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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.

  • Probability Inequalities in Multivariate Distributions

    • 1st Edition
    • Y. L. Tong
    • Z. W. Birnbaum + 1 more
    • English
    Probability Inequalities in Multivariate Distributions is a comprehensive treatment of probability inequalities in multivariate distributions, balancing the treatment between theory and applications. The book is concerned only with those inequalities that are of types T1-T5. The conditions for such inequalities range from very specific to very general. Comprised of eight chapters, this volume begins by presenting a classification of probability inequalities, followed by a discussion on inequalities for multivariate normal distribution as well as their dependence on correlation coefficients. The reader is then introduced to inequalities for other well-known distributions, including the multivariate distributions of t, chi-square, and F; inequalities for a class of symmetric unimodal distributions and for a certain class of random variables that are positively dependent by association or by mixture; and inequalities obtainable through the mathematical tool of majorization and weak majorization. The book also describes some distribution-free inequalities before concluding with an overview of their applications in simultaneous confidence regions, hypothesis testing, multiple decision problems, and reliability and life testing. This monograph is intended for mathematicians, statisticians, students, and those who are primarily interested in inequalities.

  • Representations of Commonsense Knowledge

    • 1st Edition
    • Ernest Davis
    • Ronald J. Brachman
    • English
    Representations of Commonsense Knowledge provides a rich language for expressing commonsense knowledge and inference techniques for carrying out commonsense knowledge. This book provides a survey of the research on commonsense knowledge. Organized into 10 chapters, this book begins with an overview of the basic ideas on artificial intelligence commonsense reasoning. This text then examines the structure of logic, which is roughly analogous to that of a programming language. Other chapters describe how rules of universal validity can be applied to facts known with absolute certainty to deduce other facts known with absolute certainty. This book discusses as well some prominent issues in plausible inference. The final chapter deals with commonsense knowledge about the interrelations and interactions among agents and discusses some issues in human and social interactions that have been studied in the artificial intelligence literature. This book is a valuable resource for students on a graduate course on knowledge representation.

  • Integration of Equations of Parabolic Type by the Method of Nets

    • 1st Edition
    • V. K. Saul'Yev
    • I. N. Sneddon + 2 more
    • English
    International Series of Monographs in Pure and Applied Mathematics, Volume 54: Integration of Equations of Parabolic Type by the Method of Nets deals with solving parabolic partial differential equations using the method of nets. The first part of this volume focuses on the construction of net equations, with emphasis on the stability and accuracy of the approximating net equations. The method of nets or method of finite differences (used to define the corresponding numerical method in ordinary differential equations) is one of many different approximate methods of integration of partial differential equations. The other methods, and some based on newer equations, are described. By analyzing these newer methods, older and existing methods are evaluated. For example, the asymmetric net equations; the alternating method of using certain equations; and the method of mean arithmetic and multi-nodal symmetric method point out that when the accuracy needs to be high, the requirements for stability become more defined. The methods discussed are very theoretical and methodological. The second part of the book concerns the practical numerical solution of the equations posed in Part I. Emphasis is on the commonly used iterative methods that are programmable on computers. This book is suitable for statisticians and numerical analysts and is also recommended for scientists and engineers with general mathematical knowledge.

  • Elements of Analytical Dynamics

    • 1st Edition
    • Rudolph Kurth
    • I. N. Sneddon + 1 more
    • English
    Elements of Analytical Dynamics deals with dynamics, which studies the relationship between motion of material bodies and the forces acting on them. This book is a compilation of lectures given by the author at the Georgia and Institute of Technology and formed a part of a course in Topological Dynamics. The book begins by discussing the notions of space and time and their basic properties. It then discusses the Hamilton-Jacobi theory and Hamilton's principle and first integrals. The text concludes with a discussion on Jacobi's geometric interpretation of conservative systems. This book will be of direct use to graduate students of Mathematics with minimal background in Theoretical Mechanics.

  • Handbook of Mathematics

    • 1st Edition
    • L. Kuipers + 1 more
    • English
    International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examples), Rolle's theorem, and the logarithmic function. The book also discusses extensively the functions of two variables in partial differentiation and multiple integrals. The book then describes the theory of functions, ordinary differential functions, special functions and the topic of sequences and series. The book explains vector analysis (which includes dyads and tensors), the use of numerical analysis, probability statistics, and the Laplace transform theory. Physicists, engineers, chemists, biologists, and statisticians will find this book useful.

