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Books in Mathematics and applied mathematics

This portfolio offers comprehensive coverage of pure and applied mathematics, including algebra, calculus, differential equations, and computational techniques. It supports researchers, educators, and students in advancing theoretical understanding and practical problem-solving across engineering, physics, and data science. Featuring innovative methodologies, real-world case studies, and emerging trends, these resources enable breakthroughs in modelling, simulation, and analytical skills critical for technological progress and scientific discovery.

  • Robustness in Statistics

    • 1st Edition
    • Robert L. Launer + 1 more
    • English
    Robustness in Statistics contains the proceedings of a Workshop on Robustness in Statistics held on April 11-12, 1978, at the Army Research Office in Research Triangle Park, North Carolina. The papers review the state of the art in statistical robustness and cover topics ranging from robust estimation to the robustness of residual displays and robust smoothing. The application of robust regression to trajectory data reduction is also discussed. Comprised of 14 chapters, this book begins with an introduction to robust estimation, paying particular attention to iteration schemes and error structure of estimators. Sensitivity and influence curves as well as their connection with jackknife estimates are described. The reader is then introduced to a simple analog of trimmed means that can be used for studying residuals from a robust point-of-view; a class of robust estimators (called P-estimators) based on the location and scale-invariant Pitman estimators of location; and robust estimation in the presence of outliers. Subsequent chapters deal with robust regression and its use to reduce trajectory data; tests for censoring of extreme values, especially when population distributions are incompletely defined; and robust estimation for time series autoregressions. This monograph should be of interest to mathematicians and statisticians.
  • College Algebra and Trigonometry

    • 2nd Edition
    • Bernard Kolman + 1 more
    • English
    College Algebra and Trigonometry, Second Edition provides a comprehensive approach to the fundamental concepts and techniques of college algebra and trigonometry. The book incorporates improvements from the previous edition to provide a better learning experience. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, trigonometric functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter contains a summary, including terms and symbols with appropriate page references; key ideas for review to stress the concepts; review exercises to provide additional practice; and progress tests to provide self-evaluation and reinforcement. The answers to all Review Exercises and Progress Tests appear in the back of the book. College students will find the book very useful and invaluable.
  • Nonlinear Problems of Engineering

    • 1st Edition
    • William F. Ames
    • English
    Nonlinear Problems of Engineering reviews certain nonlinear problems of engineering. This book provides a discussion of nonlinear problems that occur in four areas, namely, mathematical methods, fluid mechanics, mechanics of solids, and transport phenomena. Organized into 15 chapters, this book begins with an overview of some of the fundamental ideas of two mathematical theories, namely, invariant imbedding and dynamic programming. This text then explores nonlinear integral equations, which have long occupied a prominent place in mathematical analysis. Other chapters consider the phenomena associated with essentially divergent small-divisor series, such as may occur in the formal solution of differential equations that represent the oscillations of conservative dynamical systems. This book discusses as well the mechanics of idealized textiles consisting of inextensible filaments. The final chapter deals with the use of the Peaceman–Rachford alternating direction implicit method for solving the finite difference analogs of boundary value problems. This book is a valuable resource for engineers and mathematicians.
  • Minicomputers

    • 1st Edition
    • Peter C. Sanderson
    • English
    Minicomputers illustrate some of the potential pitfalls and benefits that can be gained if a minicomputer system is chosen wisely. This book is divided into five chapters—introductio... software, programming, selecting the minicomputer system, and applications. This text specifically discusses the advantages of the minicomputer, peripheral devices for minicomputer systems, arithmetical software, and operating systems. The nature of programming language, typical minicomputer assembly language functions, and feasibility study are also elaborated. This monograph likewise covers the preparation of tender, original equipment manufacturers (OEM) applications, and unusual applications of minicomputers. This publication is beneficial to all potential users such as scientists, research workers, process control engineers, and business managers, including educationalists concerned with computer education.
  • Tables of Weber Functions

    Mathematical Tables, Vol. 1
    • 1st Edition
    • I. Ye. Kireyeva + 1 more
    • English
    Tables of Weber Functions contains values for Weber functions or functions of a parabolic cylinder. Investigators at the Computing Centre of the Academy of Sciences, U.S.S.R. confirm these tables which have been calculated by a computer. The wave equation, expressed in parabolic coordinates, occurs in quantum mechanics, radio physics, aerodynamics, hydrodynamics and other fields. Each section of the tables contains values of the real and imaginary parts of the function Dp[x(i + i)]for 51-55 successive values of x, as determined by the interpolation with respect to x, and four values of p. On the left side are given the values of up(x) and vp(x) for positive values of x, and on the right for negative x with the same absolute values. The book contains twenty groups of sections corresponding to values of
  • Arches

    Tables for Statistical Analyses
    • 1st Edition
    • Jan Szymczyk
    • Jerzy Mutermilch
    • English
    Arches: Tables for Statistical Analyses presents a table used for simplifying the calculations of numerical determination of the magnitude of the internal forces in various cross-sections. After the evaluation of the redundancies, one of the stages in the analysis of statistically indeterminate arches is for the investigator to determine the magnitudes of the normal forces and bending moments at various cross-sections. A large number of sections should be considered in order for the investigator to get an accurate picture of the distribution of the generalized internal forces. Such number of sections varies between 10 and 20. To simplify the calculations, the book supplements the main tables for the vertical and horizontal components of reactions by auxiliary tables. These auxiliary tables give the magnitudes of normal forces and bending moments for cases usually encountered in actual practice. The book also explains the use of coefficients in the analysis of two-pinned arches with unyielding supports. The text can be useful for mathematicians, statisticians, and scientific investigators who have to deal with the analysis of numerical data.
  • Elementary Differential Geometry

    • 1st Edition
    • Barrett O'Neill
    • English
    Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.
  • A Survey of Combinatorial Theory

