Acta Mathematica Sinica-English Series最新文献_第6页

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

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

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

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, Hajo Broersma, Shenggui Zhang, Binlong Li","doi":"10.1007/s10114-025-3272-9","DOIUrl":"10.1007/s10114-025-3272-9","url":null,"abstract":"<div>The Turán number, denoted by ex (n, H), is the maximum number of edges of a graph on n vertices containing no graph H as a subgraph. Denote by kCℓ the union of k vertex-disjoint copies of Cℓ. 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 (n, kC3). We determine the Turán number ex(n, kC3) for (n geq {k^{2}+5k over 2}) when k ≤ 4, and n ≥ k2 + 2 when k ≥ 4. Moreover, we give lower and upper bounds for ex (n, kC3) with (3k leq n leq {k^{2}+5k over 2}) when k ≤ 4, and 3k ≤ n ≤ k2 + 2 when k ≥ 4. Next, we give a lower bound for the Turán number of vertex-disjoint pentagons ex (n, kC5). Finally, we determine the Turán number ex (n, kC5) for n = 5k, and propose two conjectures for ex (n, kC5) for the other values of n.</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

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, Pablo Quijada","doi":"10.1007/s10114-025-3385-1","DOIUrl":"10.1007/s10114-025-3385-1","url":null,"abstract":"<div>We study the equation<div><div>$$-Delta{u}=vert{x}vert^{alpha}u^{p_{alpha}^{ast}+varepsilon}+lambda_{varepsilon}vert{x}vert^{beta}{u}quadtext{in};Omega,$$</div></div>under the condition u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝN, N ≥ 5, which is symmetric respect to x1, x2, 2026;, xN and contains the origin, α > −2, −2 < β < N − 4, (p_{alpha}^{ast}={N+2alpha+2over{N-2}}), ε > 0 is a small parameter and λε > 0 depends on ε, with λε → 0 as ε → 0. Our main focus lies in finding positive solutions that take the form of a tower of bubbles of order α, exhibiting concentration at the origin as ε tends to zero. Furthermore, we extend our study to the equation<div><div>$$-Delta{u}=vert{x}vert^{alpha}u^{p_{alpha}^{ast}-varepsilon}-lambda_{varepsilon}vert{x}vert^{beta}{u}quadtext{in};mathbb{R}^{N};backslash;B_{1},$$</div></div>where B1 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 α, progressively flattening as ε tends to zero.</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

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

引用次数: 0

Reproducible Learning of Gaussian Graphical Models via Graphical Lasso Multiple Data Splitting 基于图形Lasso多重数据分割的高斯图形模型的可重复学习

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2025-02-15 DOI: 10.1007/s10114-025-3324-1

Kang Hu, Danning Li, Binghui Liu

引用次数: 0

Variational Bayesian Tensor Quantile Regression 变分贝叶斯张量分位数回归

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2025-02-15 DOI: 10.1007/s10114-025-3390-4

Yunzhi Jin, Yanqing Zhang

{"title":"Variational Bayesian Tensor Quantile Regression","authors":"Yunzhi Jin, Yanqing Zhang","doi":"10.1007/s10114-025-3390-4","DOIUrl":"10.1007/s10114-025-3390-4","url":null,"abstract":"<div>Quantile regression is widely used in variable relationship research for statistical learning. Traditional quantile regression model is based on vector-valued covariates and can be efficiently estimated via traditional estimation methods. However, many modern applications involve tensor data with the intrinsic tensor structure. Traditional quantile regression can not deal with tensor regression issues well. To this end, we consider a tensor quantile regression with tensor-valued covariates and develop a novel variational Bayesian estimation approach to make estimation and prediction based on the asymmetric Laplace model and the CANDECOMP/PARAFAC decomposition of tensor coefficients. To incorporate the sparsity of tensor coefficients, we consider the multiway shrinkage priors for marginal factor vectors of tensor coefficients. The key idea of the proposed method is to efficiently combine the prior structural information of tensor and utilize the matricization of tensor decomposition to simplify the complexity of tensor coefficient estimation. The coordinate ascent algorithm is employed to optimize variational lower bound. Simulation studies and a real example show the numerical performances of the proposed method.</div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 2","pages":"733 - 756"},"PeriodicalIF":0.8,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455439","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