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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.

  • Combinatorics on Words

    Progress and Perspectives
    • 1st Edition
    • Larry J. Cummings
    • English
    Combinatorics on Words: Progress and Perspectives covers the proceedings of an international meeting by the same title, held at the University of Waterloo, Canada on August 16-22, 1982. This meeting highlights the diverse aspects of combinatorics on words, including the Thue systems, topological dynamics, combinatorial group theory, combinatorics, number theory, and computer science. This book is organized into four parts encompassing 19 chapters. The first part describes the Thue systems with the Church-Rosser property. A Thue system will be called “Church-Rosser” if two strings are congruent with respect to that system if and only if they have a common descendant, that is, a string that can be obtained applying only rewriting rules that reduce length. The next part deals with the problems related to the encoding of codes and the overlapping of words in rational languages. This part also explores the features of polynomially bounded DOL systems yield codes. These topics are followed by discussions of some combinatorial properties of metrics over the free monoid and the burnside problem of semigroups of matrices. The last part considers the ambiguity types of formal grammars, finite languages, computational complexity of algebraic structures, and the Bracket-context tree functions. This book will be of value to mathematicians and advance undergraduate and graduate students.

  • Nonlinear Elasticity

    Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin—Madison April 16—18, 1973
    • 1st Edition
    • R. W. Dickey
    • English
    Nonlinear Elasticity presents a description of research and result on various nonlinear problems arising in elasticity. This book covers a variety of topics, including shallow elastic membranes, nonlinear elasticity, finite deformations of elastic solids, and nonlinear thermoelasticity. Organized into 11 chapters, this book begins with an overview of the nonlinear theory of buckling of elastic shells. This text then examines the ways in which the energy criterion supplies a necessary condition for asymptotic stability. Other chapters consider some of the phenomena, both physical and mathematical, that typify the large deformation of a nonlinearly elastic body. This book discusses as well the concepts leading to a criterion for instabilities and discusses how the criterion applies to some well-known ideal materials. The final chapter deals with the structure of strong shocks and studies the evolution of such a shock produced by a suddenly-applied strain. This book is a valuable resource for mathematicians.

  • Iterative Solution of Large Linear Systems

    • 1st Edition
    • David M. Young
    • Werner Rheinboldt
    • English
    Iterative Solution of Large Linear Systems describes the systematic development of a substantial portion of the theory of iterative methods for solving large linear systems, with emphasis on practical techniques. The focal point of the book is an analysis of the convergence properties of the successive overrelaxation (SOR) method as applied to a linear system where the matrix is "consistently ordered". Comprised of 18 chapters, this volume begins by showing how the solution of a certain partial differential equation by finite difference methods leads to a large linear system with a sparse matrix. The next chapter reviews matrix theory and the properties of matrices, as well as several theorems of matrix theory without proof. A number of iterative methods, including the SOR method, are then considered. Convergence theorems are also given for various iterative methods under certain assumptions on the matrix A of the system. Subsequent chapters deal with the eigenvalues of the SOR method for consistently ordered matrices; the optimum relaxation factor; nonstationary linear iterative methods; and semi-iterative methods. This book will be of interest to students and practitioners in the fields of computer science and applied mathematics.

  • Statistical Decision Theory and Related Topics

    • 1st Edition
    • Shanti S. Gupta + 1 more
    • English
    Statistical Decision Theory and Related Topics is a collection of the papers presented at the Symposium on Statistical Decision Theory and Related Topics which was held on November 23-25, 1970 at Purdue University. The conference brought together research workers in decision theory and related topics. This volume contains twenty papers presented during the symposium and includes works on molecular studies of evolution, globally optimal procedure for one-sided comparisons, multiple decision theory, outlier detection, empirical Bayes slippage tests, and non-optimality of likelihood ratio tests for sequential detection of signals in Gaussian noise. Mathematicians and statisticians will find the book highly insightful.

  • Graphical Representation of Multivariate Data

    • 1st Edition
    • Peter C. C. Wang
    • English
    Graphical Representation of Multivariate Data is a collection of papers that explores and expands the use of graphical methods to represent multivariate data. One paper explains the application of the graphical representation of k-dimensional data technique as a statistical tool to analyze Soviet foreign policy. The technique encompasses data files, data modifications, and transformations of Soviet foreign policy in 25 countries from 1964 to 1975. The Faces methodology (a representation of multidimensional data developed by Herman Chernoff) analyzes ten sets of these data. Another paper describes the Faces techniques, Andrew's sine curves, Anderson's metroglyphs, which are then compared to Facial representations. Examples show the application of Chernoff Faces at the Los Alamos Scientific Laboratory. The paper considers the technique's main drawback—subjectivit... a positive feature that can be overcome. Another paper agrees that computer-generated faces are a good representations to induce actions on tasks based on multivariate metrical data, The paper also acknowledges that the stereotyping of faces can be useful when making a display. One paper investigates the responsiveness to facial and verbal cues using the Syracuse person perception tool as a measuring tool. The collection is suitable for investigators, professors, or students in mathematics, computer science, or engineering courses. It will also be very helpful for researchers involved in graphical display of multivariate data from a wide range of different fields such as statistics, economics, regional planning, clinical research, social/political science, psychiatric studies, international relations, international trade, and arms transfer.

