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Elsevier

Books in Mathematics general

  • Operational Calculus

    • 2nd Edition
    • Volume 110
    • Thomas K. Boehme
    • I.N. Sneddon
    • English
    Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included. Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and non-homogeneous equations and applications of operational calculus to partial differential equations. The section section deals with the integral of an operational function and its applications, along with integral transformations. A definition of operators in terms of abstract algebra is then presented. Operators as generalized functions, power series of operators, and Laplace transform are also discussed. Formulas of the operational calculus and tables of functions round out the book. This monograph will be useful to engineers, who regard the operational calculus merely as a tool in their work, and readers who are interested in proofs of theorems and mathematical problems.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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

  • 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.

  • 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.