  • The Expected-Outcome Model of Two-Player Games

    • 1st Edition
    • Bruce Abramson
    • English
    The Expected-Outcome Model of Two-Player Games deals with the expected-outcome model of two-player games, in which the relative merit of game-tree nodes, rather than board positions, is considered. The ambiguity of static evaluation and the problems it generates in the search system are examined and the development of a domain-independent static evaluator is described. Comprised of eight chapters, this book begins with an overview of the rationale for the mathematical study of games, followed by a discussion on some previous artificial intelligence (AI) research efforts on game-trees. The next section opens with the definition of a node's expected-outcome value as the expected value of the leaves beneath it. The expected-outcome model is outlined, paying particular attention to the expected-outcome value of a game-tree node. This model was implemented on some small versions of tic-tac-toe and Othello. The book also presents results that offer strong support for both the validity of the expected-outcome model and the rationality of its underlying assumptions. This monograph is intended for specialists in AI and computer science.

  • Homology Theory on Algebraic Varieties

    • 1st Edition
    • Andrew H. Wallace
    • I. N. Sneddon
    • English
    Homology Theory on Algebraic Varieties, Volume 6 deals with the principles of homology theory in algebraic geometry and includes the main theorems first formulated by Lefschetz, one of which is interpreted in terms of relative homology and another concerns the Poincaré formula. The actual details of the proofs of these theorems are introduced by geometrical descriptions, sometimes aided with diagrams. This book is comprised of eight chapters and begins with a discussion on linear sections of an algebraic variety, with emphasis on the fibring of a variety defined over the complex numbers. The next two chapters focus on singular sections and hyperplane sections, focusing on the choice of a pencil in the latter case. The reader is then introduced to Lefschetz's first and second theorems, together with their corresponding proofs. The Poincaré formula and its proof are also presented, with particular reference to clockwise and anti-clockwise isomorphisms. The final chapter is devoted to invariant cycles and relative cycles. This volume will be of interest to students, teachers, and practitioners of pure and applied mathematics.

  • Lie Algebras

    • 1st Edition
    • Volume 104
    • Zhe-Xian Wan
    • I. N. Sneddon + 1 more
    • English
    Lie Algebras is based on lectures given by the author at the Institute of Mathematics, Academia Sinica. This book discusses the fundamentals of the Lie algebras theory formulated by S. Lie. The author explains that Lie algebras are algebraic structures employed when one studies Lie groups. The book also explains Engel's theorem, nilpotent linear Lie algebras, as well as the existence of Cartan subalgebras and their conjugacy. The text also addresses the Cartan decompositions and root systems of semi-simple Lie algebras and the dependence of structure of semi-simple Lie algebras on root systems. The text explains in details the fundamental systems of roots of semi simple Lie algebras and Weyl groups including the properties of the latter. The book addresses the group of automorphisms and the derivation algebra of a Lie algebra and Schur's lemma. The book then shows the characters of irreducible representations of semi simple Lie algebras. This book can be useful for students in advance algebra or who have a background in linear algebra.

  • Multidimensional Singular Integrals and Integral Equations

    • 1st Edition
    • S. G. Mikhlin
    • I. N. Sneddon + 2 more
    • English
    Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.

  • Lambda-Matrices and Vibrating Systems

    • 1st Edition
    • Peter Lancaster
    • I. N. Sneddon + 2 more
    • English
    Lambda-Matrices and Vibrating Systems presents aspects and solutions to problems concerned with linear vibrating systems with a finite degrees of freedom and the theory of matrices. The book discusses some parts of the theory of matrices that will account for the solutions of the problems. The text starts with an outline of matrix theory, and some theorems are proved. The Jordan canonical form is also applied to understand the structure of square matrices. Classical theorems are discussed further by applying the Jordan canonical form, the Rayleigh quotient, and simple matrix pencils with latent vectors in common. The book then expounds on Lambda matrices and on some numerical methods for Lambda matrices. These methods explain developments of known approximations and rates of convergence. The text then addresses general solutions for simultaneous ordinary differential equations with constant coefficients. The results of some of the studies are then applied to the theory of vibration by applying the Lagrange method for formulating equations of motion, after the formula establishing the energies and dissipation functions are completed. The book describes the theory of resonance testing using the stationary phase method, where the test is carried out by applying certain forces to the structure being studied, and the amplitude of response in the structure is measured. The book also discusses other difficult problems. The text can be used by physicists, engineers, mathematicians, and designers of industrial equipment that incorporates motion in the design.

  • Foundations of Galois Theory

    • 1st Edition
    • M.M. Postnikov
    • I. N. Sneddon + 2 more
    • English
    Foundations of Galois Theory is an introduction to group theory, field theory, and the basic concepts of abstract algebra. The text is divided into two parts. Part I presents the elements of Galois Theory, in which chapters are devoted to the presentation of the elements of field theory, facts from the theory of groups, and the applications of Galois Theory. Part II focuses on the development of general Galois Theory and its use in the solution of equations by radicals. Equations that are solvable by radicals; the construction of equations solvable by radicals; and the unsolvability by radicals of the general equation of degree n ? 5 are discussed as well. Mathematicians, physicists, researchers, and students of mathematics will find this book highly useful.