    • 1st Edition
    • Jagdish N. Srivastava
    • English
    A Survey of Combinatorial Theory covers the papers presented at the International Symposium on Combinatorial Mathematics and its Applications, held at Colorado State University (CSU), Fort Collins, Colorado on September 9-11, 1971. The book focuses on the principles, operations, and approaches involved in combinatorial theory, including the Bose-Nelson sorting problem, Golay code, and Galois geometries. The selection first ponders on classical and modern topics in finite geometrical structures; balanced hypergraphs and applications to graph theory; and strongly regular graph derived from the perfect ternary Golay code. Discussions focus on perfect ternary Golay code, finite projective and affine planes, Galois geometries, and other geometric structures. The book then examines the characterization problems of combinatorial graph theory, line-minimal graphs with cyclic group, circle geometry in higher dimensions, and Cayley diagrams and regular complex polygons. The text discusses combinatorial problems in finite Abelian groups, dissection graphs of planar point sets, combinatorial problems and results in fractional replication, Bose-Nelson sorting problem, and some combinatorial aspects of coding theory. The text also reviews the enumerative theory of planar maps, balanced arrays and orthogonal arrays, existence of resolvable block designs, and combinatorial problems in communication networks. The selection is a valuable source of information for mathematicians and researchers interested in the combinatorial theory.
  • Applications of Finite Groups

    • 1st Edition
    • J. S. Lomont
    • English
    Applications of Finite Groups focuses on the applications of finite groups to problems of physics, including representation theory, crystals, wave equations, and nuclear and molecular structures. The book first elaborates on matrices, groups, and representations. Topics include abstract properties, applications, matrix groups, key theorem of representation theory, properties of character tables, simply reducible groups, tensors and invariants, and representations generated by functions. The text then examines applications and subgroups and representations, as well as subduced and induced representations, fermion annihilation and creation operators, crystallographic point groups, proportionality tensors in crystals, and nonrelativistic wave equations. The publication takes a look at space group representations and energy bands, symmetric groups, and applications. Topics include molecular and nuclear structures, multiplet splitting in crystalline electric fields, construction of irreducible representations of the symmetric groups, and reality of representations. The manuscript is a dependable source of data for physicists and researchers interested in the applications of finite groups.
  • A Syntax-Oriented Translator

    • 1st Edition
    • Peter Zilahy Ingerman
    • English
    A Syntax-Oriented Translator focuses on the field of programming and the characteristics and functions of compilers and translators. The book first offers information on the metasyntactic language and the details of a parsing processor. Discussions focus on processing, recovery, and output sections, detailed flow-chart of the parsing processor, parsing form of a grammar, canonical ordering, and the metasyntactic language in general. The text then elaborates on some extensions to the metasyntactic language and metasemantic and metapragmatic language, including punctuation marks and format control, metasemantic and metapragmatic functions, basic form of the construct, and substitution MSF. The publication examines the details of an unparsing processor, as well as lists used in unparsing, subroutines, and the unparsing processor itself. The book is a dependable source of information for home compiler-writers who are interested in the use of a syntax-oriented translator.
  • Non-Linear Structures

    Matrix Methods of Analysis and Design by Computers
    • 1st Edition
    • K. I. Majid
    • English
    Non-Linear Structures: Matrix Methods of Analysis and Design by Computers presents the use of matrix methods of structural analysis suitable for computers. The book consists of 10 chapters. In the first chapter a brief introduction to the behavior of structures in general is given with reference to the linear elastic and simple plastic methods of structural analysis. Chapter 2 is devoted to linear matrix methods, both force and displacement. Chapter 3 examines the stability of an individual member with various end conditions. It also derives the stability functions used in Matrix force and Matrix displacement methods. Chapter 4 tackles the elastic stability of complete frames. Chapter 5 deals with the elastic instability of frames. The sixth chapter covers the elastic-plastic analysis of frames. This is followed in Chapter 7 by a number of approximate methods for the evaluation of the failure load of frames without following the sequence of hinge formation. The last three chapters are devoted to the design of structures and the non-linear aspects of design problems. A description of non-linear programming by piecewise linearization is included in Chapter 10. Structural engineers, architects, researchers, and engineering students will find the book useful.
  • Modern Data Analysis

    • 1st Edition
    • Robert L. Launer + 1 more
    • English
    Modern Data Analysis contains the proceedings of a Workshop on Modern Data Analysis held in Raleigh, North Carolina, on June 2-4, 1980 under the auspices of the United States Army Research Office. The papers review theories and methods of data analysis and cover topics ranging from single and multiple quantile-quantile (Q-Q) plotting procedures to biplot display and pencil-and-paper exploratory data analysis methods. Projection pursuit methods for data analysis are also discussed. Comprised of nine chapters, this book begins with an introduction to styles of data analysis techniques, followed by an analysis of single and multiple Q-Q plotting procedures. Problems involving extreme-value data and the behavior of sample averages are considered. Subsequent chapters deal with the use of smelting in guiding re-expression; geometric data analysis; and influence functions and regression diagnostics. The final chapter examines the use and interpretation of robust analysis of variance for the general non-full-rank linear model. The procedures are described in terms of their mathematical structure, which leads to efficient computational algorithms. This monograph should be of interest to mathematicians and statisticians.
  • Introduction to Finite Geometries

    • 1st Edition
    • F. Kárteszi
    • English
    North-Holland Texts in Advanced Mathematics: Introduction to Finite Geometries focuses on the advancements in finite geometries, including mapping and combinatorics. The manuscript first offers information on the basic concepts on finite geometries and Galois geometries. Discussions focus on linear mapping of a given quadrangle onto another given quadrangle; point configurations of order 2 on a Galois plane of even order; canonical equation of curves of the second order on the Galois planes of even order; and set of collineations mapping a Galois plane onto itself. The text then ponders on geometrical configurations and nets, as well as pentagon theorem and the Desarguesian configuration, two pentagons inscribed into each other, and the concept of geometrical nets. The publication takes a look at combinatorial applications of finite geometries and combinatorics and finite geometries. Topics include generalizations of the Petersen graph, combinatorial extremal problem, and theorem of closure of the hyperbolic space. The book is a valuable source of data for readers interested in finite geometries.
  • Algebraic Methods of Mathematical Logic

