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Global Well-posedness in a Two-dimensional Two-species Chemotaxis-Navier–Stokes System with Competitive Kinetics 具有竞争动力学的二维两物种趋化- navier - stokes系统全局适定性
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-04-15 DOI: 10.1007/s10114-026-4323-6
Minghua Yang, Qiang Zhao, Yatao Li, Zunwei Fu
{"title":"Global Well-posedness in a Two-dimensional Two-species Chemotaxis-Navier–Stokes System with Competitive Kinetics","authors":"Minghua Yang,&nbsp;Qiang Zhao,&nbsp;Yatao Li,&nbsp;Zunwei Fu","doi":"10.1007/s10114-026-4323-6","DOIUrl":"10.1007/s10114-026-4323-6","url":null,"abstract":"<div><p>In this article, we study the Cauchy problem for the two-species chemotaxis-Navier–Stokes system with Lotka–Volterra competitive kinetics</p><div><div><span>$$begin{cases}u_t + (u cdot nabla) u = Delta u + nabla mathbb{P} + (m+n) nabla phi, quad nabla cdot u = 0, n_t + (u cdot nabla) n = Delta n - nabla cdot (n nabla c) + n(1 - n - m), m_t + (u cdot nabla) m = Delta m - nabla cdot (m nabla c) + m(1 - n - m), c_t + u cdot nabla c = Delta c - (n + m) c.end{cases}$$</span></div></div><p>The system is a model that describes the dynamics of two species and comes from a problem on account of the influence of chemotaxis, the Lotka–Volterra kinetics and fluid. By taking advantage of a scale decomposition technique together with a microlocal analysis, we prove the global-in-time existence and uniqueness of the weak solution to the system for a large class of initial data on the whole space ℝ<sup>2</sup>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 4","pages":"1014 - 1044"},"PeriodicalIF":0.9,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147827022","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
Subgroup Identification and Variable Selection in the High-Dimensional Heterogeneous Cox Model 高维异质Cox模型的子群识别和变量选择
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-04-15 DOI: 10.1007/s10114-026-4104-2
Yunshu Huang, Jiehui Wang
{"title":"Subgroup Identification and Variable Selection in the High-Dimensional Heterogeneous Cox Model","authors":"Yunshu Huang,&nbsp;Jiehui Wang","doi":"10.1007/s10114-026-4104-2","DOIUrl":"10.1007/s10114-026-4104-2","url":null,"abstract":"<div><p>Conventional statistical analysis methods encounter challenges when addressing precise medical treatment for high-dimensional survival data. Overcoming these challenges involves accounting for heterogeneity to mitigate estimation bias and avoiding model overfitting for enhanced interpretability. This paper introduces a regularization technique based on the heterogeneous Cox model, enabling simultaneous variable selection, subgroup identification, and parameter estimation. The approach is entirely data-driven and capable of handling exponential increases in covariate dimension with sample size, as well as divergent numbers of significant variables. Under mild assumptions, we establish asymptotic properties for the proposed estimator, including the oracle property of variable selection, consistency in subgroup identification, and asymptotic normality. Leveraging the coordinate descent method and ADMM algorithm, we propose an efficient MCD-ADMM algorithm for optimization. Simulation studies further validate the effectiveness of our approach, complemented by an analysis of ovarian cancer data for illustrative purposes.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 4","pages":"913 - 939"},"PeriodicalIF":0.9,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147827018","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
Synthesis of the Weyl Matrix on the Square Lattice 方形晶格上Weyl矩阵的合成
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-04-15 DOI: 10.1007/s10114-026-4508-z
Dongjie Wu, Aiwei Guan, Natalia Pavlovna Bondarenko, Chuanfu Yang
{"title":"Synthesis of the Weyl Matrix on the Square Lattice","authors":"Dongjie Wu,&nbsp;Aiwei Guan,&nbsp;Natalia Pavlovna Bondarenko,&nbsp;Chuanfu Yang","doi":"10.1007/s10114-026-4508-z","DOIUrl":"10.1007/s10114-026-4508-z","url":null,"abstract":"<div><p>A method for successive synthesis of the Weyl matrix on the square lattice is proposed. It allows one to compute the Weyl matrix of a large graph by adding new edges and solving elementary systems of linear algebraic equations at each step. Synthesis of the Weyl matrix is useful to further study the inverse problems of the square lattice. Moreover, our approach can be extended to other types of periodic lattices.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 4","pages":"1112 - 1128"},"PeriodicalIF":0.9,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147827020","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
Escobar–Lichnerowicz–Reilly Type Eigenvalue Estimate for the Weighted p-Laplacian on Manifolds with Integral Ricci Curvature 积分Ricci曲率流形上加权p-拉普拉斯算子的Escobar-Lichnerowicz-Reilly型特征值估计
