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Elsevier

Libros en Matemáticas

  • Multiple Time Scales

    • 1 Edición
    • Jeremiah U. Brackbill + 1 más
    • Inglés
    Multiple Time Scales presents various numerical methods for solving multiple-time-scale problems. The selection first elaborates on considerations on solving problems with multiple scales; problems with different time scales; and nonlinear normal-mode initialization of numerical weather prediction models. Discussions focus on analysis of observations, nonlinear analysis, systems of ordinary differential equations, and numerical methods for problems with multiple scales. The text then examines the diffusion-synthetic acceleration of transport iterations, with application to a radiation hydrodynamics problem and implicit methods in combustion and chemical kinetics modeling. The publication ponders on molecular dynamics and Monte Carlo simulations of rare events; direct implicit plasma simulation; orbit averaging and subcycling in particle simulation of plasmas; and hybrid and collisional implicit plasma simulation models. Topics include basic moment method, electron subcycling, gyroaveraged particle simulation, and the electromagnetic direct implicit method. The selection is a valuable reference for researchers interested in pursuing further research on the use of numerical methods in solving multiple-time-scale problems.

  • Semigroups

    Proceedings of the Monash University Conference on Semigroups Held at the Monash University, Clayton, Victoria, Australia, October, 1979
    • 1 Edición
    • T. E. Hall + 2 más
    • Inglés
    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.

  • Large Problems, Small Machines

    Transforming Your Programs with Advanced Algorithms
    • 1 Edición
    • Steve Heller
    • Inglés
    Large Problems, Small Machines: Transforming Your Programs with Advanced Algorithms describes a practical, real-world approach to program optimization based on advanced algorithms. Topics covered range from how to save storage using a restricted character set and how to speed up access to records by employing hash coding (or "scatter storage") and caching. A selective mailing list system is used to illustrate rapid access to and rearrangement of information selected by criteria specified at run-time. Comprised of six chapters, this book begins by discussing factors to consider when deciding whether a program needs optimization. In the next chapter, a supermarket price lookup system is used to illustrate how to save storage by using a restricted character set and how to speed up access to records with the aid of hash coding and caching. Attention is paid to rapid retrieval of prices. A selective mailing list system is then used to illustrate rapid access to and rearrangement of information selected by criteria specified at run-time. The book also considers the Huffman coding and arithmetic coding methods of data compression before concluding with a review of the characteristics of the algorithms encountered in previous chapters, as well as the future of the art of optimization. This monograph will be a useful resource for practicing computer programmers and those who intend to be working programmers.

  • Picture Languages

    Formal Models for Picture Recognition
    • 1 Edición
    • Azriel Rosenfeld
    • Werner Rheinboldt
    • Inglés
    Computer Science and Applied Mathematics: Picture Languages: Formal Models for Picture Recognition treats pictorial pattern recognition from the formal standpoint of automata theory. This book emphasizes the capabilities and relative efficiencies of two types of automata—array automata and cellular array automata, with respect to various array recognition tasks. The array automata are simple processors that perform sequences of operations on arrays, while the cellular array automata are arrays of processors that operate on pictures in a highly parallel fashion, one processor per picture element. This compilation also reviews a collection of results on two-dimensional sequential and parallel array acceptors. Some of the analogous one-dimensional results and array grammars and their relation to acceptors are likewise covered in this text. This publication is suitable for researchers, professionals, and specialists interested in pattern recognition and automata theory.

  • A Fête of Topology

    Papers Dedicated to Itiro Tamura
    • 1 Edición
    • Y. Matsumoto + 2 más
    • Inglés
    A Fête of Topology: Papers Dedicated to Itiro Tamura focuses on the progress in the processes, methodologies, and approaches involved in topology, including foliations, cohomology, and surface bundles. The publication first takes a look at leaf closures in Riemannian foliations and differentiable singular cohomology for foliations. Discussions focus on differentiable singular chains restricted to leaves, differentiable singular cohomology for foliations, covering of pseudogroups and fundamental group, normal type of an orbit closure, and construction of a global model. The text then takes a look at measure of exceptional minimal sets of codimension one foliations, examples of exceptional minimal sets, foliations transverse to non-singular Morse-Smale flows, and Chern character for discrete groups. The manuscript ponders on characteristic classes of surface bundles and bounded cohomology, Hill's equation, isomonodromy deformation and characteristic classes, and topology of folds, cusps, and Morin singularities. Topics include system of Hill's equations, Lagrange-Grassman manifold, positive curves, Morse theory, bounded cohomology, and characteristic classes of surface bundles. The publication is a vital source of information for researchers interested in topology.

  • Analysis and Computation of Fixed Points

    Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin—Madison, May 7-8, 1979
    • 1 Edición
    • Stephen M. Robinson
    • Inglés
    Analysis and Computation of Fixed Points contains the proceedings of a Symposium on Analysis and Computation of Fixed Points, held at the University of Wisconsin-Madison on May 7-8, 1979. The papers focus on the analysis and computation of fixed points and cover topics ranging from paths generated by fixed point algorithms to strongly stable stationary solutions in nonlinear programs. A simple reliable numerical algorithm for following homotopy paths is also presented. Comprised of nine chapters, this book begins by describing the techniques of numerical linear algebra that possess attractive stability properties and exploit sparsity, and their application to the linear systems that arise in algorithms that solve equations by constructing piecewise-linear homotopies. The reader is then introduced to two triangulations for homotopy fixed point algorithms with an arbitrary grid refinement, followed by a discussion on some generic properties of paths generated by fixed point algorithms. Subsequent chapters deal with topological perturbations in the numerical study of nonlinear eigenvalue and bifurcation problems; general equilibrium analysis of taxation policy; and solving urban general equilibrium models by fixed point methods. The book concludes with an evaluation of economic equilibrium under deformation of the economy. This monograph should be of interest to students and specialists in the field of mathematics.