    • 1st Edition
    • Ladislav Rieger
    • English
    Algebraic Methods of Mathematical Logic focuses on the algebraic methods of mathematical logic, including Boolean algebra, mathematical language, and arithmetization. The book first offers information on the dialectic of the relation between mathematical and metamathematical aspects; metamathematico-math... parallelism and its natural limits; practical applications of methods of mathematical logic; and principal mathematical tools of mathematical logic. The text then elaborates on the language of mathematics and its symbolization and recursive construction of the relation of consequence. Discussions focus on recursive construction of the relation of consequence, fundamental descriptively-semant... rules, mathematical logic and mathematical language as a material system of signs, and the substance and purpose of symbolization of mathematical language. The publication examines expressive possibilities of symbolization; intuitive and mathematical notions of an idealized axiomatic mathematical theory; and the algebraic theory of elementary predicate logic. Topics include the notion of Boolean algebra based on joins, meets, and complementation, logical frame of a language and mathematical theory, and arithmetization and algebraization. The manuscript is a valuable reference for mathematicians and researchers interested in the algebraic methods of mathematical logic.
  • The Spectral Analysis of Time Series

    Probability and Mathematical Statistics, Vol. 22
    • 1st Edition
    • L. H. Koopmans
    • Z. W. Birnbaum + 1 more
    • English
    The Spectral Analysis of Time Series describes the techniques and theory of the frequency domain analysis of time series. The book discusses the physical processes and the basic features of models of time series. The central feature of all models is the existence of a spectrum by which the time series is decomposed into a linear combination of sines and cosines. The investigator can used Fourier decompositions or other kinds of spectrals in time series analysis. The text explains the Wiener theory of spectral analysis, the spectral representation for weakly stationary stochastic processes, and the real spectral representation. The book also discusses sampling, aliasing, discrete-time models, linear filters that have general properties with applications to continuous-time processes, and the applications of multivariate spectral models. The text describes finite parameter models, the distribution theory of spectral estimates with applications to statistical inference, as well as sampling properties of spectral estimates, experimental design, and spectral computations. The book is intended either as a textbook or for individual reading for one-semester or two-quarter course for students of time series analysis users. It is also suitable for mathematicians or professors of calculus, statistics, and advanced mathematics.
  • Group Theory and Its Applications

    • 1st Edition
    • Ernest M. Loebl
    • English
    Group Theory and Its Applications focuses on the applications of group theory in physics and chemistry. The selection first offers information on the algebras of lie groups and their representations and induced and subduced representations. Discussions focus on the functions of positive type and compact groups; orthogonality relations for square-integrable representations; group, topological, Borel, and quotient structures; and classification of semisimple lie algebras in terms of their root systems. The text then takes a look at the generalization of Euler's angles and projective representation of the Poincare group in a quaternionic Hilbert space. The manuscript ponders on group theory in atomic spectroscopy, group lattices and homomorphism, and group theory in solid state physics. Topics include band theory of solids, lattice vibrations in solids, stationary states in the quantum theory of matter, coupled tensors, and shell structure. The text then examines the group theory of harmonic oscillators and nuclear structure and de Sitter space and positive energy. The selection is a dependable reference for physicists and chemists interested in group theory and its applications.
  • Topology

    Volume I
    • 1st Edition
    • K. Kuratowski
    • English
    Topology, Volume I deals with topology and covers topics ranging from operations in logic and set theory to Cartesian products, mappings, and orderings. Cardinal and ordinal numbers are also discussed, along with topological, metric, and complete spaces. Great use is made of closure algebra. Comprised of three chapters, this volume begins with a discussion on general topological spaces as well as their specialized aspects, including regular, completely regular, and normal spaces. Fundamental notions such as base, subbase, cover, and continuous mapping, are considered, together with operations such as the exponential topology and quotient topology. The next chapter is devoted to the study of metric spaces, starting with more general spaces, having the limit as its primitive notion. The space is assumed to be metric separable, and this includes problems of cardinality and dimension. Dimension theory and the theory of Borei sets, Baire functions, and related topics are also discussed. The final chapter is about complete spaces and includes problems of general function theory which can be expressed in topological terms. The book includes two appendices, one on applications of topology to mathematical logics and another to functional analysis. This monograph will be helpful to students and practitioners of algebra and mathematics.
  • Mathematical Methods

    Linear Algebra / Normed Spaces / Distributions / Integration
    • 1st Edition
    • Jacob Korevaar
    • English
    Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions. The publication first offers information on algebraic theory of vector spaces and introduction to functional analysis. Discussions focus on linear transformations and functionals, rectangular matrices, systems of linear equations, eigenvalue problems, use of eigenvectors and generalized eigenvectors in the representation of linear operators, metric and normed vector spaces, and delta sequences and convergence and approximation. The text then examines the Lebesgue integral, including approximation of integrable functions and applications, integration of sequences and series, functions of bounded variation and the Stieltjes integral, and multiple integrals. Curves and integrals, holomorphic functions and integrals in the complex plane, and multiple integrals are also discussed. The book is a valuable reference for students in the physical sciences, mathematics students interested in applications, and mathematically oriented engineering students.
  • Microprocessor Architectures and Systems

