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The Binomial-Discrete Poisson-Lindley Model: Modeling and Applications to Count Regression 二项离散泊松-林德利模型:建模及其在计数回归中的应用
数学研究通讯 Pub Date : 2022-01-01 DOI: 10.4208/cmr.2021-0045
C. Chesneau
{"title":"The Binomial-Discrete Poisson-Lindley Model: Modeling and Applications to Count Regression","authors":"C. Chesneau","doi":"10.4208/cmr.2021-0045","DOIUrl":"https://doi.org/10.4208/cmr.2021-0045","url":null,"abstract":"","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516139","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: 3
Some New Results on Purely Singular Splittings 关于纯奇异分裂的一些新结果
数学研究通讯 Pub Date : 2022-01-01 DOI: 10.4208/cmr.2020-0048
P. Yuan
{"title":"Some New Results on Purely Singular Splittings","authors":"P. Yuan","doi":"10.4208/cmr.2020-0048","DOIUrl":"https://doi.org/10.4208/cmr.2020-0048","url":null,"abstract":"Let G be a finite abelian group, M a set of integers and S a subset of G. We say that M and S form a splitting of G if every nonzero element g of G has a unique representation of the form g=ms with m∈M and s∈S, while 0 has no such representation. The splitting is called purely singular if for each prime divisor p of |G|, there is at least one element of M is divisible by p. In this paper, we continue the study of purely singular splittings of cyclic groups. We prove that if k≥2 is a positive integer such that [−2k+1,2k+2]∗ splits a cyclic group Zm, then m=4k+2. We prove also that if M=[−k1,k2] ∗ splits Zm purely singularly, and 15 ≤ k1+k2 ≤ 30, then m = 1, or m = k1+k2+1, or k1 = 0 and m=2k2+1. AMS subject classifications: 20D60, 20K01, 94A17","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70515709","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
A Recursive Formula and an Estimation for a Specific Exponential Sum 一类特定指数和的递归公式及估计
数学研究通讯 Pub Date : 2022-01-01 DOI: 10.4208/cmr.2021-0030
Xiwang Cao null, Liqin Qian
{"title":"A Recursive Formula and an Estimation for a Specific Exponential Sum","authors":"Xiwang Cao null, Liqin Qian","doi":"10.4208/cmr.2021-0030","DOIUrl":"https://doi.org/10.4208/cmr.2021-0030","url":null,"abstract":"Let Fq be a finite field and Fqs be an extension of Fq. Let f (x) ∈ Fq[x] be a polynomial of degree n with gcd(n,q) = 1. We present a recursive formula for evaluating the exponential sum ∑c∈Fqs χ (s)( f (x)). Let a and b be two elements in Fq with a 6= 0, u be a positive integer. We obtain an estimate for the exponential sum ∑c∈F∗ qs χ(s)(acu+bc−1), where χ(s) is the lifting of an additive character χ of Fq. Some properties of the sequences constructed from these exponential sums are provided too. AMS subject classifications: 11T23","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516517","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
On the Nonexistence of Partial Difference Sets by Projections to Finite Fields 有限域上投影的偏差分集的不存在性
数学研究通讯 Pub Date : 2022-01-01 DOI: 10.4208/cmr.2020-0049
Yue Zhou
{"title":"On the Nonexistence of Partial Difference Sets by Projections to Finite Fields","authors":"Yue Zhou","doi":"10.4208/cmr.2020-0049","DOIUrl":"https://doi.org/10.4208/cmr.2020-0049","url":null,"abstract":"In the study of (partial) difference sets and their generalizations in groups G, the most widely used method is to translate their definition into an equation over group ring Z[G] and to investigate this equation by applying complex representations of G. In this paper, we investigate the existence of (partial) difference sets in a different way. We project the group ring equations in Z[G] to Z[N] where N is a quotient group of G isomorphic to the additive group of a finite field, and then use polynomials over this finite field to derive some existence conditions. AMS subject classifications: 05B10, 05E30, 11T06","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70515722","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
Singularly Perturbed Renormalization Group Method and Its Significance in Dynamical Systems Theory 奇摄动重整化群方法及其在动力系统理论中的意义
数学研究通讯 Pub Date : 2022-01-01 DOI: 10.4208/cmr.2021-0049
global sci
