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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.

  • Analytical Quadrics

    • 1st Edition
    • Volume 14
    • Barry Spain
    • I. N. Sneddon + 2 more
    • English
    Analytical Quadrics focuses on the analytical geometry of three dimensions. The book first discusses the theory of the plane, sphere, cone, cylinder, straight line, and central quadrics in their standard forms. The idea of the plane at infinity is introduced through the homogenous Cartesian coordinates and applied to the nature of the intersection of three planes and to the circular sections of quadrics. The text also focuses on paraboloid, including polar properties, center of a section, axes of plane section, and generators of hyperbolic paraboloid. The book also touches on homogenous coordinates. Concerns include intersection of three planes; circular sections of central quadric; straight line; and circle at infinity. The book also discusses general quadric and classification and reduction of quadric. Discussions also focus on linear systems of quadrics and plane-coordinates. The text is a valuable reference for readers interested in the analytical geometry of three dimensions.

  • 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.

  • 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.

  • Theory of Automata

    • 1st Edition
    • Arto Salomaa
    • I. N. Sneddon + 2 more
    • English
    Theory of Automata deals with mathematical aspects of the theory of automata theory, with emphasis on the finite deterministic automaton as the basic model. All other models, such as finite non-deterministic and probabilistic automata as well as pushdown and linear bounded automata, are treated as generalizations of this basic model. The formalism chosen to describe finite deterministic automata is that of regular expressions. A detailed exposition regarding this formalism is presented by considering the algebra of regular expressions. This volume is comprised of four chapters and begins with a discussion on finite deterministic automata, paying particular attention to regular and finite languages; analysis and synthesis theorems; equivalence relations induced by languages; sequential machines; sequential functions and relations; definite languages and non-initial automata; and two-way automata. The next chapter describes finite non-deterministic and probabilistic automata and covers theorems concerning stochastic languages; non-regular stochastic languages; and probabilistic sequential machines. The book then introduces the reader to the algebra of regular expressions before concluding with a chapter on formal languages and generalized automata. Theoretical exercises are included, along with ""problems"" at the end of some sections. This monograph will be a useful resource for beginning graduate or advanced undergraduates of mathematics.

  • 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.

  • 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.

  • 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.

  • Introduction to Set Theory and Topology

    • 2nd Edition
    • Kazimierz Kuratowski
    • I. S. Sneddon + 1 more
    • English
    Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.

  • 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.

  • 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.

  • 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.

  • Mathematical Statistics

    A Decision Theoretic Approach
    • 1st Edition
    • Thomas S. Ferguson
    • Z. W. Birnbaum + 1 more
    • English
    Mathematical Statistics: A Decision Theoretic Approach presents an investigation of the extent to which problems of mathematical statistics may be treated by decision theory approach. This book deals with statistical theory that could be justified from a decision-theoretic viewpoint. Organized into seven chapters, this book begins with an overview of the elements of decision theory that are similar to those of the theory of games. This text then examines the main theorems of decision theory that involve two more notions, namely the admissibility of a decision rule and the completeness of a class of decision rules. Other chapters consider the development of theorems in decision theory that are valid in general situations. This book discusses as well the invariance principle that involves groups of transformations over the three spaces around which decision theory is built. The final chapter deals with sequential decision problems. This book is a valuable resource for first-year graduate students in 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.

  • 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.

  • Lectures in General Algebra

    • 1st Edition
    • A. G. Kurosh
    • I. N. Sneddon + 2 more
    • English
    Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the convenience of constructing a single theory from the results of group experiments and ring experiments which are known to follow simple corollaries. The text also presents algebraic structures that are not of binary nature. From this parallelism arise other concepts, such as that of the lattices, complete lattices, and modular lattices. The book then proves the Schmidt-Ore theorem, and also describes linear algebra, as well as the Birkhoff-Witt theorem on Lie algebras. The text also addresses ordered groups, the Archimedean groups and rings, and Albert's theorem on normed algebras. This book can prove useful for algebra students and for professors of algebra and advanced mathematicians.