    RISC, CISC and DSP
    • 1st Edition
    • Steve Heath
    • English
    Microprocessor Architectures and Systems: RISC, CISC, and DSP focuses on the developments of Motorola's CISC, RISC, and DSP processors and the advancements of the design, functions, and architecture of microprocessors. The publication first ponders on complex instruction set computers and 32-bit CISC processors. Discussions focus on MC68881 and MC68882 floating point coprocessors, debugging support, MC68020 32-bit performance standard, bus interfaces, MC68010 SUPERVISOR resource, and high-level language support. The manuscript then covers the RISC challenge, digital signal processing, and memory management and caches. Topics include implementing memory systems, multitasking and user/supervisor conflicts, partitioning the system, cache size and organization, DSP56000 family, MC88100 programming model, M88000 family, and the 80/20 rule. The text examines the selection of a microprocessor architecture, changing design cycle, semiconductor technology, multiprocessing, and real-time software, interrupts, and exceptions. Concerns include locating associated tasks, MC88100 interrupt service routines, single- and multiple-threaded operating systems, and the MC68300 family. The publication is a valuable reference for computer engineers and researchers interested in microprocessor architectures and systems.
  • Entire Functions

    • 1st Edition
    • A. I. Markushevich
    • English
    Entire Functions focuses on complex numbers and the algebraic operations on them and the basic principles of mathematical analysis. The book first elaborates on the concept of an entire function, including the natural generalization of the concept of a polynomial and power series. The text then takes a look at the maximum absolute value and the order of an entire function, as well as calculations for the coefficients of power series representing a given function, use of integrals, and complex numbers. The publication elaborates on the zeros of an entire function and the fundamental theorem of algebra and Picard’s little theorem. Calculations for the zeros of an entire function and numerical representations of Liouville's theorem and Picard’s little theorem are presented. The book also examines algebraic relationships and addition theorems, including an explanation of Weierstrass' theorem and Picard’s little theorem. The manuscript is a vital reference for students interested in the numerical approaches involved in entire functions.
  • Geometry of Numbers

    • 1st Edition
    • C. G. Lekkerkerker
    • N. G. De Bruijn + 2 more
    • English
    Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume VIII: Geometry of Numbers focuses on bodies and lattices in the n-dimensional euclidean space. The text first discusses convex bodies and lattice points and the covering constant and inhomogeneous determinant of a set. Topics include the inhomogeneous determinant of a set, covering constant of a set, theorem of Minkowski-Hlawka, packing of convex bodies, successive minima and determinant of a set, successive minima of a convex body, extremal bodies, and polar reciprocal convex bodies. The publication ponders on star bodies, as well as points of critical lattices on the boundary, reducible, and irreducible star bodies and reduction of automorphic star bodies. The manuscript reviews homogeneous and inhomogeneous s forms and some methods. Discussions focus on asymmetric inequalities, inhomogeneous forms in more variables, indefinite binary quadratic forms, diophantine approximation, sums of powers of linear forms, spheres and quadratic forms, and a method of Blichfeldt and Mordell. The text is a dependable reference for researchers and mathematicians interested in bodies and lattices in the n-dimensional euclidean space.
  • Additive and Polynomial Representations

    • 1st Edition
    • David H. Krantz + 2 more
    • English
    Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utilization of constructive methods, and as a series of isomorphism theorems leading to consistent numerical solutions. The text also explains the counting of units in relation to an empirical relational structure which contains a concatenation operation. The book notes some special variants which arise in connection with relativity and thermodynamics. The text cites examples from physics and psychology for which additive conjoint measurement provides a possible method of fundamental measurement. The book will greatly benefit mathematicians, econometricians, and academicians in advanced mathematics or physics.
  • Arithmetic for the Mature Student

    • 1st Edition
    • F. H. George
    • F. H. George
    • English
    Arithmetic for the Mature Student provides information pertinent to the basic operations of arithmetic, including addition, subtraction, multiplication, and division. This book covers a variety of topics, including percentages, fractions, and factors. Organized into five chapters, this book begins with an overview of the instructions on how to use the book. This text then explains arithmetic, which is made up of a set of rules for performing jobs with ordinary numbers. Other chapters consider adding, subtracting, multiplying, and dividing numbers that come between 0 and 1. This book discusses as well an alternative notation for describing fractions. The final chapter deals with that particular type of standard fraction called a percentage. This book is a valuable resource for students in arithmetic.
  • Topology

    Volume II
    • 1st Edition
    • K. Kuratowski
    • English
    Topology, Volume II deals with topology and covers topics ranging from compact spaces and connected spaces to locally connected spaces, retracts, and neighborhood retracts. Group theory and some cutting problems are also discussed, along with the topology of the plane. Comprised of seven chapters, this volume begins with a discussion on the compactness of a topological space, paying particular attention to Borel, Lebesgue, Riesz, Cantor, and Bolzano-Weierstrass conditions. Semi-continuity and topics in dimension theory are also considered. The reader is then introduced to the connectedness of a space, with emphasis on the general properties and monotone mappings of connected spaces; local connectedness of a topological space; absolute retracts and contractible spaces; and general properties of commutative groups. Qualitative problems related to polygonal arcs are also examined, together with cohomotopic multiplication and duality theorems. The final chapter is devoted to the topology of a plane and evaluates the concept of the Janiszewski space. This monograph will be helpful to students and practitioners of algebra and mathematics.
  • Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations

    • 1st Edition
    • V. L. Zaguskin
    • English
    Handbook of Numerical Methods for the Solution of Algebraic and Transcendental Equations provides information pertinent to algebraic and transcendental equations. This book indicates a well-grounded plan for the solution of an approximate equation. Organized into six chapters, this book begins with an overview of the solution of various equations. This text then outlines a non-traditional theory of the solution of approximate equations. Other chapters consider the approximate methods for the calculation of roots of algebraic equations. This book discusses as well the methods for making roots more accurate, which are essential in the practical application of Berstoi's method. The final chapter deals with the methods for the solution of simultaneous linear equations, which are divided into direct methods and methods of successive approximation. This book is a valuable resource for students, engineers, and research workers of institutes and industrial enterprises who are using mathematical methods in the solution of technical problems.
  • Non-Linear Transformations of Stochastic Processes

