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The Orthogonal Bases of Exponential Functions Based on Moran-Sierpinski Measures 基于 Moran-Sierpinski 测量的指数函数正交基
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-2604-5
Qi Rong Deng, Xing Gang He, Ming Tian Li, Yuan Ling Ye
{"title":"The Orthogonal Bases of Exponential Functions Based on Moran-Sierpinski Measures","authors":"Qi Rong Deng,&nbsp;Xing Gang He,&nbsp;Ming Tian Li,&nbsp;Yuan Ling Ye","doi":"10.1007/s10114-024-2604-5","DOIUrl":"10.1007/s10114-024-2604-5","url":null,"abstract":"<div><p>Let <i>A</i><sub><i>n</i></sub> ∈ <i>M</i><sub>2</sub> (ℤ) be integral matrices such that the infinite convolution of Dirac measures with equal weights</p><div><div><span>$$mu_{{A_{n},ngeq1}}:=delta_{A_{1}^{-1}cal{D}}astdelta_{A_{1}^{-1}A_{2}^{-2}cal{D}}astcdots$$</span></div></div><p> is a probability measure with compact support, where <span>(cal{D}={(0,0)^{t},(1,0)^{t},(0,1)^{t}})</span> is the Sierpinski digit. We prove that there exists a set Λ ⊂ ℝ<sup>2</sup> such that the family {e<sup>2<i>π</i>i〈λ,<i>x</i>〉</sup>: λ ∈ Λ} is an orthonormal basis of <span>(L^{2}(mu_{{A_{n},ngeq1}}))</span> if and only if <span>({1over{3}}(1,-1)A_{n}inmathbb{Z}^{2})</span> for <i>n</i> ≥ 2 under some metric conditions on <i>A</i><sub><i>n</i></sub>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 7","pages":"1804 - 1824"},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141119794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Products of Commutator Ideals of Some Lie-admissible Algebras 某些可容许列代数的换元顶点的乘积
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-2178-2
Ivan Kaygorodov, Farukh Mashurov, Tran Giang Nam, Ze Rui Zhang
{"title":"Products of Commutator Ideals of Some Lie-admissible Algebras","authors":"Ivan Kaygorodov,&nbsp;Farukh Mashurov,&nbsp;Tran Giang Nam,&nbsp;Ze Rui Zhang","doi":"10.1007/s10114-024-2178-2","DOIUrl":"10.1007/s10114-024-2178-2","url":null,"abstract":"<div><p>In this article, we mainly study the products of commutator ideals of Lie-admissible algebras such as Novikov algebras, bicommutative algebras, and assosymmetric algebras. More precisely, we first study the properties of the lower central chains for Novikov algebras and bicommutative algebras. Then we show that for every Lie nilpotent Novikov algebra or Lie nilpotent bicommutative algebra <span>(cal{A})</span>,the ideal of <span>(cal{A})</span> generated by the set <span>({ab-ba vert a,bincal{A}})</span> is nilpotent. Finally, we study properties of the lower central chains for assosymmetric algebras, study the products of commutator ideals of assosymmetric algebras and show that the products of commutator ideals have a similar property as that for associative algebras.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 8","pages":"1875 - 1892"},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141122971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Cheeger-Müller Theorem for Delocalized L2-analytic Torsion Form 失焦 L2- 分析扭转形式的 Cheeger-Müller 定理
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-2287-y
Guo Lin An
{"title":"A Cheeger-Müller Theorem for Delocalized L2-analytic Torsion Form","authors":"Guo Lin An","doi":"10.1007/s10114-024-2287-y","DOIUrl":"10.1007/s10114-024-2287-y","url":null,"abstract":"<div><p>In this paper we define the delocalized <i>L</i><sup>2</sup>-analytic torsion form and the delocalized <i>L</i><sup>2</sup>-combinatorial torsion form. By using the method of Bismut-Goette, under the conditions of positive Novikov-Shubin invariants, nontrivial finite conjugacy class and the existence of a family of fiberwise Morse functions whose gradient fields satisfy the Thom-Smale transversality condition in every fiber, we prove the Cheeger-Müller type relation between the delocalized <i>L</i><sup>2</sup>-analytic torsion form and the delocalized <i>L</i><sup>2</sup>-combinatorial torsion form.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 11","pages":"2615 - 2670"},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141120198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tensor Decomposition-assisted Multiview Subgroup Analysis 张量分解辅助多视角分组分析
