the Poincaré formula. The actual details of the proofs of these theorems are introduced by geometrical descriptions, sometimes aided with diagrams. This book is comprised of eight chapters and begins with a discussion on linear sections of an algebraic variety, with emphasis on the fibring of a variety defined over the complex numbers. The next two chapters focus on singular sections and hyperplane sections, focusing on the choice of a pencil in the latter case. The reader is then introduced to Lefschetz's first and second theorems, together with their corresponding proofs. The Poincaré formula and its proof are also presented, with particular reference to clockwise and anti-clockwise isomorphisms. The final chapter is devoted to invariant cycles and relative cycles. This volume will be of interest to students, teachers, and practitioners of pure and applied mathematics.

  • The Algebraic Theory of Switching Circuits

    • 1st Edition
    • Gr. C. Moisil
    • English
    The Algebraic Theory of Switching Circuits covers the application of various algebraic tools to the delineation of the algebraic theory of switching circuits for automation with contacts and relays. This book is organized into five parts encompassing 31 chapters. Part I deals with the principles and application of Boolean algebra and the theory of finite fields (Galois fields). Part II emphasizes the importance of the sequential operation of the automata and the variables associated to the current and to the contacts. This part also tackles the recurrence relations that describe operations of the network and the principles of the so-called characteristic equations. Part III reviews the study of networks with secondary elements other than ordinary relays, while Part IV focuses on the fundamentals and application of multi-position contacts. Part V considers several topics related to circuit with electronic elements, including triodes, pentodes, transistors, and cryotrons. This book will be of great value to practicing engineers, mathematicians, and workers in the field of computers.

  • Multidimensional Singular Integrals and Integral Equations

    • 1st Edition
    • S. G. Mikhlin
    • I. N. Sneddon + 2 more
    • English
    Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.

  • A Many-Sorted Calculus Based on Resolution and Paramodulation

    • 1st Edition
    • Christoph Walther
    • English
    A Many-Sorted Calculus Based on Resolution and Paramodulation emphasizes the utilization of advantages and concepts of many-sorted logic for resolution and paramodulation based automated theorem proving. This book considers some first-order calculus that defines how theorems from given hypotheses by pure syntactic reasoning are obtained, shifting all the semantic and implicit argumentation to the syntactic and explicit level of formal first-order reasoning. This text discusses the efficiency of many-sorted reasoning, formal preliminaries for the RP- and ?RP-calculus, and many-sorted term rewriting and unification. The completeness and soundness of the ?RP-calculus, sort theorem, and automated theorem prover for the ?RP-calculus are also elaborated. This publication is a good source for students and researchers interested in many-sorted calculus.

  • Elements of Analytical Dynamics

    • 1st Edition
    • Rudolph Kurth
    • I. N. Sneddon + 1 more
    • English
    Elements of Analytical Dynamics deals with dynamics, which studies the relationship between motion of material bodies and the forces acting on them. This book is a compilation of lectures given by the author at the Georgia and Institute of Technology and formed a part of a course in Topological Dynamics. The book begins by discussing the notions of space and time and their basic properties. It then discusses the Hamilton-Jacobi theory and Hamilton's principle and first integrals. The text concludes with a discussion on Jacobi's geometric interpretation of conservative systems. This book will be of direct use to graduate students of Mathematics with minimal background in Theoretical Mechanics.

  • Lie Algebras

    • 1st Edition
    • Volume 104
    • Zhe-Xian Wan
    • I. N. Sneddon + 1 more
    • English
    Lie Algebras is based on lectures given by the author at the Institute of Mathematics, Academia Sinica. This book discusses the fundamentals of the Lie algebras theory formulated by S. Lie. The author explains that Lie algebras are algebraic structures employed when one studies Lie groups. The book also explains Engel's theorem, nilpotent linear Lie algebras, as well as the existence of Cartan subalgebras and their conjugacy. The text also addresses the Cartan decompositions and root systems of semi-simple Lie algebras and the dependence of structure of semi-simple Lie algebras on root systems. The text explains in details the fundamental systems of roots of semi simple Lie algebras and Weyl groups including the properties of the latter. The book addresses the group of automorphisms and the derivation algebra of a Lie algebra and Schur's lemma. The book then shows the characters of irreducible representations of semi simple Lie algebras. This book can be useful for students in advance algebra or who have a background in linear algebra.

  • Representations of Commonsense Knowledge

    • 1st Edition
    • Ernest Davis
    • Ronald J. Brachman
    • English
    Representations of Commonsense Knowledge provides a rich language for expressing commonsense knowledge and inference techniques for carrying out commonsense knowledge. This book provides a survey of the research on commonsense knowledge. Organized into 10 chapters, this book begins with an overview of the basic ideas on artificial intelligence commonsense reasoning. This text then examines the structure of logic, which is roughly analogous to that of a programming language. Other chapters describe how rules of universal validity can be applied to facts known with absolute certainty to deduce other facts known with absolute certainty. This book discusses as well some prominent issues in plausible inference. The final chapter deals with commonsense knowledge about the interrelations and interactions among agents and discusses some issues in human and social interactions that have been studied in the artificial intelligence literature. This book is a valuable resource for students on a graduate course on knowledge representation.

  • Lectures in General Algebra

    • 1st Edition
    • A. G. Kurosh
    • I. N. Sneddon + 2 more
    • English
    Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the convenience of constructing a single theory from the results of group experiments and ring experiments which are known to follow simple corollaries. The text also presents algebraic structures that are not of binary nature. From this parallelism arise other concepts, such as that of the lattices, complete lattices, and modular lattices. The book then proves the Schmidt-Ore theorem, and also describes linear algebra, as well as the Birkhoff-Witt theorem on Lie algebras. The text also addresses ordered groups, the Archimedean groups and rings, and Albert's theorem on normed algebras. This book can prove useful for algebra students and for professors of algebra and advanced mathematicians.

  • The Theory of Finitely Generated Commutative Semigroups

    • 1st Edition
    • L. Rédei
    • I. N. Sneddon + 2 more
    • English
    The Theory of Finitely Generated Commutative Semigroups describes a theory of finitely generated commutative semigroups which is founded essentially on a single "fundamental theorem" and exhibits resemblance in many respects to the algebraic theory of numbers. The theory primarily involves the investigation of the F-congruences (F is the the free semimodule of the rank n, where n is a given natural number). As applications, several important special cases are given. This volume is comprised of five chapters and begins with preliminaries on finitely generated commutative semigroups before turning to a discussion of the problem of determining all the F-congruences as the fundamental problem of the proposed theory. The next chapter lays down the foundations of the theory by defining the kernel functions and the fundamental theorem. The elementary properties of the kernel functions are then considered, along with the ideal theory of free semimodules of finite rank. The final chapter deals with the isomorphism problem of the theory, which is solved by reducing it to the determination of the equivalent kernel functions. This book should be of interest to mathematicians as well as students of pure and applied mathematics.

  • Handbook of Mathematics

    • 1st Edition
    • L. Kuipers + 1 more
    • English
    International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examples), Rolle's theorem, and the logarithmic function. The book also discusses extensively the functions of two variables in partial differentiation and multiple integrals. The book then describes the theory of functions, ordinary differential functions, special functions and the topic of sequences and series. The book explains vector analysis (which includes dyads and tensors), the use of numerical analysis, probability statistics, and the Laplace transform theory. Physicists, engineers, chemists, biologists, and statisticians will find this book useful.

  • Introduction to Set Theory and Topology

    • 2nd Edition
    • Kazimierz Kuratowski
    • I. S. Sneddon + 1 more
    • English
    Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.

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