  • Computer Aided Geometric Design

    • 1 Edición
    • Robert E. Barnhill + 1 más
    • Inglés
    Computer Aided Geometric Design covers the proceedings of the First International Conference on Computer Aided Geometric Design, held at the University of Utah on March 18-21, 1974. This book is composed of 15 chapters and starts with reviews of the properties of surface patch equation and the use of computers in geometrical design. The next chapters deal with the principles of smooth interpolation over triangles and without twist constraints, as well as the graphical representation of surfaces over triangles and rectangles. These topics are followed by discussions of the B-spline curves and surfaces; mathematical and practical possibilities of UNISURF; nonlinear splines; and some piecewise polynomial alternatives to splines under tension. Other chapters explore the smooth parametric surfaces, the space curve as a folded edge, and the interactive computer graphics application of the parametric bi-cubic surface to engineering design problems. The final chapters look into the three-dimensional human-machine communication and a class of local interpolating splines. This book will prove useful to design engineers.

  • Stochastic Economics

    Stochastic Processes, Control, and Programming
    • 1 Edición
    • Gerhard Tintner + 1 más
    • Inglés
    Stochastic Economics: Stochastic Processes, Control, and Programming presents some aspects of economics from a stochastic or probabilistic point of view. The application of stochastic processes to the theory of economic development, stochastic control theory, and various aspects of stochastic programming is discussed. Comprised of four chapters, this book begins with a short survey of the stochastic view in economics, followed by a discussion on discrete and continuous stochastic models of economic development. The next chapter focuses on methods of stochastic control and their application to dynamic economic models, with emphasis on those aspects connected especially with the theory of quantitative economic policy. Some basic operational problems of applying stochastic control, particularly in economic systems and organizations for problems such as dynamic resource allocation, growth planning, and economic coordination are considered. The last chapter is devoted to stochastic programming, paying particular attention to the decision rule theory of operations research under the chance-constrained model and a method of incorporating reliability measures into a systems reliability model. This book will be of interest to economists, statisticians, applied mathematicians, operations researchers, and systems engineers.

  • A Handbook of Integer Sequences

    • 1 Edición
    • N.J.A. Sloane
    • Inglés
    A Handbook of Integer Sequences contains a main table of 2300 sequences of integers that are collected from all branches of mathematics and science. This handbook describes how to use the main table and provides methods for analyzing and describing unknown and important sequences. This compilation also serves as an index to the literature for locating references on a particular problem and quickly finds numbers such as 712, number of partitions of 30, 18th Catalan number, or expansion of ? to 60 decimal places. Other topics include the method of differences, self-generating sequences, polyominoes, permutations, and puzzle sequences. This publication is a good source for students and researchers who are confronted with strange and important sequences.

  • Finite Permutation Groups

    • 1 Edición
    • Helmut Wielandt
    • Henry Booker + 2 más
    • Inglés
    Finite Permutation Groups provides an introduction to the basic facts of both the theory of abstract finite groups and the theory of permutation groups. This book deals with older theorems on multiply transitive groups as well as on simply transitive groups. Organized into five chapters, this book begins with an overview of the fundamental concepts of notation and Frobenius group. This text then discusses the modifications of multiple transitivity and can be used to deduce an improved form of the classical theorem. Other chapters consider the concept of simply transitive permutation groups. This book discusses as well permutation groups in the framework of representation theory. The final chapter deals with Frobenius' theory of group characters. This book is a valuable resource for engineers, mathematicians, and research workers. Graduate students and readers who are interested in finite permutation groups will also find this book useful.

  • Chaotic Dynamics and Fractals

    • 1 Edición
    • Michael F. Barnsley + 1 más
    • Inglés
    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.

  • Nonlinear Programming 4

    Proceedings of the Nonlinear Programming Symposium 4 Conducted by the Computer Sciences Department at the University of Wisconsin–Madison, July 14-16, 1980
    • 1 Edición
    • Olvi L. Mangasarian + 2 más
    • Inglés
    Nonlinear Programming, 4 focuses on linear, quadratic, and nonlinear programming, unconstrained minimization, nonsmooth and discrete optimization, ellipsoidal methods, linear complementarity problems, and software evaluation. The selection first elaborates on an upper triangular matrix method for quadratic programming, solving quadratic programs by an exact penalty function, and QP-based methods for large-scale nonlinearly constrained optimization. Discussions focus on large-scale linearly constrained optimization, search direction for superbasic variables, finite convergence, basic properties, comparison of three active set methods, and QP-based methods for dense problems. The book then examines an iterative linear programming algorithm based on an augmented Lagrangian and iterative algorithms for singular minimization problems. The publication ponders on the derivation of symmetric positive definite secant updates, preconditioned conjugate gradient methods, and finding the global minimum of a function of one variable using the method of constant signed higher order derivatives. Topics include effects of calculation errors, application to polynomial minimization, using moderate additional storage, updating Cholesky factors, and utilizing sparse second order information. The selection is a valuable source of data for researchers interested in nonlinear programming.

  • Asymptotics and Special Functions

    • 1 Edición
    • F. W. J. Olver
    • Werner Rheinbolt
    • Inglés
    Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.

