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"Here is a valuable text and research tool for scientists and engineers who use or work with theory and computation associated with practical problems relating to Markov chains and queuing networks, economic analysis, or mathematical programming. Originally published in 1979, this new edition adds material that updates the subject relative to developments from 1979 to 1993.Theory and applications of nonnegative matrices are blended here, and extensive references are included in each area. You will be led from the theory of positive operators via the Perron-Frobenius theory of nonnegative matrices and the theory of inverse positivity, to the widely used topic of M-matrices. On the way, semigroups of nonnegative matrices and symmetric nonnegative matrices are discussed. Later, applications of nonnegativity and M-matrices are given; for numerical analysis the example is convergence theory of iterative methods, for probability and statistics the examples are finite Markov chains and queuing network models, for mathematical economics the example is input-output models, and for mathematical programming the example is the linear complementarity problem.Nonnegativity constraints arise very naturally throughout the physical world. Engineers, applied mathematicians, and scientists who encounter nonnegativity or generalizations of nonegativity in their work will benefit from topics covered here, connecting them to relevant theory. Researchers in one area, such as queuing theory, may find useful the techniques involving nonnegative matrices used by researchers in another area, say, mathematical programming."

"Solutions of the wave equation or Maxwell's equations in boundary value and free space problems are analyzed. Hyperbolic systems in domains going off to infinity are studied. New results on Maxwell's equations and non-star shaped reflecting bodies are included."

"Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAE's) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of applications are used to motivate and illustrate the concepts and techniques. This classic edition, originally published in 1989, is the only general DAE book available. It not only develops guidelines for choosing different numerical methods, it is the first book to discuss DAE codes, including the popular DASSL code. An extensive discussion of backward differentiation formulas details why they have emerged as the most popular and best understood class of linear multistep methods for general DAE's. New to this edition is a chapter that brings the discussion of DAE software up to date. The objective of this monograph is to advance and consolidate the existing research results for the numerical solution of DAE's. The authors present results on the analysis of numerical methods, and also show how these results are relevant for the solution of problems from applications. They develop guidelines for problem formulation and effective use of the available mathematical software and provide extensive references for further study."

"Flow control and optimization has been an important part of experimental flow science throughout the last century. As research in computational fluid dynamics (CFD) matured, CFD codes were routinely used for the simulation of fluid flows. Subsequently, mathematicians and engineers began examining the use of CFD algorithms and codes for optimization and control problems for fluid flows. The marriage of mature CFD methodologies with state-of-the-art optimization methods has become the center of activity in computational flow control and optimization.Perspectives in Flow Control and Optimization presents flow control and optimization as a subdiscipline of computational mathematics and computational engineering. It introduces the development and analysis of several approaches for solving flow control and optimization problems through the use of modern CFD and optimization methods. The author discusses many of the issues that arise in the practical implementation of algorithms for flow control and optimization, such as choices to be made and difficulties to overcome. He provides the reader with a clear idea of what types of flow control and optimization problems can be solved, how to develop effective algorithms for solving such problems, and potential problems to be aware of when implementing the algorithms.This book is written for both those new to the field of control and optimization as well as experienced practitioners, including engineers, applied mathematicians, and scientists interested in computational methods for flow control and optimization. Both those interested in developing new algorithms and those interested in the application of existing algorithms should find useful information in this book."

"Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of "uniformity" is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method. Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems."

"How does a marble manufacturer know that the color will be consistent throughout the products being made? How can you tell if liquid at the bottom of a container is the same consistency as at the top? How does a pellet manufacturer know if the pellets are consistently the same size? How does a chemical manufacturer know if the percent purity in a sample is representative of the whole batch? These and similar questions are answered in A Primer for Sampling Solids, Liquids, and Gases: Based on the Seven Sampling Errors of Pierre Gy. Statisticians are well trained in sampling techniques if the sample is well defined. Examples of such samples include industrial parts in manufacturing, invoices in business processes, and people in surveys. However, what if the sampling unit isn't well defined? What if you are sampling bulk material such as a pile of coal? Author Patricia L. Smith illustrates what to look for in sampling devices and procedures to obtain correct samples from bulk materials. She gives sampling guidelines that can be applied immediately and shows how to analyze protocols to uncover sampling problems. Smith presents the ideas of Pierre Gy in lay terms so that his concepts and principles can be easily grasped and applied. She conveys Gy's intuitive meaning while preserving his original ideas. Synonyms have been used for some technical terms to avoid confusion."

"Presents a theory of indexing capable of ranking index terms, or subject identifiers in decreasing order of importance. This leads to the choice of good document representations, and also accounts for the role of phrases and of thesaurus classes in the indexing process. This study is typical of theoretical work in automatic information organization and retrieval, in that concepts are used from mathematics, computer science, and linguistics. A complete theory of information retrieval may emerge from an appropriate combination of these three disciplines."

"Population processes are stochastic models for systems involving a number of similar particles. Examples include models for chemical reactions and for epidemics. The model may involve a finite number of attributes, or even a continuum. This monograph considers approximations that are possible when the number of particles is large. The models considered will involve a finite number of different types of particles."

"This book offers a fundamental and practical introduction to the use of computational methods, particularly finite element methods, in the simulation of fluid flows in porous media. It is the first book to cover a wide variety of flows, including single-phase, two-phase, black oil, volatile, compositional, nonisothermal, and chemical compositional flows in both ordinary porous and fractured porous media. In addition, a range of computational methods are used, and benchmark problems of nine comparative solution projects organized by the Society of Petroleum Engineers are presented for the first time in book form.Computational Methods for Multiphase Flows in Porous Media reviews multiphase flow equations and computational methods to introduce basic terminologies and notation. A thorough discussion of practical aspects of the subjects is presented in a consistent manner, and the level of treatment is rigorous without being unnecessarily abstract. Each chapter ends with bibliographic information and exercises."

"Algorithmic, or automatic, differentiation (AD) is a growing area of theoretical research and software development concerned with the accurate and efficient evaluation of derivatives for function evaluations given as computer programs. The resulting derivative values are useful for all scientific computations that are based on linear, quadratic, or higher order approximations to nonlinear scalar or vector functions. AD has been applied in particular to optimization, parameter identification, nonlinear equation solving, the numerical integration of differential equations, and combinations of these. Apart from quantifying sensitivities numerically, AD also yields structural dependence information, such as the sparsity pattern and generic rank of Jacobian matrices. The field opens up an exciting opportunity to develop new algorithms that reflect the true cost of accurate derivatives and to use them for improvements in speed and reliability. This second edition has been updated and expanded to cover recent developments in applications and theory, including an elegant NP completeness argument by Uwe Naumann and a brief introduction to scarcity, a generalization of sparsity. There is also added material on checkpointing and iterative differentiation. To improve readability the more detailed analysis of memory and complexity bounds has been relegated to separate, optional chapters.The book consists of three parts: a stand-alone introduction to the fundamentals of AD and its software; a thorough treatment of methods for sparse problems; and final chapters on program-reversal schedules, higher derivatives, nonsmooth problems and iterative processes. Each of the 15 chapters concludes with examples and exercises."