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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.

  • The Knowledge Level in Expert Systems

    Conversations and Commentary
    • 1st Edition
    • Luc Steels + 1 more
    • English
    The Knowledge Level In Expert Systems: Conversations and Commentary deals with artificial intelligence, cognitive science, qualitative models, problem solving architectures, construction of knowledge bases, machine learning integration, knowledge sharing or reusability, and mapping problem-solving methods. The book tackles two opposing dogmas: first, that control is generic so is in the inference engine; and two, deep and surface knowledge are different so deep knowledge belongs in a performance system. The text also explains how to use SPARK, a selection method, in approaching the task features that can be used to select or construct the problem-solving method suitable for the task. An alternative method to SPARK starts with an analysis of the domain model and a classification using primitive inference steps. The book also adds that expert problem solving is a form of qualitative modeling that connects other expert systems and engineering. The text then describes very large knowledge bases, particularly, the volume of which knowledge bases can be integrated with expert systems, coherence maintenance, and use/neutral representation of knowledge. Task analysis and method selection focuses on SPARK; how theories about the relation between task features and expert system solutions can be empirically validated. The book also enumerates the benefits and limitations of a generic task approach, and how various modules with their specific internal architectures can be integrated. Programmers, computer engineers, computer technicians, and computer instructors dealing with many aspects of computers such as programming, networking, engineering or design will find the book highly useful.

  • Surveys in General Topology

    • 1st Edition
    • George M. Reed
    • English
    Surveys in General Topology presents topics relating to general topology ranging from closed mappings and ultrafilters to covering and separation properties of box products. Ordered topological spaces and the use of combinatorial techniques in functional analysis are also considered, along with product spaces and weakly compact subsets of Banach spaces. Applications of stationary sets in topology are presented as well. Comprised of 15 chapters, this volume begins with an analysis of some of the techniques and results in the area of closed mappings, followed by a discussion on the theory of ultrafilters. The reader is then introduced to the question of when a box product of compact spaces is paracompact, and how badly a box product of compact or metrizable spaces can fail to be normal. Subsequent chapters focus on the transfinite dimension; the properties of metacompactness, submetacompactness, and subparacompactness; the dimension of ordered topological spaces; the use of combinatorial techniques for the treatment and solution of fundamental problems in functional analysis, particularly in the isomorphic theory of Banach spaces; and order-theoretic base axioms. This monograph will be of significant value both to researchers in general topology and to mathematicians outside the field who wish an overview of current topics and techniques.

  • Progress in Combinatorial Optimization

    • 1st Edition
    • William R. Pulleyblank
    • English
    Progress in Combinatorial Optimization provides information pertinent to the fundamental aspects of combinatorial optimization. This book discusses how to determine whether or not a particular structure exists. Organized into 21 chapters, this book begins with an overview of a polar characterization of facets of polyhedra obtained by lifting facets of lower dimensional polyhedra. This text then discusses how to obtain bounds on the value of the objective in a graph partitioning problem in terms of spectral information about the graph. Other chapters consider the notion of a triangulation of an oriented matroid and show that oriented matroid triangulation yield triangulations of the underlying polytopes. This book discusses as well the selected results and problems on perfect ad imperfect graphs. The final chapter deals with the weighted parity problem for gammoids, which can be reduced to the weighted graphic matching problem. This book is a valuable resource for mathematicians and research workers.

  • 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.

  • Semigroups

    Proceedings of the Monash University Conference on Semigroups Held at the Monash University, Clayton, Victoria, Australia, October, 1979
    • 1st Edition
    • T. E. Hall + 2 more
    • English
    Semigroups is a collection of papers dealing with models of classical statistics, sequential computing machine, inverse semi-groups. One paper explains the structure of inverse semigroups that leads to P-semigroups or E-unitary inverse semigroups by utilizing the P-theorem of W.D. Nunn. Other papers explain the characterization of divisibility in the category of sets in terms of images and relations, as well as the universal aspects of completely simple semigroups, including amalgamation, the lattice of varieties, and the Hopf property. Another paper explains finite semigroups which are extensions of congruence-free semigroups, where their set of congruences forms a chain. The paper then shows how to construct such semigroups. A finite semigroup (which is decomposable into a direct product of cyclic semigroups which are not groups) is actually uniquely decomposable. One paper points out when a finite semigroup has such a decomposition, and how its non-group cyclic direct factors, if any, can be found. The collection can prove useful for mathematicians, statisticians, students, and professors of higher mathematics or computer science.