    • 1st Edition
    • P. I. Kuznetsov + 2 more
    • English
    Non-Linear Transformations of Stochastic Processes focuses on the approaches, methodologies, transformations, and computations involved in the non-linear transformations of stochastic processes. The selection first underscores some problems of the theory of stochastic processes and the transmission of random functions through non-linear systems. Discussions focus on the transformation of moment functions for the general non-linear transformation; conversion formulas for correlation functions; transformation of moment functions for the simplest type of non-linear transformation; and normalization of the linear system of probability distribution laws. The text then ponders on quasi-moment functions in the theory of random processes and correlation functions in the theory of the Brownian motion generalization of the Fokker-Planck equation. The manuscript elaborates on the correlation functions of random sequences of rectangular pulses; method of determining the envelope of quasi-harmonic fluctuations; and the problem of measuring electrical fluctuations with the aid of thermoelectric devices. The book then examines the effect of signal and noise on non-linear elements and the approximate method of calculating the correlation function of stochastic signals. The selection is a dependable source of information for researchers interested in the non-linear transformations of stochastic processes.
  • The Office of the Future

    Communication and Computers
    • 1st Edition
    • Ronald P. Uhlig + 2 more
    • English
    Monograph Series of the International Council for Computer Communications, Volume 1: The Office of the Future: Communication and Computers focuses on the advancements in the processes, technologies, techniques, principles, and approaches involved in communication and computers, including computer based tools, data gathering and information retrieval, and office automation. The publication first elaborates on the automated office of the future, tools to support the communication activity, and text editing tools for generating, organizing, analyzing, and transforming information. Discussions focus on generating, organizing, and analyzing information, basic message system concepts, impact of computer networks, and other processes in the office. The text then examines the integration of computer based tools, data gathering and information retrieval tools, coordination tools in the office of the future, and tools to support office processes. The manuscript ponders on the integration of the spoken word with interactive computer based office support systems, underlying technology, digital channel, and software aspects of the office environment utilizing the micro-processor. Topics include single board computer, advances in digital computer communications technology, future directions for digital networks, bandwidth availability, and storage and retrieval of voice information. The book is a dependable source of data for computer science experts and researchers interested in the relationship of communication and computers.
  • A Guidebook to Fortran on Supercomputers

    • 1st Edition
    • John M. Levesque + 1 more
    • English
    A Guidebook to Fortran on Supercomputers presents in detail both the underlying architecture of supercomputers and the manner by which a compiler maps Fortran code onto that architecture. This book outlines the constructs preventing full optimization and provides specific strategies for restructuring a program. Organized into four chapters, this book begins with an overview of the basic concepts of vector, scalar, and parallel processing. This text then provides an in-depth look at the architectural features of a variety of existing machines, with emphasis to the features common to many of them. Other chapters consider the optimization techniques used by compilers and how a programmer can take advantage of this knowledge in restructuring existing programs and in the development of new applications. The final chapter presents examples of loops from real-world programs, with a discussion of the inherent problems. This book is a valuable resource for scientists, engineers, students, and research workers.
  • Methodologies of Pattern Recognition

    • 1st Edition
    • Satosi Watanabe
    • English
    Methodologies of Pattern Recognition is a collection of papers that deals with the two approaches to pattern recognition (geometrical and structural), the Robbins-Monro procedures, and the implications of interactive graphic computers for pattern recognition methodology. Some papers describe non-supervised learning in statistical pattern recognition, parallel computation in pattern recognition, and statistical analysis as a tool to make patterns emerge from data. One paper points out the importance of cluster processing in visual perception in which proximate points of similar brightness values form clusters. At higher levels of mental activity humans are efficient in clumping complex items into clusters. Another paper suggests a recognition method which combines versatility and an efficient noise-proofness in dealing with the two main problems in the field of recognition. These difficulties are the presence of a large variety of observed signals and the presence of interference. One paper reports on a possible feature selection for pattern recognition systems employing the minimization of population entropy. Electronic engineers, physicists, physiologists, psychologists, logicians, mathematicians, and philosophers will find great rewards in reading the above collection.
  • Computer Capacity Planning

    Theory and Practice
    • 1st Edition
    • Shui F. Lam + 1 more
    • English
    Computer Capacity Planning: Theory and Practice deals with the theory and practice of computer capacity planning. Topics covered range from the tasks involved in computer capacity planning (inventory, workload measures and characterization, performance measurement, etc.) to environmental influences on computer capacity planning practices. An empirical study of computer capacity planning practices is also discussed, and the component approach is compared with the system modeling approach. Comprised of six chapters, this book begins with an introduction to the theories and techniques on computer capacity planning, along with the significance of computer capacity planning and the major elements in the process of computer capacity planning. The functions of each element are explained and the various techniques and tools for carrying out these functions are presented. The next chapter shows how these elements can be tied together to achieve the objective of computer capacity planning, that is, matching computer resources to computer workload in a cost-effective manner. The second part of the book examines how different organizations may adopt different capacity planning methods and how to improve the applicability of the theory and the quality of the practice on computer capacity planning. This monograph should be of interest to researchers, data processing managers, and analysts including those in charge of computer capacity planning and performance evaluation; auditors and quality assurance personnel; equipment manufacturers and software developers; and students in information sciences.
  • Numerical Methods for Differential Systems

    Recent Developments in Algorithms, Software, and Applications
    • 1st Edition
    • L. Lapidus + 1 more
    • English
    Numerical Methods for Differential Systems: Recent Developments in Algorithms, Software, and Applications reviews developments in algorithms, software, and applications of numerical methods for differential systems. Topics covered include numerical algorithms for ordinary and partial differential equations (ODE/PDEs); theoretical approaches to the solution of nonlinear algebraic and boundary value problems via associated differential systems; integration algorithms for initial-value ODEs with particular emphasis on stiff systems; finite difference algorithms; and general- and special-purpose computer codes for ODE/PDEs. Comprised of 15 chapters, this book begins with an introduction to high-order A-stable averaging algorithms for stiff differential systems, followed by a discussion on second derivative multistep formulas based on g-splines; numerical integration of linearized stiff ODEs; and numerical solution of large systems of stiff ODEs in a modular simulation framework. Subsequent chapters focus on numerical methods for mass action kinetics; a systematized collection of codes for solving two-point boundary value problems; general software for PDEs; and the choice of algorithms in automated method of lines solution of PDEs. The final chapter is devoted to quality software for ODEs. This monograph should be of interest to mathematicians, chemists, and chemical engineers.
  • Young Tableaux in Combinatorics, Invariant Theory, and Algebra

