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Limit Cycles of Liénard Systems with Several Equilibria 具有若干平衡点的lisamadard系统的极限环
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-04-15 DOI: 10.1007/s10114-025-3420-2
Hebai Chen, Yilei Tang, Dongmei Xiao
{"title":"Limit Cycles of Liénard Systems with Several Equilibria","authors":"Hebai Chen,&nbsp;Yilei Tang,&nbsp;Dongmei Xiao","doi":"10.1007/s10114-025-3420-2","DOIUrl":"10.1007/s10114-025-3420-2","url":null,"abstract":"<div><p>In the paper we generalize some classic results on limit cycles of Liénard system</p><div><div><span>$$dot{x}=phi(y)-F(x),quaddot{y}=-g(x)$$</span></div></div><p>having a unique equilibrium to that of the system with several equilibria. As applications, we strictly prove the number of limit cycles and obtain the distribution of limit cycles for three classes of Liénard systems, in which we correct a mistake in the literature.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 4","pages":"1104 - 1130"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908710","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
Geometric Probability on a Lattice with the 15th Type of Convex Pentagon as a Fundamental Region 以第15类凸五边形为基本域的格上的几何概率
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-04-15 DOI: 10.1007/s10114-025-3268-5
Jiangfu Zhao, Jun Jiang, Hai Liu
{"title":"Geometric Probability on a Lattice with the 15th Type of Convex Pentagon as a Fundamental Region","authors":"Jiangfu Zhao,&nbsp;Jun Jiang,&nbsp;Hai Liu","doi":"10.1007/s10114-025-3268-5","DOIUrl":"10.1007/s10114-025-3268-5","url":null,"abstract":"<div><p>In 2015, a group of mathematicians at the University of Washington, Bothell, discovered the 15th pentagon that can cover a plane, with no gaps and overlaps. However, research on its containment measure theory or geometric probability is limited. In this study, the Laplace extension of Buffon’s problem is generalized to the case of the 15th pentagon. In the solving process, the explicit expressions for the generalized support function and containment function of this irregular pentagon are derived. In addition, the chord length distribution function and density function of random distance of this pentagon are obtained in terms of the containment function.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 4","pages":"1213 - 1230"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908705","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
The Nilpotent Probability of Finite Groups 有限群的幂零概率
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-04-15 DOI: 10.1007/s10114-025-2510-5
Huaquan Wei, Xuanyou Hou, Changman Sun, Xixi Diao, Hui Wu, Liying Yang
{"title":"The Nilpotent Probability of Finite Groups","authors":"Huaquan Wei,&nbsp;Xuanyou Hou,&nbsp;Changman Sun,&nbsp;Xixi Diao,&nbsp;Hui Wu,&nbsp;Liying Yang","doi":"10.1007/s10114-025-2510-5","DOIUrl":"10.1007/s10114-025-2510-5","url":null,"abstract":"<div><p>Let <i>G</i> be a finite group. We denote by <i>ν</i>(<i>G</i>) the probability that two randomly chosen elements of <i>G</i> generate a nilpotent subgroup. In this paper, we characterize the structure of finite groups <i>G</i> with lower bounds <span>({1 over p}, , {{p^{2}+8} over {9p^{2}}})</span> and <span>({p+3} over {4p})</span> on <i>ν</i>(<i>G</i>), where <i>p</i> is a prime divisor of ∣<i>G</i>∣.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 4","pages":"1238 - 1246"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908706","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
Boundedness of Solutions for a Class of Semilinear Oscillators 一类半线性振子解的有界性
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-04-15 DOI: 10.1007/s10114-025-3505-y
Yan Zhuang, Daxiong Piao, Yanmin Niu
