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The existence of pseudoharmonic maps for small horizontal energy 小水平能量伪谐波图的存在
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0519-y
Biqiang Zhao
{"title":"The existence of pseudoharmonic maps for small horizontal energy","authors":"Biqiang Zhao","doi":"10.1007/s10473-024-0519-y","DOIUrl":"https://doi.org/10.1007/s10473-024-0519-y","url":null,"abstract":"<p>In this paper, we consider pseudoharmonic heat flow with small initial horizontal energy and give the existence of pseudoharmonic maps from closed pseudo-Hermitian manifolds into closed Riemannian manifolds.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"13 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Estimation of average differential entropy for a stationary ergodic space-time random field on a bounded area 有界区域上静态遍历时空随机场的平均微分熵估算
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0521-4
Zhanjie Song, Jiaxing Zhang
{"title":"Estimation of average differential entropy for a stationary ergodic space-time random field on a bounded area","authors":"Zhanjie Song, Jiaxing Zhang","doi":"10.1007/s10473-024-0521-4","DOIUrl":"https://doi.org/10.1007/s10473-024-0521-4","url":null,"abstract":"<p>In this paper, we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field. By estimating the probability value of a time-stationary random field in a small range, we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region. It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1. In addition, we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"71 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 empty balls of a critical or subcritical branching random walk 关于临界或亚临界分支随机游走的空球
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0525-0
Shuxiong Zhang, Jie Xiong
{"title":"On the empty balls of a critical or subcritical branching random walk","authors":"Shuxiong Zhang, Jie Xiong","doi":"10.1007/s10473-024-0525-0","DOIUrl":"https://doi.org/10.1007/s10473-024-0525-0","url":null,"abstract":"<p>Let {<i>Z</i><sub><i>n</i></sub>}<sub><i>n</i>≥0</sub> be a critical or subcritical <i>d</i>-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure on ℝ<sup><i>d</i></sup>. Denote by <i>R</i><sub><i>n</i></sub>:= sup{<i>u</i> &gt; 0: <i>Z</i><sub><i>n</i></sub>({<i>x</i> ∈ ℝ<sup><i>d</i></sup>: ∣<i>x</i>∣ &lt; <i>u</i>}) = 0} the radius of the largest empty ball centered at the origin of <i>Z</i><sub><i>n</i></sub>. In this work, we prove that after suitable renormalization, <i>R</i><sub><i>n</i></sub> converges in law to some non-degenerate distribution as <i>n</i> → ∈. Furthermore, our work shows that the renormalization scales depend on the offspring law and the dimension of the branching random walk. This completes the results of Révész [13] for the critical binary branching Wiener process.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"369 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 BSE property for some vector-valued Banach function algebras 某些向量值巴拿赫函数代数的 BSE 特性
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0518-z
Fatemeh Abtahi, Ali Rejali, Farshad Sayaf
{"title":"The BSE property for some vector-valued Banach function algebras","authors":"Fatemeh Abtahi, Ali Rejali, Farshad Sayaf","doi":"10.1007/s10473-024-0518-z","DOIUrl":"https://doi.org/10.1007/s10473-024-0518-z","url":null,"abstract":"<p>In this paper, <i>X</i> is a locally compact Hausdorff space and <span>({cal A})</span> is a Banach algebra. First, we study some basic features of <i>C</i><sub>0</sub>(<i>X</i>, <span>({cal A})</span>) related to BSE concept, which are gotten from <span>({cal A})</span>. In particular, we prove that if <i>C</i><sub>0</sub>(<i>X</i>, <span>({cal A})</span>) has the BSE property then <span>({cal A})</span> has so. We also establish the converse of this result, whenever <i>X</i> is discrete and <span>({cal A})</span> has the BSE-norm property. Furthermore, we prove the same result for the BSE property of type I. Finally, we prove that <i>C</i><sub>0</sub> (<i>X</i>, <span>({cal A})</span>) has the BSE-norm property if and only if <span>({cal A})</span> has so.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"4 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 global well-posedness of solutions to compressible isentropic two-fluid magnetohydrodynamics in a strip domain 条状域中可压缩等熵双流体磁流体力学解的全局拟合性
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0522-3
Zefu Feng, Jing Jia
{"title":"The global well-posedness of solutions to compressible isentropic two-fluid magnetohydrodynamics in a strip domain","authors":"Zefu Feng, Jing Jia","doi":"10.1007/s10473-024-0522-3","DOIUrl":"https://doi.org/10.1007/s10473-024-0522-3","url":null,"abstract":"<p>In this paper, we consider a model of compressible isentropic two-fluid magneto-hydrodynamics without resistivity in a strip domain in three dimensional space. By exploiting the two-tier energy method developed in [Anal PDE, 2013, 6: 1429–1533], we prove the global well-posedness of the governing model around a uniform magnetic field which is non-parallel to the horizontal boundary. Moreover, we show that the solution converges to the steady state at an almost exponential rate as time goes to infinity. Compared to the work of Tan and Wang [SIAM J Math Anal, 2018, 50: 1432–1470], we need to overcome the difficulties caused by particles.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"23 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Approximation problems on the smoothness classes 平滑类的近似问题