    An Anthology of Recent Work
    • 1st Edition
    • Joseph P.S. Kung
    • English
    Young Tableaux in Combinatorics, Invariant Theory, and Algebra: An Anthology of Recent Work is an anthology of papers on Young tableaux and their applications in combinatorics, invariant theory, and algebra. Topics covered include reverse plane partitions and tableau hook numbers; some partitions associated with a partially ordered set; frames and Baxter sequences; and Young diagrams and ideals of Pfaffians. Comprised of 16 chapters, this book begins by describing a probabilistic proof of a formula for the number f? of standard Young tableaux of a given shape f?. The reader is then introduced to the generating function of R. P. Stanley for reverse plane partitions on a tableau shape; an analog of Schensted's algorithm relating permutations and triples consisting of two shifted Young tableaux and a set; and a variational problem for random Young tableaux. Subsequent chapters deal with certain aspects of Schensted's construction and the derivation of the Littlewood-Richardso... rule for the multiplication of Schur functions using purely combinatorial methods; monotonicity and unimodality of the pattern inventory; and skew-symmetric invariant theory. This volume will be helpful to students and practitioners of algebra.
  • Applied Nonlinear Analysis

    Proceedings of an International Conference on Applied Nonlinear Analysis, Held at the University of Texas at Arlington, Arlington, Texas, April 20–22, 1978
    • 1st Edition
    • V. Lakshmikantham
    • English
    Applied Nonlinear Analysis contains the proceedings of an International Conference on Applied Nonlinear Analysis, held at the University of Texas at Arlington, on April 20-22, 1978. The papers explore advances in applied nonlinear analysis, with emphasis on reaction-diffusion equations; optimization theory; constructive techniques in numerical analysis; and applications to physical and life sciences. In the area of reaction-diffusion equations, the discussions focus on nonlinear oscillations; rotating spiral waves; stability and asymptotic behavior; discrete-time models in population genetics; and predator-prey systems. In optimization theory, the following topics are considered: inverse and ill-posed problems with application to geophysics; conjugate gradients; and quasi-Newton methods with applications to large-scale optimization; sequential conjugate gradient-restoration algorithm for optimal control problems with non-differentiable constraints; differential geometric methods in nonlinear programming; and equilibria in policy formation games with random voting. In the area of constructive techniques in numerical analysis, numerical and approximate solutions of boundary value problems for ordinary and partial differential equations are examined, along with finite element analysis and constructive techniques for accretive and monotone operators. In addition, the book explores turbulent fluid flows; stability problems for Hopf bifurcation; product integral representation of Volterra equations with delay; weak solutions of variational problems, nonlinear integration on measures; and fixed point theory. This monograph will be helpful to students, practitioners, and researchers in the field of mathematics.
  • Pathology, Vector Studies, and Culture

    • 1st Edition
    • Julius P. Kreier
    • English
    Malaria: Volume 2, Pathology, Vector Studies, and Culture is a collection of papers that deals with erythrocyte destruction mechanism in malaria, the pathology of malaria, colonization of laboratory mosquitoes, and their transmission of plasmodia. Other papers describe the culture of the invertebrate stages of plasmodia, of mosquito tissues, and also of erythrocytic and exoerythrocytic stages of plasmodia. One paper constructs a model to show the roles of the different destructive and regenerative processes in the mechanisms of erythrocyte destruction in malaria. Another paper describes the organ changes and physiopathological mechanism connected with Plasmodium infection. These organs concern the spleen, liver, heart, and vascular system. One paper reviews the procedures involved in malaria transmission by mosquitoes, as well as some specialized procedures unique in avian, rodent, simian, and human malarias. Another paper discusses the benefits and drawbacks of a culture medium based on the composition of adult anopheline hemolymph. This medium should lead to a rapid growth rate in primary cultures of mosquito cells and a shorter interval of adaptation for continuous cell lines. The collection can prove useful for pharmacologists, general medical practitioners, investigators, and laboratory technicians involved in mosquito borne diseases or tropical medicine research.
  • Computer Science and Multiple-Valued Logic

    Theory and Applications
    • 1st Edition
    • David C. Rine
    • English
    Computer Science and Multiple-Valued Logic: Theory and Applications focuses on the processes, methodologies, and approaches involved in multiple-valued logic and its relationship to computer science. The selection first tackles an introduction to multiple-valued logic, lattice theory of post algebras, multiple-valued logic design and applications in binary computers, smallest many-valued logic for the treatment of complemented and uncomplemented error signals, and chain based lattices. Discussions focus on formulation, representation theory, theory and circuit design, logical tables, and unary operations. The text then examines multiple-valued signal processing with limiting, development of multiple-valued logic as related to computer science, p-algebras, and an algorithm for axiomatizing every finite logic. The book takes a look at completeness properties of multiple-valued logic algebras, computer simplification of multi-valued switching functions, and minimization of multivalued functions. Topics include generation of prime implicants, realizations, minimization algorithms, decomposition algorithm for multi-valued switching functions, and relation between the sum-of-products form and array of cubes. The selection is aimed at computer engineers, computer scientists, applied mathematicians, and physicists interested in multiple-valued logic as the discipline relates to computer engineering and computer science.
  • Discrete Computational Structures

