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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.

  • Algebraic Analysis

    Papers Dedicated to Professor Mikio Sato on the Occasion of His Sixtieth Birthday
    • 1st Edition
    • Masaki Kashiwara + 1 more
    • English
    Algebraic Analysis: Papers Dedicated to Professor Mikio Sato on the Occasion of his 60th Birthday, Volume I is a collection of research papers on algebraic analysis and related topics in honor to Professor Mikio Sato’s 60th birthday. This volume is composed of 35 chapters and begins with papers concerning Sato’s early career in algebraic analysis. The succeeding chapters deal with research works on the existence of local holomorphic solutions, the holonomic q-difference systems, partial differential equations, and the properties of solvable models. Other chapters explore the fundamentals of hypergeometric functions, the Toda lattice in the complex domain, the Lie algebras, b-functions, p-adic integrals, analytic parameters of hyperfunctions, and some applicatioins of microlocal energy methods to analytic hypoeellipticity. This volume also presents studies on the complex powers of p-adic fields, operational calculus, extensions of microfunction sheaves up to the boundary, and the irregularity of holonomic modules. The last chapters feature research works on error analysis of quadrature formulas obtained by variable transformation and the analytic functional on the complex light cone, as well as their Fourier-Borel transformations. This book will prove useful to mathematicians and advance mathematics students.

  • Geometric Topology

    • 1st Edition
    • James C. Cantrell
    • English
    Geometric Topology contains the proceedings of the 1977 Georgia Topology Conference, held at the University of Georgia on August 1977. The book is comprised of contributions from leading experts in the field of geometric topology.These contributions are grouped into four sections: low dimensional manifolds, topology of manifolds, shape theory and infinite dimensional topology, and miscellaneous problems. Subjects discussed under these sections include local spanning missing loops, the structure of generalized manifolds having nonmanifold set of trivial dimension, universal open principal fibrations, and how to build a flexible polyhedral surface. Topologists, geometers, and mathematicians will find the book very interesting and insightful.

  • Regression Estimators

    A Comparative Study
    • 1st Edition
    • Marvin H. J. Gruber
    • Gerald J. Lieberman + 1 more
    • English
    Regression Estimators: A Comparative Study presents, compares, and contrasts the development and the properties of the ridge type estimators that result from both Bayesian and non-Bayesian (frequentist) methods. The book is divided into four parts. The first part (Chapters I and II) discusses the need for alternatives to least square estimators, gives a historical survey of the literature and summarizes basic ideas in Matrix Theory and Statistical Decision Theory used throughout the book. The second part (Chapters III and IV) covers the estimators from both the Bayesian and from the frequentist points of view and explores the mathematical relationships between them. The third part (Chapters V-VIII) considers the efficiency of the estimators with and without averaging over a prior distribution. Part IV, the final two chapters IX and X, suggests applications of the methods and results of Chapters III-VII to Kaiman Filters and Analysis of Variance, two very important areas of application. Statisticians and workers in fields that use statistical methods who would like to know more about the analytical properties of ridge type estimators will find the book invaluable.

  • The Mathematical Structure of Raster Graphics

    • 1st Edition
    • Eugene L. Fiume
    • English
    The Mathematical Structure of Raster Graphics presents a mathematical characterization of the structure of raster graphics, a popular and diverse form of computer graphics. The semantics and theory of the mathematical structure of raster graphics are discussed. Notations that help to clarify some of the concepts generally considered to be fundamental to computer graphics are included. Comprised of seven chapters, this book begins with a description of a general framework for specifying and manipulating scenes. Basic graphic entities, called primitive graphic objects, are defined using a simple notation over a Euclidean space. The reader is then introduced to a semantics of visibility; a mathematical semantics of rendering, developed using the very basic notion of measure; and a mathematical formalization of bit-mapped graphics. A framework for specifying illumination models is also described, along with the complexity of abstract ray tracing. This monograph will be a useful resource for undergraduate and graduate students, researchers, and practitioners in the fields of mathematics and computer graphics, and to those with some basic computer graphics background.

  • Programming Language Structures

    • 1st Edition
    • Elliott I. Organick + 2 more
    • English
    Programming Language Structures deals with the structures of programming languages and introduces the reader to five important programming languages: Algol, Fortran, Lisp, Snobol, and Pascal. The fundamental similarities and differences among these languages are discussed. A unifying framework is constructed that can be used to study the structure of other languages, such as Cobol, PL/I, and APL. Several of the tools and methodologies needed to construct large programs are also considered. Comprised of 10 chapters, this book begins with a summary of the relevant concepts and principles about algorithms, flowcharts, and computation that a student is expected to know from the first course. The discussion then turns to the semantics of procedure and function call as well as argument-parameter matching with various kinds of parameters; recursion and its relation to tree traversal; syntax formalism for context-free languages; and ALGOL 60 and block structuring. Case study programs are presented to reinforce the reader's understanding of ALGOL 60 and Fortran semantics. The remaining chapters deal with Lisp, Snobol, and Pascal. This monograph is intended for working programmers and students in computer science who have an interest in the subject of programming.

  • Transonic, Shock, and Multidimensional Flows

    Advances in Scientific Computing
    • 1st Edition
    • Richard E. Meyer
    • English
    Mathematics Research Center Symposium: Transonic, Shock, and Multidimensional Flows: Advances in Scientific Computing covers the lectures presented at a Symposium on Transonic, Shock, and Multidimensional Flows, held in Madison on May 13-15, 1981, under the auspices of the Mathematics Research Center of the University of Wisconsin. The book focuses on the advancements in the scientific computation of high-speed aerodynamic phenomena and related fluid motions. The selection first elaborates on computational fluid dynamics of airfoils and wings; shock-free configurations in two- and three-dimensional transonic flow; and steady-state solution of the Euler equations for transonic flow. Discussions focus on boundary conditions, convergence acceleration, indirect design of airfoils, and trailing edge and the boundary layer. The text then examines the calculation of transonic potential flow past three-dimensional configurations and remarks on the numerical solution of Tricomi-type equations. The manuscript ponders on the design and numerical analysis of vortex methods, shock calculations and the numerical solution of singular perturbation problems, tracking of interfaces for fluid flow, and transonic flows with viscous effects. Topics include numerical algorithm, difference approximation for scalar equations, boundary conditions, transonic flow in a tube, and governing equations. The selection is a dependable reference for researchers interested in transonic, shock, and multidimensional flows.