  • An Introduction to Data Base Design

    • 1 Edición
    • Betty Joan Salzberg
    • Inglés
    An Introduction to Data Base Design provides an understanding of how data base management systems (DBMS) work to be able to use any available commercial DBMS intelligently. This book presents the principle of independence of physical and local organization. Organized into seven chapters, this book begins with an overview of normal form theory. This text then describes the three types of DBMS. Other chapters consider the difficulties in processing queries where the names of the files are not mentioned. This book discusses as well how to group data hierarchically, how to use a preorder tree traversal to represent the data, and how to convert a network organization to a hierarchical one. The final chapter deals with four essential issues in data base theory, namely, recovery, security, integrity, and concurrency. This book is a valuable resource for computer science students in the junior or senior year, and people in industry who are doing technical work using data bases.

  • Rewriting Techniques

    Resolution of Equations in Algebraic Structures
    • 1 Edición
    • Hassan Aït-Kaci + 1 más
    • Inglés
    Resolution of Equations in Algebraic Structures: Volume 2, Rewriting Techniques is a collection of papers dealing with the construction of canonical rewrite systems, constraint handling in logic programming, and completion algorithms for conditional rewriting systems. Papers discuss the Knuth-Bendix completion method which constructs a complete system for a given set of equations, including extensions of the method dealing with termination, unfailing completion, and associative-communic... completion. One paper examines the various practical techniques that can be used to extend Prolog as a constraint solver, particularly on techniques that solve boolean equations, imposing inequality, disequality, and finitary domain constraints on variables. Another paper presents a sufficient condition for confluence of conditional rewriting, and a practical unification algorithm modulo conditional rewriting through the notion of conditional narrowing. One paper analyzes the possibility of using completion for inductive proofs in the initial algebra of an equational variety without explicit induction. Another papers discusses solving systems of word equations in the free monoid and the free group, where a solution is defined as a word homomorphism. Programmers, mathematicians, students, and instructors involved in computer science and computer logic will find this collection valuable.

  • Mathematical Aspects of Finite Elements in Partial Differential Equations

    Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, April 1 – 3, 1974
    • 1 Edición
    • Carl de Boor
    • Inglés
    Mathematical Aspects of Finite Elements in Partial Differential Equations addresses the mathematical questions raised by the use of finite elements in the numerical solution of partial differential equations. This book covers a variety of topics, including finite element method, hyperbolic partial differential equation, and problems with interfaces. Organized into 13 chapters, this book begins with an overview of the class of finite element subspaces with numerical examples. This text then presents as models the Dirichlet problem for the potential and bipotential operator and discusses the question of non-conforming elements using the classical Ritz- and least-squares-method... Other chapters consider some error estimates for the Galerkin problem by such energy considerations. This book discusses as well the spatial discretization of problem and presents the Galerkin method for ordinary differential equations using polynomials of degree k. The final chapter deals with the continuous-time Galerkin method for the heat equation. This book is a valuable resource for mathematicians.

  • Interval Mathematics 1980

    • 1 Edición
    • Karl L. E. Nickel
    • Inglés
    Interval Mathematics 1980 contains the proceedings of an International Symposium on Interval Mathematics held in Germany on May 27-31, 1980. The book introduces the reader to some of the most important work done in the field of interval mathematics and its application to computing. Topics covered range from purely theoretical to computational methods and computer architecture. Comprised of 41 chapters, this book begins with an overview of set functions and their applications, followed by a discussion on global constrained optimization using interval analysis. A model for the propagation of rounding error in floating arithmetic is then presented, and the importance of 3-valued notions for interval mathematics is highlighted. Subsequent chapters focus on the transformation of interval programs into convergent interval programs; specifications for interval programming languages; interval contractions for the solution of integral equations; and mean convergence enclosing of solutions of operator equations with convex and inverse monotonic operators. This monograph will be of value to both students and specialists in the fields of mathematics and computer science.

  • Nonlinear Programming 2

    Proceedings of the Special Interest Group on Mathematical Programming Symposium Conducted by the Computer Sciences Department at the University of Wisconsin - Madison, April 15-17, 1974
    • 1 Edición
    • O. L. Mangasarian + 2 más
    • Inglés
    Nonlinear Programming 2 covers the proceedings of the Special Interest Group on Mathematical Programming Symposium conducted by the Computer Sciences Department at the University of Wisconsin, Madison, on April 15-17, 1974. This book is divided into 13 chapters and begins with a survey of the global and superlinear convergence of a class of algorithms obtained by imposing changing bounds on the variables of the problem. The succeeding chapters deal with the convergence of the well-known reduced gradient method under suitable conditions and a superlinearly convergent quasi-Newton method for unconstrained minimization. These topics are followed by discussion of a superlinearly convergent algorithm for linearly constrained optimization problems and the effective methods for constrained optimization, namely the method of augmented Lagrangians. Other chapters explore a method for handling minimization problems with discontinuous derivatives and the advantages of factorizations of updating for Jacobian-related matrices in minimization problems. The last chapters present the Newton-like methods for the solution of nonlinear equations and inequalities, along with the various aspects of integer programming. This book will prove useful to mathematicians and computer scientists.

