A one-stop reference to fractional factorials and relatedorthogonal arrays. Presenting one of the most dynamic areas of statistical research,this book offers a systematic, rigorous, and up-to-date treatmentof fractional factorial designs and related combinatorialmathematics. Leading statisticians Aloke Dey and Rahul Mukerjeeconsolidate vast amounts of material from the professionalliterature--expertly weaving fractional replication, orthogonalarrays, and optimality aspects. They develop the basic theory offractional factorials using the calculus of factorial arrangements,thereby providing a unified approach to the study of fractionalfactorial plans. An indispensable guide for statisticians inresearch and industry as well as for graduate students, FractionalFactorial Plans features: * Construction procedures of symmetric and asymmetric orthogonalarrays. * Many up-to-date research results on nonexistence. * A chapter on optimal fractional factorials not based onorthogonal arrays. * Trend-free plans, minimum aberration plans, and search andsupersaturated designs. * Numerous examples and extensive references.
The purpose of this book is to present the basic elements of numerical methods for compressible flows. It is appropriate for advanced undergraduate and graduate students and specialists working in high speed flows. The focus is on the unsteady one-dimensional Euler equations which form the basis for numerical algorithms in compressible fluid mechanics. The book is restricted to the basic concepts of finite volume methods, and even in this regard is not intended to be exhaustive in its treatment. Although the practical applications of the one-dimensional Euler equations are limited, virtually all numerical algorithms for inviscid compressible flow in two and three dimensions owe their origin to techniques developed in the context of the one-dimensional Euler equations. The author believes it is therefore essential to understand the development and implementation of these algorithms in their original one-dimensional context. The text is supplemented by numerous end-of-chapter exercises.
In this book, Professor Copson gives a rigorous account of the theory of partial differential equations of the first order and of linear partial differential equations of the second order, using the methods of classical analysis. In spite of the advent of computers and the applications of the methods of functional analysis to the theory of partial differential equations, the classical theory retains its relevance in several important respects. Many branches of classical analysing have their origins in the rigourous discussion of problems in applies mathematics and theoretical physics, and the classical treatment of the theory of partial differential equations still provides the best method of treating many physical problems. A knowledge of the classical theory is essential for pure mathematics who intend to undertake research in this field, whatever approach they ultimately adopt. The numerical analyst needs a knowledge of classical theory in order to decide whether a problem has a unique solution or not.
Why do some ethnic parties succeed in attracting the support of their target ethnic group while others fail? In a world in which ethnic parties flourish in both established and emerging democracies alike, understanding the conditions under which such parties rise and fall is of critical importance to both political scientists and policy makers. Drawing on a study of variation in the performance of ethnic parties in India, this book builds a theory of ethnic party performance in 'patronage democracies'. Chandra shows why individual voters and political entrepreneurs in such democracies condition their strategies not on party ideologies or policy platforms, but on a headcount of co-ethnics and others across party personnel and among the electorate.
In eighteenth-century Germany the universal harmony of God's creation and the perfection of its proportions still held philosophical, moral and devotional significance. Reproducing proportions close to the unity (1:1) across compositions could render them beautiful, perfect and even eternal. Using the principles of her groundbreaking theory of proportional parallelism and the latest source study research, Ruth Tatlow reveals how Bach used the number of bars to create numerical perfection across his published collections, and explains why he did so. The first part of the book illustrates the wide-ranging application of belief in the unity, showing how planning a well-proportioned structure was a normal compositional procedure in Bach's time. In the second part Tatlow presents practical demonstrations of this in Bach's works, illustrating the layers of proportion that appear within a movement, a work, between two works in a collection, across a collection and between collections.
The theory of integer partitions is a subject of enduring interest. A major research area in its own right, it has found numerous applications, and celebrated results such as the Rogers-Ramanujan identities make it a topic filled with the true romance of mathematics. The aim in this introductory textbook is to provide an accessible and wide ranging introduction to partitions, without requiring anything more of the reader than some familiarity with polynomials and infinite series. Many exercises are included, together with some solutions and helpful hints. The book has a short introduction followed by an initial chapter introducing Euler's famous theorem on partitions with odd parts and partitions with distinct parts. This is followed by chapters titled: Ferrers Graphs, The Rogers-Ramanujan Identities, Generating Functions, Formulas for Partition Functions, Gaussian Polynomials, Durfee Squares, Euler Refined, Plane Partitions, Growing Ferrers Boards, and Musings.
Numerical Methods for Roots of Polynomials - Part I (along with volume 2 covers most of the traditional methods for polynomial root-finding such as Newton, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincent method, simultaneous iterations, and matrix methods. There is an extensive chapter on evaluation of polynomials, including parallel methods and errors. There are pointers to robust and efficient programs. In short, it could be entitled Handbook of Methods for Polynomial Root-finding . This book will be invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic.First comprehensive treatment of Root-Finding in several decadesGives description of high-grade software and where it can be down-loadedVery up-to-date in mid-2006; long chapter on matrix methodsIncludes Parallel methods, errors where appropriateInvaluable for research or graduate course
Numerical Methods for Fluids, Part 3
As we approach the 21st century, the Advances in Computers serial remains the oldes continuously published anthology chronicling the evolution of the information technology field. Since 1960, this series has described the ever-changing nature of computing. In this volume, we will emphasize the major themes that have dominated computing in these latter days of the 1990s. Of course we mean the distributed nature of information technology. The growth of networking, the Internet and the World Wide Web have greatly changed the role of the computer, and in turn, our lives as well. Starting as a computer science research topic in 1969, the ARPANET, funded by the U.S. government's Advanced Research Projects Agency (ARPA), tied together university, research, and military computing centers. By the mid-1980s the ARPANET evolved into the Internet under funding by the U.S. National Science Foundation (NSF). The computer experimenter, the so-called "computer geek," discovered the Internet and joined the fun. By the early 1990s, the World Wide Web (WWW) grew as a subnet of the Internet, and email and Web browsing became available to all. Today millions of "computer illiterate" individuals daily use these resources to send mail and search for online information. No longer is the Internet the domain of the serious computer researcher. In this volume we will describe some of the changes the Internet has brought us.
Advances in Imaging & Electron Physics merges two long-running serials--Advances in Electronics and Electron Physics and Advances in Optical & Electron Microscopy. The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains.Volume 100 is a cumulative index for all in-print volumes of Advances in Electronics and Electron Physics, Advances in Imaging & Electron Physics , and Advances in Optical & Electron Microscopy
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