  • Mastering C Pointers

    Tools for Programming Power
    • 1st Edition
    • Robert J. Traister
    • English
    Mastering C Pointers: Tools for Programming Power focuses on the pointer operations of the C programming language, explaining exactly what pointers are and how to master them through easy-to-understand phrasing and by presenting many simple program examples. The functions of pointers with respect to memory access and memory allocation are also discussed. Comprised of 10 chapters, this book begins with the author's personal reflection on his first encounters with the C programming language and its pointers. The next two chapters presents steps to learning pointers, with emphasis on the essential processes that occur (invisibly and internally) when declaring standard numeric variables in C language and how to deal with C language character arrays and C strings. The reader is then introduced to string pointers and declared pointers of numeric types; the use of C language pointers and the memory allocation functions; and C language functions. The book also explores some of the other "entities" that pointers are used to access, including structures and unions, before concluding with an examination of the source code format of C language. This monograph is intended for both beginning and experienced C language programmers.

  • Zero-Symmetric Graphs

    Trivalent Graphical Regular Representations of Groups
    • 1st Edition
    • H. S. M. Coxeter + 2 more
    • English
    Zero-Symmetric Graphs: Trivalent Graphical Regular Representations of Groups describes the zero-symmetric graphs with not more than 120 vertices.The graphs considered in this text are finite, connected, vertex-transitive and trivalent. This book is organized into three parts encompassing 25 chapters. The first part reviews the different classes of zero-symmetric graphs, according to the number of essentially different edges incident at each vertex, namely, the S, T, and Z classes. The remaining two parts discuss the theorem and characteristics of type 1Z and 3Z graphs. These parts explore Cayley graphs of specific groups, including the parameters of Cayley graphs of groups. This book will prove useful to mathematicians, computer scientists, and researchers.

  • From Pixels to Animation

    An Introduction to Graphics Programming
    • 1st Edition
    • James Alan Farrell
    • English
    From Pixels to Animation: An Introduction to Graphics Programming deals with the C programming language, particularly for the Borland C and Microsoft C languages. The book reviews the basics of graphics programming, including graphics hardware, graphs, charts, changing colors, 3D graphics, high level functions provided by Borland and Microsoft C. The text also explains low-level graphics, getting around the limitations of standard, graphics libraries, SVGA programming, and creating graphics functions. Advanced topics include linear transformations, ray tracing, and fractals. The book explains in detail the aspect ratio of pixels (length of the pixel dot divided by its width), pixel colors, line styles, and the functions to create the graphic. The text also describes the presentation of a three-dimensional object by using perspective, shading, and texturing. Between the operating system, which carries out the instruction of the program, and the hardware, which displays the output of the program, is the Basic Input/Output Services (BIOS). The BIOS is a set of routine instruction inside the different parts or hardware devices in the computer. The book explains programing animation effects by utilizing routines provided by Microsoft or Borland. The text also notes that a programmer can create good animation effects by directly addressing the graphics adapter, bypassing the BIOS or the high-level routines created by Microsoft or Borland. The book is suitable for beginning programmers, computer science, operators, animators, and artists involved with computer aided designs.

  • Applied Time Series Analysis

    Proceedings of the First Applied Time Series Symposium Held in Tulsa, Oklahoma, May 14-15, 1976
    • 1st Edition
    • David F. Findley
    • English
    Applied Time Series Analysis contains the proceedings of the First Applied Time Series Symposium held in Tulsa, Oklahoma, on May 14-15, 1976. The symposium provided a forum for reviewing various applications of time series analysis and covered topics ranging from nonlinear time series modeling and G-spectral estimation to multivariate autoregression estimation using residuals. Adaptive processing of seismic data and the application of homomorphic filtering to seismic data processing are also discussed. Comprised of 10 chapters, this book begins by describing the application of parametric models to the analysis and control of time series using some numerical examples. The reader is then introduced to nonlinear time series modeling; two-dimensional recursive filtering in theory and practice; and spectral estimators. Waves propagating in random media as statistical time series are also considered. The book concludes with a chapter that illustrates how the intensity of a Poisson process is estimated, with emphasis on a time series approach to the fixed signal case, invariant testing, and spline estimation. This monograph will be a useful resource for students and practitioners in the fields of mathematics and statistics, electrical engineering, and computer science.

  • Geometric Measure Theory

    A Beginner's Guide
    • 1st Edition
    • Frank Morgan
    • English
    Geometric Measure Theory: A Beginner's Guide provides information pertinent to the development of geometric measure theory. This book presents a few fundamental arguments and a superficial discussion of the regularity theory. Organized into 12 chapters, this book begins with an overview of the purpose and fundamental concepts of geometric measure theory. This text then provides the measure-theoretic foundation, including the definition of Hausdorff measure and covering theory. Other chapters consider the m-dimensional surfaces of geometric measure theory called rectifiable sets and introduce the two basic tools of the regularity theory of area-minimizing surfaces. This book discusses as well the fundamental theorem of geometric measure theory, which guarantees solutions to a wide class of variational problems in general dimensions. The final chapter deals with the basic methods of geometry and analysis in a generality that embraces manifold applications. This book is a valuable resource for graduate students, mathematicians, and research workers.