  • 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 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • Subharmonic Functions

    Volume 2
    • 1st Edition
    • Volume 2
    • W. K. Hayman
    • P. M. Cohn + 1 more
    • English
    Building on the foundation laid in the first volume of Subharmonic Functions, which has become a classic, this second volume deals extensively with applications to functions of a complex variable. The material also has applications in differential equations and differential equations and differential geometry. It reflects the increasingly important role that subharmonic functions play in these areas of mathematics. The presentation goes back to the pioneering work of Ahlfors, Heins, and Kjellberg, leading to and including the more recent results of Baernstein, Weitsman, and many others. The volume also includes some previously unpublished material. It addresses mathematicians from graduate students to researchers in the field and will also appeal to physicists and electrical engineers who use these tools in their research work. The extensive preface and introductions to each chapter give readers an overview. A series of examples helps readers test their understatnding of the theory and the master the applications.

  • The Retinoids: v. 2

    • 1st Edition
    • BAERT ET BAERT ET AL
    • English
    The Retinoids is a collection of papers that deals with the biochemistry and metabolism of the retinoids and of specific retinoid-binding proteins that are found in plasma and in cells. Some papers describes the biosynthesis and metabolism of retinol, with plasma retinol-binding protein, with intracellular retinoid-binding proteins, as well as with the metabolism and role of retinoids in the eye. Other papers review the metabolism of retinoic acid and synthetic retinoids, the cellular and molecular mechanisms of action of the retinoids, and applied biology of the retinoids. Several papers discuss toxicology, teratology, immunology, and the applications of retinoids in the fields of cancer and dermatology. One paper describes the transport of retinoic acid and other acidic retinoids in plasma in association with serum albumin. Another paper hypothesizes that vitamin A affects differentiation at the cellular level and addresses how tissue specificity of this action can arise. One paper examines the role of retinoid-binding proteins in vertebrate visual system, particularly how these proteins transport retinoids in the serum, cell sap, and interstitial spaces of the eye. The collection can prove useful for biologists, microbiologists, cellular biologists, students and professors of biology, oncology, ophthalmology or dermatology.

  • Developments in Statistics

    • 1st Edition
    • Volume 2
    • Paruchuri R. Krishnaiah
    • English
    Development in Statistics, Volume 2 is a collection of papers that deals with one- and two- dimensional structures, the statistical theory of linear systems, bispectra, and energy transfer in grid-generated turbulence. Several papers discuss simultaneous test procedures, stochastic Markovian fields, as well as the stopping of invariant sequential probability ratio tests. One paper examines the relationships between excitation and response statistics for one-dimensional structures, and then as extended to two-dimensional structures. The special features issuing from these extensions are related to simple supported rectangular and square plates excited by a stationary random force applied at a single point. Another paper discuses the relationship between the measurable bispectra and the one-dimensional energy transfer terms, and which bispectra will vanish in an isotropic turbulent flow field. One paper reviews simultaneous test procedures, including the evaluation of the probability integrals of multivariates, multivariate gamma distributions, distributions of correlated quadratic forms. Another paper analyzes two concerns regarding the random sample size N, also known as stopping time. These are if N is finite with a probability of one, or the rate that the tail probabilities in the distribution of N go to zero. Mathematicians, statisticians, students, and professors of calculus or advanced mathematics will surely appreciate the collection.

