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Toughness and the Existence of 2-factors 韧性与2因子的存在
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-09-15 DOI: 10.1007/s10114-026-4288-5
Leyou Xu, Bo Zhou
{"title":"Toughness and the Existence of 2-factors","authors":"Leyou Xu,&nbsp;Bo Zhou","doi":"10.1007/s10114-026-4288-5","DOIUrl":"10.1007/s10114-026-4288-5","url":null,"abstract":"<div><p>In 1985, Enomoto et al. showed that each 2-tough graph with at least three vertices has a 2-factor, but for any <i>ε</i> &gt; 0, there exists a (2 − <i>ε</i>)-tough graph on at least 3 vertices having no 2-factor. In recent years, the study of sufficient conditions for graphs with toughness in [1, 2) having a 2-factor has attracted substantial interest. In this paper, we give new sufficient conditions for a <i>t</i>-tough graph having a 2-factor when <i>t</i> ∈ [1, 2) by involving independence number, minimum degree, connectivity and forbidden forests, improving and extending some known results.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 9","pages":"2241 - 2251"},"PeriodicalIF":0.9,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007356","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 Bijections on NBC Subsets NBC子集上的两个双反
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-09-15 DOI: 10.1007/s10114-026-4536-8
Houshan Fu, Baoren Peng, Suijie Wang, Jinxing Yang
{"title":"Two Bijections on NBC Subsets","authors":"Houshan Fu,&nbsp;Baoren Peng,&nbsp;Suijie Wang,&nbsp;Jinxing Yang","doi":"10.1007/s10114-026-4536-8","DOIUrl":"10.1007/s10114-026-4536-8","url":null,"abstract":"<div><p>We establish two explicit bijections: from acyclic reorientations of an oriented matroid to no broken circuit (NBC) subsets of its underlying matroid, and from regions of a real hyperplane arrangement to its affine NBC subsets.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 9","pages":"2281 - 2294"},"PeriodicalIF":0.9,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007380","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 Average Behavior of Fourier Coefficients of j-th Symmetric Power L-function over Certain Sequences 第j次对称幂l函数在若干序列上的傅里叶系数的平均性质
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-08-15 DOI: 10.1007/s10114-026-5406-0
Youjun Wang
{"title":"The Average Behavior of Fourier Coefficients of j-th Symmetric Power L-function over Certain Sequences","authors":"Youjun Wang","doi":"10.1007/s10114-026-5406-0","DOIUrl":"10.1007/s10114-026-5406-0","url":null,"abstract":"<div><p>Let <i>j</i> ≥ 2 be a given integer. Let <i>f</i> be a normalized primitive holomorphic cusp form of even integral weight for the full modular group Γ = SL(2, ℤ). Denote by <span>(lambda_{text{sym}^{j}f}(n))</span> the <i>n</i>th normalized coefficient of the Dirichlet expansion of the <i>j</i>th symmetric power <i>L</i>-function <i>L</i>(<i>s</i>, sym<sup><i>j</i></sup><i>f</i>). In this paper, we are interested in the average behavior of <span>(lambda_{text{sym}^{j}f}(n))</span> over some certain sequences, which improved the previous results.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 8","pages":"2139 - 2150"},"PeriodicalIF":0.9,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878120","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
First Eigenvalue of Embedded Minimal Surfaces in S3 S3中嵌入极小曲面的第一特征值
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-08-15 DOI: 10.1007/s10114-026-5125-6
Yuhang Zhao
{"title":"First Eigenvalue of Embedded Minimal Surfaces in S3","authors":"Yuhang Zhao","doi":"10.1007/s10114-026-5125-6","DOIUrl":"10.1007/s10114-026-5125-6","url":null,"abstract":"<div><p>We prove that for an embedded minimal surface Σ in <i>S</i><sup>3</sup>, the first eigenvalue of the Lapla-cian operator λ<sub>1</sub> satisfies λ<sub>1</sub> ≥ 1 + <i>C</i>(cot<sup>−1</sup> λ<sub>max</sub>)<sup>6</sup>, where λ<sub>max</sub> is the maximum of the (positive) principal curvature and <i>C</i> &gt; 0 is an absolute constant. This improves previous result of Choi–Wang.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 8","pages":"2025 - 2037"},"PeriodicalIF":0.9,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878096","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
