Uniform Distribution of Sequences

Uniform Distribution of Sequences

Author: L. Kuipers

Publisher: Courier Corporation

Published: 2012-05-24

Total Pages: 416

ISBN-13: 0486149994

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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.


Book Synopsis Uniform Distribution of Sequences by : L. Kuipers

Download or read book Uniform Distribution of Sequences written by L. Kuipers and published by Courier Corporation. This book was released on 2012-05-24 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Uniform Distribution of Sequences

Uniform Distribution of Sequences

Author: Lauwerens Kuipers

Publisher:

Published: 1986

Total Pages: 390

ISBN-13:

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Book Synopsis Uniform Distribution of Sequences by : Lauwerens Kuipers

Download or read book Uniform Distribution of Sequences written by Lauwerens Kuipers and published by . This book was released on 1986 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt:


Uniform Distribution of Sequences of Integers in Residue Classes

Uniform Distribution of Sequences of Integers in Residue Classes

Author: W. Narkiewicz

Publisher: Springer

Published: 2006-12-08

Total Pages: 133

ISBN-13: 3540390634

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Book Synopsis Uniform Distribution of Sequences of Integers in Residue Classes by : W. Narkiewicz

Download or read book Uniform Distribution of Sequences of Integers in Residue Classes written by W. Narkiewicz and published by Springer. This book was released on 2006-12-08 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt:


Sequences, Discrepancies and Applications

Sequences, Discrepancies and Applications

Author: Michael Drmota

Publisher: Springer

Published: 2006-11-14

Total Pages: 517

ISBN-13: 354068333X

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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.


Book Synopsis Sequences, Discrepancies and Applications by : Michael Drmota

Download or read book Sequences, Discrepancies and Applications written by Michael Drmota and published by Springer. This book was released on 2006-11-14 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Distribution of Sequences

Distribution of Sequences

Author: Oto Strauch

Publisher: Peter Lang Publishing

Published: 2005

Total Pages: 576

ISBN-13:

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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.


Book Synopsis Distribution of Sequences by : Oto Strauch

Download or read book Distribution of Sequences written by Oto Strauch and published by Peter Lang Publishing. This book was released on 2005 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Uniform Distribution of Sequences of Integers in Residue Classes

Uniform Distribution of Sequences of Integers in Residue Classes

Author: Wadysaw Narkiewicz

Publisher:

Published: 2014-01-15

Total Pages: 140

ISBN-13: 9783662192191

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Book Synopsis Uniform Distribution of Sequences of Integers in Residue Classes by : Wadysaw Narkiewicz

Download or read book Uniform Distribution of Sequences of Integers in Residue Classes written by Wadysaw Narkiewicz and published by . This book was released on 2014-01-15 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:


Uniform distribution of sequences of integers in residue classes

Uniform distribution of sequences of integers in residue classes

Author:

Publisher:

Published: 1984

Total Pages:

ISBN-13: 9780387138725

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Download or read book Uniform distribution of sequences of integers in residue classes written by and published by . This book was released on 1984 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:


The Theory of Uniform Distribution

The Theory of Uniform Distribution

Author: Edmund Hlawka

Publisher:

Published: 1984

Total Pages: 160

ISBN-13:

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Book Synopsis The Theory of Uniform Distribution by : Edmund Hlawka

Download or read book The Theory of Uniform Distribution written by Edmund Hlawka and published by . This book was released on 1984 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:


The Uniform Distribution of Sequences

The Uniform Distribution of Sequences

Author: Charles Vanden Eynden

Publisher:

Published: 1962

Total Pages: 48

ISBN-13:

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Book Synopsis The Uniform Distribution of Sequences by : Charles Vanden Eynden

Download or read book The Uniform Distribution of Sequences written by Charles Vanden Eynden and published by . This book was released on 1962 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:


An Introduction to Uniform Distributions and Weyl's Criterion

An Introduction to Uniform Distributions and Weyl's Criterion

Author: Rachel M. Andriunas

Publisher:

Published: 2020

Total Pages:

ISBN-13:

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This report is an exploration into the basics of the uniform distribution of sequences and a proof of Weyl's Criterion. After describing what it means for a sequence to be uniformly distributed, we develop the tools to prove Weyl's Criterion. In order to do this, we split Weyl's Criterion into two theorems and prove each of them. Finally, we will show an example which applies Weyl's Criterion to prove that a certain sequence of irrational numbers is uniformly distributed.


Book Synopsis An Introduction to Uniform Distributions and Weyl's Criterion by : Rachel M. Andriunas

Download or read book An Introduction to Uniform Distributions and Weyl's Criterion written by Rachel M. Andriunas and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This report is an exploration into the basics of the uniform distribution of sequences and a proof of Weyl's Criterion. After describing what it means for a sequence to be uniformly distributed, we develop the tools to prove Weyl's Criterion. In order to do this, we split Weyl's Criterion into two theorems and prove each of them. Finally, we will show an example which applies Weyl's Criterion to prove that a certain sequence of irrational numbers is uniformly distributed.