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-3310-z
Xun Zhao, Ling Zhou, Weijia Zhang, Huazhen Lin
{"title":"Tensor Decomposition-assisted Multiview Subgroup Analysis","authors":"Xun Zhao,&nbsp;Ling Zhou,&nbsp;Weijia Zhang,&nbsp;Huazhen Lin","doi":"10.1007/s10114-024-3310-z","DOIUrl":"10.1007/s10114-024-3310-z","url":null,"abstract":"<div><p>To learn the subgroup structure generated by multidimensional interaction, we propose a novel multiview subgroup integration technique based on tensor decomposition. Compared to the traditional subgroup analysis that can only handle single-view heterogeneity, our proposed method achieves a greater level of homogeneity within the subgroups, leading to enhanced interpretability and predictive power. For computational readiness of the proposed method, we build an algorithm that incorporates pairwise shrinkage-encouraging penalties and ADMM techniques. Theoretically, we establish the asymptotic consistency and normality of the proposed estimators. Extensive simulation studies and real data analysis demonstrate that our proposal outperforms other methods in terms of prediction accuracy and grouping consistency. In addition, the analysis based on the proposed method indicates that intergenerational care significantly increases the risk of chronic diseases associated with diet and fatigue in all provinces while only reducing the risk of emotion-related chronic diseases in the eastern coastal and central regions of China.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 2","pages":"588 - 618"},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141119101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Example of Embedded Singular Continuous Spectrum for Discrete Schrödinger Operators 离散薛定谔算子的嵌入式奇异连续谱实例
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-2574-7
Zheng Qi Fu, Xiong Li
{"title":"An Example of Embedded Singular Continuous Spectrum for Discrete Schrödinger Operators","authors":"Zheng Qi Fu,&nbsp;Xiong Li","doi":"10.1007/s10114-024-2574-7","DOIUrl":"10.1007/s10114-024-2574-7","url":null,"abstract":"<div><p>We present an example of a potential such that the corresponding discrete Schrödinger operator has singular continuous spectrum embedded in the absolutely continuous spectrum.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 8","pages":"1837 - 1849"},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141118812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Precise Asymptotics in Limit Theorems for a Supercritical Branching Process with Immigration in a Random Environment 随机环境中带有移民的超临界分支过程极限定理中的精确渐近线
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-2493-7
Chun Mao Huang, Rui Zhang, Zhi Qiang Gao
{"title":"Precise Asymptotics in Limit Theorems for a Supercritical Branching Process with Immigration in a Random Environment","authors":"Chun Mao Huang,&nbsp;Rui Zhang,&nbsp;Zhi Qiang Gao","doi":"10.1007/s10114-024-2493-7","DOIUrl":"10.1007/s10114-024-2493-7","url":null,"abstract":"<div><p>Let (<i>Z</i><sub><i>n</i></sub>) be a supercritical branching process with immigration in an independent and identically distributed random environment. Under necessary moment conditions, we show the exact convergence rate in the central limit theorem on log <i>Z</i><sub><i>n</i></sub> and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm. By similar approach and with the help of a change of measure, we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 8","pages":"1850 - 1874"},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141120037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Trudinger–Moser Inequalities on a Closed Riemann Surface with a Symmetric Conical Metric 具有对称圆锥公设的封闭黎曼曲面上的特鲁丁格-莫泽不等式
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-2566-7
Yu Fang, Yun Yan Yang
