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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.

  • Entire Functions

    • 1st Edition
    • A. I. Markushevich
    • English
    Entire Functions focuses on complex numbers and the algebraic operations on them and the basic principles of mathematical analysis. The book first elaborates on the concept of an entire function, including the natural generalization of the concept of a polynomial and power series. The text then takes a look at the maximum absolute value and the order of an entire function, as well as calculations for the coefficients of power series representing a given function, use of integrals, and complex numbers. The publication elaborates on the zeros of an entire function and the fundamental theorem of algebra and Picard’s little theorem. Calculations for the zeros of an entire function and numerical representations of Liouville's theorem and Picard’s little theorem are presented. The book also examines algebraic relationships and addition theorems, including an explanation of Weierstrass' theorem and Picard’s little theorem. The manuscript is a vital reference for students interested in the numerical approaches involved in entire functions.

  • Failure-Tolerant Computer Design

    • 1st Edition
    • William H. Pierce
    • English
    Failure-Tolerant Computer Design focuses on the use of redundancy theory in improving the reliability of computers. The book first offers information on redundancy theory and limit theorems. Discussions focus on applications in determining the optimum placement of restoring organs; time asymptotes for log failure probability for exponential survival probability; reliability of multiple-function system with paralleled individual units; and basic concepts for making reliable computers out of unreliable parts. The text then examines decision theory in redundant systems and adaptive decision elements. The publication examines the interconnection structure for redundant logic and redundant relay theory. Topics include Moore-Shannon limit theorem; systematic groupings of inputs in single-layer error-correcting interwoven redundant logic; interwoven logic with alternating-layer error correction; and interwoven logic with single-layer error correction. The book also elaborates on transition analyses in reliability theory, including Markov chain theory and probability bounds in Markov chains having many states or inexactly known transition matrices. The manuscript is a vital source of data for engineers and researchers interested in failure-tolerant computer design.

  • Functional Equations in Probability Theory

    • 1st Edition
    • Ramachandran Balasubrahmanyan + 1 more
    • English
    Functional Equations in Probability Theory deals with functional equations in probability theory and covers topics ranging from the integrated Cauchy functional equation (ICFE) to stable and semistable laws. The problem of identical distribution of two linear forms in independent and identically distributed random variables is also considered, with particular reference to the context of the common distribution of these random variables being normal. Comprised of nine chapters, this volume begins with an introduction to Cauchy functional equations as well as distribution functions and characteristic functions. The discussion then turns to the nonnegative solutions of ICFE on R+; ICFE with a signed measure; and application of ICFE to the characterization of probability distributions. Subsequent chapters focus on stable and semistable laws; ICFE with error terms on R+; independent/identica... distributed linear forms and the normal laws; and distribution problems relating to the arc-sine, the normal, and the chi-square laws. The final chapter is devoted to ICFE on semigroups of Rd. This book should be of interest to mathematicians and statisticians.

  • Topology

    Volume I
    • 1st Edition
    • K. Kuratowski
    • English
    Topology, Volume I deals with topology and covers topics ranging from operations in logic and set theory to Cartesian products, mappings, and orderings. Cardinal and ordinal numbers are also discussed, along with topological, metric, and complete spaces. Great use is made of closure algebra. Comprised of three chapters, this volume begins with a discussion on general topological spaces as well as their specialized aspects, including regular, completely regular, and normal spaces. Fundamental notions such as base, subbase, cover, and continuous mapping, are considered, together with operations such as the exponential topology and quotient topology. The next chapter is devoted to the study of metric spaces, starting with more general spaces, having the limit as its primitive notion. The space is assumed to be metric separable, and this includes problems of cardinality and dimension. Dimension theory and the theory of Borei sets, Baire functions, and related topics are also discussed. The final chapter is about complete spaces and includes problems of general function theory which can be expressed in topological terms. The book includes two appendices, one on applications of topology to mathematical logics and another to functional analysis. This monograph will be helpful to students and practitioners of algebra and mathematics.

  • Computer Programming and Computer Systems

    • 1st Edition
    • Anthony Hassitt
    • Anthony Ralston
    • English
    Computer Programming and Computer Systems imparts a “reading knowledge” of computer systems. This book describes the aspects of machine-language programming, monitor systems, computer hardware, and advanced programming that every thorough programmer should be acquainted with. This text discusses the automatic electronic digital computers, symbolic language, Reverse Polish Notation, and Fortran into assembly language. The routine for reading blocked tapes, dimension statements in subroutines, general-purpose input routine, and efficient use of memory are also elaborated. This publication is intended as an introduction to modern programming practices for professional programmers, but is also valuable to research workers in science, engineering, academic, and industrial fields who are using computers.