    • 1st Edition
    • Robert R. Korfhage
    • Werner Rheinboldt
    • English
    Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasizes combinatorics and probability. Examples show different techniques of the general process of enumerating objects. Combinatorics cover permutations, enumerators for combinations, Stirling numbers, cycle classes of permutations, partitions, and compositions. The book cites as example the interplay between discrete mathematics and computing using a system of distinct representatives (SDR) problem. The problem, originating from group theory, graph theory, and set theory can be worked out by the student with a network model involving computers to generate and analyze different scenarios. The book is intended for sophomore or junior level, corresponding to the course B3, "Introduction to Discrete Structures," in the ACM Curriculum 68, as well as for mathematicians or professors of computer engineering and advanced mathematics.
  • Protecting Information on Local Area Networks

    • 1st Edition
    • James A Schweitzer
    • English
    Protecting Information on Local Area Networks presents the various types of networks and explains why they are being expanded at such a rapid pace. This book considers how management can gain control of the valuable network-services information resources generally available. Organized into three parts encompassing seven chapters, this book begins with an overview of the various networks and their operations. This text then discusses the appropriate management actions to ensure some control over the use of networks and the business information resource. Other chapters consider the management rationale for network information security and explain the development of a company information network security policy. This book discusses as well security or network-connected personal computers. The final chapter deals with a number of major vulnerabilities of information when communicated or processed on network-connected personal computers. This book is a valuable resource for research scientists, technical security specialists, information systems specialists, and systems administrators.
  • Symposia Mathematica

    • 1st Edition
    • Sam Stuart
    • English
    Symposia Mathematica, Volume I focuses on research in the field of mathematics and its applications. This book discusses the definition of S-semigroup, extensions of R modules, structure of H, laws of conservation and equations of motion, and measures of strain. The basic equations for continua with internal rotations, general concepts of the discrete particle mechanics of matter, and implications of the first law of thermodynamics are also elaborated. This text likewise covers the homomorphism theorem, magneto-elastic interactions, transition from discrete particle mechanics to continuum mechanics, and passage to the continuum. This publication is suitable for mathematicians, specialists, and students interested in mathematical structures.
  • Distributed Computer Systems

    Theory and Practice
    • 1st Edition
    • H. S. M. Zedan
    • English
    Distributed Computer Systems: Theory and Practice is a collection of papers dealing with the design and implementation of operating systems, including distributed systems, such as the amoeba system, argus, Andrew, and grapevine. One paper discusses the concepts and notations for concurrent programming, particularly language notation used in computer programming, synchronization methods, and also compares three classes of languages. Another paper explains load balancing or load redistribution to improve system performance, namely, static balancing and adaptive load balancing. For program efficiency, the user can choose from various debugging approaches to locate or fix errors without significantly disturbing the program behavior. Examples of debuggers pertain to the ada language and the occam programming language. Another paper describes the architecture of a real-time distributed database system used for computer network management, monitoring integration, as well as administration and control of both local area or wide area communications networks. The book can prove helpful to programmers, computer engineers, computer technicians, and computer instructors dealing with many aspects of computers, such as programming, hardware interface, networking, engineering or design.
  • The Desktop Fractal Design Handbook

    • 1st Edition
    • Michael F. Barnsley
    • English
    The Desktop Fractal Design Handbook is a four-chapter introductory text to fractal geometry. The underlying algorithms are derived from mathematics, which is reflected in the images they produce. Chapter 1 provides an overview of the products of the desktop fractal design system. Chapter 2 describes the installation and operation of hardware and operating system of the design system, along with its maintenance. Chapter 3 outlines the use of the desktop fractal design system, specifically on hot to design fractals on the fractal design screen, maps, paintings, and help screens. Chapter 4 focuses on the many practical applications of fractals. This book will be of value to mathematicians, engineers, graphic artists, teachers, and students.
  • Study Guide for College Algebra and Trigonometry

    • 1st Edition
    • James W. Snow + 2 more
    • English
    Study Guide for College Algebra and Trigonometry is a supplement material to the basic text, College Algebra and Trigonometry. It is written to assist the student in learning mathematics effectively. The book provides detailed solutions to exercises found in the text. Students are encouraged to use these solutions to find a way to approach a problem. The Study Guide and Solutions Manual consists of four major components: basic concepts that should be learned from each unit, what was learned upon completion of each unit, solutions to selected problems, and a short chapter quiz, including the answers, covering the concepts and problem types. Students of algebra and trigonometry in the college level will find the book very useful.
  • Programming Primer for the Macintosh®

    Volume 1
    • 1st Edition
    • John M. May + 1 more
    • English
    Programming Primer for the Macintosh, Volume 1 focuses on the principles and operations of the Macintosh system. The publication first offers information on the development environment, creating a simple program with Symantec C++, and a review of C++. Discussions focus on pointers, handles, patterns, points, creating a source file, compiling the program, adding libraries, adding file to the subject, building an application, and useful tools. The text then takes a look at the Macintosh ROM, Mac programs and system software, and toolbox managers. Topics include menu, window, control, and dialog manager, alerts, desktop interface, event-driven programming, trap mechanism, interface and library files, stack frame incompatibility, and the relationship between an application and toolbox. The book examines QuickDraw, alerts, and dialogs, memory manager, and object-oriented programming. Concerns include structures, linked list example, new and delete operators, and handling lines, rectangles, round rectangles, ovals, arcs, and polygons The publication is a dependable reference for computer programmers and researchers interested in the Macintosh system.
  • Pattern-Directed Inference Systems

    • 1st Edition
    • D. A. Waterman + 1 more
    • English
    Pattern-Directed Inference Systems provides a description of the design and implementation of pattern-directed inference systems (PDIS) for various applications. The book also addresses the theoretical significance of PDIS for artificial intelligence and cognitive psychology. The book is divided into eight sections. The introduction provides a brief overview of pattern-directed inference systems, including a historical perspective, a review of basic concepts, and a survey of work in this area. Subsequent chapters address topics on architecture and design, methods for accessing and controlling rule based systems, methods for obtaining adaptive behavior via rule-based systems and cognitive modeling. Constructing models of human information processing, natural language understanding and multilevel systems and complexity are described as well. The last section discusses the earlier chapters in the book and provides a unifying set of principles for the PDIS formalism. Computer scientists, psychologists, engineers, and researchers in artificial intelligence will find the book very informative.
  • Generalized Inverses and Applications