{"title":"Boundedness of Solutions for a Class of Semilinear Oscillators","authors":"Yan Zhuang,&nbsp;Daxiong Piao,&nbsp;Yanmin Niu","doi":"10.1007/s10114-025-3505-y","DOIUrl":"10.1007/s10114-025-3505-y","url":null,"abstract":"<div><p>We are concerned with the boundedness for the equation <i>x</i>″ + <i>f</i>(<i>x</i>, <i>x</i>′) + <i>ω</i><sup>2</sup><i>x</i> = <i>p</i>(<i>t</i>), where <i>p</i> is quasi-periodic function. Since the corresponding system is non-Hamiltonian, we transform the original system into a new reversible one, the Poincaré mapping of which satisfies the twist theorem for quasi-periodic reversible mappings of low smoothness, or is close to its linear part by normal form theorem. We then obtain results concerning the boundedness of solutions based on the recently work. The above two cases need some smooth and growth assumptions for <i>f</i> and <i>p</i>, which are precisely the innovations of this paper.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 4","pages":"1165 - 1180"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908707","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
On a Centro-equiaffine Area-preserving Flow 关于中心等仿射保面积流
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-04-15 DOI: 10.1007/s10114-025-3082-0
Yunlong Yang, Yanlong Zhang
{"title":"On a Centro-equiaffine Area-preserving Flow","authors":"Yunlong Yang,&nbsp;Yanlong Zhang","doi":"10.1007/s10114-025-3082-0","DOIUrl":"10.1007/s10114-025-3082-0","url":null,"abstract":"<div><p>This paper will deal with a nonlocal geometric flow in centro-equiaffine geometry, which keeps the enclosed area of the evolving curve and converges smoothly to an ellipse. This model can be viewed as the affine version of Gage’s area-preserving flow in Euclidean geometry.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 4","pages":"1091 - 1103"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908711","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
Turán Numbers for Vertex-disjoint Triangles and Pentagons Turán顶点不相交三角形和五边形的数字
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-04-15 DOI: 10.1007/s10114-025-3272-9
Fangfang Wu, Hajo Broersma, Shenggui Zhang, Binlong Li
{"title":"Turán Numbers for Vertex-disjoint Triangles and Pentagons","authors":"Fangfang Wu,&nbsp;Hajo Broersma,&nbsp;Shenggui Zhang,&nbsp;Binlong Li","doi":"10.1007/s10114-025-3272-9","DOIUrl":"10.1007/s10114-025-3272-9","url":null,"abstract":"<div><p>The Turán number, denoted by ex (<i>n</i>, <i>H</i>), is the maximum number of edges of a graph on <i>n</i> vertices containing no graph <i>H</i> as a subgraph. Denote by <i>kC</i><sub><i>ℓ</i></sub> the union of <i>k</i> vertex-disjoint copies of <i>C</i><sub><i>ℓ</i></sub>. In this paper, we present new results for the Turán numbers of vertex-disjoint cycles. Our first results deal with the Turán number of vertex-disjoint triangles ex (<i>n</i>, <i>kC</i><sub>3</sub>). We determine the Turán number ex(<i>n</i>, <i>kC</i><sub>3</sub>) for <span>(n geq {k^{2}+5k over 2})</span> when <i>k</i> ≤ 4, and <i>n</i> ≥ <i>k</i><sup>2</sup> + 2 when <i>k</i> ≥ 4. Moreover, we give lower and upper bounds for ex (<i>n</i>, <i>kC</i><sub>3</sub>) with <span>(3k leq n leq {k^{2}+5k over 2})</span> when <i>k</i> ≤ 4, and 3<i>k</i> ≤ <i>n</i> ≤ <i>k</i><sup>2</sup> + 2 when <i>k</i> ≥ 4. Next, we give a lower bound for the Turán number of vertex-disjoint pentagons ex (<i>n</i>, <i>kC</i><sub>5</sub>). Finally, we determine the Turán number ex (<i>n</i>, <i>kC</i><sub>5</sub>) for <i>n</i> = 5<i>k</i>, and propose two conjectures for ex (<i>n</i>, <i>kC</i><sub>5</sub>) for the other values of <i>n</i>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 4","pages":"1181 - 1195"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908704","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
Some Problems about Consonant and Co-Consonant Spaces 关于辅音和辅音空间的几个问题
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-04-15 DOI: 10.1007/s10114-025-3080-2
Zhengmao He, Bin Zhao
{"title":"Some Problems about Consonant and Co-Consonant Spaces","authors":"Zhengmao He,&nbsp;Bin Zhao","doi":"10.1007/s10114-025-3080-2","DOIUrl":"10.1007/s10114-025-3080-2","url":null,"abstract":"<div><p>In this paper, we first prove that the retract of a consonant space (or co-consonant space) is consonant (co-consonant). Simultaneously, we consider the co-consonance of two powerspace constructions and proved that (1) the co-consonance of the Smyth powerspace <i>P</i><sub><i>S</i></sub>(<i>X</i>) implies the co-consonance of <i>X</i> if <i>X</i> is strongly compact; (2) the co-consonance of <i>X</i> implies the co-consonance of the Smyth powerspace under some conditions; (3) if the lower powerspace <i>P</i><sub><i>H</i></sub>(<i>X</i>) is co-consonant, then <i>X</i> is co-consonant; (4) for a continuous poset <i>P</i>, the lower powerspace <i>P</i><sub><i>H</i></sub>(Σ<i>P</i>) is co-consonant.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 4","pages":"1152 - 1164"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908708","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