Teodorescu Transform for Slice Monogenic Functions and Applications 切片单基因函数的Teodorescu变换及其应用
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-08-15 DOI: 10.1007/s10114-026-5029-5
Chao Ding, Zhenghua Xu
{"title":"Teodorescu Transform for Slice Monogenic Functions and Applications","authors":"Chao Ding,&nbsp;Zhenghua Xu","doi":"10.1007/s10114-026-5029-5","DOIUrl":"10.1007/s10114-026-5029-5","url":null,"abstract":"<div><p>In the past few years, the theory of slice monogenic functions has been fully developed, especially in its applications to the noncommutative <i>S</i>-functional calculus. In this article, we introduce the Teodorescu transform in the theory of slice monogenic functions, which turns out to be a right inverse of the slice Cauchy–Riemann operator. The boundednesses of the Teodorescu transform and its derivatives are investigated as well. These results successfully generalize the classical results in the complex plane to higher dimensions. As applications, a Hodge decomposition of the Banach space of slice <i>L</i><sup><i>p</i></sup> functions and the corresponding generalized Bergman projection are investigated.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 8","pages":"2101 - 2124"},"PeriodicalIF":0.9,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878122","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
Banach–Tarski Type Paradox Preserving Self-similar Measure Banach-Tarski型悖论保持自相似测度
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-08-15 DOI: 10.1007/s10114-026-4663-2
Ying Lu, Lifeng Xi
{"title":"Banach–Tarski Type Paradox Preserving Self-similar Measure","authors":"Ying Lu,&nbsp;Lifeng Xi","doi":"10.1007/s10114-026-4663-2","DOIUrl":"10.1007/s10114-026-4663-2","url":null,"abstract":"<div><p>In this paper, we obtain a Banach–Tarski type paradox preserving the self-similar measure: Let <i>K</i> be a self-similar set on a complete metric space and <i>ν</i> a self-similar measure on <i>K</i>, then there are bijections <i>g</i><sub><i>i</i></sub>: <i>K</i> → <i>K</i> preserving <i>ν</i>-measure such that </p><div><div><span>$$K = biguplus_{i=1}^{n} A_i = biguplus_{i=1}^{k} g_i(A_i) = biguplus_{i=k+1}^{n} g_i(A_i) quad text{with } k &lt; n,$$</span></div></div><p> where <span>(biguplus)</span> means the disjoint union.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 8","pages":"2151 - 2167"},"PeriodicalIF":0.9,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878121","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 and Small Hankel Operators on the Harmonic Bergman Space 调和Bergman空间上的可交换Toeplitz算子和Small Hankel算子
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-08-15 DOI: 10.1007/s10114-026-4467-4
Jie Zhang, Xianfeng Zhao
{"title":"Commuting Toeplitz and Small Hankel Operators on the Harmonic Bergman Space","authors":"Jie Zhang,&nbsp;Xianfeng Zhao","doi":"10.1007/s10114-026-4467-4","DOIUrl":"10.1007/s10114-026-4467-4","url":null,"abstract":"<div><p>Let <i>φ</i> and <i>ψ</i> be two bounded harmonic functions on the open unit disk, <span>(mathbb{T}_{varphi})</span> and <span>(mathbb{H}_{psi})</span> be the Toeplitz and small Hankel operators on the harmonic Bergman space, respectively. In this paper, we establish a number of necessary conditions and sufficient conditions for <span>(mathbb{T}_{varphi})</span> to commute with <span>(mathbb{H}_{psi})</span>. Moreover, we obtain equivalent characterizations for such commutativity problem in two cases: (i) <i>φ</i> is analytic and <i>ψ</i> is harmonic; (ii) <i>φ</i> is harmonic and the coefficients of the Taylor series of the harmonic function <i>ψ</i> are all real.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 8","pages":"2051 - 2072"},"PeriodicalIF":0.9,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878115","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
