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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.

  • Object-Oriented Simulation with Hierarchical, Modular Models

    Intelligent Agents and Endomorphic Systems
    • 1st Edition
    • Bernard P. Zeigler
    • English
    Object-Oriented Simulation with Hierarchical, Modular Models: Intelligent Agents and Endomorphic Systems describes an approach to object-oriented discrete event simulation and the concepts of hierarchical, modular model construction, The implementation of the concepts of multifaceted modeling methodology in the DEVS-Scheme modeling and simulation environment is discussed. The use of the DEVS-Scheme environment in modeling artificial intelligent agents is also considered, along with the concept of endomorphism to characterize the application of self-embedded models, including models of self. Comprised of 15 chapters, this book begins with an overview of the dimensions of knowledge representation in simulation environments, followed by a discussion on object-oriented programming as well as the concepts of modular, hierarchical models and the system entity structure. Subsequent chapters focus on digraph-models and experimental frames; DEVS formalism and DEVS-Scheme simulation environment; a model base for simple multi-computer architectures; and rule-based specification of atomic models. Model bases in endomorphic systems and intelligent agents are also examined. This monograph will be of interest to simulation theorists as well as practitioners and researchers in the fields of artificial intelligence, systems engineering, computer science and engineering, and operations research.

  • Generalized Inverses and Applications

    Proceedings of an Advanced Seminar Sponsored by the Mathematics Research Center, the University of Wisconsin—Madison, October 8 - 10, 1973
    • 1st Edition
    • M. Zuhair Nashed
    • English
    Generalized Inverses and Applications, contains the proceedings of an Advanced Seminar on Generalized Inverses and Applications held at the University of Wisconsin-Madison on October 8-10, 1973 under the auspices of the university's Mathematics Research Center. The seminar provided a forum for discussing the basic theory of generalized inverses and their applications to analysis and operator equations. Numerical analysis and approximation methods are considered, along with applications to statistics and econometrics, optimization, system theory, and operations research. Comprised of 14 chapters, this book begins by describing a unified approach to generalized inverses of linear operators, with particular reference to algebraic, topological, extremal, and proximinal properties. The reader is then introduced to the algebraic aspects of the generalized inverse of a rectangular matrix; the Fredholm pseudoinverse; and perturbations and approximations for generalized inverses and linear operator equations. Subsequent chapters deal with various applications of generalized inverses, including programming, games, and networks, as well as estimation and aggregation in econometrics. This monograph will be of interest to mathematicians and students of mathematics.

  • Constrained Optimization and Lagrange Multiplier Methods

    • 1st Edition
    • Dimitri P. Bertsekas
    • Werner Rheinboldt
    • English
    Computer Science and Applied Mathematics: Constrained Optimization and Lagrange Multiplier Methods focuses on the advancements in the applications of the Lagrange multiplier methods for constrained minimization. The publication first offers information on the method of multipliers for equality constrained problems and the method of multipliers for inequality constrained and nondifferentiable optimization problems. Discussions focus on approximation procedures for nondifferentiable and ill-conditioned optimization problems; asymptotically exact minimization in the methods of multipliers; duality framework for the method of multipliers; and the quadratic penalty function method. The text then examines exact penalty methods, including nondifferentiable exact penalty functions; linearization algorithms based on nondifferentiable exact penalty functions; differentiable exact penalty functions; and local and global convergence of Lagrangian methods. The book ponders on the nonquadratic penalty functions of convex programming. Topics include large scale separable integer programming problems and the exponential method of multipliers; classes of penalty functions and corresponding methods of multipliers; and convergence analysis of multiplier methods. The text is a valuable reference for mathematicians and researchers interested in the Lagrange multiplier methods.

  • Algebra, Topology, and Category Theory

    A Collection of Papers in Honor of Samuel Eilenberg
    • 1st Edition
    • Alex Heller + 1 more
    • English
    Algebra, Topology, and Category Theory: A Collection of Papers in Honor of Samuel Eilenberg is a collection of papers dealing with algebra, topology, and category theory in honor of Samuel Eilenberg. Topics covered range from large modules over artin algebras to two-dimensional Poincaré duality groups, along with the homology of certain H-spaces as group ring objects. Variable quantities and variable structures in topoi are also discussed. Comprised of 16 chapters, this book begins by looking at the relationship between the representation theories of finitely generated and large (not finitely generated) modules over an artin algebra. The reader is then introduced to reduced bar constructions on deRham complexes; some properties of two-dimensional Poincaré duality groups; and properties invariant within equivalence types of categories. Subsequent chapters explore the work of Samuel Eilenberg in topology; local complexity of finite semigroups; global dimension of ore extensions; and the spectrum of a ringed topos. This monograph will be a useful resource for students and practitioners of algebra and mathematics.

