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Mathematical Techniques of Operational Research

  • 1st Edition
  • Volume 38
  • July 17, 2014
  • L. S. Goddard
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 8 0 6 0 - 1
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.

Abelian Groups

  • 3rd Edition
  • Volume 12
  • July 15, 2014
  • L. Fuchs
  • J. P. Kahane + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 8 0 9 0 - 5
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.

Linear Representations of the Lorentz Group

  • 1st Edition
  • Volume 63
  • July 15, 2014
  • M. A. Naimark
  • H. K. Farahat
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 8 4 9 8 - 2
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.

Mathematical Analysis

  • 1st Edition
  • Volume 69
  • July 15, 2014
  • L. A. Lyusternik + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 9 4 3 6 - 3
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.

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

  • 1st Edition
  • Volume 97
  • July 15, 2014
  • L. Redei
  • I. N. Sneddon + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 8 2 7 0 - 1
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.

Some Topics in Complex Analysis

  • 1st Edition
  • Volume 86
  • July 15, 2014
  • E. G. Phillips
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 8 2 7 2 - 5
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.

The Theory of Lebesgue Measure and Integration

  • 1st Edition
  • Volume 15
  • July 14, 2014
  • S. Hartman + 1 more
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 8 0 3 3 - 2
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.

Elements of Linear Space

  • 1st Edition
  • Volume 26
  • July 14, 2014
  • A. R. Amir-Moez + 1 more
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 7 9 0 9 - 1
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.

A Collection of Problems on a Course of Mathematical Analysis

  • 1st Edition
  • July 14, 2014
  • G. N. Berman
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 8 4 8 4 - 5
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.

Non-Linear Differential Equations

  • 1st Edition
  • Volume 67
  • July 14, 2014
  • G. Sansone + 1 more
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 8 5 0 5 - 7
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.