  • Statistical Decision Theory and Related Topics III

    • 1st Edition
    • Shanti S. Gupta + 1 more
    • English
    Statistical Decision Theory and Related Topics III, Volume 2 is a collection of papers presented at the Third Purdue Symposium on Statistical Decision Theory and Related Topics, held at Purdue University in June 1981. The symposium brought together many prominent leaders and a number of younger researchers in statistical decision theory and related areas. This volume contains the research papers presented at the symposium and includes works on general decision theory, multiple decision theory, optimum experimental design, sequential and adaptive inference, Bayesian analysis, robustness, and large sample theory. These research areas have seen rapid developments since the preceding Purdue Symposium in 1976, developments reflected by the variety and depth of the works in this volume. Statisticians and mathematicians will find the book very insightful.

  • Artificial Intelligence

    • 1st Edition
    • Earl B. Hunt
    • Edward C. Carterette + 1 more
    • English
    Artificial Intelligence provides information pertinent to the fundamental aspects of artificial intelligence. This book presents the basic mathematical and computational approaches to problems in the artificial intelligence field. Organized into four parts encompassing 16 chapters, this book begins with an overview of the various fields of artificial intelligence. This text then attempts to connect artificial intelligence problems to some of the notions of computability and abstract computing devices. Other chapters consider the general notion of computability, with focus on the interaction between computability theory and artificial intelligence. This book discusses as well the concepts of pattern recognition, problem solving, and machine comprehension. The final chapter deals with the study of machine comprehension and reviews the fundamental mathematical and computing techniques underlying artificial intelligence research. This book is a valuable resource for seniors and graduate students in any of the computer-related sciences, or in experimental psychology. Psychologists, general systems theorists, and scientists will also find this book useful.

  • Group Theory and Its Applications

    Volume II
    • 1st Edition
    • Ernest M. Loebl
    • English
    Group Theory and its Applications, Volume II 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 the representation and tensor operators of the unitary groups. The next chapter describes wave equations, both Schrödinger’s and Dirac’s for a wide variety of potentials. These topics are followed by discussions of the applications of dynamical groups in dealing with bound-state problems of atomic and molecular physics. A chapter explores the connection between the physical constants of motion and the unitary group of the Hamiltonian, the symmetry adaptation with respect to arbitrary finite groups, and the Dixon method for computing irreducible characters without the occurrence of numerical errors. The last chapter deals with the study of the extension, representation, and applications of Galilei group. This book will prove useful to mathematicians, practicing engineers, and physicists.

  • Oriented Projective Geometry

    A Framework for Geometric Computations
    • 1st Edition
    • Jorge Stolfi
    • English
    Oriented Projective Geometry: A Framework for Geometric Computations proposes that oriented projective geometry is a better framework for geometric computations than classical projective geometry. The aim of the book is to stress the value of oriented projective geometry for practical computing and develop it as a rich, consistent, and effective tool for computer programmers. The monograph is comprised of 20 chapters. Chapter 1 gives a quick overview of classical and oriented projective geometry on the plane, and discusses their advantages and disadvantages as computational models. Chapters 2 through 7 define the canonical oriented projective spaces of arbitrary dimension, the operations of join and meet, and the concept of relative orientation. Chapter 8 defines projective maps, the space transformations that preserve incidence and orientation; these maps are used in chapter 9 to define abstract oriented projective spaces. Chapter 10 introduces the notion of projective duality. Chapters 11, 12, and 13 deal with projective functions, projective frames, relative coordinates, and cross-ratio. Chapter 14 tells about convexity in oriented projective spaces. Chapters 15, 16, and 17 show how the affine, Euclidean, and linear vector spaces can be emulated with the oriented projective space. Finally, chapters 18 through 20 discuss the computer representation and manipulation of lines, planes, and other subspaces. Computer scientists and programmers will find this text invaluable.

  • Computer Science and Scientific Computing

    Proceedings of the Third ICASE Conference on Scientific Computing, Williamsburg, Virginia, April 1 and 2, 1976
    • 1st Edition
    • James M. Ortega
    • English
    Computer Science and Scientific Computing contains the proceedings of the Third ICASE Conference on Scientific Computing held in Williamsburg, Virginia, on April l and 2, 1976, under the auspices of the Institute for Computer Applications in Systems Engineering at the NASA Langley Research Center. The conference provided a forum for reviewing all the aspects of scientific computing and covered topics ranging from computer-aided design (CAD) and computer science technology to the design of large hydrodynamics codes. Case studies in reliable computing are also presented. Comprised of 13 chapters, this book begins with an introduction to the use of the hierarchical family concept in the development of scientific programming systems. The discussion then turns to the data structures of scientific computing and their representation and management; some important CAD capabilities required to support aerospace design in the areas of interactive support, information management, and computer hardware advances as well as some computer science developments which may contribute significantly to making such capabilities possible; and the use of symbolic computation systems for problem solving in scientific research. Subsequent chapters deal with computer applications in astrophysics; the possibility of computing turbulence and numerical wind tunnels; and the basis for a general-purpose program for finite element analysis. Software tools for computer graphics are also considered. This monograph will be of value to scientists, systems designers and engineers, and students in computer science who have an interest in the subject of scientific computing.

  • Algorithm-Structured Computer Arrays and Networks

    Architectures and Processes for Images, Percepts, Models, Information
    • 1st Edition
    • Leonard Uhr
    • Werner Rheinboldt
    • English
    Computer Science and Applied Mathematics: Algorithm-Structured Computer Arrays and Networks: Architectures and Processes for Images, Percepts, Models, Information examines the parallel-array, pipeline, and other network multi-computers. This book describes and explores arrays and networks, those built, being designed, or proposed. The problems of developing higher-level languages for systems and designing algorithm, program, data flow, and computer structure are also discussed. This text likewise describes several sequences of successively more general attempts to combine the power of arrays with the flexibility of networks into structures that reflect and embody the flow of information through their processors. This publication is useful as a textbook or auxiliary textbook for students taking courses on computer architecture, parallel computers, arrays and networks, and image processing and pattern recognition.