  • Boundary Value Problems

    • 1st Edition
    • F. D. Gakhov
    • I. N. Sneddon + 2 more
    • English
    Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions. The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels. Although the book treats the theory of boundary value problems, emphasis is on linear problems with one unknown function. The definition of the Cauchy type integral, examples, limiting values, behavior, and its principal value are explained. The Riemann boundary value problem is emphasized in considering the theory of boundary value problems of analytic functions. The book then analyzes the application of the Riemann boundary value problem as applied to singular integral equations with Cauchy kernel. A second fundamental boundary value problem of analytic functions is the Hilbert problem with a Hilbert kernel; the application of the Hilbert problem is also evaluated. The use of Sokhotski's formulas for certain integral analysis is explained and equations with logarithmic kernels and kernels with a weak power singularity are solved. The chapters in the book all end with some historical briefs, to give a background of the problem(s) discussed. The book will be very valuable to mathematicians, students, and professors in advanced mathematics and geometrical functions.

  • The Algebraic Theory of Switching Circuits

    • 1st Edition
    • Gr. C. Moisil
    • English
    The Algebraic Theory of Switching Circuits covers the application of various algebraic tools to the delineation of the algebraic theory of switching circuits for automation with contacts and relays. This book is organized into five parts encompassing 31 chapters. Part I deals with the principles and application of Boolean algebra and the theory of finite fields (Galois fields). Part II emphasizes the importance of the sequential operation of the automata and the variables associated to the current and to the contacts. This part also tackles the recurrence relations that describe operations of the network and the principles of the so-called characteristic equations. Part III reviews the study of networks with secondary elements other than ordinary relays, while Part IV focuses on the fundamentals and application of multi-position contacts. Part V considers several topics related to circuit with electronic elements, including triodes, pentodes, transistors, and cryotrons. This book will be of great value to practicing engineers, mathematicians, and workers in the field of computers.

  • TREAT

    A New and Efficient Match Algorithm for AI Production System
    • 1st Edition
    • Daniel P. Miranker
    • English
    TREAT: A New and Efficient Match Algorithm for AI Production Systems describes the architecture and software systems embodying the DADO machine, a parallel tree-structured computer designed to provide significant performance improvements over serial computers of comparable hardware complexity in the execution of large expert systems implemented in production system form. This book focuses on TREAT as a match algorithm for executing production systems that is presented and comparatively analyzed with the RETE match algorithm. TREAT, originally designed specifically for the DADO machine architecture, handles efficiently both temporally redundant and non-temporally redundant production system programs. This publication is suitable for developers and specialists interested in match algorithms for AI production systems.

  • Nonparametric Functional Estimation

    • 1st Edition
    • B. L. S. Prakasa Rao
    • Z. W. Birnbaum + 1 more
    • English
    Nonparametric Functional Estimation is a compendium of papers, written by experts, in the area of nonparametric functional estimation. This book attempts to be exhaustive in nature and is written both for specialists in the area as well as for students of statistics taking courses at the postgraduate level. The main emphasis throughout the book is on the discussion of several methods of estimation and on the study of their large sample properties. Chapters are devoted to topics on estimation of density and related functions, the application of density estimation to classification problems, and the different facets of estimation of distribution functions. Statisticians and students of statistics and engineering will find the text very useful.

  • Multivariate Statistical Inference

    • 1st Edition
    • Narayan C. Giri
    • Z. W. Birnbaum + 1 more
    • English
    Multivariate Statistical Inference is a 10-chapter text that covers the theoretical and applied aspects of multivariate analysis, specifically the multivariate normal distribution using the invariance approach. Chapter I contains some special results regarding characteristic roots and vectors, and partitioned submatrices of real and complex matrices, as well as some special theorems on real and complex matrices useful in multivariate analysis. Chapter II deals with the theory of groups and related results that are useful for the development of invariant statistical test procedures, including the Jacobians of some specific transformations that are useful for deriving multivariate sampling distributions. Chapter III is devoted to basic notions of multivariate distributions and the principle of invariance in statistical testing of hypotheses. Chapters IV and V deal with the study of the real multivariate normal distribution through the probability density function and through a simple characterization and the maximum likelihood estimators of the parameters of the multivariate normal distribution and their optimum properties. Chapter VI tackles a systematic derivation of basic multivariate sampling distributions for the real case, while Chapter VII explores the tests and confidence regions of mean vectors of multivariate normal populations with known and unknown covariance matrices and their optimum properties. Chapter VIII is devoted to a systematic derivation of tests concerning covariance matrices and mean vectors of multivariate normal populations and to the study of their optimum properties. Chapters IX and X look into a treatment of discriminant analysis and the different covariance models and their analysis for the multivariate normal distribution. These chapters also deal with the principal components, factor models, canonical correlations, and time series. This book will prove useful to statisticians, mathematicians, and advance mathematics students.