  • Statistical Methods and the Improvement of Data Quality

    • 1st Edition
    • Tommy Wright
    • English
    Statistical Methods and the Improvement of Data Quality contains the proceedings of The Small Conference on the Improvement of the Quality of Data Collected by Data Collection Systems, held on November 11-12, 1982, in Oak Ridge, Tennessee. The conference provided a forum for discussing the use of statistical methods to improve data quality, with emphasis on the problems of data collection systems and how to handle them using state-of-the-art techniques. Comprised of 16 chapters, this volume begins with an overview of some of the limitations of surveys, followed by an annotated bibliography on frames from which the probability sample is selected. The reader is then introduced to sample designs and methods for collecting data over space and time; response effects to behavior and attitude questions; and how to develop and use error profiles. Subsequent chapters focus on principles and methods for handling outliers in data sets; influence functions, outlier detection, and data editing; and application of pattern recognition techniques to data analysis. The use of exploratory data analysis as an aid in modeling and statistical forecasting is also described. This monograph is likely to be of primary benefit to students taking a general course in survey sampling techniques, and to individuals and groups who deal with large data collection systems and are constantly seeking ways to improve the overall quality of their data.

  • Numerical and Computer Methods in Structural Mechanics

    • 1st Edition
    • Steven J. Fenves + 2 more
    • English
    Numerical and Computer Methods in Structural Mechanics is a compendium of papers that deals with the numerical methods in structural mechanics, computer techniques, and computer capabilities. Some papers discus the analytical basis of the computer technique most widely used in software, that is, the finite element method. This method includes the convergence (in terms of variation principles) isoparametrics, hybrid models, and incompatible displacement models. Other papers explain the storage or retrieval of data, as well as equation-solving algorithms. Other papers describe general-purpose structural mechanics programs, alternatives to, and extension of the usual finite element approaches. Another paper explores nonlinear, dynamic finite element problems, and a direct physical approach to determine finite difference models. Special papers explain structural mechanics used in computing, particularly, those related to integrated data bases, such as in the Structures Oriented Exchange System of the Office of Naval Research and the integrated design of tanker structures. Other papers describe software and hardware capabilities, for example, in ship design, fracture mechanics, biomechanics, and crash safety. The text is suitable for programmers, computer engineers, researchers, and scientists involved in materials and industrial design.

  • Computer Arithmetic and Self-Validating Numerical Methods

    • 1st Edition
    • Christian Ullrich
    • English
    Notes and Reports in Mathematics in Science and Engineering, Volume VII: Computer Arithmetic and Self-Validating Numerical Methods compiles papers presented at the first international conference on “Computer Arithmetic and Self-Validating Numerical Methods,” held in Basel from October 2 to 6, 1989. This book begins by providing a tutorial introduction to computer arithmetic with operations of maximum accuracy, differentiation arithmetic and enclosure methods, and programming languages for self-validating numerical methods. The rest of the chapters discuss the determination of guaranteed bounds for eigenvalues by variational methods and guaranteed inclusion of solutions of differential equations. An appendix covering the IMACS-GAMM resolution on computer arithmetic is provided at the end of this publication. This volume is recommended for researchers and professionals working on computer arithmetic and self-validating numerical methods.

  • Introduction to Probability Models

    • 5th Edition
    • Sheldon M. Ross
    • English
    Introduction to Probability Models, Fifth Edition focuses on different probability models of natural phenomena. This edition includes additional material in Chapters 5 and 10, such as examples relating to analyzing algorithms, minimizing highway encounters, collecting coupons, and tracking the AIDS virus. The arbitrage theorem and its relationship to the duality theorem of linear program are also covered, as well as how the arbitrage theorem leads to the Black-Scholes option pricing formula. Other topics include the Bernoulli random variable, Chapman-Kolmogorov equations, and properties of the exponential distribution. The continuous-time Markov chains, single-server exponential queueing system, variations on Brownian motion; and variance reduction by conditioning are also elaborated. This book is a good reference for students and researchers conducting work on probability models.

  • Introduction to Numerical Computations

    • 2nd Edition
    • James S. Vandergraft
    • Werner Rheinboldt
    • English
    Computer Science and Applied Mathematics: Introduction to Numerical Computations, Second Edition introduces numerical algorithms as they are used in practice. This edition covers the usual topics contained in introductory numerical analysis textbooks that include all of the well-known and most frequently used algorithms for interpolation and approximation, numerical differentiation and integration, solution of linear systems and nonlinear equations, and solving ordinary differential equations. A complete discussion of computer arithmetic, problems that arise in the computer evaluation of functions, and cubic spline interpolation are also provided. This text likewise discusses the Newton formulas for interpolation and adaptive methods for integration. The level of this book is suitable for advanced undergraduate students and readers with elementary mathematical background.

  • Mathematical Techniques of Applied Probability

    Discrete Time Models: Basic Theory
    • 1st Edition
    • Jeffrey J. Hunter
    • J. William Schmidt
    • English
    Mathematical Techniques of Applied Probability, Volume 1: Discrete Time Models: Basic Theory provides information pertinent to the basic theory of discrete time models. This book introduces the tools of generating functions and matrix theory to facilitate a detailed study of such models. Organized into five chapters, this volume begins with an overview of the elementary theory of probability for discrete random variables. This text then reviews the concepts of convergence, absolute convergence, uniform convergence, continuity, differentiation, and integration. Other chapters consider the occurrence of general patterns of successes and failures in Bernoulli trials. This book discusses as well the matrix theory, which is used in the study of stochastic processes, particularly in the analysis of the behavior of Markov chains. The final chapter deals with the properties of a special class of discrete time chains. This book is a valuable resource for students and teachers.

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