  • Group Theory and Its Applications

    Volume III
    • 1 Edición
    • Ernest M. Loebl
    • Inglés
    Group Theory and its Applications, Volume III covers the two broad areas of applications of group theory, namely, all atomic and molecular phenomena, as well as all aspects of nuclear structure and elementary particle theory. This volume contains five chapters and begins with an introduction to Wedderburn’s theory to establish the structure of semisimple algebras, algebras of quantum mechanical interest, and group algebras. The succeeding chapter deals with Dynkin’s theory for the embedding of semisimple complex Lie algebras in semisimple complex Lie algebras. These topics are followed by a review of the Frobenius algebra theory, its centrum, its irreducible, invariant subalgebras, and its matric basis. The discussion then shifts to the concepts and application of the Heisenberg-Weyl ring to quantum mechanics. Other chapters explore some well-known results about canonical transformations and their unitary representations; the Bargmann Hilbert spaces; the concept of complex phase space; and the concept of quantization as an eigenvalue problem. The final chapter looks into a theoretical approach to elementary particle interactions based on two-variable expansions of reaction amplitudes. This chapter also demonstrates the use of invariance properties of space-time and momentum space to write down and exploit expansions provided by the representation theory of the Lorentz group for relativistic particles, or the Galilei group for nonrelativistic ones. This book will prove useful to mathematicians, engineers, physicists, and advance students.

  • Solutions for Networked Databases

    How to Move from Heterogeneous Structures to Federated Concepts
    • 1 Edición
    • Dimitris N. Chorafas + 1 más
    • Inglés
    Solutions for Networked Databases: How to Move from Heterogeneous Structures to Federated Concepts reviews developments in standards and ad hoc solutions aimed at providing cross-database connectivity for networked databases. The emphasis is on how to move from heterogeneous structures to federated concepts. The advent of the multidatabase is discussed, along with schemata, dictionaries, and protocols. Applications with federated databases are also considered. Comprised of 18 chapters, this book begins with an introduction to database and knowledge bank concepts; reliability and availability characteristics; and the synergy necessary to create and sustain federated databases. Centralized and distributed databases are then compared, and the different ways of managing distributed databases are outlined. Subsequent chapters focus on the importance of treating the networked database as a corporate resource; the use of schemata to solve cross-database problems; the Information Resource Dictionary System; and application programming interface and remote data access. A solution to heterogeneous distributed databases, the Data Access Integrated Services (DAIS), is described. This monograph is written for specialists in computers and communications.

  • Recent Advances in Numerical Analysis

    Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin-Madison, May 22-24, 1978
    • 1 Edición
    • Carl De Boor + 1 más
    • Inglés
    Recent Advances in Numerical Analysis provides information pertinent to the developments in numerical analysis. This book covers a variety of topics, including positive functions, Sobolev spaces, computing paths, partial differential equations, and perturbation theory. Organized into 12 chapters, this book begins with an overview of stability conditions for numerical methods that can be expressed in the form that some associated function is positive. This text then examines the polynomial approximation theory having applications to finite element Galerkin methods. Other chapters consider the numerical condition of polynomials by examining three particular problem areas, namely, the representation of polynomials, algebraic equations, and the problem of orthogonalization. This book discusses as well a general theory that leads to a systematic way to prepare the initial data. The final chapter deals with the derivation of the Kronecker canonical form. This book is a valuable resource for applied mathematicians, numerical analysts, physicists, engineers, and research workers.

  • Optimal Control of Differential and Functional Equations

    • 1 Edición
    • J. Warga
    • Inglés
    Optimal Control of Differential and Functional Equations presents a mathematical theory of deterministic optimal control, with emphasis on problems involving functional-integral equations and functional restrictions. The book reviews analytical foundations, and discusses deterministic optimal control problems requiring original, approximate, or relaxed solutions. Original solutions involve mathematicians, and approximate solutions concern engineers. Relaxed solutions yield a complete theory that encompasses both existence theorems and necessary conditions. The text also presents general optimal control problems, optimal control of ordinary differential equations, and different types of functional-integral equations. The book discusses control problems defined by equations in Banach spaces, the convex cost functionals, and the weak necessary conditions for an original minimum. The text illustrates a class of ordinary differential problems with examples, and explains some conflicting control problems with relaxed adverse controls, as well as conflicting control problems with hyper-relaxed adverse controls. The book is intended for mature mathematicians, graduate students in analysis, and practitioners of optimal control whose primary interests and training are in science or engineering.

  • Algebraic Geometry and Commutative Algebra

    In Honor of Masayoshi Nagata
    • 1 Edición
    • Hiroaki Hijikata + 2 más
    • Inglés
    Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Nagata presents a collection of papers on algebraic geometry and commutative algebra in honor of Masayoshi Nagata for his significant contributions to commutative algebra. Topics covered range from Weierstrass models and endomorphism algebras of abelian varieties to the generic Torelli theorem for hypersurfaces in compact irreducible hermitian symmetric spaces. Coarse moduli spaces for curves are also discussed, along with discriminants of curves of genus 2 and arithmetic surfaces. Comprised of 14 chapters, this volume begins by describing a basic fibration as a Weierstrass model, with emphasis on elliptic threefolds with a section. The reader is then introduced to canonical bundles of analytic surfaces of class VII0 with curves; Lifting Problem on ideal-adically complete noetherian rings; and the canonical ring of a curve. Subsequent chapters deal with algebraic surfaces for regular systems of weights; elementary transformations of algebraic vector bundles; the irreducibility of the first differential equation of Painlevé; and F-pure normal rings of dimension two. The book concludes with an assessment of the existence of some curves. This monograph will be a useful resource for practitioners and researchers in algebra and geometry.

  • Special Purpose Computers

    • 1 Edición
    • Berni J. Alder
    • Inglés
    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.