  • Pascal-SC

    A Computer Language for Scientific Computation
    • 1st Edition
    • Gerd Bohlender + 2 more
    • Werner Rheinboldt + 1 more
    • English
    Perspectives in Computing, Vol. 17: Pascal-SC: A Computer Language for Scientific Computation focuses on the application of Pascal-SC, a programming language developed as an extension of standard Pascal, in scientific computation. The publication first elaborates on the introduction to Pascal-SC, a review of standard Pascal, and real floating-point arithmetic. Discussions focus on optimal scalar product, standard functions, real expressions, program structure, simple extensions, real floating-point arithmetic, vector and matrix arithmetic, and dynamic arrays. The text then examines functions and operators with arbitrary result types and solving problems with Pascal-SC. The book ponders on strings and text processing, dynamic arrays, and modules. Topics include declaration and use of modules, compatibility of static and dynamic arrays, dynamic result types of functions and operators, strings in procedures, functions, and operators, and declaration of string variables. The publication is a dependable reference for computer science experts and researchers interested in the application of Pascal-SC in scientific computation.

  • Multivariate Statistics and Probability

    Essays in Memory of Paruchuri R. Krishnaiah
    • 1st Edition
    • C. R. Rao + 1 more
    • English
    Multivariate Statistics and Probability: Essays in Memory of Paruchuri R. Krishnaiah is a collection of essays on multivariate statistics and probability in memory of Paruchuri R. Krishnaiah (1932-1987), who made significant contributions to the fields of multivariate statistical analysis and stochastic theory. The papers cover the main areas of multivariate statistical theory and its applications, as well as aspects of probability and stochastic analysis. Topics range from finite sampling and asymptotic results, including aspects of decision theory, Bayesian analysis, classical estimation, regression, and time-series problems. Comprised of 35 chapters, this book begins with a discussion on the joint asymptotic distribution of marginal quantiles and quantile functions in samples from a multivariate population. The reader is then introduced to kernel estimators of density function of directional data; moment conditions for valid formal edgeworth expansions; and ergodicity and central limit theorems for a class of Markov processes. Subsequent chapters focus on minimal complete classes of invariant tests for equality of normal covariance matrices and sphericity; normed likelihood as saddlepoint approximation; generalized Gaussian random fields; and smoothness properties of the conditional expectation in finitely additive white noise filtering. This monograph should be of considerable interest to researchers as well as to graduate students working in theoretical and applied statistics, multivariate analysis, and random processes.

  • Neural Networks for Perception

    Computation, Learning, and Architectures
    • 1st Edition
    • Harry Wechsler
    • English
    Neural Networks for Perception, Volume 2: Computation, Learning, and Architectures explores the computational and adaptation problems related to the use of neuronal systems, and the corresponding hardware architectures capable of implementing neural networks for perception and of coping with the complexity inherent in massively distributed computation. This book addresses both theoretical and practical issues related to the feasibility of both explaining human perception and implementing machine perception in terms of neural network models. The text is organized into two sections. The first section, computation and learning, discusses topics on learning visual behaviors, some of the elementary theory of the basic backpropagation neural network architecture, and computation and learning in the context of neural network capacity. The second section is on hardware architecture. The chapters included in this part of the book describe the architectures and possible applications of recent neurocomputing models. The Cohen-Grossberg model of associative memory, hybrid optical/digital architectures for neorocomputing, and electronic circuits for adaptive synapses are some of the subjects elucidated. Neuroscientists, computer scientists, engineers, and researchers in artificial intelligence will find the book useful.

  • 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.

  • Statistical Decision Theory and Related Topics

    Proceedings of a Symposium Held at Purdue University, May 17-19, 1976
    • 1st Edition
    • Shanti S. Gupta + 1 more
    • English
    Statistical Decision Theory and Related Topics II is a compendium of papers presented at an international symposium on Statistical Decision Theory and Related Topics held at Purdue University in May, 1976. The researchers invited to participate, and to author papers for this volume, are among the leaders in the field of Statistical Decision Theory. This collection features works on general decision theory, multiple decision theory, optimal experimental design, and robustness. Mathematicians and statisticians will find the book highly insightful and informative.

  • A Second Course in Elementary Differential Equations

    • 1st Edition
    • Paul Waltman
    • English
    A Second Course in Elementary Differential Equations deals with norms, metric spaces, completeness, inner products, and an asymptotic behavior in a natural setting for solving problems in differential equations. The book reviews linear algebra, constant coefficient case, repeated eigenvalues, and the employment of the Putzer algorithm for nondiagonalizable coefficient matrix. The text describes, in geometrical and in an intuitive approach, Liapunov stability, qualitative behavior, the phase plane concepts, polar coordinate techniques, limit cycles, the Poincaré-Bendixson theorem. The book explores, in an analytical procedure, the existence and uniqueness theorems, metric spaces, operators, contraction mapping theorem, and initial value problems. The contraction mapping theorem concerns operators that map a given metric space into itself, in which, where an element of the metric space M, an operator merely associates with it a unique element of M. The text also tackles inner products, orthogonality, bifurcation, as well as linear boundary value problems, (particularly the Sturm-Liouville problem). The book is intended for mathematics or physics students engaged in ordinary differential equations, and for biologists, engineers, economists, or chemists who need to master the prerequisites for a graduate course in mathematics.

  • The Mathematical Theory of Coding

    • 1st Edition
    • Ian F. Blake + 1 more
    • English
    The Mathematical Theory of Coding focuses on the application of algebraic and combinatoric methods to the coding theory, including linear transformations, vector spaces, and combinatorics. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on self-dual and quasicyclic codes, quadratic residues and codes, balanced incomplete block designs and codes, bounds on code dictionaries, code invariance under permutation groups, and linear transformations of vector spaces over finite fields. The text then takes a look at coding and combinatorics and the structure of semisimple rings. Topics include structure of cyclic codes and semisimple rings, group algebra and group characters, rings, ideals, and the minimum condition, chains and chain groups, dual chain groups, and matroids, graphs, and coding. The book ponders on group representations and group codes for the Gaussian channel, including distance properties of group codes, initial vector problem, modules, group algebras, andrepresentations, orthogonality relationships and properties of group characters, and representation of groups. The manuscript is a valuable source of data for mathematicians and researchers interested in the mathematical theory of coding.

