发布求助
文献互助 智能选刊 最新文献

Uniform distribution theory最新文献

筛选
英文 中文
Une Propriété Topologique de Certains Ensembles de Mills 某些轧机集的拓扑性质
Uniform distribution theory Pub Date : 2017-06-27 DOI: 10.1515/udt-2017-0009
B. Deschamps
{"title":"Une Propriété Topologique de Certains Ensembles de Mills","authors":"B. Deschamps","doi":"10.1515/udt-2017-0009","DOIUrl":"https://doi.org/10.1515/udt-2017-0009","url":null,"abstract":"Abstract In this article , we show that the set of Mills constants (real numbers M such that [M3ⁿ] is prime for all n ≥ 0) is the increasing limit of sets homeomorphic to the triadic Cantor’s set. More generally, for a given function ϕ and a set A of integers, we studying the Mills set Mϕ(A) = {α ∈ ℝ/ ∀n ∈ ℕ, [ϕn(α)] ∈ A} (where ϕn = ϕ∘...∘ϕ n times). We show that, under certain assumptions over ϕ and A, for all real w > infMϕ(A) the set Mϕ(A) ∩ [2, w] is homeomorphic to the triadic Cantor’s set.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"73 1","pages":"139 - 153"},"PeriodicalIF":0.0,"publicationDate":"2017-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90420538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Fifth International Conference on Uniform Distribution Theory (UDT 2016) Sopron, Hungary, July 5–8, 2016 第五届均匀分配理论国际会议(UDT 2016)，匈牙利Sopron, 2016年7月5-8日
Uniform distribution theory Pub Date : 2017-06-27 DOI: 10.1515/udt-2017-0010
K. Gueth, T. Herendi, L. Németh, L. Szalay
{"title":"The Fifth International Conference on Uniform Distribution Theory (UDT 2016) Sopron, Hungary, July 5–8, 2016","authors":"K. Gueth, T. Herendi, L. Németh, L. Szalay","doi":"10.1515/udt-2017-0010","DOIUrl":"https://doi.org/10.1515/udt-2017-0010","url":null,"abstract":"Abstract This volume contains papers originally presented or inspired by the Fifth International Conference on Uniform Distribution Theory which was held in Sopron, Hungary, July 5-8, 2016.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"47 1","pages":"i - vii"},"PeriodicalIF":0.0,"publicationDate":"2017-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84997081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Statistical Distribution of Roots of a Polynomial Modulo Primes II 模素数多项式根的统计分布II
Uniform distribution theory Pub Date : 2017-06-27 DOI: 10.1515/udt-2017-0007
Y. Kitaoka
{"title":"Statistical Distribution of Roots of a Polynomial Modulo Primes II","authors":"Y. Kitaoka","doi":"10.1515/udt-2017-0007","DOIUrl":"https://doi.org/10.1515/udt-2017-0007","url":null,"abstract":"Abstract Continuing the previous paper, we give several data on the distribution of roots modulo primes of an irreducible polynomial, and based on them, we propose problems on the distribution.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"12 1","pages":"109 - 122"},"PeriodicalIF":0.0,"publicationDate":"2017-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87590084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, I. (General Results) 二值数列相对于等差数列分布的不规则性，I.(一般结果)
Uniform distribution theory Pub Date : 2017-06-27 DOI: 10.1515/udt-2017-0004
Cécile Dartyge, Katalin Gyarmati, A. Sárközy
{"title":"On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, I. (General Results)","authors":"Cécile Dartyge, Katalin Gyarmati, A. Sárközy","doi":"10.1515/udt-2017-0004","DOIUrl":"https://doi.org/10.1515/udt-2017-0004","url":null,"abstract":"Abstract In 1964 K. F. Roth initiated the study of irregularities of distribution of binary sequences relative to arithmetic progressions and since that numerous papers have been written on this subject. In the applications one needs binary sequences which are well distributed relative to arithmetic progressions, in particular, in cryptography one needs binary sequences whose short subsequences are also well-distributed relative to arithmetic progressions. Thus we introduce weighted measures of pseudorandomness of binary sequences to study this property. We study the typical and minimal values of this measure for binary sequences of a given length.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"15 1","pages":"55 - 67"},"PeriodicalIF":0.0,"publicationDate":"2017-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87362545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On The Classification of Ls-Sequences l -序列的分类问题
Uniform distribution theory Pub Date : 2017-06-27 DOI: 10.2478/udt-2018-0012
Christian Weiss
{"title":"On The Classification of Ls-Sequences","authors":"Christian Weiss","doi":"10.2478/udt-2018-0012","DOIUrl":"https://doi.org/10.2478/udt-2018-0012","url":null,"abstract":"Abstract This paper addresses the question whether the LS-sequences constructed in [Car12] yield indeed a new family of low-discrepancy sequences. While it is well known that the case S = 0 corresponds to van der Corput sequences, we prove here that the case S = 1 can be traced back to symmetrized Kronecker sequences and moreover that for S ≥ 2 none of these two types occurs anymore. In addition, our approach allows for an improved discrepancy bound for S = 1 and L arbitrary.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"23 1","pages":"83 - 92"},"PeriodicalIF":0.0,"publicationDate":"2017-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76936833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
An Extension of the Digital Method Based on b-Adic Integers 基于b进整数的数字方法的推广
Uniform distribution theory Pub Date : 2017-06-20 DOI: 10.1515/udt-2018-0005
Roswitha Hofer, Isabel Pirsic