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0505-4
Yongping Liu, Man Lu
{"title":"Approximation problems on the smoothness classes","authors":"Yongping Liu, Man Lu","doi":"10.1007/s10473-024-0505-4","DOIUrl":"https://doi.org/10.1007/s10473-024-0505-4","url":null,"abstract":"<p>This paper investigates the relative Kolmogorov <i>n</i>-widths of 2<i>π</i>-periodic smooth classes in <span>(widetilde{L}_{q})</span>. We estimate the relative widths of <span>(widetilde{W}^{r}H^{omega}_{p})</span> and its generalized class <i>K</i><sub><i>p</i></sub><i>H</i><sup><i>ω</i></sup> (<i>P</i><sub><i>r</i></sub>), where <i>K</i><sub><i>p</i></sub><i>H</i><sup><i>ω</i></sup> (<i>P</i><sub><i>r</i></sub>) is defined by a self-conjugate differential operator <i>P</i><sub><i>r</i></sub> (<i>D</i>) induced by</p><span>$$P_{r}(t):= t^{sigma} Pi_{j=1}^{l}(t^{2}- t_{j}^{2}),~t_{j} &gt; 0,~j=1, 2,cdots, l,~l geq 1,~sigma geq 1,~r=2l+sigma.$$</span><p>Also, the modulus of continuity of the <i>r</i>-th derivative, or <i>r</i>-th self-conjugate differential, does not exceed a given modulus of continuity <i>ω</i>. Then we obtain the asymptotic results, especially for the case <i>p</i> = ∞, 1 ≤ <i>q</i> ≤ ∞.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"166 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A strong positivity property and a related inverse source problem for multi-term time-fractional diffusion equations 多期时间分形扩散方程的强正性属性和相关反源问题
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0523-2
Li Hu, Zhiyuan Li, Xiaona Yang
{"title":"A strong positivity property and a related inverse source problem for multi-term time-fractional diffusion equations","authors":"Li Hu, Zhiyuan Li, Xiaona Yang","doi":"10.1007/s10473-024-0523-2","DOIUrl":"https://doi.org/10.1007/s10473-024-0523-2","url":null,"abstract":"<p>In this article, we consider the diffusion equation with multi-term time-fractional derivatives. We first derive, by a subordination principle for the solution, that the solution is positive when the initial value is non-negative. As an application, we prove the uniqueness of solution to an inverse problem of determination of the temporally varying source term by integral type information in a subdomain. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"41 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A derivative-Hilbert operator acting from logarithmic Bloch spaces to Bergman spaces 从对数布洛赫空间作用于伯格曼空间的导数-希尔伯特算子
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0516-1
Shanli Ye, Yun Xu
{"title":"A derivative-Hilbert operator acting from logarithmic Bloch spaces to Bergman spaces","authors":"Shanli Ye, Yun Xu","doi":"10.1007/s10473-024-0516-1","DOIUrl":"https://doi.org/10.1007/s10473-024-0516-1","url":null,"abstract":"<p>Let <i>μ</i> be a positive Borel measure on the interval [0, 1). The Hankel matrix <span>(cal{H}_{mu}=(mu_{n,k})_{n,kgeq 0})</span> with entries <i>μ</i><sub><i>n,k</i></sub> = <i>μ</i><sub><i>n</i>+<i>k</i></sub>, where <i>μ</i><sub><i>n</i></sub> = ⨜<sub>[0,1)</sub> <i>t</i><sup><i>n</i></sup>d<i>μ</i>(<i>t</i>), induces, formally, the operator</p><span>$$cal{DH}_mu(f)(z)=sumlimits_{n=0}^inftyleft(sumlimits_{k=0}^infty mu_{n,k}a_kright)(n+1)z^n, ~zin mathbb{D},$$</span><p>where <span>(f(z)=sumlimits_{n=0}^infty a_nz^n)</span> is an analytic function in ⅅ. We characterize the measures <i>μ</i> for which <span>(cal{DH}_mu)</span> is bounded (resp., compact) operator from the logarithmic Bloch space <span>(mathscr{B}_{L^{alpha}})</span> into the Bergman space <span>(cal{A}^p)</span>, where 0 ≤ <i>α</i> &lt; ∞, 0 &lt; <i>p</i> &lt; ∞. We also characterize the measures <i>μ</i> for which <span>(cal{DH}_mu)</span> is bounded (resp., compact) operator from the logarithmic Bloch space <span>(mathscr{B}_{L^{alpha}})</span> into the classical Bloch space <span>(mathscr{B})</span>.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"64 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Heat kernel on Ricci shrinkers (II) 里奇收缩器上的热核 (II)
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0502-7
Yu Li, Bing Wang
{"title":"Heat kernel on Ricci shrinkers (II)","authors":"Yu Li, Bing Wang","doi":"10.1007/s10473-024-0502-7","DOIUrl":"https://doi.org/10.1007/s10473-024-0502-7","url":null,"abstract":"<p>This paper is the sequel to our study of heat kernel on Ricci shrinkers [29]. In this paper, we improve many estimates in [29] and extend the recent progress of Bamler [2]. In particular, we drop the compactness and curvature boundedness assumptions and show that the theory of <span>(mathbb{F})</span>-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"9 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Elliptic equations in divergence form with discontinuous coefficients in domains with corners 带角域中具有不连续系数的发散形式椭圆方程
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2024-08-27 DOI: 10.1007/s10473-024-0515-2
Jun Chen, Xuemei Deng
{"title":"Elliptic equations in divergence form with discontinuous coefficients in domains with corners","authors":"Jun Chen, Xuemei Deng","doi":"10.1007/s10473-024-0515-2","DOIUrl":"https://doi.org/10.1007/s10473-024-0515-2","url":null,"abstract":"<p>We study equations in divergence form with piecewise <i>C</i><sup><i>α</i></sup> coefficients. The domains contain corners and the discontinuity surfaces are attached to the edges of the corners. We obtain piecewise <i>C</i><sup>1,<i>α</i></sup> estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"10 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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