  • The Architecture of Supercomputers

    Titan, a Case Study
    • 1st Edition
    • Daniel P. Siewiorek + 1 more
    • English
    The Architecture of Supercomputers: Titan, A Case Study describes the architecture of the first member of an entirely new computing class, the graphic supercomputing workstation known as Titan. This book is divided into seven chapters. Chapter 1 provides an overview of the Titan architecture, including the motivation, organization, and processes that created it. A survey of all the techniques to speed up computation is presented in Chapter 2. Chapter 3 reviews the issue of particular benchmarks and measures, while Chapter 4 analyzes a model of a concurrency hierarchy extending from the register set to the entire operating system. The architecture of Titan graphics supercomputer and its implementation are considered in Chapter 5. Chapter 6 examines the performance of Titan in terms of the various information flow data rates. The last chapter is devoted to the actual performance on benchmark kernels and how the architecture and implementation affect performance. This publication is recommended for architects and engineers designing processors and systems.

  • Transformations

    Mathematical Approaches to Culture Change
    • 1st Edition
    • Colin Renfrew + 1 more
    • English
    Transformations: Mathematical Approaches to Culture Change focuses on the application of contemporary mathematical techniques to the study of culture change and formulates problems in archaeology, anthropology, and historiography in such a way that they are susceptible to treatment of a mathematical kind. Mathematical models, extending from the almost purely quantitative methods of physics to the purely verbal conceptual explanations, are described. Emphasis is placed on catastrophe theoretic models that exemplify the use of soft mathematics in situations in which the use of hard quantitative models is not possible. Comprised of 21 chapters, this book begins with an overview of the role of mathematics in theoretical archaeology, followed by a discussion on two general categories of mathematical methods that seem to be suitable for modeling cultural transformations: methods of dynamical systems theory and methods that give greater emphasis on discrete entities and the structural relations or patterns among them. Subsequent chapters deal with the use of mathematics in history; morphogenesis in biological and social systems; simulation of the growth of hierarchies; and logistic trends in Southwest population growth. A reconstruction of political units in the Valley of Mexico during the Toltec period is also presented. This monograph will be of interest to archaeologists, anthropologists, historians, biologists, sociologists, and mathematicians.

  • Stochastic Modelling of Social Processes

    • 1st Edition
    • Andreas Diekmann + 1 more
    • English
    Stochastic Modelling of Social Processes provides information pertinent to the development in the field of stochastic modeling and its applications in the social sciences. This book demonstrates that stochastic models can fulfill the goals of explanation and prediction. Organized into nine chapters, this book begins with an overview of stochastic models that fulfill normative, predictive, and structural–analytic roles with the aid of the theory of probability. This text then examines the study of labor market structures using analysis of job and career mobility, which is one of the approaches taken by sociologists in research on the labor market. Other chapters consider the characteristic trends and patterns from data on divorces. This book discusses as well the two approaches of stochastic modeling of social processes, namely competing risk models and semi-Markov processes. The final chapter deals with the practical application of regression models of survival data. This book is a valuable resource for social scientists and statisticians.

  • Discovering Causal Structure

    Artificial Intelligence, Philosophy of Science, and Statistical Modeling
    • 1st Edition
    • Clark Glymour + 2 more
    • English
    Discovering Causal Structure: Artificial Intelligence, Philosophy of Science, and Statistical Modeling provides information pertinent to the fundamental aspects of a computer program called TETRAD. This book discusses the version of the TETRAD program, which is designed to assist in the search for causal explanations of statistical data. or alternative models. This text then examines the notion of applying artificial intelligence methods to problems of statistical model specification. Other chapters consider how the TETRAD program can help to find god alternative models where they exist, and how it can help detect the existence of important neglected variables. This book discusses as well the procedures for specifying a model or models to account for non-experimental or quasi-experimental data. The final chapter presents a description of the format of input files and a description of each command. This book is a valuable resource for social scientists and researchers.

  • Classification and Clustering

    Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin at Madison, May 3–5, 1976
    • 1st Edition
    • J. Van Ryzin
    • English
    Classification and Clustering documents the proceedings of the Advanced Seminar on Classification and Clustering held in Madison, Wisconsin on May 3-5, 1976. This compilation discusses the relationship between multidimensional scaling and clustering, distribution problems in clustering, and botryology of botryology. The graph theoretic techniques for cluster analysis algorithms, data dependent clustering techniques, and linguistic approach to pattern recognition are also elaborated. This text likewise covers the discriminant analysis when scale contamination is present in the initial sample and statistical basis of computerized diagnosis using the electrocardiogram. Other topics include the simple histogram method for nonparametric classification and optimal smoothing of density estimates. This book is intended for mathematicians, biological scientists, social scientists, computer scientists, statisticians, and engineers interested in classification and clustering.

  • Integer Programming

    Theory, Applications, and Computations
    • 1st Edition
    • Hamdy A. Taha
    • J. William Schmidt
    • English
    Integer Programming: Theory, Applications, and Computations provides information pertinent to the theory, applications, and computations of integer programming. This book presents the computational advantages of the various techniques of integer programming. Organized into eight chapters, this book begins with an overview of the general categorization of integer applications and explains the three fundamental techniques of integer programming. This text then explores the concept of implicit enumeration, which is general in a sense that it is applicable to any well-defined binary program. Other chapters consider the branch-and-bound methods, the cutting-plane method, and its closely related asymptotic problem. This book discusses as well several specialized algorithms for certain well-known integer models and provides an alternative approach to the solution of the integer problem. The final chapter deals with a number of observations about the formulations and executions of integer programming models. This book is a valuable resource for industrial engineers and research workers.