{"title":"An Extension of the Digital Method Based on b-Adic Integers","authors":"Roswitha Hofer, Isabel Pirsic","doi":"10.1515/udt-2018-0005","DOIUrl":"https://doi.org/10.1515/udt-2018-0005","url":null,"abstract":"Abstract We introduce a hybridization of digital sequences with uniformly distributed sequences in the domain of b-adic integers, ℤb,b ∈ℕ {1}, by using such sequences as input for generating matrices. The generating matrices are then naturally required to have finite row-lengths. We exhibit some relations of the ‘classical’ digital method to our extended version, and also give several examples of new constructions with their respective quality assessments in terms of t, T and discrepancy.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"36 1","pages":"107 - 87"},"PeriodicalIF":0.0,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78048273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal Quantization for Piecewise Uniform Distributions 分段均匀分布的最优量化
Uniform distribution theory Pub Date : 2017-01-16 DOI: 10.2478/udt-2018-0009
J. Rosenblatt, M. Roychowdhury
{"title":"Optimal Quantization for Piecewise Uniform Distributions","authors":"J. Rosenblatt, M. Roychowdhury","doi":"10.2478/udt-2018-0009","DOIUrl":"https://doi.org/10.2478/udt-2018-0009","url":null,"abstract":"Abstract Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite number of points. In this paper, firstly a general approach to this process is outlined using independent random variables and ergodic maps; these give asymptotically the optimal sets of n-means and the nth quantization errors for all positive integers n. Secondly two piecewise uniform distributions are considered on R: one with infinite number of pieces and one with finite number of pieces. For these two probability measures, we describe the optimal sets of n-means and the nth quantization errors for all n ∈ N. It is seen that for a uniform distribution with infinite number of pieces to determine the optimal sets of n-means for n ≥ 2 one needs to know an optimal set of (n − 1)-means, but for a uniform distribution with finite number of pieces one can directly determine the optimal sets of n-means and the nth quantization errors for all n ∈ N.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"43 1","pages":"23 - 55"},"PeriodicalIF":0.0,"publicationDate":"2017-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78612300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 19
Higher Order Oscillation and Uniform Distribution 高阶振荡与均匀分布
Uniform distribution theory Pub Date : 2016-12-26 DOI: 10.2478/udt-2019-0001
S. Akiyama, Yunping Jiang
{"title":"Higher Order Oscillation and Uniform Distribution","authors":"S. Akiyama, Yunping Jiang","doi":"10.2478/udt-2019-0001","DOIUrl":"https://doi.org/10.2478/udt-2019-0001","url":null,"abstract":"Abstract It is known that the Möbius function in number theory is higher order oscillating. In this paper we show that there is another kind of higher order oscillating sequences in the form (e2πiαβn g(β))n∈𝕅, for a non-decreasing twice differentiable function g with a mild condition. This follows the result we prove in this paper that for a fixed non-zero real number α and almost all real numbers β> 1 (alternatively, for a fixed real number β> 1 and almost all real numbers α) and for all real polynomials Q(x), sequences (αβng(β)+ Q(n)) n∈𝕅 are uniformly distributed modulo 1.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"263 1","pages":"1 - 10"},"PeriodicalIF":0.0,"publicationDate":"2016-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73277511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
On the Constant in the Average Digit Sum for a Recurrence-Based Numeration 基于递归计数的平均数字和中的常数
Uniform distribution theory Pub Date : 2016-12-01 DOI: 10.1515/udt-2016-0016
C. Ballot
{"title":"On the Constant in the Average Digit Sum for a Recurrence-Based Numeration","authors":"C. Ballot","doi":"10.1515/udt-2016-0016","DOIUrl":"https://doi.org/10.1515/udt-2016-0016","url":null,"abstract":"Abstract Given an integral, increasing, linear-recurrent sequence A with initial term 1, the greedy algorithm may be used on the terms of A to represent all positive integers. For large classes of recurrences, the average digit sum is known to equal cA log n+O(1), where cA is a positive constant that depends on A. This asymptotic result is re-proved with an elementary approach for a class of special recurrences larger than, or distinct from, that of former papers. The focus is on the constants cA for which, among other items, explicit formulas are provided and minimal values are found, or conjectured, for all special recurrences up to a certain order.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"26 1","pages":"125 - 150"},"PeriodicalIF":0.0,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82259941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Tractability of Multivariate Integration Using Low-Discrepancy Sequences 基于低差异序列的多元积分的可跟踪性
Uniform distribution theory Pub Date : 2016-12-01 DOI: 10.1515/udt-2016-0013
S. Tezuka
{"title":"Tractability of Multivariate Integration Using Low-Discrepancy Sequences","authors":"S. Tezuka","doi":"10.1515/udt-2016-0013","DOIUrl":"https://doi.org/10.1515/udt-2016-0013","url":null,"abstract":"Abstract We propose a notion of (t, e, s)-sequences in multiple bases, which unifies the Halton sequence and (t, s)-sequences under one roof, and obtain an upper bound of their discrepancy consisting only of the leading term. By using this upper bound, we improve the tractability results currently known for the Halton sequence, the Niederreiter sequence, the Sobol’ sequence, and the generalized Faure sequence, and also give tractability results for the Xing-Niederreiter sequence and the Hofer-Niederreiter sequence, for which no results have been known so far.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"11 1","pages":"23 - 43"},"PeriodicalIF":0.0,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86444076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信