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Times of a Branching Process with Immigration in Varying Environments Attaining a Fixed Level 在不同环境中迁移的分支过程达到固定水平的时间
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI: 10.1007/s10114-025-4035-3
Huaming Wang
{"title":"Times of a Branching Process with Immigration in Varying Environments Attaining a Fixed Level","authors":"Huaming Wang","doi":"10.1007/s10114-025-4035-3","DOIUrl":"10.1007/s10114-025-4035-3","url":null,"abstract":"<div><p>Consider a branching process {<i>Z</i><sub><i>n</i></sub>}<sub><i>n</i>≥0</sub> with immigration in varying environments. For <i>a</i> ∈ {0, 1, 2, …}, let <i>C</i>(<i>a</i>) = {<i>n</i> ≥ 0: <i>Z</i><sub><i>n</i></sub> = <i>a</i>} be the collection of times at which the population size of the process attains level <i>a</i>. We give a criterion to determine whether the set <i>C</i>(<i>a</i>) is finite or not. For the critical Galton–Watson process, based on a moment method, we show that <span>({{| {C(a) cap [1,n]} |} over {log ;n to S}})</span> in distribution, where <i>S</i> is an exponentially distributed random variable with <i>P</i>(<i>S</i> &gt; <i>t</i>) = e<sup>−<i>t</i></sup>, <i>t</i> &gt; 0.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 7","pages":"1789 - 1806"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145100647","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
Part-Silting Presilting Complexes 部分预淤复合体
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI: 10.1007/s10114-025-4309-9
Jiaqun Wei
{"title":"Part-Silting Presilting Complexes","authors":"Jiaqun Wei","doi":"10.1007/s10114-025-4309-9","DOIUrl":"10.1007/s10114-025-4309-9","url":null,"abstract":"<div><p>Let <i>A</i> be an Artin algebra and <i>M</i> be a presilting radical complex. We show that <i>M</i> is silting provided its some left part or some right part is silting.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 7","pages":"1944 - 1952"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145100688","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
Nonstandard Limit Theorems and Large Deviation for β-Jacobi Ensembles with a Different Scaling 不同尺度下β-Jacobi系综的非标准极限定理和大偏差
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI: 10.1007/s10114-025-3133-6
Yutao Ma, Yonghua Mao, Siyu Wang
{"title":"Nonstandard Limit Theorems and Large Deviation for β-Jacobi Ensembles with a Different Scaling","authors":"Yutao Ma,&nbsp;Yonghua Mao,&nbsp;Siyu Wang","doi":"10.1007/s10114-025-3133-6","DOIUrl":"10.1007/s10114-025-3133-6","url":null,"abstract":"<div><p>We consider <i>β</i>-Jacobi ensembles with parameters <i>p</i><sub>1</sub>, <i>p</i><sub>2</sub> ≥ <i>n</i>. We prove that the empirical measure of the rescaled <i>β</i>-Jacobi ensembles converges weakly to a modified Wachter law via the spectral measure method. We also provide the central limit theorem and the large deviation for the corresponding rescaled spectral measure.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 7","pages":"1753 - 1774"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145100690","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
Two New Families of Fourth-Order Explicit Exponential Runge–Kutta Methods with Four Stages for First-Order Differential Systems 一阶微分系统的两种新的四阶显式四阶指数龙格-库塔方法
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI: 10.1007/s10114-025-4348-2
Xianfa Hu, Yonglei Fang, Bin Wang
