Uniform Distribution Modulo One
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| Author | : Yann Bugeaud |
| Publisher | : Cambridge University Press |
| Total Pages | : 317 |
| Release | : 2012-07-05 |
| Genre | : Mathematics |
| ISBN | : 0521111692 |
Download Distribution Modulo One and Diophantine Approximation Book in PDF, Epub and Kindle
A treatment of cutting-edge research on the distribution modulo one of sequences and related topics, much of it from the last decade. There are numerous exercises to aid student understanding of the topic, and researchers will appreciate the notes at the end of each chapter, extensive references and open problems.
| Author | : Frederik Michel Dekking |
| Publisher | : |
| Total Pages | : 12 |
| Release | : 1981 |
| Genre | : |
| ISBN | : |
Download Uniform distribution modulo one Book in PDF, Epub and Kindle
| Author | : Stacy Jo Robinson |
| Publisher | : |
| Total Pages | : 108 |
| Release | : 2011 |
| Genre | : Uniform distribution (Probability theory) |
| ISBN | : |
Download An Introduction to Uniform Distribution Modulo 1 Book in PDF, Epub and Kindle
In this thesis, we study the theory of uniform distribution of sequences of real numbers. We first give an exposition of the necessary mathematical tools including a rare type of Mean-Value Theorems, Fourier series, Fourier transforms, and the uniform boundedness of sequences of functions. We devote the main body of the thesis to prove theorems based on the well-known Weyl's Criterion and investigate their applications. In particular, we prove and utilize Fejér's Theorem to determine the uniform distribution of several single and double sequences. The contribution of this can be mainly manifested in its thoroughness and completeness of the proofs provided which, in our opinion, is lacking or inaccessible in the current literature. The effort undertaken here will help practitioners to fully understand the intricacy of the theory and enable them to master its applications. Furthermore, we use alternative ways to analyze a few examples, which will facilitate implementation of these mathematical methods.
| Author | : L. Kuipers |
| Publisher | : Courier Corporation |
| Total Pages | : 416 |
| Release | : 2012-05-24 |
| Genre | : Mathematics |
| ISBN | : 0486149994 |
Download Uniform Distribution of Sequences Book in PDF, Epub and Kindle
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.
| Author | : M. L. Robinson |
| Publisher | : |
| Total Pages | : 12 |
| Release | : 1989 |
| Genre | : Distribution modulo one |
| ISBN | : |
Download On Certain Properties Stronger Than Uniform Distribution Modulo One Book in PDF, Epub and Kindle
| Author | : Jozsef Beck |
| Publisher | : #N/A |
| Total Pages | : 458 |
| Release | : 2017-07-07 |
| Genre | : Mathematics |
| ISBN | : 9814740764 |
Download Strong Uniformity And Large Dynamical Systems Book in PDF, Epub and Kindle
It is the first book about a new aspect of Uniform distribution, called Strong Uniformity. Besides developing the theory of Strong Uniformity, the book also includes novel applications in the underdeveloped field of Large Dynamical Systems.
| Author | : Josef Dick |
| Publisher | : Cambridge University Press |
| Total Pages | : 619 |
| Release | : 2010-09-09 |
| Genre | : Computers |
| ISBN | : 1139490052 |
Download Digital Nets and Sequences Book in PDF, Epub and Kindle
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.
| Author | : Shigeki Akiyama |
| Publisher | : Springer Nature |
| Total Pages | : 456 |
| Release | : 2020-12-05 |
| Genre | : Mathematics |
| ISBN | : 3030576663 |
Download Substitution and Tiling Dynamics: Introduction to Self-inducing Structures Book in PDF, Epub and Kindle
This book presents a panorama of recent developments in the theory of tilings and related dynamical systems. It contains an expanded version of courses given in 2017 at the research school associated with the Jean-Morlet chair program. Tilings have been designed, used and studied for centuries in various contexts. This field grew significantly after the discovery of aperiodic self-similar tilings in the 60s, linked to the proof of the undecidability of the Domino problem, and was driven futher by Dan Shechtman's discovery of quasicrystals in 1984. Tiling problems establish a bridge between the mutually influential fields of geometry, dynamical systems, aperiodic order, computer science, number theory, algebra and logic. The main properties of tiling dynamical systems are covered, with expositions on recent results in self-similarity (and its generalizations, fusions rules and S-adic systems), algebraic developments connected to physics, games and undecidability questions, and the spectrum of substitution tilings.
| Author | : Michael Drmota |
| Publisher | : Springer |
| Total Pages | : 517 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 354068333X |
Download Sequences, Discrepancies and Applications Book in PDF, Epub and Kindle
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.
| Author | : Themistocles M. Rassias |
| Publisher | : Springer |
| Total Pages | : 811 |
| Release | : 2014-10-13 |
| Genre | : Mathematics |
| ISBN | : 3319065548 |
Download Topics in Mathematical Analysis and Applications Book in PDF, Epub and Kindle
This volume presents significant advances in a number of theories and problems of Mathematical Analysis and its applications in disciplines such as Analytic Inequalities, Operator Theory, Functional Analysis, Approximation Theory, Functional Equations, Differential Equations, Wavelets, Discrete Mathematics and Mechanics. The contributions focus on recent developments and are written by eminent scientists from the international mathematical community. Special emphasis is given to new results that have been obtained in the above mentioned disciplines in which Nonlinear Analysis plays a central role. Some review papers published in this volume will be particularly useful for a broader readership in Mathematical Analysis, as well as for graduate students. An attempt is given to present all subjects in this volume in a unified and self-contained manner, to be particularly useful to the mathematical community.