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-04-15 DOI: 10.1007/s10114-026-4479-0
Yongtao Liu
{"title":"Escobar–Lichnerowicz–Reilly Type Eigenvalue Estimate for the Weighted p-Laplacian on Manifolds with Integral Ricci Curvature","authors":"Yongtao Liu","doi":"10.1007/s10114-026-4479-0","DOIUrl":"10.1007/s10114-026-4479-0","url":null,"abstract":"<div><p>Under the assumption of integral <i>m</i>-Bakry–Émery Ricci curvature, we give an Escobar–Lichnerowicz–Reilly type eigenvalue estimate for the weighted <i>p</i>-Laplacian on compact smooth metric measure spaces with or without boundaries. This conclusion is a generalization and improvement of Wang–Li’s result in the case of integral Bakry–Émery Ricci curvature, and of Seto–Wei’s one to the compact metric measure space setting. Our main tools are the weighted <i>p</i>-Bochner formula and the weighted <i>p</i>-Reilly formula.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 4","pages":"1045 - 1061"},"PeriodicalIF":0.9,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147827025","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
Fundamental Group and Symmetric Differentials on an Elliptic Fibration 椭圆型纤曲上的基群和对称微分
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-04-15 DOI: 10.1007/s10114-026-5069-x
Wanyuan Xu
{"title":"Fundamental Group and Symmetric Differentials on an Elliptic Fibration","authors":"Wanyuan Xu","doi":"10.1007/s10114-026-5069-x","DOIUrl":"10.1007/s10114-026-5069-x","url":null,"abstract":"<div><p>Let <i>f</i>: <i>X</i> → <i>C</i> be an elliptic fibration. We prove that if the fundamental group π<sub>1</sub>(<i>X</i>) of <i>X</i> is infinite, then there exists a positive integer <i>m</i> such that <i>H</i><sup>0</sup>(<i>X, S</i><sup><i>m</i></sup>Ω<span>\u0000 <sup>1</sup><sub><i>X</i></sub>\u0000 \u0000 </span>) ≠ 0. This answers a question of H. Esnault for an elliptic fibration.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 4","pages":"1129 - 1134"},"PeriodicalIF":0.9,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147827021","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
Equicontinuity and Sensitivity Under Weak Mean Metric 弱平均度量下的等连续性和灵敏度
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-04-15 DOI: 10.1007/s10114-026-4238-2
Zhongxuan Yang, Xiaojun Huang
{"title":"Equicontinuity and Sensitivity Under Weak Mean Metric","authors":"Zhongxuan Yang,&nbsp;Xiaojun Huang","doi":"10.1007/s10114-026-4238-2","DOIUrl":"10.1007/s10114-026-4238-2","url":null,"abstract":"<div><p>In this paper, we study the weak mean metric and give some properties by replacing the Besicovitch pseudometric with weak mean metric in the definition of mean equicontinuity and mean sensitivity. We study an opposite side of weak mean equicontinuity, namely strong mean sensitivity and we obtain some dichotomies: minimal topological dynamical systems are either weakly mean equicontinuous or strongly mean sensitive and transitive topological dynamical systems are either almost weakly mean equicontinuous or strongly mean sensitive. Furthermore, motivated by the localized idea of sensitivity, we introduce some notions of new version sensitive tuples and study the properties of these sensitive tuples, we show that a transitive dynamical system is strongly mean sensitive if and only if it admits a strongly mean sensitive tuple. Finally, we introduce the notion of weak mean equicontinuity of a topological dynamical system with respect to a given continuous function <i>f</i>, and we show that a topological dynamical system is weakly mean equicontinuous then it is weakly mean equicontinuous with respect to every continuous function.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 4","pages":"961 - 1004"},"PeriodicalIF":0.9,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147827023","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
Averaging Approach to the Limit Cycles of A Class of Discontinuous Piecewise Differential Systems 一类不连续分段微分系统极限环的平均方法
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-04-15 DOI: 10.1007/s10114-026-2316-0
Jie Li, Jaume Llibre
{"title":"Averaging Approach to the Limit Cycles of A Class of Discontinuous Piecewise Differential Systems","authors":"Jie Li,&nbsp;Jaume Llibre","doi":"10.1007/s10114-026-2316-0","DOIUrl":"10.1007/s10114-026-2316-0","url":null,"abstract":"<div><p>These last years an increasing interest appeared for studying the discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. One of the difficulties for understanding the dynamics of these systems is the study of their limit cycles. In this paper we study the limit cycles of the discontinuous piecewise differential systems separated by one straight line and formed by two distinct cubic reversible isochronous centers, whose first integrals are neither polynomial nor rational. We prove that 9 is the number of limit cycles of this kind of discontinuous piecewise differential systems that can be obtained using the averaging theory up to seven order.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 4","pages":"940 - 960"},"PeriodicalIF":0.9,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147827019","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