  • Strong Approximations in Probability and Statistics

    • 1st Edition
    • M. Csörgo + 1 more
    • Z. W. Birnbaum + 1 more
    • English
    Strong Approximations in Probability and Statistics presents strong invariance type results for partial sums and empirical processes of independent and identically distributed random variables (IIDRV). This seven-chapter text emphasizes the applicability of strong approximation methodology to a variety of problems of probability and statistics. Chapter 1 evaluates the theorems for Wiener and Gaussian processes that can be extended to partial sums and empirical processes of IIDRV through strong approximation methods, while Chapter 2 addresses the problem of best possible strong approximations of partial sums of IIDRV by a Wiener process. Chapters 3 and 4 contain theorems concerning the one-time parameter Wiener process and strong approximation for the empirical and quantile processes based on IIDRV. Chapter 5 demonstrate the validity of previously discussed theorems, including Brownian bridges and Kiefer process, for empirical and quantile processes. Chapter 6 illustrate the approximation of defined sequences of empirical density, regression, and characteristic functions by appropriate Gaussian processes. Chapter 7 deal with the application of strong approximation methodology to study weak and strong convergence properties of random size partial sum and empirical processes. This book will prove useful to mathematicians and advance mathematics students.

  • Measure and Integral

    • 1st Edition
    • Konrad Jacobs
    • Z. W. Birnbaum + 1 more
    • English
    Probability and Mathematical Statistics: Measure and Integral provides information pertinent to the general mathematical notions and notations. This book discusses how the machinery of ?-extension works and how ?-content is derived from ?-measure. Organized into 16 chapters, this book begins with an overview of the classical Hahn–Banach theorem and introduces the Banach limits in the form of a major exercise. This text then presents the Daniell extension theory for positive ?-measures. Other chapters consider the transform of ?-contents and ?-measures by measurable mappings and kernels. This text is also devoted to a thorough study of the vector lattice of signed contents. This book discusses as well an abstract regularity theory and applied to the standard cases of compact, locally compact, and Polish spaces. The final chapter deals with the rudiments of the Krein–Milman theorem, along with some of their applications. This book is a valuable resource for graduate students.

  • Stochastic Integration

    • 1st Edition
    • Michel Metivier + 1 more
    • Z. W. Birnbaum + 1 more
    • English
    Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Stochastic Integration focuses on the processes, methodologies, and approaches involved in stochastic integration. The publication first takes a look at the Ito formula, stochastic integral equations, and martingales and semimartingales. Discussions focus on Meyer process and decomposition theorem, inequalities, examples of stochastic differential equations, general stochastic integral equations, and applications of the Ito formula. The text then elaborates on stochastic measures, including stochastic measures and related integration and the Riesz representation theorem. The manuscript tackles the special features of infinite dimensional stochastic integration, as well as the isometric integral of a Hubert-valued square integrable martingale, cylindrical processes, and stochastic integral with respect to 2-cylindrical martingales with finite quadratic variation. The book is a valuable reference for mathematicians and researchers interested in stochastic integration.

  • Martingale Limit Theory and Its Application

    • 1st Edition
    • P. Hall + 1 more
    • Z. W. Birnbaum + 1 more
    • English
    Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.

  • Probability Algebras and Stochastic Spaces

    • 1st Edition
    • Demetrios A. Kappos
    • Z. W. Birnbaum + 1 more
    • English
    Probability Algebras and Stochastic Spaces explores the fundamental notions of probability theory in the so-called “point-free” way. The space of all elementary random variables defined over a probability algebra in a “point-free” way is a base for the stochastic space of all random variables, which can be obtained from it by lattice-theoretic extension processes. This book is composed of eight chapters and begins with discussions of the definition, properties, scope, and extension of probability algebras. The succeeding chapters deal with the Cartesian product of probability algebras and the principles of stochastic spaces. These topics are followed by surveys of the expectation, moments, and spaces of random variables. The final chapters define generalized random variables and the Boolean homomorphisms of these variables. This book will be of great value to mathematicians and advance mathematics students.

  • Probabilistic Programming

    • 1st Edition
    • S. Vajda
    • Z. W. Birnbaum + 1 more
    • English
    Probabilistic Programming discusses a high-level language known as probabilistic programming. This book consists of three chapters. Chapter I deals with “wait-and-see” problems that require waiting until an observation is made on the random elements, while Chapter II contains the analysis of decision problems, particularly of so-called two-stage problems. The last chapter focuses on “chance constraints,” such as constraints that are not expected to be always satisfied, but only in a proportion of cases or “with given probabilities.” This text specifically deliberates the decision regions for optimality, probability distributions, Kall's Theorem, and two-stage programming under uncertainty. The complete problem, active approach, quantile rules, randomized decisions, and nonzero order rules are also covered. This publication is suitable for developers aiming to define and automatically solve probability models.

