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Differences of Composition Operators from Classical Zygmund Space to Bloch-type Space 经典Zygmund空间与bloch型空间复合算子的差异
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI: 10.1007/s10114-025-3224-4
Jinhao Liu, Yuxia Liang, Zicong Yang
{"title":"Differences of Composition Operators from Classical Zygmund Space to Bloch-type Space","authors":"Jinhao Liu,&nbsp;Yuxia Liang,&nbsp;Zicong Yang","doi":"10.1007/s10114-025-3224-4","DOIUrl":"10.1007/s10114-025-3224-4","url":null,"abstract":"<div><p>The aim of this paper is to explore the equivalent characterizations for the boundedness and compactness of <i>C</i><sub><i>φ</i></sub> − <i>C</i><sub><i>ψ</i></sub> acting from classical (little) Zygmund space <span>({cal{Z}}({cal{Z}}_{0}))</span> to (little) Bloch-type space <span>({cal{B}}^{alpha};({cal{B}}_{0}^{alpha}))</span>. Especially, we creatively develop a useful lemma, which not only plays a crucial role in the estimations but also offers a sufficient condition for the bounded below property of composition operators.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 5","pages":"1431 - 1446"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165394","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
Twisted and Absolute Degrees of Maps into the Projective Plane 扭曲度和绝对度映射到投影平面
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI: 10.1007/s10114-025-3336-x
Marcio Colombo Fenille, Daciberg Lima Gonçalves
{"title":"Twisted and Absolute Degrees of Maps into the Projective Plane","authors":"Marcio Colombo Fenille,&nbsp;Daciberg Lima Gonçalves","doi":"10.1007/s10114-025-3336-x","DOIUrl":"10.1007/s10114-025-3336-x","url":null,"abstract":"<div><p>For each based map <i>f</i>: <i>X</i> → ℝP<sup>2</sup> from a closed surface into the real projective plane, we compute its absolute and twisted degrees and describe the action of the fundamental group of ℝP<sup>2</sup> over the based homotopy class of <i>f</i>. We emphasize the finding that for any nonorientable closed surface, there exists only one based homotopy class of maps from it into ℝP<sup>2</sup> whose maps have twisted degree zero and absolute degree nonzero–which shows that, unlike the absolute degree, the twisted degree is not able to detect the strong surjectivity in this setting. In all the other scenarios, the absolute degree of each map is either equal to the twisted degree or its absolute value–and so the twisted degree detects strong surjectivity.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 5","pages":"1393 - 1406"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165400","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
Concentration of Dimension in Extremal Points of Left-half Lines in the Lagrange Spectrum 拉格朗日谱左半线极值点的维数集中
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI: 10.1007/s10114-025-3683-7
Carlos Gustavo Moreira, Christian Camilo Silva Villamil
{"title":"Concentration of Dimension in Extremal Points of Left-half Lines in the Lagrange Spectrum","authors":"Carlos Gustavo Moreira,&nbsp;Christian Camilo Silva Villamil","doi":"10.1007/s10114-025-3683-7","DOIUrl":"10.1007/s10114-025-3683-7","url":null,"abstract":"<div><p>We prove that for any <i>η</i> that belongs to the closure of the interior of the Markov and Lagrange spectra, the sets <i>k</i><sup>−1</sup>((−∞, <i>η</i>]) and <i>k</i><sup>−1</sup>(<i>η</i>), which are the sets of irrational numbers with best constant of Diophantine approximation bounded by <i>η</i> and exactly <i>η</i> respectively, have the same Hausdorff dimension. We also show that, as <i>η</i> varies in the interior of the spectra, this Hausdorff dimension is a strictly increasing function.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 5","pages":"1328 - 1352"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165401","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 the Existence of Solutions for Prescribing Fractional Q-curvature Problem on ({mathbb S}^{n}) 关于规定分数阶q曲率问题解的存在性 ({mathbb S}^{n})
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI: 10.1007/s10114-025-3630-7
Yan Li, Zhongwei Tang
{"title":"On the Existence of Solutions for Prescribing Fractional Q-curvature Problem on ({mathbb S}^{n})","authors":"Yan Li,&nbsp;Zhongwei Tang","doi":"10.1007/s10114-025-3630-7","DOIUrl":"10.1007/s10114-025-3630-7","url":null,"abstract":"<div><p>The aim of this paper is to investigate the existence of solutions to the prescribing fractional <i>Q</i>-curvature problem on <span>({mathbb S}^{n})</span> under some reasonable assumption of the Laplacian sign at the critical point of prescribing curvature function <i>K</i>. Due to the lack of compactness, we choose to return to the basic elements of variational theory and study the deformation along the flow lines. The novelty of the paper is that we obtain the existence without assuming any symmetry and periodicity on <i>K</i>. In addition, to overcome the loss of compactness for high-order operator problem, we need more delicate estimates with the second order cases.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 5","pages":"1296 - 1314"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165396","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
Morse Index and Maslov-type Index of the Discrete Hamiltonian System 离散哈密顿系统的Morse指数和maslov型指数
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI: 10.1007/s10114-025-2580-4
Gaosheng Zhu
{"title":"Morse Index and Maslov-type Index of the Discrete Hamiltonian System","authors":"Gaosheng Zhu","doi":"10.1007/s10114-025-2580-4","DOIUrl":"10.1007/s10114-025-2580-4","url":null,"abstract":"<div><p>In this paper, we give the definition of Maslov-type index of the discrete Hamiltonian system, and obtain the relation of Morse index and Maslov-type index of the discrete Hamiltonian system which is a generalization of the case <i>ω</i> = 1 to <i>ω</i> ∈ <b>U</b> degenerate case via direct method which is different from that of the known literatures. Moreover the well-posedness of the splitting numbers <span>(cal{S}_{h,omega}^{pm})</span> is proven, then the index iteration theories of Bott and Long are also valid for the discrete case, and those can be also applied to the study of the symplectic algorithm.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 5","pages":"1353 - 1392"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10114-025-2580-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165398","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
Ground State Solutions to Some Indefinite Nonlinear Schrödinger Equations on Lattice Graphs 点阵图上一些不定非线性Schrödinger方程的基态解
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI: 10.1007/s10114-025-3111-z
Wendi Xu
{"title":"Ground State Solutions to Some Indefinite Nonlinear Schrödinger Equations on Lattice Graphs","authors":"Wendi Xu","doi":"10.1007/s10114-025-3111-z","DOIUrl":"10.1007/s10114-025-3111-z","url":null,"abstract":"<div><p>In this paper, we consider the Schrödinger type equation −Δ<i>u</i> + <i>V</i> (<i>x</i>)<i>u</i> = <i>f</i>(<i>x, u</i>) on the lattice graph ℤ<sup><i>N</i></sup> with indefinite variational functional, where Δ is the discrete Laplacian. Specifically, we assume that <i>V</i> (<i>x</i>) and <i>f</i>(<i>x, u</i>) are periodic in <i>x, f</i> satisfies some growth condition and 0 lies in a finite spectral gap of (−Δ + <i>V</i>). We obtain ground state solutions by using the method of generalized Nehari manifold which has been introduced by Pankov.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 5","pages":"1279 - 1295"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165393","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 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
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