  • Mathematical Functions and Their Approximations

    • 1 Edición
    • Yudell L. Luke
    • Inglés
    Mathematical Functions and their Approximations is an updated version of the Applied Mathematics Series 55 Handbook based on the 1954 Conference on Mathematical Tables, held at Cambridge, Massachusetts. The aim of the conference is to determine the need for mathematical tables in view of the availability of high speed computing machinery. This work is composed of 14 chapters that cover the machinery for the expansion of the generalized hypergeometric function and other functions in infinite series of Jacobi and Chebyshev polynomials of the first kind. Numerical coefficients for Chebyshev expansions of the more common functions are tabulated. Other chapters contain polynomial and rational approximations for certain class of G-functions, the coefficients in the early polynomials of these rational approximations, and the Padé approximations for many of the elementary functions and the incomplete gamma functions. The remaining chapters describe the development of analytic approximations and expansions. This book will prove useful to mathematicians, advance mathematics students, and researchers.

  • Generalized Inverses and Applications

    Proceedings of an Advanced Seminar Sponsored by the Mathematics Research Center, the University of Wisconsin—Madison, October 8 - 10, 1973
    • 1 Edición
    • M. Zuhair Nashed
    • Inglés
    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.

  • Introduction to Ordinary Differential Equations

    Second Enlarged Edition with Applications
    • 2 Edición
    • Albert L. Rabenstein
    • Inglés
    Introduction to Ordinary Differential Equations, Second Edition provides an introduction to differential equations. This book presents the application and includes problems in chemistry, biology, economics, mechanics, and electric circuits. Organized into 12 chapters, this edition begins with an overview of the methods for solving single differential equations. This text then describes the important basic properties of solutions of linear differential equations and explains higher-order linear equations. Other chapters consider the possibility of representing the solutions of certain linear differential equations in terms of power series. This book discusses as well the important properties of the gamma function and explains the stability of solutions and the existence of periodic solutions. The final chapter deals with the method for the construction of a solution of the integral equation and explains how to establish the existence of a solution of the initial value system. This book is a valuable resource for mathematicians, students, and research workers.

  • The Knowledge Level in Expert Systems

    Conversations and Commentary
    • 1 Edición
    • Luc Steels + 1 más
    • Inglés
    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.

  • Advanced Programming with Microsoft QuickC

    • 1 Edición
    • Keith Weiskamp
    • Inglés
    Advanced Programming with Microsoft QuickC provides the necessary programming tools for programmers who are interested in learning new skills in developing some useful tools and PC applications using the QuickC programming language. The book emphasizes practical and useful programming examples. It is organized into five sections. The first section introduces the proposed ANSI standard features, tips and techniques about C programming style, working with the C preprocessor, and tips for using pointers and managing memory allocation tasks. Section 2 presents data structures, discussing techniques for constructing useful and reliable data structures from linked lists to binary trees. The third section covers the many tools that QuickC provides for accessing files and other I/O devices. Section 4 explains the techniques for interacting with DOS and the special features of QuickC. The final chapter presents the tools and techniques for developing QuickC-like user interfaces. Computer programmers will find the text very useful.

  • Dynamics and Modelling of Reactive Systems

    Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin—Madison, October 22–24, 1979
    • 1 Edición
    • Warren E. Stewart + 2 más
    • Inglés
    Dynamics and Modelling of Reactive Systems contains the proceedings of the Advanced Seminar on Dynamics and Modeling of Reactive Systems, held at the University of Wisconsin on October 1979. The book presents papers that assess the level of understanding of the dynamics of chemically reacting systems. The topics discussed include the hierarchies of models in reactive systems; model reduction of chemically reacting systems; and some consequences of nonlinearity in the diffusion process. Time-periodic and spatially irregular patterns; important aspects in simulating the dynamics of aerosols; and the diffusion and reaction in carbon burning are covered as well. Engineers and applied mathematicians will find the book highly insightful.

  • Numerical Methods for Partial Differential Equations

    • 2 Edición
    • William F. Ames
    • Werner Rheinboldt + 1 más
    • Inglés
    Numerical Methods for Partial Differential Equations, Second Edition deals with the use of numerical methods to solve partial differential equations. In addition to numerical fluid mechanics, hopscotch and other explicit-implicit methods are also considered, along with Monte Carlo techniques, lines, fast Fourier transform, and fractional steps methods. Comprised of six chapters, this volume begins with an introduction to numerical calculation, paying particular attention to the classification of equations and physical problems, asymptotics, discrete methods, and dimensionless forms. Subsequent chapters focus on parabolic and hyperbolic equations, elliptic equations, and special topics ranging from singularities and shocks to Navier-Stokes equations and Monte Carlo methods. The final chapter discuss the general concepts of weighted residuals, with emphasis on orthogonal collocation and the Bubnov-Galerkin method. The latter procedure is used to introduce finite elements. This book should be a valuable resource for students and practitioners in the fields of computer science and applied mathematics.

  • Group Analysis of Differential Equations

    • 1 Edición
    • L. V. Ovsiannikov
    • Inglés
    Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations. This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the given differential equation with a known admitted group. The theory of differential invariants that is developed on an infinitesimal basis is elaborated in Chapter VII. The last chapter outlines the ways in which the methods of group analysis are used in special issues involving differential equations. This publication is a good source for students and specialists concerned with areas in which ordinary and partial differential equations play an important role.