L-function for Sp(4) × GL(2) via a Non-unique Model 非唯一模型下Sp(4) × GL(2)的l函数
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-08-15 DOI: 10.1007/s10114-026-4579-x
Pan Yan
{"title":"L-function for Sp(4) × GL(2) via a Non-unique Model","authors":"Pan Yan","doi":"10.1007/s10114-026-4579-x","DOIUrl":"10.1007/s10114-026-4579-x","url":null,"abstract":"<div><p>In this paper we prove a conjecture of Ginzburg and Soudry on an integral representation for the <i>L</i>-function <i>L</i><sup><i>S</i></sup>(<i>s, π × τ</i>) attached to a pair (<i>π, τ</i>) of irreducible automorphic cuspidal representations of <span>(text{Sp}_{4}(mathbb{A}))</span> and <span>(text{GL}_{2}(mathbb{A}))</span>, which is derived from the generalized doubling method of Cai, Friedberg, Ginzburg and Kaplan. We show that the integral unfolds to a non-unique model and analyze it using the New Way method of Piatetski-Shapiro and Rallis. Two applications are given. First, we relate the existence of the poles of <i>L</i><sup><i>S</i></sup>(<i>s,π × τ</i>) to the non-vanishing of certain period integrals. Second, for certain family of cuspidal representations, we prove that <i>L</i><sup><i>S</i></sup>(<i>s,π × τ</i>) is holomorphic.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 8","pages":"1957 - 1999"},"PeriodicalIF":0.9,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878117","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 Higher-power Moments of Hecke Eigenvalues for Congruence Group 关于同余群Hecke特征值的高次矩
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-08-15 DOI: 10.1007/s10114-026-4498-x
Jing Huang, Wenguang Zhai, Deyu Zhang
{"title":"On Higher-power Moments of Hecke Eigenvalues for Congruence Group","authors":"Jing Huang,&nbsp;Wenguang Zhai,&nbsp;Deyu Zhang","doi":"10.1007/s10114-026-4498-x","DOIUrl":"10.1007/s10114-026-4498-x","url":null,"abstract":"<div><p>Let <i>H</i><sub>ℓ</sub>(<i>N</i>) denote the set of normalized primitive holomorphic cusp forms of even integral weight ℓ for the congruence group Γ<sub>0</sub>(<i>N</i>). In this paper, our main goal is to derive asymptotic formulas of </p><div><div><span>$$int_{1}^{T} S_{f}^{l}(x; N) dx,$$</span></div></div><p> where <i>f</i> ∈ <i>H</i><sub>ℓ</sub>(<i>N</i>) and </p><div><div><span>$$S_f(x; N) = sum_{n leq x} lambda_f(n).$$</span></div></div><p>Here <i>λ</i><sub>f</sub>(<i>n</i>) is the <i>n</i>-th Hecke eigenvalue of <i>f</i>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 8","pages":"2073 - 2084"},"PeriodicalIF":0.9,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878124","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
(mathscr{F})-Sensitivity for Linear Dynamics and Its Induced Hyperspace Dynamics (mathscr{F})线性动力学及其诱导的超空间动力学的灵敏度
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-08-15 DOI: 10.1007/s10114-026-4462-9
Song-Gwang Won, Jin-Hyon Kim
{"title":"(mathscr{F})-Sensitivity for Linear Dynamics and Its Induced Hyperspace Dynamics","authors":"Song-Gwang Won,&nbsp;Jin-Hyon Kim","doi":"10.1007/s10114-026-4462-9","DOIUrl":"10.1007/s10114-026-4462-9","url":null,"abstract":"<div><p>In this paper we study <span>(mathscr{F})</span>-sensitivity for a bounded linear operator <i>T</i> on Banach space and its induced hyperspace dynamics. First, we suggest the necessary and sufficient condition for <span>(mathscr{F})</span>-sensitivity for a bounded linear operator <i>T</i> on Banach space. Next, we consider the natural hyperspace extensions <span>(overline{T})</span> and <span>(tilde{T})</span> of <i>T</i> to the space <i>K</i>(<i>X</i>) of compact subsets of <i>X</i> and <i>C</i>(<i>X</i>) of convex compact subsets of <i>X</i>, respectively. We show that <span>(mathscr{F})</span>-sensitivity is equivalent for the maps <i>T</i>, <span>(overline{T})</span> and <span>(tilde{T})</span>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 8","pages":"2038 - 2050"},"PeriodicalIF":0.9,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878125","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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