{"title":"Singularly Perturbed Renormalization Group Method and Its Significance in Dynamical Systems Theory","authors":"global sci","doi":"10.4208/cmr.2021-0049","DOIUrl":"https://doi.org/10.4208/cmr.2021-0049","url":null,"abstract":"","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516542","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: 3
Global Well-Posedness of the Inviscid Heat-Conductive Resistive Compressible MHD in a Strip Domain 条形域上无粘导热电阻可压缩MHD的全局适定性
数学研究通讯 Pub Date : 2022-01-01 DOI: 10.4208/cmr.2021-0061
Yan Xin
{"title":"Global Well-Posedness of the Inviscid Heat-Conductive Resistive Compressible MHD in a Strip Domain","authors":"Yan Xin","doi":"10.4208/cmr.2021-0061","DOIUrl":"https://doi.org/10.4208/cmr.2021-0061","url":null,"abstract":"","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516237","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
Gevrey Well-Posedness of the Hyperbolic Prandtl Equations 双曲型Prandtl方程的Gevrey适定性
数学研究通讯 Pub Date : 2021-12-20 DOI: 10.4208/cmr.2021-0104
Wei-Xi Li, R. Xu
{"title":"Gevrey Well-Posedness of the Hyperbolic Prandtl Equations","authors":"Wei-Xi Li, R. Xu","doi":"10.4208/cmr.2021-0104","DOIUrl":"https://doi.org/10.4208/cmr.2021-0104","url":null,"abstract":"We study the 2D and 3D Prandtl equations of degenerate hyperbolic type, and establish without any structural assumption the Gevrey well-posedness with Gevrey index ≤ 2. Compared with the classical parabolic Prandtl equations, the loss of the derivatives, caused by the hyperbolic feature coupled with the degeneracy, can’t be overcame by virtue of the classical cancellation mechanism that developed for the parabolic counterpart. Inspired by the abstract Cauchy-Kowalewski theorem and by virtue of the hyperbolic feature, we give in this text a straightforward proof, basing on an elementary L energy estimate. In particular our argument does not involve the cancellation mechanism used efficiently for the classical Prandtl equations.","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45362682","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
First Order Hardy Inequalities Revisited 一阶Hardy不等式的修正
数学研究通讯 Pub Date : 2021-09-12 DOI: 10.4208/cmr.2021-0085
Xia Huang, D. Ye
{"title":"First Order Hardy Inequalities Revisited","authors":"Xia Huang, D. Ye","doi":"10.4208/cmr.2021-0085","DOIUrl":"https://doi.org/10.4208/cmr.2021-0085","url":null,"abstract":"Abstract. In this paper, we consider the first order Hardy inequalities using simple equalities. This basic setting not only permits to derive quickly many well-known Hardy inequalities with optimal constants, but also supplies improved or new estimates in miscellaneous situations, such as multipolar potential, the exponential weight, hyperbolic space, Heisenberg group, the edge Laplacian, or the Grushin type operator.","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42327008","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: 3
Global-in-Time $L^p−L^q$ Estimates for Solutions of the Kramers-Fokker-Planck Equation Kramers-Fokker-Planck方程解的全局时间$L^p−L^q$估计
数学研究通讯 Pub Date : 2021-07-07 DOI: 10.4208/cmr.2021-0081
Xue Ping Wang, Lu Zhu
{"title":"Global-in-Time $L^p−L^q$ Estimates for Solutions of the Kramers-Fokker-Planck Equation","authors":"Xue Ping Wang, Lu Zhu","doi":"10.4208/cmr.2021-0081","DOIUrl":"https://doi.org/10.4208/cmr.2021-0081","url":null,"abstract":"In this work, we prove an optimal global-in-time Lp−Lq estimate for solutions to the Kramers-Fokker-Planck equation with short range potential in dimension three. Our result shows that the decay rate as t → +∞ is the same as the heat equation in x-variables and the divergence rate as t → 0+ is related to the sub-ellipticity with loss of 1/3 derivatives of the Kramers-Fokker-Planck operator.","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48168516","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
The $L^*$ Partial Order on the Set of Group Matrices 群矩阵集合上的$L^*$偏序
数学研究通讯 Pub Date : 2021-06-01 DOI: 10.4208/cmr.2021-0012
global sci
{"title":"The $L^*$ Partial Order on the Set of Group Matrices","authors":"global sci","doi":"10.4208/cmr.2021-0012","DOIUrl":"https://doi.org/10.4208/cmr.2021-0012","url":null,"abstract":"","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48823281","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
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