  • FORTRAN

    • 1 Edición
    • Samuel L. Marateck
    • Inglés
    FORTRAN is written for students who have no prior knowledge of computers or programming. The book aims to teach students how to program using the FORTRAN language. The publication first elaborates on an introduction to computers and programming, introduction to FORTRAN, and calculations and the READ statement. Discussions focus on flow charts, rounding numbers, strings, executing the program, the WRITE and FORMAT statements, performing an addition, input and output devices, and algorithms. The text then takes a look at functions and the IF statement and the DO Loop, the IF-THEN-ELSE and the WHILE loop, including applications of the DO loop, the LOGICAL declaration statement, library functions, other applications of the IF statement, and writing REAL constants in exponential form. The manuscript ponders on subscripted variables, the DATA statement, and the implied DO loop, doubly subscripted variables and matrix multiplication, input/output, and functions, subprograms, and subroutines. Topics include statement functions, subprograms calling other subprograms, reading using X format, control characters, reading using F format, INTEGER subscripted variables, and matrix multiplication. The publication is a dependable source of data for computer programmers and students interested in the FORTRAN language.

  • Advanced Turbo C Programming

    • 1 Edición
    • Keith Weiskamp
    • Inglés
    Advanced Turbo C Programming provides the necessary programming tools for programmers who are interested in learning new skills in developing some useful tools and PC applications using the Turbo C Version 1.5 programming language and environment. This book covers both the advanced programming features of the IBM PC and Turbo C. It is organized into five sections. In Section 1 the proposed ANSI standard features, tips and techniques about C programming style, working with the C preprocessor, and tips for using pointers and managing memory allocation tasks are introduced. Section 2 discusses techniques for constructing useful and reliable data structures from linked lists to binary trees. The third section provides the complete Turbo C I/O system and takes an in-depth look at the many tools that Turbo C provides for accessing files and other I/O devices. Section 4 explains the techniques for interacting with DOS and the special features of Turbo C such as the Borland Graphic Interface (BGI). The final section, Section 5 presents the tools and techniques for developing Turbo C-like user interfaces, such as pop-up windows, pop-up menus, and pulldown menus. Computer programmers will find the text invaluable.

  • Complex Variables

    • 1 Edición
    • Robert B. Ash
    • Inglés
    Complex Variables deals with complex variables and covers topics ranging from Cauchy's theorem to entire functions, families of analytic functions, and the prime number theorem. Major applications of the basic principles, such as residue theory, the Poisson integral, and analytic continuation are given. Comprised of seven chapters, this book begins with an introduction to the basic definitions and concepts in complex variables such as the extended plane, analytic and elementary functions, and Cauchy-Riemann equations. The first chapter defines the integral of a complex function on a path in the complex plane and develops the machinery to prove an elementary version of Cauchy's theorem. Some applications, including the basic properties of power series, are then presented. Subsequent chapters focus on the general Cauchy theorem and its applications; entire functions; families of analytic functions; and the prime number theorem. The geometric intuition underlying the concept of winding number is emphasized. The linear space viewpoint is also discussed, along with analytic number theory, residue theory, and the Poisson integral. This book is intended primarily for students who are just beginning their professional training in mathematics.

  • Stochastic Analysis

    Liber Amicorum for Moshe Zakai
    • 1 Edición
    • Eddy Mayer-Wolf + 2 más
    • Inglés
    Stochastic Analysis: Liber Amicorum for Moshe Zakai focuses on stochastic differential equations, nonlinear filtering, two-parameter martingales, Wiener space analysis, and related topics. The selection first ponders on conformally invariant and reflection positive random fields in two dimensions; real time architectures for the Zakai equation and applications; and quadratic approximation by linear systems controlled from partial observations. Discussions focus on predicted miss, review of basic sequential detection problems, multigrid algorithms for the Zakai equation, invariant test functions and regularity, and reflection positivity. The text then takes a look at a model of stochastic differential equation in Hubert spaces applicable to Navier Stokes equation in dimension 2; wavelets as attractors of random dynamical systems; and Markov properties for certain random fields. The publication examines the anatomy of a low-noise jump filter, nonlinear filtering with small observation noise, and closed form characteristic functions for certain random variables related to Brownian motion. Topics include derivation of characteristic functions for the examples, proof of the theorem, sequential quadratic variation test, asymptotic optimal filters, mean decision time, and asymptotic optimal filters. The selection is a valuable reference for researchers interested in stochastic analysis.

  • Theory and Application of Special Functions

    Proceedings of an Advanced Seminar Sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31-April 2, 1975
    • 1 Edición
    • Richard Askey
    • Inglés
    Theory and Application of Special Functions contains the proceedings of the Advanced Seminar on Special Functions sponsored by the Mathematics Research Center of the University of Wisconsin-Madison and held from March 31 to April 2, 1975. The seminar tackled the theory and application of special functions and covered topics ranging from the asymptotic estimation of special functions to association schemes and coding theory. Some interesting results, conjectures, and problems are given. Comprised of 13 chapters, this book begins with a survey of computational methods in special functions, followed by a discussion on unsolved problems in the asymptotic estimation of special functions. The reader is then introduced to periodic Bernoulli numbers, summation formulas, and applications; problems and prospects for basic hypergeometric functions; and linear growth models with many types and multidimensional Hahn polynomials. Subsequent chapters explore two-variable analogues of the classical orthogonal polynomials; special functions of matrix and single argument in statistics; and some properties of the determinants of orthogonal polynomials. This monograph is intended primarily for students and practitioners of mathematics.

