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Four Dimensional Hypersurfaces with Proper Mean Curvature Vector Field in Pseudo-Riemannian Space Forms 伪黎曼空间形式中具有固有平均曲率向量场的四维超曲面
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-01-15 DOI: 10.1007/s10114-026-4492-3
Chao Yang, Jiancheng Liu, Li Du
{"title":"Four Dimensional Hypersurfaces with Proper Mean Curvature Vector Field in Pseudo-Riemannian Space Forms","authors":"Chao Yang,&nbsp;Jiancheng Liu,&nbsp;Li Du","doi":"10.1007/s10114-026-4492-3","DOIUrl":"10.1007/s10114-026-4492-3","url":null,"abstract":"<div><p>In this paper, we prove that four-dimensional hypersurface <i>M</i><span>\u0000 <sup>4</sup><sub><i>r</i></sub>\u0000 \u0000 </span> with proper mean curvature vector field (i.e., <span>(Delta{vec H})</span> is proportional to <span>({vec H})</span>) in pseudo-Riemannian space form <i>N</i><span>\u0000 <sup>5</sup><sub><i>s</i></sub>\u0000 \u0000 </span>(<i>c</i>) has constant mean curvature, and give the value or range of this constant. As an application, we obtain that biharmonic hypersurfaces in <i>N</i><span>\u0000 <sup>5</sup><sub><i>s</i></sub>\u0000 \u0000 </span>(<i>c</i>) are minimal in some specific case.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 1","pages":"201 - 223"},"PeriodicalIF":0.9,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339365","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
Full Conformal Oscillator Representations of (mathfrak{o}(2n+2)) and Combinatorial Identities (mathfrak{o}(2n+2))与组合恒等式的全共形振子表示
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-01-15 DOI: 10.1007/s10114-026-4286-7
Zhenyu Zhou
{"title":"Full Conformal Oscillator Representations of (mathfrak{o}(2n+2)) and Combinatorial Identities","authors":"Zhenyu Zhou","doi":"10.1007/s10114-026-4286-7","DOIUrl":"10.1007/s10114-026-4286-7","url":null,"abstract":"<div><p>Zhao and Xu (2013) constructed a functor from <span>(mathfrak{o}(n))</span>-<b>Mod</b> to <span>(mathfrak{o}(n+2))</span>-<b>Mod</b>. In this paper, we use the functor successively to obtain full conformal oscillator representation of <span>(mathfrak{o}(2n+2))</span> in <i>n</i>(<i>n</i> + 1) variables and determine the corresponding finite-dimensional irreducible module explicitly when the highest weight is dominant integral. We also find an equation of counting the dimension of an irreducible <span>(mathfrak{o}(2n+2))</span>-module in terms of certain alternating sum of the dimensions of irreducible <span>(mathfrak{o}(2n))</span>-modules, which leads to new combinatorial identities of classical type in the case of the Steinberg modules. One can use the results to study tensor decomposition of finite-dimensional irreducible modules by solving certain first-order linear partial differential equations, and thereby obtain the corresponding physically interested Clebsch–Gordan coefficients and exact solutions of Knizhnik–Zamolodchikov equation in WZW model of conformal field theory.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 1","pages":"1 - 49"},"PeriodicalIF":0.9,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339363","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
Study on Chaotic Behavior of the (N + 1)-Body Ring Problem （N + 1）-体环问题混沌行为研究
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-01-15 DOI: 10.1007/s10114-026-4245-3
Xuhua Cheng, Mengqian Li
{"title":"Study on Chaotic Behavior of the (N + 1)-Body Ring Problem","authors":"Xuhua Cheng,&nbsp;Mengqian Li","doi":"10.1007/s10114-026-4245-3","DOIUrl":"10.1007/s10114-026-4245-3","url":null,"abstract":"<div><p>In this paper, we study chaotic behavior of the (<i>N</i> + 1)-body planar ring problem. Firstly, based on the perturbation theory of integrable Hamiltonian systems, we utilize mass ratio as a disturbance parameter so that this ring problem is regarded as a perturbation of the two-body problem. Then, by applying the extended Melnikov method, we address that there are transversal homoclinic orbits in the ring problem. Afterwards, since the standard Smale–Birkhoff homoclinic theorem cannot be directly applied to the case of a degenerate saddle, we construct an invertible map <i>f</i> satisfying Conley–Moser condition and finally conclude that the ring problem possesses chaotic behavior of the Smale horseshoe type.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 1","pages":"189 - 200"},"PeriodicalIF":0.9,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339459","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
