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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.

  • 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 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.

  • Order Statistics & Inference

    Estimation Methods
    • 1st Edition
    • Narayanaswamy Balakrishnan + 1 more
    • English
    The literature on order statistics and inferenc eis quite extensive and covers a large number of fields ,but most of it is dispersed throughout numerous publications. This volume is the consolidtion of the most important results and places an emphasis on estimation. Both theoretical and computational procedures are presented to meet the needs of researchers, professionals, and students. The methods of estimation discussed are well-illustrated with numerous practical examples from both the physical and life sciences, including sociology,psychology... nd electrical and chemical engineering. A complete, comprehensive bibliography is included so the book can be used both aas a text and reference.

  • Introduction to Structural Equation Models

    • 1st Edition
    • Otis Dudley Duncan
    • English
    Introduction to Structural Equation Models prepares the reader to understand the recent sociological literature on the use of structural equation models in research, and discusses methodological questions pertaining to such models. The material in first seven chapters is almost entirely standard, with the remaining four introducing progressively more open-ended issues, seducing the reader into beginning to think for himself about the properties of models or even to suggest problems that may intrigue the advanced student.

  • Topoi

    The Categorial Analysis of Logic
    • 2nd Edition
    • Volume 98
    • R. Goldblatt
    • English
    The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-varia... classical real number''.The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes. The aim of this chapter is to explain why Deligne's theorem about the existence of points of coherent topoi is equivalent to the classical Completeness theorem for ``geometric'' first-order formulae.

  • 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.

  • 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?

  • 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.

  • 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.

  • 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.

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