  • An Introduction to Stochastic Modeling

    • 1 Edición
    • Howard M. Taylor + 1 más
    • Inglés
    An Introduction to Stochastic Modeling, Revised Edition provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

  • Software for Roundoff Analysis of Matrix Algorithms

    • 1 Edición
    • Webb Miller + 1 más
    • Inglés
    Computer Science and Applied Mathematics: A Series of Monographs and Textbooks: Software for Roundoff Analysis of Matrix Algorithms focuses on the presentation of techniques and software tools for analyzing the propagation of rounding error in matrix algorithms. The publication looks into some elements of error analysis, concepts from linear algebra and analysis, and directed graphs. Discussions focus on arithmetic graphs, sums of path products, linear transformations, Minkowski sums and Cartesian products, and elementary concepts from analysis. The text then examines software for roundoff analysis, including rounding and perturbations of the computational problem, comparing rounding errors with problem sensitivity, reverse condition numbers, and comparing two algorithms. The book ponders on case studies, as well as Gaussian elimination with iterative improvement, Cholesky factorization, Gauss-Jordan elimination, variants of the Gram-Schmidt method, and Cholesky factors after rank-one modifications. The text is a valuable reference for researchers interested in the techniques and software tools involved in the analysis of the propagation of rounding error in matrix algorithms.

  • Algebraic Analysis

    Papers Dedicated to Professor Mikio Sato on the Occasion of His Sixtieth Birthday
    • 1 Edición
    • Masaki Kashiwara + 1 más
    • Inglés
    Algebraic Analysis: Papers Dedicated to Professor Mikio Sato on the Occasion of his 60th Birthday, Volume II is a collection of research papers on algebraic analysis and related topics in honor to Professor Mikio Sato’s 60th birthday. This volume is divided into 29 chapters and starts with research works concerning the fundamentals of KP equations, strings, Schottky problem, and the applications of transformation theory for nonlinear integrable systems to linear prediction problems and isospectral deformations,. The subsequent chapters contain papers on the approach to nonlinear integrable systems, the Hodge numbers, the stochastic different equation for the multi-dimensional weakly stationary process, and a method of harmonic analysis on semisimple symmetric spaces. These topics are followed by studies on the quantization of extended vortices, moduli space for Fuchsian groups, microfunctions for boundary value problems, and the issues of multi-dimensional integrable systems. The remaining chapters explore the practical aspects of pseudodifferential operators in hyperfunction theory, the elliptic solitons, and Carlson’s theorem for holomorphic functions. This book will prove useful to mathematicians and advance mathematics students.

  • Statistical Methods and the Improvement of Data Quality

    • 1 Edición
    • Tommy Wright
    • Inglés
    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.

  • Nonnegative Matrices in the Mathematical Sciences

    • 1 Edición
    • Abraham Berman + 1 más
    • Inglés
    Nonnegative Matrices in the Mathematical Sciences provides information pertinent to the fundamental aspects of the theory of nonnegative matrices. This book describes selected applications of the theory to numerical analysis, probability, economics, and operations research. Organized into 10 chapters, this book begins with an overview of the properties of nonnegative matrices. This text then examines the inverse-positive matrices. Other chapters consider the basic approaches to the study of nonnegative matrices, namely, geometrical and combinatorial. This book discusses as well some useful ideas from the algebraic theory of semigroups and considers a canonical form for nonnegative idempotent matrices and special types of idempotent matrices. The final chapter deals with the linear complementary problem (LCP). This book is a valuable resource for mathematical economists, mathematical programmers, statisticians, mathematicians, and computer scientists.

  • Probabilistic Methods in Applied Mathematics

    Volume 3
    • 1 Edición
    • A. T. Bharucha-Reid
    • Inglés
    Probabilistic Methods in Applied Mathematics, Volume 3 focuses on the influence of the probability theory on the formulation of mathematical models and development of theories in many applied fields. The selection first offers information on statistically well-set Cauchy problems and wave propagation in random anisotropic media. Discussions focus on extension to biaxial anisotropic random media; an effective medium description for a random uniaxial anisotropic medium and the resulting dyadic Green's function; evolution of the spectral matrix measure; and well-set Cauchy problems. The text then examines stochastic processes in heat and mass transport, including mass transport, velocity field, temperature transport, and coupling of mass and heat transport. The manuscript takes a look at the potential theory for Markov chains and stochastic differential games. Topics include formal solutions for some classes of stochastic linear pursuit-evasion games; solution of a stochastic linear pursuit-evasion game with nonrandom controls; problems of potential theory; and hitting distributions. The selection is a vital source of data for mathematicians and researchers interested in the probability theory.

  • Contributions to Survey Sampling and Applied Statistics

    Papers in Honor of H.O Hartley
    • 1 Edición
    • H. O. Hartley
    • H. A. David
    • Inglés
    Contributions to Survey Sampling and Applied Statistics: Papers in Honor of H. O. Hartley covers the significant advances in survey sampling, modeling, and applied statistics. This book is organized into five parts encompassing 20 chapters. The opening part looks into some aspects of statistics, sampling, randomization, predictive estimation, and internal congruency. This part also considers the properties of variance estimation for a specified multiple frame survey design and some sampling designs involving unequal probabilities of selection and robust estimation of a finite population total. The next parts present the analysis and the theoretical and practical aspects of linear models, as well as the applications of time series analysis. These topics are followed by discussions of the testing for outliers in linear regression; the robustness of location estimators; and completeness comparisons among sample sequences. The closing part deals with the properties of norm estimators in regression and geometric programming. This part also provides tables of the normal conditioned on t-distribution. This book will prove useful to mathematicians and statisticians.