  • Mathematical Programming

    Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin, and the U. S. Army at Madison, September 11-13, 1972
    • 1st Edition
    • T. C. Hu + 1 more
    • English
    Mathematical Programming provides information pertinent to the developments in mathematical programming. This book covers a variety of topics, including integer programming, dynamic programming, game theory, nonlinear programming, and combinatorial equivalence. Organized into nine chapters, this book begins with an overview of optimization of very large-scale planning problems that can be achieved on significant problems. This text then introduces non-stationary policies and determines certain operating characteristics of the optimal policy for a very long planning horizon. Other chapters consider the perfect graph theorem by defining some well-known integer-valued functions of an arbitrary graph. This book discusses as well integer programming that deals with the class of mathematical programming problems in which some or all of the variables are required to be integers. The final chapter deals with the basic theorem of game theory. This book is a valuable resource for readers who are interested in mathematical programming. Mathematicians will also find this book useful.

  • Computational Probability

    The Proceedings of the Actuarial Research Conference on Computational Probability Held at Brown University, Providence, Rhode Island, on August 28-30, 1975
    • 1st Edition
    • P. M. Kahn
    • English
    Computational Probability is a collection of papers presented at the Actuarial Research Conference on Computational Probability and related topics, held at Brown University on August 28-30, 1975. This 19-chapter book explores the development of computational techniques in probability and statistics and their application to problems in insurance. It covers six general topics, including computational probability, computational statistics, computational risk theory, analysis of algorithms, numerical methods, and notation and computation. Applications covered both life and nonlife insurance. This book will prove useful to applied mathematicians, statisticians, and computer scientists.

  • Applications of Number Theory to Numerical Analysis

    • 1st Edition
    • S. K. Zaremba
    • English
    Applications of Number Theory to Numerical Analysis contains the proceedings of the Symposium on Applications of Number Theory to Numerical Analysis, held in Quebec, Canada, on September 9-14, 1971, under the sponsorship of the University of Montreal's Center for Research in Mathematics. The symposium provided a forum for discussing number theory and its applications to numerical analysis, tackling topics ranging from methods used in estimating discrepancy to the structure of linear congruential sequences. Comprised of 17 chapters, this book begins by considering some combinatorial problems studied experimentally on computing machines. The discussion then turns to experiments on optimal coefficients; a distribution problem in finite sets; and the statistical interdependence of pseudo-random numbers generated by the linear congruential method. Subsequent chapters deal with lattice structure and reduced bases of random vectors generated by linear recurrences; modulo optimization problems and integer linear programming; equivalent forms of zero-one programs; and number theoretic foundations of finite precision arithmetic. This monograph will be of interest to students and practitioners in the field of applied mathematics.

  • Singular Perturbations and Asymptotics

    Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin—Madison, May 28-30, 1980
    • 1st Edition
    • Richard E. Meyer + 1 more
    • English
    Mathematics Research Center Symposia and Advanced Seminar Series: Singular Perturbations and Asymptotics covers the lectures presented at an Advanced Seminar on Singular Perturbation and Asymptotics, held in Madison, Wisconsin on May 28-30, 1980 under the auspices of the Mathematics Research Center of the University of Wisconsin—Madison. The book focuses on the processes, methodologies, reactions, and principles involved in singular perturbations and asymptotics, including boundary value problems, equations, perturbations, water waves, and gas dynamics. The selection first elaborates on basic concepts in the analysis of singular perturbations, limit process expansions and approximate equations, and results on singularly perturbed boundary value problems. Discussions focus on quasi-linear and nonlinear problems, semilinear systems, water waves, expansion in gas dynamics, asymptotic matching principles, and classical perturbation analysis. The text then takes a look at multiple solutions of singularly perturbed systems in the conditionally stable case and singular perturbations, stochastic differential equations, and applications. The book ponders on connection problems in the parameterless case; general connection-formula problem for linear differential equations of the second order; and turning-point problems for ordinary differential equations of hydrodynamic type. Topics include the comparison equation method, boundary layer flows, compound matrix method, asymptotic solution of the connection-formula problem, and higher order equations. The selection is a valuable source of information for researchers interested in singular perturbations and asymptotics.

  • Statistical Inference and Related Topics

    Proceedings of the Summer Research Institute on Statistical Inference for Stochastic Processes, Bloomington, Indiana, July 31 – August 9, 1975
    • 1st Edition
    • Madan Lal Puri
    • English
    Statistical Inference and Related Topics, Volume 2 presents the proceedings of the Summer Research Institute on Statistical Inference for Stochastic Processes, held in Bloomingdale, Indiana on July 31 to August 9, 1975. This book focuses on the theory of statistical inference for stochastic processes. Organized into 15 chapters, this volume begins with an overview of the case of continuous distributions with one real parameter. This text then reviews some results for multidimensional empirical processes and Brownian sheets when they are indexed by families of sets. Other chapters consider a class of cubic spline estimators of probability density functions over a finite interval. This book discusses as well the method to construct nonelimination type sequential procedures to select a subset containing all the superior populations. The final chapter deals with Markov sequences, which are among the most interesting available for study with a rich theory and varied applications. This book is a valuable resource for graduate students and research workers.

  • Table of Integrals, Series, and Products

    • 1st Edition
    • I. S. Gradshteyn + 1 more
    • English
    Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.

  • Precalculus

    Functions & Graphs
    • 1st Edition
    • Bernard Kolman + 1 more
    • English
    Precalculus: Functions & Graphs provides a complete and self-contained presentation of the basic mathematical techniques and ideas required for the successful completion of a calculus course. The book emphasizes the learning and understanding of the concept of a function, using function notation, and being able to sketch graphs of functions with ease. The text employs a number of pedagogic devices that have been proven effective in teaching college mathematics. The mathematical concepts are presented in a style that is informal, supportive, and "user-friendly". Progress checks, warnings, and features are inserted. Every chapter contains a summary, including terms and symbols with appr This textbook is intended for college students.