{"title":"Two New Families of Fourth-Order Explicit Exponential Runge–Kutta Methods with Four Stages for First-Order Differential Systems","authors":"Xianfa Hu,&nbsp;Yonglei Fang,&nbsp;Bin Wang","doi":"10.1007/s10114-025-4348-2","DOIUrl":"10.1007/s10114-025-4348-2","url":null,"abstract":"<div><p>In this paper, we formulate two new families of fourth-order explicit exponential Runge–Kutta (ERK) methods with four stages for solving first-order differential systems <i>y</i>′(<i>t</i>)+ <i>My</i>(<i>t</i>) = <i>f</i>(<i>y</i>(<i>t</i>)). The order conditions of these ERK methods are derived by comparing the Taylor series of the exact solution, which are exactly identical to the order conditions of explicit Runge–Kutta methods, and these ERK methods reduce to classical Runge–Kutta methods once <i>M</i> → 0. Moreover, we analyze the stability properties and the convergence of these new methods. Several numerical examples are implemented to illustrate the accuracy and efficiency of these ERK methods by comparison with standard exponential integrators.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 7","pages":"1923 - 1943"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145100687","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
Structure of Perfect and Complete Lie Conformal Algebras 完备李共形代数的结构
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI: 10.1007/s10114-025-3220-8
Tianqi Feng, Jun Zhao, Liangyun Chen, Chenrui Yao
{"title":"Structure of Perfect and Complete Lie Conformal Algebras","authors":"Tianqi Feng,&nbsp;Jun Zhao,&nbsp;Liangyun Chen,&nbsp;Chenrui Yao","doi":"10.1007/s10114-025-3220-8","DOIUrl":"10.1007/s10114-025-3220-8","url":null,"abstract":"<div><p>Perfect and complete Lie conformal algebras will be discussed in this paper. We give the characterizations of complete Lie conformal algebras. We demonstrate that every perfectly complete Lie conformal algebra can be uniquely decomposed to a direct sum of indecomposable perfectly complete ideals. And we show the existence of a sympathetic decomposition in every perfect Lie conformal algebra. Finally, we study a class of ideals of Lie conformal algebras such that the quotients are perfectly complete Lie conformal algebras.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 7","pages":"1868 - 1890"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145100693","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
Rigidity of k-extremal Submanifolds in a Sphere 球面上k-极值子流形的刚性
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI: 10.1007/s10114-025-3379-z
Hang Chen, Yaru Wang
{"title":"Rigidity of k-extremal Submanifolds in a Sphere","authors":"Hang Chen,&nbsp;Yaru Wang","doi":"10.1007/s10114-025-3379-z","DOIUrl":"10.1007/s10114-025-3379-z","url":null,"abstract":"<div><p>In this paper, we study the rigidity of <i>k</i>(≥ 1)-extremal submanifolds in a sphere and prove various pinching theorems under different curvature conditions, including sectional and Ricci curvatures in pointwise and integral sense.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 7","pages":"1832 - 1854"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145100696","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
Scattering for the Non-Radial Focusing Inhomogeneous Nonlinear Schrödinger–Choquard Equation 非径向聚焦非齐次非线性Schrödinger-Choquard方程的散射
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI: 10.1007/s10114-025-4015-7
Chengbin Xu
{"title":"Scattering for the Non-Radial Focusing Inhomogeneous Nonlinear Schrödinger–Choquard Equation","authors":"Chengbin Xu","doi":"10.1007/s10114-025-4015-7","DOIUrl":"10.1007/s10114-025-4015-7","url":null,"abstract":"<div><p>In this paper, we study the long-time behavior of global solutions to the Schrödinger–Choquard equation </p><div><div><span>$${rm{i}}{partial _t}u + Delta u = - ( {{I_alpha } * {{vert cdot vert}^b}{{vert u vert}^p}} ){vert cdot vert^b}{vert u vert^{p - 2}}u.$$</span></div></div><p>Inspired by Murphy who gave a simple proof of scattering for the non-radial INLS, we find that the inhomogeneous term ∣<i>x</i>∣<sup><i>b</i></sup> can replace the radial Sobolev embedding theorem, which allows us to prove scattering theory below the ground state for the intercritical case in energy space without radial assumption.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 7","pages":"1891 - 1905"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145100691","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
Commuting Toeplitz Operators on the 2-analytic Bergman Space 2解析Bergman空间上的可交换Toeplitz算子