  • Special Purpose Computers

    • 1st Edition
    • Berni J. Alder
    • English
    Special Purpose Computers describes special-purpose computers and compares them to general-purpose computers in terms of speed and cost. Examples of computers that were designed for the efficient solution of long established algorithms are given, including Navier-Stokes hydrodynamic solvers, classical molecular dynamic machines, and Ising model computers. Comprised of seven chapters, this volume begins by documenting the progress of the CalTech Concurrent Computation Program and its evolution from computational high-energy physics to a supercomputer initiative, with emphasis on the lessons learned including computer architecture issues and the trade-offs between in-house and commercial development. The reader is then introduced to the QCD Machine, a special-purpose parallel supercomputer that was designed and built to solve the lattice quantum chromodynamics problem. Subsequent chapters focus on the Geometry-Defining Processors and their application to the solution of partial differential equations; the Navier-Stokes computer; parallel processing using the Loosely Coupled Array of Processors (LCAP) system; and the Delft Ising system processor. The design and implementation of the Delft molecular-dynamics processor are also described. This book will be of interest to computer engineers and designers.

  • Methods of Numerical Integration

    • 2nd Edition
    • Philip J. Davis + 1 more
    • Werner Rheinbolt
    • English
    Methods of Numerical Integration, Second Edition describes the theoretical and practical aspects of major methods of numerical integration. Numerical integration is the study of how the numerical value of an integral can be found. This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials. This book will be of great value to theoreticians and computer programmers.

  • Parallel Computations

    • 1st Edition
    • Garry Rodrigue
    • English
    Parallel Computations focuses on parallel computation, with emphasis on algorithms used in a variety of numerical and physical applications and for many different types of parallel computers. Topics covered range from vectorization of fast Fourier transforms (FFTs) and of the incomplete Cholesky conjugate gradient (ICCG) algorithm on the Cray-1 to calculation of table lookups and piecewise functions. Single tridiagonal linear systems and vectorized computation of reactive flow are also discussed. Comprised of 13 chapters, this volume begins by classifying parallel computers and describing techniques for performing matrix operations on them. The reader is then introduced to FFTs and the tridiagonal linear system as well as the ICCG method. Different versions of the conjugate gradient method for solving the time-dependent diffusion equation are considered. Subsequent chapters deal with two- and three-dimensional fluid flow calculations, paying particular attention to the principal issues in designing efficient numerical methods for hydrodynamic calculations; the decisions that a numerical modeler must make to optimize chemically reactive flow simulations; and how to handle disk-to-core data transfer and storage allocation for the solution of the implicit equations for three-dimensional flows. The book also describes the time-split finite difference scheme for solving the two-dimensional Navier-Stokes equation for flows through slotted nozzles. Finally, the large-scale stimulation of plasmas, as carried out on a small computer with an array processor, is discussed. This monograph should be of interest to specialists in computer science.

  • Optical Computing Hardware

    Optical Computing
    • 1st Edition
    • Jürgen Jahns + 1 more
    • Sing H. Lee
    • English
    Optical Computing Hardware provides information pertinent to the advances in the development of optical computing hardware. This book discusses the two application areas, namely, high-performance computing and high-throughput photonic switching. Organized into 11 chapters, this book begins with an overview of the requirements on hardware from s system perspective. This text then presents the self-electro-optic-e... devices (SPEED), the vertical-cavity-surf... emitting microlasers (VCSEL), and the vertical-to-surface transmission electrophotonic device (VSTEP). Other chapters consider the fundamental principles of the devices and their operation either as logic devices or for optical interconnection applications. This book discusses as well the planar optical microlens as an example of a refractive microlens of the gradient-index type and explains the diffractive optical elements. The final chapter describes a method for writing and reading optically in parallel from a three-dimensional matrix by means of two-photon interaction in photochromic organic materials. This book is a valuable resource for engineers, scientists, and researchers.

  • Chaotic Dynamics and Fractals

    • 1st Edition
    • Michael F. Barnsley + 1 more
    • English
    Chaotic Dynamics and Fractals covers the proceedings of the 1985 Conference on Chaotic Dynamics, held at the Georgia Institute of Technology. This conference deals with the research area of chaos, dynamical systems, and fractal geometry. This text is organized into three parts encompassing 16 chapters. The first part describes the nature of chaos and fractals, the geometric tool for some strange attractors, and other complicated sets of data associated with chaotic systems. This part also considers the Henon-Hiles Hamiltonian with complex time, a Henon family of maps from C2 into itself, and the idea of turbulent maps in the course of presenting results on iteration of continuous maps from the unit interval to itself. The second part discusses complex analytic dynamics and associated fractal geometry, specifically the bursts into chaos, algorithms for obtaining geometrical and combinatorial information, and the parameter space for iterated cubic polynomials. This part also examines the differentiation of Julia sets with respects to a parameter in the associated rational map, permitting the formulation of Taylor series expansion for the sets. The third part highlights the applications of chaotic dynamics and fractals. This book will prove useful to mathematicians, physicists, and other scientists working in, or introducing themselves to, the field.

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