  • Directions in Partial Differential Equations

    Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 28—30, 1985
    • 1 Edición
    • Michael G. Crandall + 2 más
    • Inglés
    Directions in Partial Differential Equations covers the proceedings of the 1985 Symposium by the same title, conducted by the Mathematics Research Center, held at the University of Wisconsin, Madison. This book is composed of 13 chapters and begins with reviews of the calculus of variations and differential geometry. The subsequent chapters deal with the study of development of singularities, regularity theory, hydrodynamics, mathematical physics, asymptotic behavior, and critical point theory. Other chapters discuss the use of probabilistic methods, the modern theory of Hamilton-Jacobi equations, the interaction between theory and numerical methods for partial differential equations. The remaining chapters explore attempts to understand oscillatory phenomena in solutions of nonlinear equations. This book will be of great value to mathematicians and engineers.

  • Data Structures, Computer Graphics, and Pattern Recognition

    • 1 Edición
    • A. Klinger + 2 más
    • Inglés
    Data Structures, Computer Graphics, and Pattern Recognition focuses on the computer graphics and pattern recognition applications of data structures methodology. This book presents design related principles and research aspects of the computer graphics, system design, data management, and pattern recognition tasks. The topics include the data structure design, concise structuring of geometric data for computer aided design, and data structures for pattern recognition algorithms. The survey of data structures for computer graphics systems, application of relational data structures in computer graphics, and observations on linguistics for scene analysis are also elaborated. This text likewise covers the design of satellite graphics systems, interactive image segmentation, surface representation for computer aided design, and error-correcting parsing for syntactic pattern recognition. This publication is valuable to practitioners in data structures, particularly those who are applying real computer systems to problems involving image, speech, and medical data.

  • Numerical Methods for Partial Differential Equations

    Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin-Madison, October 23-25, 1978
    • 1 Edición
    • Seymour V. Parter
    • Inglés
    Numerical Methods for Partial Differential Equations is a collection of papers dealing with techniques and practical solutions to problems concerning continuum mechanics, fluid dynamics, and plasma physics. One paper discusses the important considerations that lead to an efficient nonlinear dynamic finite element analysis using improved analysis techniques. Another paper describes the results obtained from fully discrete methods of higher order in time (order 3 and 4) for second order parabolic initial boundary value problems in which the equations have time dependent (or nonlinear) coefficients. Another paper reviews concepts of ellipticity of finite-difference approximations to general elliptic partial differential systems, with examples utilizing Cauchy-Riemann equations or Navier-Stokes equations. One paper describes fluid-dynamic computing using basic equations, boundary conditions, time dependent gas dynamics, shock waves, stream-function-vort... methods, and an example on the formation of a spherical vortex. Another paper evaluates a specific problem arising in the study of the equilibrium of plasma confined in a machine of the Tokomak type. The collection is suitable for mathematicians, physicists, and investigators in the field of continuum mechanics, fluid dynamics, plasma physics.

  • Ideas and Their Reception

    Proceedings of the Symposium on the History of Modern Mathematics, Vassar College, Poughkeepsie, New York, June 20-24, 1989
    • 1 Edición
    • David E. Rowe + 1 más
    • Inglés
    The History of Modern Mathematics, Volume I: Ideas and their Reception documents the proceedings of the Symposium on the History of Modern Mathematics held at Vassar College in Poughkeepsie, New York on June 20-24, 1989. This book is concerned with the emergence and reception of major ideas in fields that range from foundations and set theory, algebra and invariant theory, and number theory to differential geometry, projective and algebraic geometry, line geometry, and transformation groups. Other topics include the theory of reception for the history of mathematics and British synthetic vs. French analytic styles of algebra in the early American Republic. The early geometrical works of Sophus Lie and Felix Klein, background to Gergonne's treatment of duality, and algebraic geometry in the late 19th century are also elaborated. This volume is intended for students and researchers interested in developments in pure mathematics.

  • Nonlinear Problems in Abstract Cones

    • 1 Edición
    • Dajun Guo + 1 más
    • William F. Ames
    • Inglés
    Notes and Reports in Mathematics in Science and Engineering, Volume 5: Nonlinear Problems in Abstract Cones presents the investigation of nonlinear problems in abstract cones. This book uses the theory of cones coupled with the fixed point index to investigate positive fixed points of various classes of nonlinear operators. Organized into four chapters, this volume begins with an overview of the fundamental properties of cones coupled with the fixed point index. This text then employs the fixed point theory developed to discuss positive solutions of nonlinear integral equations. Other chapters consider several examples from integral and differential equations to illustrate the abstract results. This book discusses as well the fixed points of increasing and decreasing operators. The final chapter deals with the development of the theory of nonlinear differential equations in cones. This book is a valuable resource for graduate students in mathematics. Mathematicians and researchers will also find this book useful.

  • Control Theory of Systems Governed by Partial Differential Equations

    • 1 Edición
    • A.K. Aziz + 2 más
    • Inglés
    Control Theory of Systems Governed by Partial Differential Equations covers the proceedings of the 1976 Conference by the same title, held at the Naval Surface Weapons Center, Silver Spring, Maryland. The purpose of this conference is to examine the control theory of partial differential equations and its application. This text is divided into five chapters that primarily focus on tutorial lecture series on the theory of optimal control of distributed systems. It describes the many manifestations of the theory and its applications appearing in the other chapters. This work also presents the principles of the duality and asymptotic methods in control theory, including the variational principle for the heat equation. A chapter highlights systems that are not of the linear quadratic type. This chapter also explores the control of free surfaces and the geometrical control variables. The last chapter provides a summary of the features and applications of the numerical approximation of problems of optimal control. This book will prove useful to mathematicians, engineers, and researchers.

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