  • Probability Measures on Metric Spaces

    • 1st Edition
    • K. R. Parthasarathy
    • Z. W. Birnbaum + 1 more
    • English
    Probability Measures on Metric Spaces presents the general theory of probability measures in abstract metric spaces. This book deals with complete separable metric groups, locally impact abelian groups, Hilbert spaces, and the spaces of continuous functions. Organized into seven chapters, this book begins with an overview of isomorphism theorem, which states that two Borel subsets of complete separable metric spaces are isomorphic if and only if they have the same cardinality. This text then deals with properties such as tightness, regularity, and perfectness of measures defined on metric spaces. Other chapters consider the arithmetic of probability distributions in topological groups. This book discusses as well the proofs of the classical extension theorems and existence of conditional and regular conditional probabilities in standard Borel spaces. The final chapter deals with the compactness criteria for sets of probability measures and their applications to testing statistical hypotheses. This book is a valuable resource for statisticians.

  • Tables of the Function w (z)- e-z2 ? ex2 dx

    Mathematical Tables Series, Vol. 27
    • 1st Edition
    • K. A. Karpov
    • English
    Tables of the Function w(z) = e-z2 z?0ex2dx in the Complex Domain contains tables of the function in connection with the problem of the radio wave propagation. These tables are compiled in the Experimental-Computi... Laboratories of the Institute of Exact Mechanics and Computational Methods of the U.S.S.R. Academy of Sciences. The function w(z) is represented in the upper half-plane by the asymptotic series. Description of the tables and method of computation is provided. This book will prove useful to mathematicians and researchers.

  • Stochastic Convergence

    • 2nd Edition
    • Eugene Lukacs
    • Z. W. Birnbaum + 1 more
    • English
    Stochastic Convergence, Second Edition covers the theoretical aspects of random power series dealing with convergence problems. This edition contains eight chapters and starts with an introduction to the basic concepts of stochastic convergence. The succeeding chapters deal with infinite sequences of random variables and their convergences, as well as the consideration of certain sets of random variables as a space. These topics are followed by discussions of the infinite series of random variables, specifically the lemmas of Borel-Cantelli and the zero-one laws. Other chapters evaluate the power series whose coefficients are random variables, the stochastic integrals and derivatives, and the characteristics of the normal distribution of infinite sums of random variables. The last chapter discusses the characterization of the Wiener process and of stable processes. This book will prove useful to mathematicians and advance mathematics students.

  • Classical and Modern Integration Theories

    • 1st Edition
    • Ivan N. Pesin
    • Z. W. Birnbaum + 1 more
    • English
    Classical and Modern Integration Theories discusses classical integration theory, particularly that part of the theory directly associated with the problems of area. The book reviews the history and the determination of primitive functions, beginning from Cauchy to Daniell. The text describes Cauchy's definition of an integral, Riemann's definition of the R-integral, the upper and lower Darboux integrals. The book also reviews the origin of the Lebesgue-Young integration theory, and Borel's postulates that define measures of sets. W.H. Young's work provides a construction of the integral equivalent to Lebesque's construction with a different generalization of integrals leading to different approaches in solutions. Young's investigations aim at generalizing the notion of length for arbitrary sets by means of a process which is more general than Borel's postulates. The text notes that the Lebesgue measure is the unique solution of the measure problem for the class of L-measurable sets. The book also describes further modifications made into the Lebesgue definition of the integral by Riesz, Pierpont, Denjoy, Borel, and Young. These modifications bring the Lebesgue definition of the integral closer to the Riemann or Darboux definitions, as well as to have it associated with the concepts of classical analysis. The book can benefit mathematicians, students, and professors in calculus or readers interested in the history of classical mathematics.

  • Fourier Transforms of Distributions and Their Inverses

    A Collection of Tables
    • 1st Edition
    • Fritz Oberhettinger
    • Z. W. Birnbaum + 1 more
    • English
    Fourier Transforms of Distributions and Their Inverses: A Collection of Tables is a collection of tables on the integrals of Fourier transforms of distributions and their inverses involving the class of functions which are nonnegative and integrable over the interval. The emphasis is on the probability densities, and a number of examples are provided. This book is organized into two parts and begins with an introduction to those properties of characteristic functions which are important in probability theory, followed by a description of the tables and their use. The first three tables contain Fourier transforms of absolutely continuous distribution functions, namely, even functions (including Legendre functions); functions vanishing identically for negative values of the argument (including arbitrary powers); and functions that do not belong to either of the above classes. The transform pairs are numbered consecutively and arranged systematically according to the analytical character of the frequency function. The next two tables give the inverse transforms of the functions listed in the first and third tables, respectively. This monograph will appeal to students and specialists in the fields of probability and mathematical statistics.

  • Probability Theory

    A Historical Sketch
    • 1st Edition
    • L. E. Maistrov
    • Samuel Kotz
    • English
    Probability Theory: A Historical Sketch covers the probability theory, mainly axiomatization problems. The book discusses the prehistory of the probability theory; the first stage in the development of probability theory; and the development of probability theory to the middle of the 19th century. The text also describes the probability theory in the second half of the 19th century; and the axiomatic foundations of the probability theory. Historians and mathematicians will find the book invaluable.

