The theory of uniform distribution began with Hermann Weyl's celebrated paper of 1916. In later decades, the theory moved beyond its roots in diophantine approximations to provide common ground for topics as diverse as number theory, probability theory, functional analysis, and topological algebra. This book summarizes the theory's development from its beginnings to the mid-1970s, with comprehensive coverage of both methods and their underlying principles. A practical introduction for students of number theory and analysis as well as a reference for researchers in the field, this book covers uniform distribution in compact spaces and in topological groups, in addition to examinations of sequences of integers and polynomials. Notes at the end of each section contain pertinent bibliographical references and a brief survey of additional results. Exercises range from simple applications of theorems to proofs of propositions that expand upon results stated in the text.

One notable new direction this century in the study of primes has been the influx of ideas from probability. The goal of this book is to provide insights into the prime numbers and to describe how a sequence so tautly determined can incorporate such a striking amount of randomness. The book opens with some classic topics of number theory. It ends with a discussion of some of the outstanding conjectures in number theory. In between are an excellent chapter on the stochastic properties of primes and a walk through an elementary proof of the Prime Number Theorem. This book is suitable for anyone who has had a little number theory and some advanced calculus involving estimates. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.

It has been said that every generation of historians seeks to rewrite what a previous generation had established as the standard interpretations of the motives and circumstances shaping the fabric of historical events. It is not that the facts of history have changed. No one will dispute that the battle of Waterloo occurred on June 11, 1815 or that the allied invasion of Europe began on June 6, 1944. What each new age of historians are attempting to do is to reinterpret the motives of men and the force of circumstance impacting the direction of past events based on the factual, social, intellectual, and cultural milieu of their own generation. By examining the facts of history from a new perspective, today's historians hope to reveal some new truth that will not only illuminate the course of history but also validate contempo rary values and societal ideals. Although it is true that tackling the task of developing a new text on logistics and distribution channel management focuses less on schools of philosophical and social analysis and more on the calculus of managing sales campaigns, inventory replenishment, and income statements, the goal of the management scientist, like the historian, is to merge the facts and figures of the discipline with today's organizational, cultural, and economic realities. Hopefully, the result will be a new synthesis, where a whole new perspective will break forth, exposing new directions and opportunities.

The Dirichlet distribution appears in many areas of application, which include modelling of compositional data, Bayesian analysis, statistical genetics, and nonparametric inference. This book provides a comprehensive review of the Dirichlet distribution and two extended versions, the Grouped Dirichlet Distribution (GDD) and the Nested Dirichlet Distribution (NDD), arising from likelihood and Bayesian analysis of incomplete categorical data and survey data with non-response. The theoretical properties and applications are also reviewed in detail for other related distributions, such as the inverted Dirichlet distribution, Dirichlet-multinomial distribution, the truncated Dirichlet distribution, the generalized Dirichlet distribution, Hyper-Dirichlet distribution, scaled Dirichlet distribution, mixed Dirichlet distribution, Liouville distribution, and the generalized Liouville distribution. Key Features: Presents many of the results and applications that are scattered throughout the literature in one single volume. Looks at the most recent results such as survival function and characteristic function for the uniform distributions over the hyper-plane and simplex; distribution for linear function of Dirichlet components; estimation via the expectation-maximization gradient algorithm and application; etc. Likelihood and Bayesian analyses of incomplete categorical data by using GDD, NDD, and the generalized Dirichlet distribution are illustrated in detail through the EM algorithm and data augmentation structure. Presents a systematic exposition of the Dirichlet-multinomial distribution for multinomial data with extra variation which cannot be handled by the multinomial distribution. S-plus/R codes are featured along with practical examples illustrating the methods. Practitioners and researchers working in areas such as medical science, biological science and social science will benefit from this book.

Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.

As the digital revolution has democratised film production, a new hybrid model of distribution is the way independent filmmakers can take control of their own distribution. This approach is not just DIY or Web-based - it combines the best techniques from each distribution arena, old and new. In Think Outside the Box Office, Reiss explains audience identification and targeting, negotiating split-rights agreements, the new role of film festivals and more.

Of the "big three" components of electrical infrastructure, distribution typically gets the least attention. In fact, a thorough, up-to-date treatment of the subject hasn’t been published in years, yet deregulation and technical changes have increased the need for better information. Filling this void, the Electric Power Distribution Handbook delivers comprehensive, cutting-edge coverage of the electrical aspects of power distribution systems. The first few chapters of this pragmatic guidebook focus on equipment-oriented information and applications such as choosing transformer connections, sizing and placing capacitors, and setting regulators. The middle portion discusses reliability and power quality, while the end tackles lightning protection, grounding, and safety. The Second Edition of this CHOICE Award winner features: 1 new chapter on overhead line performance and 14 fully revised chapters incorporating updates from several EPRI projects New sections on voltage optimization, arc flash, and contact voltage Full-color illustrations throughout, plus fresh bibliographic references, tables, graphs, methods, and statistics Updates on conductor burndown, fault location, reliability programs, tree contacts, automation, and grounding and personnel protection Access to an author-maintained support website, distributionhandbook.com, with problems sets, resources, and online apps An unparalleled source of tips and solutions for improving performance, the Electric Power Distribution Handbook, Second Edition provides power and utility engineers with the technical information and practical tools they need to understand the applied science of distribution.