Bounded Directional Complexity and Rigidity for ℤq-actions q-作用的有界方向复杂度和刚性
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-01-15 DOI: 10.1007/s10114-026-4222-x
Runju Wei, Leiye Xu, Liqi Zheng, Xiaomin Zhou
{"title":"Bounded Directional Complexity and Rigidity for ℤq-actions","authors":"Runju Wei,&nbsp;Leiye Xu,&nbsp;Liqi Zheng,&nbsp;Xiaomin Zhou","doi":"10.1007/s10114-026-4222-x","DOIUrl":"10.1007/s10114-026-4222-x","url":null,"abstract":"<div><p>We introduce directional complexities for ℤ<sup><i>q</i></sup>-measure preserving dynamical systems via a collection of new metrics along non-zero directions in ℝ<sup><i>q</i></sup>. It turns out that a ℤ<sup><i>q</i></sup>-measure preserving dynamical system is rigid if and only if the invariant measure has bounded directional complexity. We also obtain ergodic decomposition formula for the measure-theoretic directional entropy of a ℤ<sup><i>q</i></sup>-measure preserving dynamical system.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 1","pages":"173 - 188"},"PeriodicalIF":0.9,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10114-026-4222-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasi-stationary Distribution for the Explosive Single-birth Process 爆炸单胎过程的准平稳分布
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-01-15 DOI: 10.1007/s10114-026-4225-7
Zhekang Fang, Yonghua Mao, Yuhui Zhang
{"title":"Quasi-stationary Distribution for the Explosive Single-birth Process","authors":"Zhekang Fang,&nbsp;Yonghua Mao,&nbsp;Yuhui Zhang","doi":"10.1007/s10114-026-4225-7","DOIUrl":"10.1007/s10114-026-4225-7","url":null,"abstract":"<div><p>For the minimal process corresponding to an explosive single-birth (or upwardly skip-free) <i>Q</i>-matrix on the non-negative integers, we prove the existence and uniqueness of quasi-stationary distribution, provide an explicit representation to it and show that it is the limit of quasi-stationary distributions of its truncated processes.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 1","pages":"151 - 172"},"PeriodicalIF":0.9,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339463","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
Derivatives of Local Times and Hausdorff Dimension of Inverse Images of Space-time Anisotropic Gaussian Random Fields 时空各向异性高斯随机场逆像的局部时间导数和Hausdorff维数
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-01-15 DOI: 10.1007/s10114-026-4355-y
Peng Xu, Zhenlong Chen
{"title":"Derivatives of Local Times and Hausdorff Dimension of Inverse Images of Space-time Anisotropic Gaussian Random Fields","authors":"Peng Xu,&nbsp;Zhenlong Chen","doi":"10.1007/s10114-026-4355-y","DOIUrl":"10.1007/s10114-026-4355-y","url":null,"abstract":"<div><p>Let <i>X</i> = {<i>X</i>(<i>t</i>), <i>t</i> ∈ ∝<sup><i>N</i></sup>} be a centered space-time anisotropic Gaussian random field with values in ℝ<sup><i>d</i></sup>. Under some general conditions, the existence, joint continuity and Hölder conditions of higher-order derivative of local times of <i>X</i> are studied. Moreover, we obtain the uniform Hausdorff dimension of the inverse images of <i>X</i>. The existing results of Gaussian random fields are extended to space-time anisotropic Gaussian random fields with approximate independent components.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 1","pages":"224 - 238"},"PeriodicalIF":0.9,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10114-026-4355-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hardy Space Estimate of the Maximal Wave Operator 极大波算子的Hardy空间估计
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-01-15 DOI: 10.1007/s10114-026-4215-9
Jiecheng Chen, Dashan Fan, Junyan Zhao
{"title":"Hardy Space Estimate of the Maximal Wave Operator","authors":"Jiecheng Chen,&nbsp;Dashan Fan,&nbsp;Junyan Zhao","doi":"10.1007/s10114-026-4215-9","DOIUrl":"10.1007/s10114-026-4215-9","url":null,"abstract":"<div><p>In this paper, we obtain the sharp Hardy space estimate of the maximal wave operator. Some applications on spherical averages and their combinations are also given.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 1","pages":"127 - 150"},"PeriodicalIF":0.9,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339519","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