  • Real Analysis and Probability

    Probability and Mathematical Statistics: A Series of Monographs and Textbooks
    • 1st Edition
    • Robert B. Ash
    • Z. W. Birnbaum + 1 more
    • English
    Real Analysis and Probability provides the background in real analysis needed for the study of probability. Topics covered range from measure and integration theory to functional analysis and basic concepts of probability. The interplay between measure theory and topology is also discussed, along with conditional probability and expectation, the central limit theorem, and strong laws of large numbers with respect to martingale theory. Comprised of eight chapters, this volume begins with an overview of the basic concepts of the theory of measure and integration, followed by a presentation of various applications of the basic integration theory. The reader is then introduced to functional analysis, with emphasis on structures that can be defined on vector spaces. Subsequent chapters focus on the connection between measure theory and topology; basic concepts of probability; and conditional probability and expectation. Strong laws of large numbers are also examined, first from the classical viewpoint, and then via martingale theory. The final chapter is devoted to the one-dimensional central limit problem, paying particular attention to the fundamental role of Prokhorov's weak compactness theorem. This book is intended primarily for students taking a graduate course in probability.

  • Statistics of Directional Data

    • 1st Edition
    • K. V. Mardia
    • Z. W. Birnbaum + 1 more
    • English
    Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Statistics of Directional Data aims to provide a systematic account of statistical theory and methodology for observations which are directions. The publication first elaborates on angular data and frequency distributions, descriptive measures, and basic concepts and theoretical models. Discussions focus on moments and measures of location and dispersion, distribution function, corrections for grouping, calculation of the mean direction and the circular variance, interrelations between different units of angular measurement, and diagrammatical representation. The book then examines fundamental theorems and distribution theory, point estimation, and tests for samples from von Mises populations. The text takes a look at non-parametric tests, distributions on spheres, and inference problems on the sphere. Topics include tests for axial data, point estimation, distribution theory, moments and limiting distributions, and tests of goodness of fit and tests of uniformity. The publication is a dependable reference for researchers interested in probability and mathematical statistics.

  • Fixed Effects Analysis of Variance

    • 1st Edition
    • Lloyd Fisher + 1 more
    • Z. W. Birnbaum + 1 more
    • English
    Fixed Effects Analysis of Variance covers the mathematical theory of the fixed effects analysis of variance. The book discusses the theoretical ideas and some applications of the analysis of variance. The text then describes topics such as the t-test; two-sample t-test; the k-sample comparison of means (one-way analysis of variance); the balanced two-way factorial design without interaction; estimation and factorial designs; and the Latin square. Confidence sets, simultaneous confidence intervals, and multiple comparisons; orthogonal and nonorthologonal designs; and multiple regression analysis and related matters are also encompassed. Mathematicians, statisticians, and students taking related courses will find the book useful.

  • Convexity Theory and its Applications in Functional Analysis

    • 1st Edition
    • L. Asimow
    • English
    Convexity Theory and its Applications in Functional Analysis is a five-chapter text that provides a geometric perspective of the convexity theory and its practical applications. Chapter 1 reviews the functional analytic preliminaries, including the Krein-Smulyan Theorem, the basic Choquet Theory, and the Bishop-Phelps Theorem. Chapter 2 gives the basic duality results, lattice theory and concrete representation theorems for order unit spaces and Banach lattices of type Mand L. Chapters 3 and 4 deal with the real affine function spaces through examining the Choquet simplex and the application of the study of real A(K) spaces to complex-values function spaces by means of a complex state space. Chapter 5 highlights the application of the theory to the study of non-commutative Banach algebras. This book will prove useful to mathematicians, engineers, and physicists.

  • Matrix Logic

    Theory and Applications
    • 1st Edition
    • A. Stern
    • English
    In this pioneering work, the author develops a fundamental formulation of logic in terms of theory of matrices and vector spaces. The discovery of matrix logic represents a landmark in the further formalization of logic. For the first time the power of direct mathematical computation is applied to the whole set of logic operations, allowing the derivation of both the classical and modal logics from the same formal base.The new formalism allows the author to enlarge the alphabet of the truth-values with negative logic antivalues and to link matrix logic descriptions with the Dirac formulation of quantum theory - a result having fundamental implications and repercussions for science as a whole.As a unified language which permits a logical examination of the underlying phenomena of quantum field theory and vice versa, matrix logic opens new avenues for the study of fundamental interactions and gives rise to a revolutionary conclusion that physics as such can be viewed and studied as a logic in the fundamental sense.Finally, modelling itself on exact sciences, matrix logic does not refute the classical logic but instead incorporates it as a special deterministic limit. The book requires multidisciplinary knowledge and will be of interest to physicists, mathematicians, computer scientists and engineers.