  • Mathematical Problems and Puzzles

    from the Polish Mathematical Olympiads
    • 1st Edition
    • S. Straszewicz
    • I. N. Sneddon + 1 more
    • English
    Popular Lectures in Mathematics, Volume 12: Mathematical Problems and Puzzles: From the Polish Mathematical Olympiads contains sample problems from various fields of mathematics, including arithmetic, algebra, geometry, and trigonometry. The contest for secondary school pupils known as the Mathematical Olympiad has been held in Poland every year since 1949/50. This book is composed of two main parts. Part I considers the problems and solutions about integers, polynomials, algebraic fractions and irrational experience. Part II focuses on the problems of geometry and trigonometric transformation, along with their solutions. The provided solutions aim to extend the student’s knowledge of mathematics and train them in mathematical thinking. This book will prove useful to secondary school mathematics teachers and students.

  • 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.

  • 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.

  • Wavelets

    Theory, Algorithms, and Applications
    • 1st Edition
    • Volume 5
    • Laura Montefusco + 1 more
    • English
    Wavelets: Theory, Algorithms, and Applications is the fifth volume in the highly respected series, WAVELET ANALYSIS AND ITS APPLICATIONS. This volume shows why wavelet analysis has become a tool of choice infields ranging from image compression, to signal detection and analysis in electrical engineering and geophysics, to analysis of turbulent or intermittent processes. The 28 papers comprising this volume are organized into seven subject areas: multiresolution analysis, wavelet transforms, tools for time-frequency analysis, wavelets and fractals, numerical methods and algorithms, and applications. More than 135 figures supplement the text.

  • 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.

  • A Course in Probability Theory

    • 2nd Edition
    • Kai Lai Chung
    • English
    This book contains about 500 exercises consisting mostly of special cases and examples, second thoughts and alternative arguments, natural extensions, and some novel departures. With a few obvious exceptions they are neither profound nor trivial, and hints and comments are appended to many of them. If they tend to be somewhat inbred, at least they are relevant to the text and should help in its digestion. As a bold venture I have marked a few of them with a * to indicate a "must", although no rigid standard of selection has been used. Some of these are needed in the book, but in any case the reader's study of the text will be more complete after he has tried at least those problems.

  • Computational Morphology

    A Computational Geometric Approach to the Analysis of Form
    • 1st Edition
    • Volume 6
    • G.T. Toussaint
    • English
    Computational Geometry is a new discipline of computer science that deals with the design and analysis of algorithms for solving geometric problems. There are many areas of study in different disciplines which, while being of a geometric nature, have as their main component the extraction of a description of the shape or form of the input data. This notion is more imprecise and subjective than pure geometry. Such fields include cluster analysis in statistics, computer vision and pattern recognition, and the measurement of form and form-change in such areas as stereology and developmental biology.This volume is concerned with a new approach to the study of shape and form in these areas. Computational morphology is thus concerned with the treatment of morphology from the computational geometry point of view. This point of view is more formal, elegant, procedure-oriented, and clear than many previous approaches to the problem and often yields algorithms that are easier to program and have lower complexity.

  • 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.

  • 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'.

  • 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.

  • 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.

  • 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.

  • Systematic Glossary of the Terminology of Statistical Methods

    English/French/Spanish/Russian
    • 1st Edition
    • I. Paenson
    • English
    Systematic Glossary of the Terminology of Statistical Methods focuses on the elaboration of terms used in statistical methods. The publication first elaborates on the subject and basic methods of statistics, collection of statistical data, and classification and tabulation of statistical data. Discussions focus on the basic methods of statistics, units used in statistics, statistical inquiry, and the subject of statistics. The text then ponders on graphic presentation, averages, and measurements of variation. The manuscript examines essential theoretical distributions, moments of a frequency distribution, and statistical inference. Topics include point and interval estimations, binomial and normal distributions, nature of theoretical distributions, and elements of the theory of probability. The text also evaluates the theory of attributes, correlation, analysis of variance, and time series, including decomposition of time series, multiple correlation, and variance analysis with two or more principles of classification. The publication is a valuable reference for readers interested in the terms used in statistical methods.

  • 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.

