Multidimensional Analysis And Discrete Models

Multidimensional Analysis and Discrete Models, a thorough and detailed reference, covers the main structures of multidimensional analysis and the intrinsically defined discrete models in applied mathematics, mathematical physics, and related fields. The material is presented in a clear and straightforward manner, with background information provided to define finite models and to clarify the concepts of multidimensional analysis. The book covers special difference models of the mathematical physics equations, models of boundary value problems, and objects of quantum mechanics. Considerable attention is also given to differential operators on Riemannian manifolds and the interpretation of classical vector analysis. The primary focus of Multidimensional Analysis and Discrete Models is on the description of regular methods of constructing intrinsically defined discrete models for special classes of continual objects, but emphasis is also given to the interaction of ideas and methods that exist throughout the field of mathematics. For example, the connections between theories derived from classical and functional analysis, Riemannian geometry, and algebraic topology are illustrated, and are discussed in terms of their relevance to computing solutions.

Multidimensional Analysis and Discrete Models, a thorough and detailed reference, covers the main structures of multidimensional analysis and the intrinsically defined discrete models in applied mathematics, mathematical physics, and related fields. The material is presented in a clear and straightforward manner, with background information provided to define finite models and to clarify the concepts of multidimensional analysis. The book covers special difference models of the mathematical physics equations, models of boundary value problems, and objects of quantum mechanics. Considerable attention is also given to differential operators on Riemannian manifolds and the interpretation of classical vector analysis. The primary focus of Multidimensional Analysis and Discrete Models is on the description of regular methods of constructing intrinsically defined discrete models for special classes of continual objects, but emphasis is also given to the interaction of ideas and methods that exist throughout the field of mathematics. For example, the connections between theories derived from classical and functional analysis, Riemannian geometry, and algebraic topology are illustrated, and are discussed in terms of their relevance to computing solutions.

“A welcome addition to multivariate analysis. The discussion is lucid and very leisurely, excellently illustrated with applications drawn from a wide variety of fields. A good part of the book can be understood without very specialized statistical knowledge. It is a most welcome contribution to an interesting and lively subject.” -- Nature Originally published in 1974, this book is a reprint of a classic, still-valuable text.

This work considers Kronecker-based models with finite as well as countably infinite state spaces for multidimensional Markovian systems by paying particular attention to those whose reachable state spaces are smaller than their product state spaces. Numerical methods for steady-state and transient analysis of Kronecker-based multidimensional Markovian models are discussed in detail together with implementation issues. Case studies are provided to explain concepts and motivate use of methods. Having grown out of research from the past twenty years, this book expands upon the author’s previously published book Analyzing Markov Chains using Kronecker Products (Springer, 2012). The subject matter is interdisciplinary and at the intersection of applied mathematics and computer science. The book will be of use to researchers and graduate students with an understanding of basic linear algebra, probability, and discrete mathematics.

One of the major achievements in computational fluid dynamics has been the development of numerical methods for simulating compressible flows, combining higher-order accuracy in smooth regions with a sharp, oscillation-free representation of embedded shocks methods and now known as "high-resolution schemes". Together with introductions from the editors written from the modern vantage point this volume collects in one place many of the most significant papers in the development of high-resolution schemes as occured at ICASE.

This book deals with the mathematical properties of dimensioned quantities, such as length, mass, voltage, and viscosity. Beginning with a careful examination of how one expresses the numerical results of a measurement and uses these results in subsequent manipulations, the author rigorously constructs the notion of dimensioned numbers and discusses their algebraic structure. The result is a unification of linear algebra and traditional dimensional analysis that can be extended from the scalars to which the traditional analysis is perforce restricted to multidimensional vectors of the sort frequently encountered in engineering, systems theory, economics, and other applications.

This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.

Balancing simplicity with technical rigour, this practical guide to the statistical techniques essential to research in marketing and related fields, describes each method as well as showing how they are applied. The book is accompanied by two real data sets to replicate examples and with exercises to solve, as well as detailed guidance on the use of appropriate software including: - 750 powerpoint slides with lecture notes and step-by-step guides to run analyses in SPSS (also includes screenshots) - 136 multiple choice questions for tests This is augmented by in-depth discussion of topics including: - Sampling - Data management and statistical packages - Hypothesis testing - Cluster analysis - Structural equation modelling