Distribution Of Sequences
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Uniform Distribution Of Sequences
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Author : L. Kuipers
language : en
Publisher: Courier Corporation
Release Date : 2012-05-24
Uniform Distribution Of Sequences written by L. Kuipers and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.
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.
Distribution Of Sequences
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Author : Oto Strauch
language : en
Publisher: Peter Lang Publishing
Release Date : 2005
Distribution Of Sequences written by Oto Strauch and has been published by Peter Lang Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
The monograph covers material scattered throughout books and journals and focuses on the distribution properties of sequences which may be expressed in terms of distribution function, upper and lower distribution function, the discrepancy, diaphony, dispersion etc. The individual character of sequences reflected in their distribution properties may be an object of study from various points of view, and as such they are often the primary goal of investigation. In that case the studied properties are caught in separate results and are consequently accessible in a displayed form. On the other hand, the various distribution properties of sequences play only a subsidiary role in proofs and thus remain often hidden and are not manifested in a visible form. The enormous wealth of information contained in both cases may be of value not only to those working directly in the field, but also to those working in related branches of number theory, combinatorics, real or numerical analysis in the process of finding sequence possessing the required properties. Last, but not least browsing throughout the book may provide the impetus for prospective further research. This is what we hope may address a wide class of working mathematicians.
Distribution Of Sequences
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Author : Oto Strauch
language : en
Publisher:
Release Date : 2019
Distribution Of Sequences written by Oto Strauch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
Sequences Discrepancies And Applications
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Author : Michael Drmota
language : en
Publisher: Springer
Release Date : 2006-11-14
Sequences Discrepancies And Applications written by Michael Drmota and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory.
Uniform Distribution Of Sequences
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Author : Lauwerens Kuipers
language : en
Publisher:
Release Date : 1974
Uniform Distribution Of Sequences written by Lauwerens Kuipers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
The Theory Of Distributions
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Author : El Mustapha Ait Ben Hassi
language : en
Publisher: John Wiley & Sons
Release Date : 2023-08-31
The Theory Of Distributions written by El Mustapha Ait Ben Hassi and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-31 with Mathematics categories.
Many physical, chemical, biological and even economic phenomena can be modeled by differential or partial differential equations, and the framework of distribution theory is the most efficient way to study these equations. A solid familiarity with the language of distributions has become almost indispensable in order to treat these questions efficiently. This book presents the theory of distributions in as clear a sense as possible while providing the reader with a background containing the essential and most important results on distributions. Together with a thorough grounding, it also provides a series of exercises and detailed solutions. The Theory of Distributions is intended for master’s students in mathematics and for students preparing for the agrégation certification in mathematics or those studying the physical sciences or engineering.
Extremes And Related Properties Of Random Sequences And Processes
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Author : M. R. Leadbetter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Extremes And Related Properties Of Random Sequences And Processes written by M. R. Leadbetter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.
Partial Identification Of Probability Distributions
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Author : Charles F. Manski
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-29
Partial Identification Of Probability Distributions written by Charles F. Manski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-29 with Mathematics categories.
Sample data alone never suffice to draw conclusions about populations. Inference always requires assumptions about the population and sampling process. Statistical theory has revealed much about how strength of assumptions affects the precision of point estimates, but has had much less to say about how it affects the identification of population parameters. Indeed, it has been commonplace to think of identification as a binary event – a parameter is either identified or not – and to view point identification as a precondition for inference. Yet there is enormous scope for fruitful inference using data and assumptions that partially identify population parameters. This book explains why and shows how. The book presents in a rigorous and thorough manner the main elements of Charles Manski's research on partial identification of probability distributions. One focus is prediction with missing outcome or covariate data. Another is decomposition of finite mixtures, with application to the analysis of contaminated sampling and ecological inference. A third major focus is the analysis of treatment response. Whatever the particular subject under study, the presentation follows a common path. The author first specifies the sampling process generating the available data and asks what may be learned about population parameters using the empirical evidence alone. He then ask how the (typically) setvalued identification regions for these parameters shrink if various assumptions are imposed. The approach to inference that runs throughout the book is deliberately conservative and thoroughly nonparametric.
Digital Nets And Sequences
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Author : Josef Dick
language : en
Publisher: Cambridge University Press
Release Date : 2010-09-09
Digital Nets And Sequences written by Josef Dick and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-09 with Computers categories.
Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi–Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi–Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses with numerous examples, exercises and illustrations.
Uniform Distribution Of Sequences Of Integers In Residue Classes
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Author :
language : en
Publisher:
Release Date : 1984
Uniform Distribution Of Sequences Of Integers In Residue Classes written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.