  • Crime, the Police and Criminal Statistics

    An Analysis of Official Statistics for England and Wales Using Econometric Methods
    • 1st Edition
    • R. A. Carr-Hill + 1 more
    • Peter H. Rossi
    • English
    Crime, The Police and Criminal Statistics: An Analysis of Official Statistics for England and Wales Using Econometric Methods presents a study of the relation between official criminal statistics and the activities which they are supposed to reflect. The book is comprised of three sections: the theoretical background, the empirical argument, and certain implications of the study. The first section discusses the criminological, sociological, and economic theories under consideration in the light of available evidence, and their relevance to the countries and period of the study: England and Wales in the 1960s. The second section describes the techniques employed and the interpretations of the obtained results. The final section considers the examination of the use of official criminal statistics in discussions of policy; and the review of models of suitable or optimum strategies of punishment and deterrence. The monograph will be of interest to criminologists, economists, sociologists, and statisticians.

  • Contributions to Probability

    A Collection of Papers Dedicated to Eugene Lukacs
    • 1st Edition
    • J. Gani + 1 more
    • English
    Contributions to Probability: A Collection of Papers Dedicated to Eugene Lukacs is a collection of papers that reflect Professor Eugene Lukacs’ broad range of research interests. This text celebrates the 75th birthday of Eugene Lukacs, mathematician, teacher, and research worker in probability and mathematical statistics. This book is organized into two parts encompassing 23 chapters. Part I consists of papers in probability theory, limit theorems, and stochastic processes. This part also deals with the continuation and arithmetic of distribution functions, the arc sine law, Fourier transform methods, and nondifferentiality of the Wiener sheet. Part II includes papers in information and statistical theories. This book will prove useful to statisticians, mathematicians, and advance mathematics students.

  • Geometry and Combinatorics

    • 1st Edition
    • J. J. Seidel
    • D. G. Corneil + 1 more
    • English
    Geometry and Combinatorics: Selected Works of J. J. Seidel brings together some of the works of J. J. Seidel in geometry and combinatorics. Seidel's selected papers are divided into four areas: graphs and designs; lines with few angles; matrices and forms; and non-Euclidean geometry. A list of all of Seidel's publications is included. Comprised of 29 chapters, this book begins with a discussion on equilateral point sets in elliptic geometry, followed by an analysis of strongly regular graphs of L2-type and of triangular type. The reader is then introduced to strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3; graphs related to exceptional root systems; and equiangular lines. Subsequent chapters deal with the regular two-graph on 276 vertices; the congruence order of the elliptic plane; equi-isoclinic subspaces of Euclidean spaces; and Wielandt's visibility theorem. This monograph will be of interest to students and practitioners in the field of mathematics.

  • Reliability in Computing

    The Role of Interval Methods in Scientific Computing
    • 1st Edition
    • Ramon E. Moore
    • English
    Perspectives in Computing, Vol. 19: Reliability in Computing: The Role of Interval Methods in Scientific Computing presents a survey of the role of interval methods in reliable scientific computing, including vector arithmetic, language description, convergence, and algorithms. The selection takes a look at arithmetic for vector processors, FORTRAN-SC, and reliable expression evaluation in PASCAL-SC. Discussions focus on interval arithmetic, optimal scalar product, matrix and vector arithmetic, transformation of arithmetic expressions, development of FORTRAN-SC, and language description with examples. The text then examines floating-point standards, algorithms for verified inclusions, applications of differentiation arithmetic, and interval acceleration of convergence. The book ponders on solving systems of linear interval equations, interval least squares, existence of solutions and iterations for nonlinear equations, and interval methods for algebraic equations. Topics include interval methods for single equations, diagnosing collinearity, interval linear equations, effects of nonlinearity, and bounding the solutions. The publication is a valuable source of data for computer science experts and researchers interested in the role of interval methods in reliable scientific computing.

  • Optimizing Methods in Statistics

    Proceedings of a Symposium Held at the Center for Tomorrow, the Ohio State University, June 14-16, 1971
    • 1st Edition
    • Jagdish S. Rustagi
    • English
    Optimizing Method in Statistics is a compendium of papers dealing with variational methods, regression analysis, mathematical programming, optimum seeking methods, stochastic control, optimum design of experiments, optimum spacings, and order statistics. One paper reviews three optimization problems encountered in parameter estimation, namely, 1) iterative procedures for maximum likelihood estimation, based on complete or censored samples, of the parameters of various populations; 2) optimum spacings of quantiles for linear estimation; and 3) optimum choice of order statistics for linear estimation. Another paper notes the possibility of posing various adaptive filter algorithms to make the filter learn the system model while the system is operating in real time. By reducing the time necessary for process modeling, the time required to implement the acceptable system design can also be reduced One paper evaluates the parallel structure between duality relationships for the linear functional version of the generalized Neyman-Pearson problem, as well as the duality relationships of linear programming as these apply to bounded-variable linear programming problems. The compendium can prove beneficial to mathematicians, students, and professor of calculus, statistics, or advanced mathematics.

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