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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
Greedy Lattice Paths with General Weights 具有一般权重的贪婪网格路径
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-2388-7
Yin Shan Chang, An Qi Zheng
{"title":"Greedy Lattice Paths with General Weights","authors":"Yin Shan Chang,&nbsp;An Qi Zheng","doi":"10.1007/s10114-024-2388-7","DOIUrl":"10.1007/s10114-024-2388-7","url":null,"abstract":"<div><p>Let {<i>X</i><sub><i>υ</i></sub>: <i>υ</i> ∈ ℤ<sup><i>d</i></sup>} be i.i.d. random variables. Let <span>(S(pi) = sumnolimits_{upsilonin pi} {{X_upsilon}})</span> be the weight of a self-avoiding lattice path <i>π</i>. Let </p><div><div><span>$${M_n} = max{ S(pi):,,pi,{text{has}},{text{length}},n,{text{and}},{text{starts}},{text{from}},{text{origin}}}.$$</span></div></div><p>We are interested in the asymptotics of <i>M</i><sub><i>n</i></sub> as <i>n</i> → ∞. This model is closely related to the first passage percolation when the weights {<i>X</i><sub><i>υ</i></sub>: <i>υ</i> ∈ ℤ<sup><i>d</i></sup>} are non-positive and it is closely related to the last passage percolation when the weights {<i>X</i><sub><i>υ</i></sub>, <i>υ</i> ∈ ℤ<sup><i>d</i></sup>} are non-negative. For general weights, this model could be viewed as an interpolation between first passage models and last passage models. Besides, this model is also closely related to a variant of the position of right-most particles of branching random walks. Under the two assumptions that <span>(exists alpha &gt; 0,,E{(X_0^ + )^d}{({log ^ + }X_0^ + )^{d + alpha }} &lt; + ,infty)</span> and that <span>(E[X_0^ - ] &lt; + ,infty)</span>, we prove that there exists a finite real number <i>M</i> such that <i>M</i><sub><i>n</i></sub>/<i>n</i> converges to a deterministic constant <i>M</i> in <i>L</i><sup>1</sup> as <i>n</i> tends to infinity. And under the stronger assumptions that <span>(exists alpha &gt; 0,,,E{(X_0^ + )^d}{({log ^ + },X_0^ + )^{d + alpha }} &lt; , + ,infty)</span> and that <span>(E[{(X_0^ - )^4}] &lt; , + ,infty)</span>, we prove that <i>M</i><sub><i>n</i></sub>/<i>n</i> converges to the same constant <i>M</i> almost surely as <i>n</i> tends to infinity.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 9","pages":"2213 - 2222"},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141147297","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 Local Tb Theorem for Square Functions and Parabolic Layer Potentials 平方函数和抛物线层势的局部 Tb 定理
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-2576-5
Zhi Dan Wang, Guo Ming Zhang
{"title":"A Local Tb Theorem for Square Functions and Parabolic Layer Potentials","authors":"Zhi Dan Wang,&nbsp;Guo Ming Zhang","doi":"10.1007/s10114-024-2576-5","DOIUrl":"10.1007/s10114-024-2576-5","url":null,"abstract":"<div><p>In this paper, we give a locally parabolic version of <i>Tb</i> theorem for a class of vector-valued operators with off-diagonal decay in <i>L</i><sup>2</sup> and certain quasi-orthogonality on a subspace of <i>L</i><sup>2</sup>, in which the testing functions themselves are also vector-valued. As an application, we establish the boundedness of layer potentials related to parabolic operators in divergence form, defined in the upper half-space ℝ<span>\u0000 <sup><i>n</i>+2</sup><sub>+</sub>\u0000 \u0000 </span> ≔ {(<i>x</i>, <i>t</i>, <i>λ</i>) ∈ ℝ<sup><i>n</i>+1</sup> × (0, ∞)}, with uniformly complex elliptic, <i>L</i><sup>∞</sup>, <i>t</i>, <i>λ</i>-independent coefficients, and satisfying the De Giorgi/Nash estimates.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 8","pages":"1941 - 1966"},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141118541","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