  • Stochastic Differential Equations and Diffusion Processes

    • 2nd Edition
    • Volume 24
    • N. Ikeda + 1 more
    • English
    Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sections discussing complex (conformal) martingales and Kahler diffusions have been added.

  • Pursuit-Evasion Differential Games

    • 1st Edition
    • Volume 14
    • Y. Yavin + 1 more
    • English
    Twenty papers are devoted to the treatment of a wide spectrum of problems in the theory and applications of dynamic games with the emphasis on pursuit-evasion differential games. The problem of capturability is thoroughly investigated, also the problem of noise-corrupted (state) measurements. Attention is given to aerial combat problems and their attendant modelling issues, such as variable speed of the combatants, the three-dimensionality of physical space, and the combat problem, i.e. problems related to 'role determination'.

  • System-Theoretic Methods in Economic Modelling I

    • 1st Edition
    • Volume 19
    • S. Mittnik
    • English
    The value of applying system-theoretic concepts to economic modelling problems arises from the fact that it offers a unifying framework for modelling dynamic systems. In addition to offering this powerful conceptual framework, it provides a wide range of tools useful in applied work. System-theoretic techniques enter predominantly two stages of economic modelling efforts: the stage of model construction and the stage of model application in accordance with the modelling. The objective of this and subsequent volumes on System-Theoretic Methods in Economic Modelling I is to initiate and/or intensify dialogues between researchers and practitioners within and across the disciplines involved. This first volume brings together papers exhibiting a wide range of system-theoretic techniques and applications to economic problems. The papers have been divided into two groups, following roughly--but not necessarily--the above classification into the construction and application stages of economic modelling. The papers in the first group focus on the identification of dynamic and static systems, while the papers in the second group address dynamic optimization problems.

  • Finite Elements for Analysis and Design

    Computational Mathematics and Applications Series
    • 1st Edition
    • J. E. Akin
    • English
    The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material.

  • Handbook of Set-Theoretic Topology

    • 1st Edition
    • K. Kunen + 1 more
    • English
    This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest.In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.

  • The Econometric Analysis of Non-Uniqueness in Rational Expectations Models

    • 1st Edition
    • Volume 201
    • L. Broze + 1 more
    • English
    This book is devoted to the econometric analysis of linear multivariate rational expectation models. It shows that the interpretation of multiplicity in terms of "new degrees of freedom" is consistent with a rigorous econometric reasoning. Non-uniqueness is the central theme of this book. Each chapter is concerned with a specific econometric aspect of rational expectations equilibria. The most constructive result lies in the possibility of an empirical determination of the equilibrium followed by the economy.

  • Ordinary Differential Equations

    Introduction to the Theory of Ordinary Differential Equations in the Real Domain
    • 1st Edition
    • Volume 13
    • J. Kurzweil
    • English
    The author, Professor Kurzweil, is one of the world's top experts in the area of ordinary differential equations - a fact fully reflected in this book. Unlike many classical texts which concentrate primarily on methods of integration of differential equations, this book pursues a modern approach: the topic is discussed in full generality which, at the same time, permits us to gain a deep insight into the theory and to develop a fruitful intuition. The basic framework of the theory is expanded by considering further important topics like stability, dependence of a solution on a parameter, Carathéodory's theory and differential relations.The book is very well written, and the prerequisites needed are minimal - some basics of analysis and linear algebra. As such, it is accessible to a wide circle of readers, in particular to non-mathematicians.

  • Hilbertian Kernels and Spline Functions

    • 1st Edition
    • Volume 4
    • M. Atteia
    • English
    In this monograph, which is an extensive study of Hilbertian approximation, the emphasis is placed on spline functions theory. The origin of the book was an effort to show that spline theory parallels Hilbertian Kernel theory, not only for splines derived from minimization of a quadratic functional but more generally for splines considered as piecewise functions type.Being as far as possible self-contained, the book may be used as a reference, with information about developments in linear approximation, convex optimization, mechanics and partial differential equations.

  • Scientific Computing

    An Introduction with Parallel Computing
    • 1st Edition
    • Gene H. Golub + 1 more
    • English
    This book introduces the basic concepts of parallel and vector computing in the context of an introduction to numerical methods. It contains chapters on parallel and vector matrix multiplication and solution of linear systems by direct and iterative methods. It is suitable for advanced undergraduate and beginning graduate courses in computer science, applied mathematics, and engineering. Ideally, students will have access to a parallel or Vector computer, but the material can be studied profitably in any case.