Positive Solutions for some almost Critical Brezis-Nirenberg Type Problems in Bounded and Exterior Domains 有界和外域上一些几乎临界Brezis-Nirenberg型问题的正解
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-04-15 DOI: 10.1007/s10114-025-3385-1
Salomón Alarcón, Pablo Quijada
{"title":"Positive Solutions for some almost Critical Brezis-Nirenberg Type Problems in Bounded and Exterior Domains","authors":"Salomón Alarcón,&nbsp;Pablo Quijada","doi":"10.1007/s10114-025-3385-1","DOIUrl":"10.1007/s10114-025-3385-1","url":null,"abstract":"<div><p>We study the equation</p><div><div><span>$$-Delta{u}=vert{x}vert^{alpha}u^{p_{alpha}^{ast}+varepsilon}+lambda_{varepsilon}vert{x}vert^{beta}{u}quadtext{in};Omega,$$</span></div></div><p>under the condition <i>u</i> = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝ<sup><i>N</i></sup>, <i>N</i> ≥ 5, which is symmetric respect to <i>x</i><sub>1</sub>, <i>x</i><sub>2</sub>, 2026;, <i>x</i><sub><i>N</i></sub> and contains the origin, <i>α</i> &gt; −2, −2 &lt; <i>β</i> &lt; <i>N</i> − 4, <span>(p_{alpha}^{ast}={N+2alpha+2over{N-2}})</span>, <i>ε</i> &gt; 0 is a small parameter and <i>λ</i><sub><i>ε</i></sub> &gt; 0 depends on <i>ε</i>, with <i>λ</i><sub><i>ε</i></sub> → 0 as <i>ε</i> → 0. Our main focus lies in finding positive solutions that take the form of a tower of bubbles of order <i>α</i>, exhibiting concentration at the origin as <i>ε</i> tends to zero. Furthermore, we extend our study to the equation</p><div><div><span>$$-Delta{u}=vert{x}vert^{alpha}u^{p_{alpha}^{ast}-varepsilon}-lambda_{varepsilon}vert{x}vert^{beta}{u}quadtext{in};mathbb{R}^{N};backslash;B_{1},$$</span></div></div><p>where <i>B</i><sub>1</sub> is the unit ball centered at the origin, under Dirichlet zero boundary condition and an additional vanishing condition at infinity. In this context, we discover positive solutions that take the form of a tower of bubbles of order <i>α</i>, progressively flattening as <i>ε</i> tends to zero.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 4","pages":"1131 - 1151"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908709","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 Solvable Groups Whose Prime Graphs have Diameter 3 素数图直径为3的有限可解群
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-03-15 DOI: 10.1007/s10114-025-2021-4
Guohua Qian
{"title":"Finite Solvable Groups Whose Prime Graphs have Diameter 3","authors":"Guohua Qian","doi":"10.1007/s10114-025-2021-4","DOIUrl":"10.1007/s10114-025-2021-4","url":null,"abstract":"<div><p>Let <i>G</i> be a finite group and <i>π</i>(<i>G</i>) be the set of prime divisors of ∣<i>G</i>∣. The prime graph Γ(<i>G</i>) of <i>G</i> is the graph with vertex set <i>π</i>(<i>G</i>), and different <i>p, q</i> ∈ <i>π</i>(<i>G</i>) are joined by an edge if and only if <i>G</i> has an element of order <i>pq</i>. In this paper, we characterize the finite solvable groups whose prime graphs have diameter 3.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 3","pages":"975 - 984"},"PeriodicalIF":0.8,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688319","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
Preface of the Special Issue on Statistics 《统计专刊》序言
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-02-20 DOI: 10.1007/s10114-025-4551-1
Zhiming Ma, Fuzhou Gong, Liuquan Sun
{"title":"Preface of the Special Issue on Statistics","authors":"Zhiming Ma,&nbsp;Fuzhou Gong,&nbsp;Liuquan Sun","doi":"10.1007/s10114-025-4551-1","DOIUrl":"10.1007/s10114-025-4551-1","url":null,"abstract":"","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 2","pages":"497 - 497"},"PeriodicalIF":0.8,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455582","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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