Generic Existence of Infinitely Many Non-contractible Closed Geodesics on Compact Space Forms 紧凑空间形式上无限多非收缩闭合大地线的一般存在性
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-20 DOI: 10.1007/s10114-024-3009-1
Hui Liu, Yu Chen Wang
{"title":"Generic Existence of Infinitely Many Non-contractible Closed Geodesics on Compact Space Forms","authors":"Hui Liu,&nbsp;Yu Chen Wang","doi":"10.1007/s10114-024-3009-1","DOIUrl":"10.1007/s10114-024-3009-1","url":null,"abstract":"<div><p>Let <i>M</i> = <i>S</i><sup><i>n</i></sup> /Γ and <i>h</i> be a nontrivial element of finite order <i>p</i> in <i>π</i><sub>1</sub>(<i>Μ</i>), where the integers <i>n</i>, <i>p</i> ≥ 2, Γ is a finite abelian group which acts freely and isometrically on the <i>n</i>-sphere and therefore <i>M</i> is diffeomorphic to a compact space form. In this paper, we prove that there are infinitely many non-contractible closed geodesics of class [<i>h</i>] on the compact space form with <i>C</i><sup><i>r</i></sup>-generic Finsler metrics, where 4 ≤ <i>r</i> ≤ ∞. The conclusion also holds for <i>C</i><sup><i>r</i></sup>-generic Riemannian metrics for 2 ≤ <i>r</i> ≤ ∞. The proof is based on the resonance identity of non-contractible closed geodesics on compact space forms.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 7","pages":"1674 - 1684"},"PeriodicalIF":0.8,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141120952","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
Differential Operator Approach to ıquantum Groups and Their Oscillator Representations 量子群及其振子表示的微分算子方法
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-15 DOI: 10.1007/s10114-024-2151-0
Zhao Bing Fan, Ji Cheng Geng, Shao Long Han
{"title":"Differential Operator Approach to ıquantum Groups and Their Oscillator Representations","authors":"Zhao Bing Fan,&nbsp;Ji Cheng Geng,&nbsp;Shao Long Han","doi":"10.1007/s10114-024-2151-0","DOIUrl":"10.1007/s10114-024-2151-0","url":null,"abstract":"<div><p>For a quasi-split Satake diagram, we define a modified <i>q</i>-Weyl algebra, and show that there is an algebra homomorphism between it and the corresponding <i>ı</i>quantum group. In other words, we provide a differential operator approach to <i>ı</i>quantum groups. Meanwhile, the oscillator representations of <i>ı</i>quantum groups are obtained. The crystal basis of the irreducible subrepresentations of these oscillator representations are constructed.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 5","pages":"1360 - 1374"},"PeriodicalIF":0.8,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411990","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
Finite Groups with Some Bounded Codegrees 具有某些有界编码的有限群
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-05-09 DOI: 10.1007/s10114-024-1236-0
Dong Fang Yang, Yu Zeng, Heng Lv
{"title":"Finite Groups with Some Bounded Codegrees","authors":"Dong Fang Yang,&nbsp;Yu Zeng,&nbsp;Heng Lv","doi":"10.1007/s10114-024-1236-0","DOIUrl":"10.1007/s10114-024-1236-0","url":null,"abstract":"<div><p>For a character <i>χ</i> of a finite group <i>G</i>, the number cod(<i>χ</i>)≔ ∣<i>G</i>: ker(<i>χ</i>)∣/<i>χ</i>(1) is called the codegree of <i>χ</i>. In this paper, we give a solvability criterion for a finite group <i>G</i> depending on the minimum of the ratio <i>χ</i>(1)<sup>2</sup>/cod(<i>χ</i>), when <i>χ</i> varies among the irreducible characters of <i>G</i>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 7","pages":"1778 - 1784"},"PeriodicalIF":0.8,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410804","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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