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI: 10.1007/s10114-025-3195-5
Yanyue Shi, Yunpeng Li, Bo Zhang, Yufeng Lu
{"title":"Commuting Toeplitz Operators on the 2-analytic Bergman Space","authors":"Yanyue Shi,&nbsp;Yunpeng Li,&nbsp;Bo Zhang,&nbsp;Yufeng Lu","doi":"10.1007/s10114-025-3195-5","DOIUrl":"10.1007/s10114-025-3195-5","url":null,"abstract":"<div><p>On the classical Bergman space, Toeplitz operators with radial symbols are diagonal and those operators commute. However, on the <i>n</i>-analytic Bergman space <span>(A_{n}^{2}(mathbb D))</span> when <i>n</i> ≥ 2, the case is different. In this paper, our focus is on the problem of commuting Toeplitz operators with quasiho-mogeneous symbols, specifically in the context of the function space <span>(A_{2}^{2}(mathbb D))</span>. We show a kind of block matrice expression of Toeplitz operators on <span>(A_{2}^{2}(mathbb D))</span>. Based on the block expression, we give several important properties. Our results indicate that in some cases, two Toeplitz operators are commutative if and only if both operators are analytic or differ by a constant multiple.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 7","pages":"1855 - 1867"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145100692","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
Strongly HN-Positivity, Uniformly RC k-Positivity and Rational Connectedness 强hn -正性、一致RC - k-正性和有理连通性
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI: 10.1007/s10114-025-3217-3
Yong Chen
{"title":"Strongly HN-Positivity, Uniformly RC k-Positivity and Rational Connectedness","authors":"Yong Chen","doi":"10.1007/s10114-025-3217-3","DOIUrl":"10.1007/s10114-025-3217-3","url":null,"abstract":"<div><p>In this paper, we discuss the concept of HN-semipositive (HN-positive) vector bundle and also introduce strongly HN-semipositive vector bundle over compact complex manifold. Let <i>M</i> be a projective manifold with HN-semipositive tangent bundle. If <i>M</i> is rationally connected, we show that <i>T</i><sup>1,0</sup><i>M</i> is strongly HN-positive. We give a characterization of rationally connected compact Kähler manifolds with strongly HN-semipositive tangent bundle. In the second part, we show that a uniformly RC <i>k</i>-positivity implies mean curvature positivity.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 7","pages":"1906 - 1922"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145100694","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
Solution of Linear Damped Fractional Wave Equation on Triebel–Lizorkin Spaces triiebel - lizorkin空间上线性阻尼分数阶波动方程的解
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI: 10.1007/s10114-025-3294-3
Meizhong Wang, Jiecheng Chen, Dashan Fan, Ziyao Liu
{"title":"Solution of Linear Damped Fractional Wave Equation on Triebel–Lizorkin Spaces","authors":"Meizhong Wang,&nbsp;Jiecheng Chen,&nbsp;Dashan Fan,&nbsp;Ziyao Liu","doi":"10.1007/s10114-025-3294-3","DOIUrl":"10.1007/s10114-025-3294-3","url":null,"abstract":"<div><p>In the article we study the solution <i>u</i>(<i>x, t</i>) of the Cauchy problem of linear damped fractional wave equation. We prove that <i>u</i>(<i>x, t</i>) has some sharp boundedness estimates on the Triebel–Lizorkin space. The proof of the necessity part is based on obtaining the precise asymptotic forms of the kernels of operators <span>({rm e}^{-t} cosh(t{sqrt L}))</span> and <span>({rm e}^{-t} {{sinh(t{sqrt L})} over {sqrt L}})</span> with <i>L</i> = 1 − ∣Δ∣<sup><i>α</i></sup>, where Δ is the Laplacian, as well as the method of stationary phase. Additionally, we study the Riesz mean of the solution and show its convergence in the Triebel–Lizorkin space norm.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 7","pages":"1807 - 1831"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145100695","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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