  • Numerical Analysis

    • 1st Edition
    • John Todd
    • Ch. Blanc + 2 more
    • English
    Basic Numerical Mathematics, Volume 1: Numerical Analysis focuses on numerical analysis, with emphasis on the ideas of "controlled computational experiments" and "bad examples". The concepts of convergence and continuity are discussed, along with the rate of convergence, acceleration, and asymptotic series. The more traditional topics of interpolation, quadrature, and differential equations are also explored. Comprised of 10 chapters, this volume begins with an analysis of the algorithms of Gauss, Borchardt, and Carlson in relation to the rate of convergence. The reader is then introduced to orders of magnitude and rates of convergence; recurrence relations for powers; and the solution of equations. Subsequent chapters deal with uniform convergence and approximation; the acceleration processes of Aitken and Euler; asymptotic series; interpolation; and quadrature. The final chapter is devoted to linear difference equations with constant coefficients, along with differentiation and differential equations. This book will be of interest to mathematicians and students of mathematics.

  • Analysis of Qualitative Data

    Introductory Topics
    • 1st Edition
    • Shelby J Haberman
    • English
    Analysis of Qualitative Data: Volume 1, Introductory Topics introduces log-linear models oriented toward the social scientist, including assessments of the variability of parameter estimates using algebraic equations and summation notation. The book also contains examples involving basic problems in survey research, such as memory error. Other examples pertain to the General Social Survey of the National Opinion Research Center that examines public opinion on abortion, as well as the variations in homicide rates related to variables (such as race or sex of victim). The text explains the quantitative assessment of the size of departures from independence of polytomous variables by investigating the linear combinations of log cells means, known as log cross-product ratios. The book discusses the use of log odds, conditional log odds, cross-product ratios, and conditional cross-product ratios in interpreting hierarchical models such as those found in the General Social Surveys. The text describes logit models, namely, the Newton-Raphson algorithm used to explore the relationship of a dichotomous dependent variable to one or more independent variables. The book can serve and benefit mathematicians, students, or professor of calculus, statistics, and advanced mathematics.

  • Introduction to Group Theory with Applications

    Materials Science and Technology
    • 1st Edition
    • Gerald Burns
    • Allen M. Alper + 1 more
    • English
    Introduction to Group Theory with Applications covers the basic principles, concepts, mathematical proofs, and applications of group theory. This book is divided into 13 chapters and begins with discussions of the elementary topics related to the subject, including symmetry operations and group concepts. The succeeding chapters deal with the properties of matrix representations of finite groups, the vibrations of molecular and crystals, vibrational wave function, selection rules, and molecular approximations. These topics are followed by reviews of the basic of quantum mechanics, crystal field theory, atomic physics, hybrid functions, and molecular orbital theory. The last chapters describe the symmetry of crystal lattices, the band theory of solids, and the full rotation group. This book will be of value to undergraduate mathematics and physics students.

  • Computer Literacy

    Issues and Directions for 1985
    • 1st Edition
    • Robert J. Seidel + 2 more
    • English
    Computer Literacy: Issues and Directions for 1985 is based on a conference entitled "National Goals for Computer Literacy in 1985", held in Reston, Virginia, on December 18-20, 1980, under the auspices of the National Science Foundation. The conference provided a forum for discussing views on computer literacy, as well as methods for infusion of computer-related objectives and activities into existing curricula for different age levels. Issues and barriers to developing national goals for achieving a computer-literate society in the United States are also examined. Comprised of 31 chapters, this book begins by presenting four major approaches to a perspective on computer literacy: impact of computer literacy on the citizenry; major national components of a computer literacy program; development of an information handling curriculum for an evolving computer literacy concept; and a 30-year historical overview of "computer events in three strands" (research/developmen... education, and social/political institutional). The next section considers the definitions and requirements of computer literacy as they impact society, students, and teachers. The use of the computer in cognitive research and in problem solving is also discussed, together with curriculum development in computer literacy. This monograph will be of interest to students, teachers, school administrators, and educational policymakers.

  • Contributions to the Theory and Application of Statistics

    A Volume in Honor of Herbert Solomon
    • 1st Edition
    • Alan E. Gelfand
    • English
    Contributions to the Theory and Application of Statistics: A Volume in Honor of Herbert Solomon is a collection of 20 papers that cover the significant contributions of Herbert Solomon in the field of statistics. This text is organized into four sections encompassing 20 chapters. Each section defines an area in which Herb has made a contribution and the papers are ordered alphabetically. The first section consists of four papers in the area of operations research and applied probability, while the second section gathers six papers looking into problems in distribution theory and geometric probability. The third section contains five applied articles in the areas of law and justice, medicine, and psychology. The fourth section covers five papers that explore several inference issues. This book will be of value to statisticians and advance students.

  • Differential Equations

    • 1st Edition
    • Shair Ahmad + 2 more
    • English
    Differential Equations is a collection of papers from the "Eight Fall Conference on Differential Equations" held at Oklahoma State University in October 1979. The papers discuss hyperbolic problems, bifurcation function, boundary value problems for Lipschitz equations, and the periodic solutions of systems of ordinary differential equations. Some papers deal with the existence of periodic solutions for nonlinearly perturbed conservative systems, the saddle-point theorem, the periodic solutions of the forced pendulum equation, as well as the structural identification (inverse) problem for illness-death processes. One paper presents an elementary proof of the work of deOliveira and Hale, and applies the stability for autonomous systems in the critical case of one zero root. Another paper explains the necessary and sufficient conditions for structural identification prior to application in states of illness-death processes. An illness-death process is a continuous Markov model with n illness (transient) states each having one (and only one) transfer into a death state. The paper examines two theorems whether these apply to an illness-death process under certain given elements. The collection is an ideal source of reference for mathematicians, students, and professor of calculus and advanced mathematics.

  • Introduction to Probabilistic Automata

    • 1st Edition
    • Azaria Paz
    • Werner Rheinboldt
    • English
    Introduction to Probabilistic Automata deals with stochastic sequential machines, Markov chains, events, languages, acceptors, and applications. The book describes mathematical models of stochastic sequential machines (SSMs), stochastic input-output relations, and their representation by SSMs. The text also investigates decision problems and minimization-of-stat... problems arising from concepts of equivalence and coverings for SSMs. The book presents the theory of nonhomogeneous Markov chains and systems in mathematical terms, particularly in relation to asymptotic behavior, composition (direct sum or product), and decomposition. "Word functions," induced by Markov chains and valued Markov systems, involve characterization, equivalence, and representability by an underlying Markov chain or system. The text also discusses the closure properties of probabilistic languages, events and their relation to regular events, particularly with reference to definite, quasidefinite, and exclusive events. Probabilistic automata theory has applications in information theory, control, learning theory, pattern recognition, and time sharing in computer programming. Programmers, computer engineers, computer instructors, and students of computer science will find the collection highly valuable.