  • Statistical Inferences for Stochastic Processes

    Theory and Methods
    • 1st Edition
    • Ishwar V. Basawa + 1 more
    • English
    Statistical Inference Stochastic Processes provides information pertinent to the theory of stochastic processes. This book discusses stochastic models that are increasingly used in scientific research and describes some of their applications. Organized into three parts encompassing 12 chapters, this book begins with an overview of the basic concepts and procedures of statistical inference. This text then explains the inference problems for Galton–Watson process for discrete time and Markov-branching processes for continuous time. Other chapters consider problems of prediction, filtering, and parameter estimation for some simple discrete-time linear stochastic processes. This book discusses as well the ergodic type chains with finite and countable state-spaces and describes some results on birth and death processes that are of a non-ergodic type. The final chapter deals with inference procedures for stochastic processes through sequential procedures. This book is a valuable resource for graduate students.

  • Annual Review in Automatic Programming

    International Tracts in Computer Science and Technology and Their Application, Vol. 4
    • 1st Edition
    • Richard Goodman
    • English
    Annual Review in Automatic Programming, Volume 4 is a collection of papers that deals with the GIER ALGOL compiler, a parameterized compiler based on mechanical linguistics, and the JOVIAL language. A couple of papers describes a commercial use of stacks, an IBM system, and what an ideal computer program support system should be. One paper reviews the system of compilation, the development of a more advanced language, programming techniques, machine independence, and program transfer to other machines. Another paper describes the ALGOL 60 system for the GIER machine including running ALGOL programs, storage allocation, addressing of variables, program references, procedure calls, storage problem of the translator, and writing the translator. Another paper investigates the internal operation of the ALGOL translator, the source and target languages, the parts of the translator, Polish postfix notation, symbol table in the translator, and the realization of the stack concept. One paper examines the components for a large digital computer, specific features, and compares these to IBM's IBSYS. The collection will prove valuable for programmers, computer engineers, computer instructors, and students of computer science.

  • 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.

  • Introduction to Non-Euclidean Geometry

    • 1st Edition
    • EISENREICH
    • English
    An Introduction to Non-Euclidean Geometry covers some introductory topics related to non-Euclidian geometry, including hyperbolic and elliptic geometries. This book is organized into three parts encompassing eight chapters. The first part provides mathematical proofs of Euclid’s fifth postulate concerning the extent of a straight line and the theory of parallels. The second part describes some problems in hyperbolic geometry, such as cases of parallels with and without a common perpendicular. This part also deals with horocycles and triangle relations. The third part examines single and double elliptic geometries. This book will be of great value to mathematics, liberal arts, and philosophy major students.

  • The Fix-Point Approach to Interdependent Systems

    • 1st Edition
    • Volume 132
    • H. Wold
    • English
    Contributions to Economic Analysis, 132: The Fix-Point Approach to Interdependent Systems focuses on the Fix-Point method for the estimation of interdependent systems, including the Algebraic Fix-Point, Parametric Fix-Point, and Parametric Fractional Fix-Point methods. The selection first ponders on the fix-point approach to interdependent systems, iterative algorithms for fix-point estimation, and GEID specification. Discussions focus on the GEID estimator, convergence to multiple parameter sets, design of iterative algorithms, and challenges of simultaneous equations systems. The text then takes a look at the Parametric Fix-Point (PFP) and the Algebraic Fix-Point (AFP) methods; estimation of real-world models by fix-point and other methods; and a search for asymptotically efficient estimators. Topics include autoregressive errors, estimation of the Klein-Goldberger model, estimation of a model of the Czechoslovak economy, and the Parametric Fractional Fix-Point (PFFP) and Parametric Recursive Fix-Point (PRFP) methods. The text elaborates on fix-point estimates of the structure of a model using different Y proxy starts; analysis of the nonlinear Klein-Goldberger model using fix-point estimation and other methods; and fix-point estimation in interdependent systems with specification errors. The selection is a vital reference for researchers interested in the Fix-Point method for the estimation of interdependent systems.

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