  • Distributed Computer Systems

    Theory and Practice
    • 1st Edition
    • H. S. M. Zedan
    • English
    Distributed Computer Systems: Theory and Practice is a collection of papers dealing with the design and implementation of operating systems, including distributed systems, such as the amoeba system, argus, Andrew, and grapevine. One paper discusses the concepts and notations for concurrent programming, particularly language notation used in computer programming, synchronization methods, and also compares three classes of languages. Another paper explains load balancing or load redistribution to improve system performance, namely, static balancing and adaptive load balancing. For program efficiency, the user can choose from various debugging approaches to locate or fix errors without significantly disturbing the program behavior. Examples of debuggers pertain to the ada language and the occam programming language. Another paper describes the architecture of a real-time distributed database system used for computer network management, monitoring integration, as well as administration and control of both local area or wide area communications networks. The book can prove helpful to programmers, computer engineers, computer technicians, and computer instructors dealing with many aspects of computers, such as programming, hardware interface, networking, engineering or design.

  • Mathematical Theory of Probability and Statistics

    • 1st Edition
    • Richard von Mises
    • Hilda Geiringer
    • English
    Mathematical Theory of Probability and Statistics focuses on the contributions and influence of Richard von Mises on the processes, methodologies, and approaches involved in the mathematical theory of probability and statistics. The publication first elaborates on fundamentals, general label space, and basic properties of distributions. Discussions focus on Gaussian distribution, Poisson distribution, mean value variance and other moments, non-countable label space, basic assumptions, operations, and distribution function. The text then ponders on examples of combined operations and summation of chance variables characteristic function. The book takes a look at the asymptotic distribution of the sum of chance variables and probability inference. Topics include inference from a finite number of observations, law of large numbers, asymptotic distributions, limit distribution of the sum of independent discrete random variables, probability of the sum of rare events, and probability density. The text also focuses on the introduction to the theory of statistical functions and multivariate statistics. The publication is a dependable source of information for researchers interested in the mathematical theory of probability and statistics

  • Nonlinear Systems and Applications

    An International Conference
    • 1st Edition
    • V. Lakshmikantham
    • English
    Nonlinear Systems and Applications: An International Conference contains the proceedings of an International Conference on Nonlinear Systems and Applications held at the University of Texas at Arlington, on July 19-23, 1976. The conference provided a forum for reviewing advances in nonlinear systems and their applications and tackled a wide array of topics ranging from abstract evolution equations and nonlinear semigroups to controllability and reachability. Various methods used in solving equations are also discussed, including approximation techniques for delay systems. Most of the applications are in the area of the life sciences. Comprised of 59 chapters, this book begins with a discussion on monotonically convergent upper and lower bounds for classes of conflicting populations, followed by an analysis of constrained problems. The reader is then introduced to approximation techniques for delay systems in biological models; differential inequalities for Liapunov functions; and stability or chaos in discrete epidemic models. Subsequent chapters deal with nonlinear boundary value problems for elliptic systems; bounds for solutions of reaction-diffusion equations; monotonicity and measurability; and periodic solutions of some integral equations from the theory of epidemics. This monograph will be helpful to students, practitioners, and researchers in the field of mathematics.

  • Topological Spaces

    • 1st Edition
    • H. J. Kowalsky
    • English
    Topological Spaces focuses on the applications of the theory of topological spaces to the different branches of mathematics. The book first offers information on elementary principles, topological spaces, and compactness and connectedness. Discussions focus on locally compact spaces, local connectedness, fundamental concepts and their reformulations, lattice of topologies, axioms of separation, fundamental concepts of set theory, and ordered sets and lattices. The manuscript then ponders on mappings and extensions and characterization of topological spaces, including completely regular spaces, transference of topologies, Wallman compactification, and embeddings. The publication takes a look at metric and uniform spaces and applications of topological groups. Topics include the Stone-Weierstrass Approximation Theorem, extensions and completions of topological groups, topological rings and fields, extension and completion of uniform spaces, uniform continuity and uniform convergence, metric spaces, and metritization. The text is a valuable reference for mathematicians and researchers interested in the study of topological spaces.

  • Functional Analysis and Numerical Mathematics

    • 1st Edition
    • Lothar Collatz
    • English
    Functional Analysis and Numerical Mathematics focuses on the structural changes which numerical analysis has undergone, including iterative methods, vectors, integral equations, matrices, and boundary value problems. The publication first examines the foundations of functional analysis and applications, including various types of spaces, convergence and completeness, operators in Hilbert spaces, vector and matrix norms, eigenvalue problems, and operators in pseudometric and other special spaces. The text then elaborates on iterative methods. Topics include the fixed-point theorem for a general iterative method in pseudometric spaces; special cases of the fixed-point theorem and change of operator; iterative methods for differential and integral equations; and systems of equations and difference methods. The manuscript takes a look at monotonicity, inequalities, and other topics, including monotone operators, applications of Schauder's theorem, matrices and boundary value problems of monotone kind, discrete Chebyshev approximation and exchange methods, and approximation of functions. The publication is a valuable source of data for mathematicians and researchers interested in functional analysis and numerical mathematics.

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