Endpoint Sobolev Regularity of One-sided Multilinear Maximal Functions 单侧多线性极大函数的端点Sobolev规律性
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-04-15 DOI: 10.1007/s10114-026-4487-0
Daiqing Zhang, Pu Zhang
{"title":"Endpoint Sobolev Regularity of One-sided Multilinear Maximal Functions","authors":"Daiqing Zhang,&nbsp;Pu Zhang","doi":"10.1007/s10114-026-4487-0","DOIUrl":"10.1007/s10114-026-4487-0","url":null,"abstract":"<div><p>In the present paper, we study the endpoint Sobolev regularity of the one-sided multilinear maximal operators <span>(frak{M}_{alpha}^{+})</span> and <span>(frak{M}_{alpha}^{-})</span>, where <i>m</i> is a positive integer and 0 ≤ <i>a</i> ≤ <i>m</i>. We prove that both the maps <span>(overrightarrow{f}mapsto({frak{M}}_{alpha}^{+}(overrightarrow{f}))^{prime})</span> and <span>(overrightarrow{f}mapsto({frak{M}}_{alpha}^{-}(overrightarrow{f}))^{prime})</span> are bounded and continuous from <i>w</i><sup>1,1</sup>(ℝ) × ⋯ × <i>w</i><sup>1,1</sup>(ℝ) to <i>L</i><sup><i>q</i></sup>(ℝ) if <span>(q in ({{1 over {m - alpha}},infty}))</span>, and bounded and continuous from <i>W</i><sup>1,1</sup> (ℝ) × ⋯ × <i>W</i><sup>1,1</sup> (ℝ) to <i>L</i><sup><i>q</i></sup>(ℝ) if α ∈ [1, <i>m</i>) and <span>(q in ({{1 over {m - alpha +1}},infty}))</span>. Here <i>w</i><sup>1,1</sup>(ℝ) is the set of all functions <i>f</i> ∈ <i>W</i><sup>1,1</sup>(ℝ) with <span>(Vert f^{prime}Vert_{L^{infty}(mathbb{R})}&lt;infty)</span>. Besides, we show that the boundedness of <span>(overrightarrow{f}mapsto({frak{M}}_{alpha}^{+}(overrightarrow{f}))^{prime})</span> from <i>W</i><sup>1,1</sup>(ℝ) × ⋯ × <i>W</i><sup>1,1</sup>(ℝ) to <i>L</i><sup><i>q</i></sup>(ℝ) with any <span>(q in ({{1 over {m - alpha +1}},infty}))</span> implies its continuity. The above claim also holds for <span>(frak{M}_{alpha}^{-})</span>. It should be pointed out that all of main results are new even in the linear case <i>m</i> = 1.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 4","pages":"1062 - 1086"},"PeriodicalIF":0.9,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147827026","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
New Results On James’ Questions 詹姆斯问题的新结果
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-04-15 DOI: 10.1007/s10114-026-4311-x
Haoyang Sun
{"title":"New Results On James’ Questions","authors":"Haoyang Sun","doi":"10.1007/s10114-026-4311-x","DOIUrl":"10.1007/s10114-026-4311-x","url":null,"abstract":"<div><p>In 1958, I. M. James raised two fundamental questions about octonionic Stiefel spaces <span>(V_{k}(mathbb{O}^{n}))</span>. The first breakthrough was made by Qian, Tang, Yan in 2022. The present paper is divided into two parts. The first one shows that neither of two natural projections <span>(V_{k+2}(mathbb{O}^n) xrightarrow{pi_2} V_k(mathbb{O}^n))</span> and <span>(V_{k+3}(mathbb{O}^n) xrightarrow{pi_3} V_k(mathbb{O}^n))</span> is a fiber bundle. The second one proves the parallelizability of closed manifold Ω<sub><i>l,m</i></sub>, which contains <span>(V_{3}(mathbb{O}^n))</span> as a special case.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 4","pages":"1099 - 1111"},"PeriodicalIF":0.9,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147827028","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
Liouville Theorems for Ancient Solutions to the V-harmonic Map Heat Flows II v调和映射热流古解的Liouville定理2
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-04-15 DOI: 10.1007/s10114-026-4255-1
Qun Chen, Hongbing Qiu
{"title":"Liouville Theorems for Ancient Solutions to the V-harmonic Map Heat Flows II","authors":"Qun Chen,&nbsp;Hongbing Qiu","doi":"10.1007/s10114-026-4255-1","DOIUrl":"10.1007/s10114-026-4255-1","url":null,"abstract":"<div><p>When the domain is a complete noncompact Riemannian manifold with nonnegative Bakry–Emery Ricci curvature and the target is a complete Riemannian manifold with sectional curvature bounded above by a positive constant, by carrying out refined gradient estimates, we obtain a better Liouville theorem for ancient solutions to the <i>V</i>-harmonic map heat flows. Furthermore, we can also derive a Liouville theorem for quasi-harmonic maps under an exponential growth condition.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 4","pages":"1005 - 1013"},"PeriodicalIF":0.9,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147827024","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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