  • Algebraic Techniques

    Resolution of Equations in Algebraic Structures
    • 1st Edition
    • Hassan Aït-Kaci + 1 more
    • English
    Resolution of Equations in Algebraic Structures: Volume 1, Algebraic Techniques is a collection of papers from the "Colloquium on Resolution of Equations in Algebraic Structures" held in Texas in May 1987. The papers discuss equations and algebraic structures relevant to symbolic computation and to the foundation of programming. One paper discusses the complete lattice of simulation congruences associated with the ground atomic theory of hierarchical specification, retrieving as the lattice's maximum element Milner's strong bisimulation for CCS. Another paper explains algebraic recognizability of subsets of free T-algebras, or equational theories, and covers discrete structures like those of words, terms, finite trees, and finite graphs. One paper proposes a general theory of unification using a category theoretic framework for various substitution systems including classical unification, E-unification, and order-sorted unification. Another paper shows the universality of algebraic equations in computer science. Fixpoint theorems in ordered algebraic structures can be applied in computer science. These theorems, or their variations, include semantics and proof theory, logic programming, as well as efficient strategies for answering recursive queries in deductive data bases. The collection is suitable for programmers, mathematicians, students, and instructors involved in computer science and computer technology.

  • 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.

  • Robustness of Statistical Tests

    • 1st Edition
    • Takeaki Kariya + 1 more
    • Gerald L. Lieberman + 1 more
    • English
    Robustness of Statistical Tests provides a general, systematic finite sample theory of the robustness of tests and covers the application of this theory to some important testing problems commonly considered under normality. This eight-chapter text focuses on the robustness that is concerned with the exact robustness in which the distributional or optimal property that a test carries under a normal distribution holds exactly under a nonnormal distribution. Chapter 1 reviews the elliptically symmetric distributions and their properties, while Chapter 2 describes the representation theorem for the probability ration of a maximal invariant. Chapter 3 explores the basic concepts of three aspects of the robustness of tests, namely, null, nonnull, and optimality, as well as a theory providing methods to establish them. Chapter 4 discusses the applications of the general theory with the study of the robustness of the familiar Student’s r-test and tests for serial correlation. This chapter also deals with robustness without invariance. Chapter 5 looks into the most useful and widely applied problems in multivariate testing, including the GMANOVA (General Multivariate Analysis of Variance). Chapters 6 and 7 tackle the robust tests for covariance structures, such as sphericity and independence and provide a detailed description of univariate and multivariate outlier problems. Chapter 8 presents some new robustness results, which deal with inference in two population problems. This book will prove useful to advance graduate mathematical statistics students.

  • Mechanisms for Reliable Distributed Real-Time Operating Systems

    The Alpha Kernel
    • 1st Edition
    • J. Duane Northcutt
    • W. Rheinboldt + 1 more
    • English
    Mechanisms for Reliable Distributed Real-Time Operating Systems: The Alpha Kernel deals with the Alpha kernel, a set of mechanisms that support the construction of reliable, modular, decentralized operating systems for real-time control applications. An initial snapshot of the kernel design and implementation is provided. Comprised of seven chapters, this volume begins with a background on the Alpha operating system kernel and its implementation, followed by a description of the programming abstractions created for the Alpha kernel. The third chapter defines the client interface provided by the kernel in support of the given programming abstractions, while the fourth chapter focuses on the functional design of the kernel. The hardware on which the kernel was constructed, as well as the implications of this hardware on the design and implementation of the kernel, is also examined. The final chapter compares Alpha with other relevant operating systems such as Hydra, Cronus, Eden, Argus, Accent, and Locus. This book will appeal to computer scientists, systems designers, and undergraduate and graduate students of computer science.

  • Handbook of Mathematical Formulas

    • 1st Edition
    • Hans-Jochen Bartsch
    • English
    Handbook of Mathematical Formulas presents a compilation of formulas to provide the necessary educational aid. This book covers the whole field from the basic rules of arithmetic, via analytic geometry and infinitesimal calculus through to Fourier's series and the basics of probability calculus. Organized into 12 chapters, this book begins with an overview of the fundamental notions of set theory. This text then explains linear expression wherein the variables are only multiplied by constants and added to constants or expressions of the same kind. Other chapters consider a variety of topics, including matrices, statistics, linear optimization, Boolean algebra, and Laplace's transforms. This book discusses as well the various systems of coordinates in analytical geometry. The final chapter deals with algebra of logic and its development into a two-value Boolean algebra as switching algebra. This book is intended to be suitable for students of technical schools, colleges, and universities.

  • Mathematics Applied to Science

    In Memoriam Edward D. Conway
    • 1st Edition
    • Jerome Goldstein + 2 more
    • English
    Mathematics Applied to Science: In Memoriam Edward D. Conway presents a compilation of articles as a lasting tribute to Edward Conway III. This book covers a variety of topics, including molecular electronic energies, partial differential equations, density matrix, electron density functional, and climate change. Organized into 13 chapters, this book begins with an overview of the large-time behavior of one-dimensional motion in a model gas whose particles have a discrete set of allowed velocities. This text then explores the operator splitting techniques for the solution of time dependent differential equations. Other chapters describe a Monte Carlo simulation procedure for evaluating the relaxation rate of an excited state vibrational population of a diatomic in a simple solvent. This book discusses as well the numerical solution of nonlinear differential equations. The final chapter deals with the physical, thermal, and dynamical properties near the surface of the Earth. This book is a valuable resource for mathematicians.

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