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

    Human and Machine Perception
    • 1st Edition
    • Harry Wechsler
    • English
    Neural Networks for Perception, Volume 1: Human and Machine Perception focuses on models for understanding human perception in terms of distributed computation and examples of PDP models for machine perception. 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 book is organized into two parts. The first part focuses on human perception. Topics on network model of object recognition in human vision, the self-organization of functional architecture in the cerebral cortex, and the structure and interpretation of neuronal codes in the visual system are detailed under this part. Part two covers the relevance of neural networks for machine perception. Subjects considered under this section include the multi-dimensional linear lattice for Fourier and Gabor transforms, multiple- scale Gaussian filtering, and edge detection; aspects of invariant pattern and object recognition; and neural network for motion processing. Neuroscientists, computer scientists, engineers, and researchers in artificial intelligence will find the book useful.
  • Vector and Operator Valued Measures and Applications

    • 1st Edition
    • Don H. Tucker + 1 more
    • English
    Vector and Operator Valued Measures and Applications is a collection of papers presented at the Symposium on Vector and Operator Valued Measures and Applications held in Alta, Utah, on August 7-12, 1972. The symposium provided a forum for discussing vector and operator valued measures and their applications to various areas such as stochastic integration, electrical engineering, control theory, and scattering theory. Comprised of 37 chapters, this volume begins by presenting two remarks related to the result due to Kolmogorov: the first is a theorem holding for nonnegative definite functions from T X T to C (where T is an arbitrary index set), and the second applies to separable Hausdorff spaces T, continuous nonnegative definite functions ? from T X T to C, and separable Hilbert spaces H. The reader is then introduced to the extremal structure of the range of a controlled vector measure ? with values in a Hausdorff locally convex space X over the field of reals; how the theory of vector measures is connected with the theory of compact and weakly compact mappings on certain function spaces; and Daniell and Daniell-Bochner type integrals. Subsequent chapters focus on the disintegration of measures and lifting; products of spectral measures; and mean convergence of martingales of Pettis integrable functions. This book should be of considerable use to workers in the field of mathematics.
  • Study Guide for Applied Finite Mathematics

    • 3rd Edition
    • Nicholas A. Macri
    • English
    Study Guide for Applied Finite Mathematics, Third Edition is a study guide that introduces beginners to the fundamentals of finite mathematics and its various realistic and relevant applications. Some applications of probability, game theory, and Markov chains are given. Each chapter includes exercises, and each set begins with basic computational "drill" problems and then progresses to problems with more substance. Comprised of 10 chapters, this book begins with exercises related to set theory and concepts such as the union and intersection of sets. Exercises on Cartesian coordinate systems and graphs as well as linear programming from a geometric and algebraic point of view are then given. Subsequent chapters deal with matrices, the solution of linear systems, and applications; the simplex method for solving linear programming problems; and probability and probability models for finite sample spaces as well as permutations, combinations, and counting methods. Basic concepts in statistics are also considered, along with the mathematics of finance. Some applications of probability, game theory, and Markov chains are also considered. This monograph is intended for students and instructors of applied mathematics.
  • Workbook for Introductory Statistics for the Behavioral Sciences

    • 2nd Edition
    • Robert B. Ewen
    • English
    Workbook for Introductory Statistics for the Behavioral Sciences, Second Edition provides an introduction to the concepts of statistics. This book aims to help students obtain the necessary practice in a first course in statistics, which is essential to learning and understanding the material. This edition begins with an overview of summation notation exercises with additional computational practices. This text then provides computational exercises for regular frequency distributions, grouped frequency distributions, cumulative frequency distribution, graphic representations, measures of central tendency, measures of variability, and general transformations. This book discusses as well the probability and the general strategy of inferential statistics as well as the differences between the means of two populations. The reader is also introduced to the main advantage of nonparametric and distribution-free statistical tests in which they do not require the population being sampled to the normally distributed. This book is a valuable resource for students of behavioral and social sciences.
  • Introduction to Asymptotics and Special Functions

    • 1st Edition
    • F. W. J. Olver
    • English
    Introduction to Asymptotics and Special Functions is a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable are discussed, along with contour integrals and differential equations with regular and irregular singularities. The Liouville-Green approximation is also considered. Comprised of seven chapters, this volume begins with an overview of the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on integrals of a real variable. Contour integrals are then examined, paying particular attention to Laplace integrals with a complex parameter and Bessel functions of large argument and order. Subsequent chapters focus on differential equations having regular and irregular singularities, with emphasis on Legendre functions as well as Bessel and confluent hypergeometric functions. A chapter devoted to the Liouville-Green approximation tackles asymptotic properties with respect to parameters and to the independent variable, eigenvalue problems, and theorems on singular integral equations. This monograph is intended for students needing only an introductory course to asymptotics and special functions.
  • Handbook of Networking & Connectivity

    • 1st Edition
    • Gary R. McClain
    • English
    Handbook of Networking & Connectivity focuses on connectivity standards in use, including hardware and software options. The book serves as a guide for solving specific problems that arise in designing and maintaining organizational networks. The selection first tackles open systems interconnection, guide to digital communications, and implementing TCP/IP in an SNA environment. Discussions focus on elimination of the SNA backbone, routing SNA over internets, connectionless versus connection-oriented networks, internet concepts, application program interfaces, basic principles of layering, protocols and services, application layer, and conformance testing. The book then takes a look at integrated services digital network, an overview of the synchronous optical network, and X.25 and worldwide networking. The publication ponders on Metropolitan Area Networks (MAN), an overview of the switched multimegabit data service, and Ethernet/802.3 and Token Ring/802.5. Topics include Ethernet versus token ring, Ethernet/802.3, customer network management, MAN conception and technology, and SMDS specifications and sources and interface protocol. The selection is a vital source of data for systems professionals and researchers interested in networking and connectivity.