  • The IEA Study of Mathematics III

    Student Growth and Classroom Processes
    • 1st Edition
    • Rami Burstein
    • English
    The Second International Mathematics Study was conducted in the schools of 20 education systems under the sponsorship of the International Association for the Evaluation of Educational Achievement (IEA). This is the third of three international reports, each of which focus on a major component of the study. This volume describes the main findings from analyses of classroom processes and mathematic growth by posing such questions as: how successful have the national education systems been in providing the opportunity to learn mathematics by the end of the lower secondary school; what do students at the lower secondary level know across educational systems and what have they learned during their most recent schooling experiences; and what teaching practices are utilized in the mathematics classroom of the various systems and to what extent can these classroom processes explain differences in student achievements?

  • Discrete Optimization

    • 1st Edition
    • R. Gary Parker + 1 more
    • English
    This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas of linear programming, graph theory, and combinatorics--prere... for readers of the text. Numerous exercises are included at the end of each chapter.

  • Numerical Methods for Partial Differential Equations

    • 3rd Edition
    • William F. Ames
    • English
    This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation.

  • Statistical Methods in Longitudinal Research

    Principles and Structuring Change
    • 1st Edition
    • Volume 1
    • Alexander von Eye
    • English
    These edited volumes present new statistical methods in a way that bridges the gap between theoretical and applied statistics. The volumes cover general problems and issues and more specific topics concerning the structuring of change, the analysis of time series, and the analysis of categorical longitudinal data. The book targets students of development and change in a variety of fields - psychology, sociology, anthropology, education, medicine, psychiatry, economics, behavioural sciences, developmental psychology, ecology, plant physiology, and biometry - with basic training in statistics and computing.

  • Curves and Surfaces for Computer-Aided Geometric Design

    A Practical Guide
    • 3rd Edition
    • Gerald Farin
    • English
    A leading expert in CAGD, Gerald Farin covers the representation, manipulation, and evaluation of geometric shapes in this the Third Edition of Curves and Surfaces for Computer Aided Geometric Design. The book offers an introduction to the field that emphasizes Bernstein-Bezier methods and presents subjects in an informal, readable style, making this an ideal text for an introductory course at the advanced undergraduate or graduate level.The Third Edition includes a new chapter on Topology, offers new exercises and sections within most chapters, combines the material on Geometric Continuity into one chapter, and updates existing materials and references. Implementation techniques are addressed for practitioners by the inclusion of new C programs for many of the fundamental algorithms. The C programs are available on a disk included with the text. System Requirements:IBM PC or compatibles, DOS version 2.0 or higher.

  • Machine Intelligence and Pattern Recognition

    • 1st Edition
    • Volume 2
    • Godfried T. Toussaint
    • English
    Machine Intelligence and Pattern Recognition, Volume 2: Computational Geometry focuses on the operations, processes, methodologies, and approaches involved in computational geometry, including algorithms, polygons, convex hulls, and bucketing techniques. The selection first ponders on optimal parallel algorithms for selection, sorting, and computing convex hulls, simple on-line algorithms for convex polygons, and geometric algorithms that use the furthest-point Voronoi diagram. Discussions focus on algorithms that use the furthest-point Voronoi diagram, intersection of a convex polygon and a halfplane, point insertion, convex hulls and polygons and their representations, and parallel algorithm for selection and computing convex hulls. The text then examines optimal convex decompositions, expected time analysis of algorithms in computational geometry, and practical use of bucketing techniques in computational geometry. The book takes a look at minimum decompositions of polygonal objects, framework for computational morphology, display of visible edges of a set of convex polygons, and implementation study of two algorithms for the minimum spanning circle problem. Topics include rolling algorithm, shape of point sets, and decomposition of rectilinear and simple polygons and polygons with holes. The selection is a valuable source of data for researchers interested in computational geometry.

  • System-Theoretic Methods in Economic Modelling II

    • 1st Edition
    • Volume 22
    • S. Mittnik
    • English
    System-Theoretic Methods in Economic Modelling II complements the editor's earlier volume, bringing together current research efforts integrating system-theoretic concepts with economic modelling processes. The range of papers presented here goes beyond the long-accepted control-theoretic contributions in dynamic optimization and focuses on system-theoretic methods in the construction as well as the application stages of economic modelling. This volume initiates new and intensifies existing debate between researchers and practitioners within and across the disciplines involved, with the objective of encouraging interdisciplinary research. The papers are split into four sections - estimation, filtering and smoothing problems in the context of state space modelling; applying the state space concept to financial modelling; modelling rational expectation; and a miscellaneous section including a follow-up case study by Tse and Khilnani on their integrated system model for a fishery management process, which featured in the first volume.

  • Inequalities

    Theory of Majorization and Its Applications
    • 1st Edition
    • Volume 143
    • Ingram Olkin + 1 more
    • English
    Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying "theory of inequalities." For certain kinds of inequalities, the notion of majorization leads to such a theory that is sometimes extremely useful and powerful for deriving inequalities. Moreover, the derivation of an inequality by methods of majorization is often very helpful both for providing a deeper understanding and for suggesting natural generalizations.Anyo... wishing to employ majorization as a tool in applications can make use of the theorems; for the most part, their statements are easily understood.

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