{"title":"Trudinger–Moser Inequalities on a Closed Riemann Surface with a Symmetric Conical Metric","authors":"Yu Fang,&nbsp;Yun Yan Yang","doi":"10.1007/s10114-024-2566-7","DOIUrl":"10.1007/s10114-024-2566-7","url":null,"abstract":"<div><p>This is a continuation of our previous work (<i>Ann. Sc. Norm. Super. Pisa Cl. Sci.</i>, <b>20</b>, 1295–1324, 2020). Let (Σ, <i>g</i>) be a closed Riemann surface, where the metric <i>g</i> has conical singularities at finite points. Suppose <b>G</b> is a group whose elements are isometries acting on (Σ, <i>g</i>). Trudinger–Moser inequalities involving <b>G</b> are established via the method of blow-up analysis, and the corresponding extremals are also obtained. This extends previous results of Chen (<i>Proc. Amer. Math. Soc.</i>, 1990), Iula–Manicini (<i>Nonlinear Anal.</i>, 2017), and the authors (2020).</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 9","pages":"2263 - 2284"},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141121255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Block dual Toeplitz Operators on the Orthogonal Complements of Fock Spaces 福克空间正交补集上的整块对偶托普利兹算子
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-2587-2
Jian Xiang Dong, Chun Xu Xu, Yu Feng Lu
{"title":"Block dual Toeplitz Operators on the Orthogonal Complements of Fock Spaces","authors":"Jian Xiang Dong,&nbsp;Chun Xu Xu,&nbsp;Yu Feng Lu","doi":"10.1007/s10114-024-2587-2","DOIUrl":"10.1007/s10114-024-2587-2","url":null,"abstract":"<div><p>In this paper, we characterize the boundedness and compactness of the block dual Toeplitz operators acting on the orthogonal complement of the Fock spaces, and the compactness of the finite sum of two dual Toeplitz operators products. The commutator and semi-commutator induced by the block dual Toeplitz operators are considered.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 8","pages":"1967 - 1988"},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141121442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exponentially Bounded C-semigroup and the Cauchy Initial Value Problems in Complete Random Normed Modules 指数有界 C-半群与完全随机规范模中的考希初值问题
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-2584-5
Son Ta Cong, Thang Dang Hung, Oanh Le Thi
{"title":"Exponentially Bounded C-semigroup and the Cauchy Initial Value Problems in Complete Random Normed Modules","authors":"Son Ta Cong,&nbsp;Thang Dang Hung,&nbsp;Oanh Le Thi","doi":"10.1007/s10114-024-2584-5","DOIUrl":"10.1007/s10114-024-2584-5","url":null,"abstract":"<div><p>In this paper, the notion of <i>C</i>-semigroup of continuous module homomorphisms on a complete random normal (RN) module is introduced and investigated. The existence and uniqueness of solution to the Cauchy problem with respect to exponentially bounded <i>C</i>-semigroups of continuous module homomorphisms in a complete RN module are established.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 9","pages":"2195 - 2212"},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141119493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Extension of the Non-central Wishart Distribution with Integer Shape Vector 带整数形状向量的非中心维沙特分布的扩展
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-2549-8
Kaouthar Kammoun
{"title":"An Extension of the Non-central Wishart Distribution with Integer Shape Vector","authors":"Kaouthar Kammoun","doi":"10.1007/s10114-024-2549-8","DOIUrl":"10.1007/s10114-024-2549-8","url":null,"abstract":"<div><p>This research paper deals with an extension of the non-central Wishart introduced in 1944 by Anderson and Girshick, that is the non-central Riesz distribution when the scale parameter is derived from a discrete vector. It is related to the matrix of normal samples with monotonous missing data. We characterize this distribution by means of its Laplace transform and we give an algorithm for generating it. Then we investigate, based on the method of the moment, the estimation of the parameters of the proposed model. The performance of the proposed estimators is evaluated by a numerical study.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 9","pages":"2153 - 2168"},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141120823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","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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