Left-invariant Metrics on a Class of Solvable Lie Groups 一类可解李群上的左不变度量
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-01-15 DOI: 10.1007/s10114-026-4284-9
Zhiqi Chen, Ke Yan, Hui Zhang
{"title":"Left-invariant Metrics on a Class of Solvable Lie Groups","authors":"Zhiqi Chen,&nbsp;Ke Yan,&nbsp;Hui Zhang","doi":"10.1007/s10114-026-4284-9","DOIUrl":"10.1007/s10114-026-4284-9","url":null,"abstract":"<div><p>Left-invariant Riemannian metrics on Lie groups <span>(G_{{{mathbb R}{rm H}}^{n-1}} times {mathbb R})</span> and <span>(G_{{{mathbb R}{rm H}}^{2}} times {{mathbb R}^{n-2}})</span> (<i>n</i> ≥ 3) have been classified by Hiroshi, Takahara and Tamaru. It is easily seen that <span>(G_{{{mathbb R}{rm H}}^{n-1}} times {mathbb R})</span> and <span>(G_{{{mathbb R}{rm H}}^{2}} times {{mathbb R}^{n-2}})</span> (<i>n</i> ≥ 3) have the same automorphism group, which is denoted by <i>L</i><sub><i>n</i></sub>. In this paper, we first classify <i>n</i>-dimensional simply connected Lie groups with automorphism group <i>L</i><sub><i>n</i></sub>, then we classify the left-invariant Riemannian metrics on such Lie groups. As an application, we get the <i>m</i>-quasi Einstein metrics.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 1","pages":"250 - 268"},"PeriodicalIF":0.9,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339461","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
Limit Theorems for Supercritical Remaining-lifetime Age-structured Branching Processes 超临界剩余寿命年龄结构分支过程的极限定理
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-01-15 DOI: 10.1007/s10114-026-4134-9
Ziling Cheng
{"title":"Limit Theorems for Supercritical Remaining-lifetime Age-structured Branching Processes","authors":"Ziling Cheng","doi":"10.1007/s10114-026-4134-9","DOIUrl":"10.1007/s10114-026-4134-9","url":null,"abstract":"<div><p>We study supercritical age-structured branching models starting from a single particle with a random lifetime, where the reproduction law depends on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. A necessary and sufficient condition is provided for the convergence of the Malthusian normalized random measures. The Malthusian type limit theory in a functional form can be strengthened to hold with probability one under some “<i>L</i> log <i>L</i>” conditions. We further prove a central limit theory with a random normalization factor.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 1","pages":"50 - 84"},"PeriodicalIF":0.9,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339462","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
Generalized Turán Number for Edge Blow-up of Paths and Cycles 路径与环边爆破的广义Turán数
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-01-15 DOI: 10.1007/s10114-026-4223-9
Yuanpei Wang, Liying Kang
{"title":"Generalized Turán Number for Edge Blow-up of Paths and Cycles","authors":"Yuanpei Wang,&nbsp;Liying Kang","doi":"10.1007/s10114-026-4223-9","DOIUrl":"10.1007/s10114-026-4223-9","url":null,"abstract":"<div><p>Given a graph <i>H</i> and an integer <i>p</i> ≥ 2, the edge blow-up graph <i>H</i><sup><i>p</i>+1</sup> of <i>H</i> is the graph obtained by replacing each edge in <i>H</i> with a clique of order <i>p</i> + 1, where the new vertices of the cliques are all distinct. The generalized Turán number ex(<i>n, K</i><sub><i>m</i></sub>, <i>F</i>) denote the maximum number of copies of <i>K</i><sub><i>m</i></sub> in an <i>n</i>-vertex <i>F</i>-free graph. Let <i>C</i><sub><i>t</i></sub> and <i>P</i><sub><i>t</i></sub> denote the cycle and path with <i>t</i> vertices, respectively. In this paper, we obtain the generalized Turán numbers ex(<i>n, K</i><sub><i>m</i></sub>, <i>P</i><span>\u0000 <sup><i>p</i>+1</sup><sub><i>t</i></sub>\u0000 \u0000 </span>), ex(<i>n, K</i><sub><i>m</i></sub>, <i>C</i><span>\u0000 <sup><i>p</i>+1</sup><sub><i>t</i></sub>\u0000 \u0000 </span>) and characterize the unique graph for <i>P</i><span>\u0000 <sup><i>p</i>+1</sup><sub><i>t</i></sub>\u0000 \u0000 </span> and <i>C</i><span>\u0000 <sup><i>p</i>+1</sup><sub><i>t</i></sub>\u0000 \u0000 </span> respectively, when <i>t</i> ≥ 3, <i>p</i> ≥ <i>m</i> ≥ 3 and <i>n</i> is sufficiently large.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 1","pages":"239 - 249"},"PeriodicalIF":0.9,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147339366","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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