On Generalizations of p-Sets and their Applications

doi:10.4208/nmtma.OA-2017-0145

	On Generalizations of p-Sets and their Applications
	Zhou, Heng 1; Xu, Zhiqiang2,3
	2019-05-01
发表期刊	NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
ISSN	1004-8979
卷号	12 期号:2 页码:453-466
摘要	The p-set, which is in a simple analytic form, is well distributed in unit cubes. The well-known Weil's exponential sum theorem presents an upper bound of the exponential sum over the p-set. Based on the result, one shows that the p-set performs well in numerical integration, in compressed sensing as well as in uncertainty quantification. However, p-set is somewhat rigid since the cardinality of the p-set is a prime p and the set only depends on the prime number p. The purpose of this paper is to present generalizations of p-sets, say P-d,p(a,epsilon) which is more flexible. Particularly, when a prime number p is given, we have many different choices of the new p-sets. Under the assumption that Goldbach conjecture holds, for any even number m, we present a point set, say L-p,L-q, with cardinality m - 1 by combining two different new p-sets, which overcomes a major bottleneck of the p-set. We also present the upper bounds of the exponential sums over P-d,p(a,epsilon) and L-p,L-q, which imply these sets have many potential applications.
关键词	p-set deterministic sampling numerical integral exponential sum
DOI	10.4208/nmtma.OA-2017-0145
语种	英语
资助项目	NSFC[91630203] ; NSFC[11331012] ; NSFC[11688101] ; NSFC[61602341] ; National Basic Research Program of China (973 Program)[2015CB856000]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000453759200006
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31988
专题	计算数学与科学工程计算研究所
通讯作者	Zhou, Heng
作者单位	1.Tianjin Polytech Univ, Sch Sci, Tianjin 300160, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Zhou, Heng,Xu, Zhiqiang. On Generalizations of p-Sets and their Applications[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2019,12(2):453-466.
APA	Zhou, Heng,&Xu, Zhiqiang.(2019).On Generalizations of p-Sets and their Applications.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,12(2),453-466.
MLA	Zhou, Heng,et al."On Generalizations of p-Sets and their Applications".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS 12.2(2019):453-466.