发布求助
文献互助 智能选刊 最新文献

Acta Mathematica Scientia最新文献

筛选
英文 中文
Notes on the log-Brunn-Minkowski inequality 关于log-Brunn-Minkowski不等式的注记
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-06 DOI: 10.1007/s10473-023-0601-x
Yunlong Yang, Nan Jiang, Deyan Zhang
{"title":"Notes on the log-Brunn-Minkowski inequality","authors":"Yunlong Yang,&nbsp;Nan Jiang,&nbsp;Deyan Zhang","doi":"10.1007/s10473-023-0601-x","DOIUrl":"10.1007/s10473-023-0601-x","url":null,"abstract":"<div><p>Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality. In this paper, we investigate the relative positive center set of planar convex bodies. As an application of the relative positive center, we prove the log-Minkowski inequality and the log-Brunn-Minkowski inequality.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2333 - 2346"},"PeriodicalIF":1.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71908995","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 regularity criteria of weak solutions to 3D axisymmetric incompressible Boussinesq equations 三维轴对称不可压缩Boussinesq方程弱解的正则性准则
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-06 DOI: 10.1007/s10473-023-0604-7
Yu Dong, Yaofang Huang, Li Li, Qing Lu
{"title":"The regularity criteria of weak solutions to 3D axisymmetric incompressible Boussinesq equations","authors":"Yu Dong,&nbsp;Yaofang Huang,&nbsp;Li Li,&nbsp;Qing Lu","doi":"10.1007/s10473-023-0604-7","DOIUrl":"10.1007/s10473-023-0604-7","url":null,"abstract":"<div><p>In this paper, we obtain new regularity criteria for the weak solutions to the three dimensional axisymmetric incompressible Boussinesq equations. To be more precise, under some conditions on the swirling component of vorticity, we can conclude that the weak solutions are regular.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2387 - 2397"},"PeriodicalIF":1.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71908937","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 existence of ground state normalized solutions for Chern-Simons-Schrödinger systems Chern-Simons-Schrödinger系统基态归一化解的存在性
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-06 DOI: 10.1007/s10473-023-0620-7
Yu Mao, Xingping Wu, Chunlei Tang
{"title":"The existence of ground state normalized solutions for Chern-Simons-Schrödinger systems","authors":"Yu Mao,&nbsp;Xingping Wu,&nbsp;Chunlei Tang","doi":"10.1007/s10473-023-0620-7","DOIUrl":"10.1007/s10473-023-0620-7","url":null,"abstract":"<div><p>In this paper, we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in <i>H</i><sup>1</sup>(ℝ)<sup>2</sup>. When the nonlinearity satisfies some general 3-superlinear conditions, we obtain the existence of ground state normalized solutions by using the minimax procedure proposed by Jeanjean in [L. Jeanjean, Existence of solutions with prescribed norm for semilinear elliptic equations, Nonlinear Anal. (1997)].</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2649 - 2661"},"PeriodicalIF":1.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909001","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 on Hardy spaces 作用于Hardy空间的导数Hilbert算子
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-06 DOI: 10.1007/s10473-023-0605-6
Shanli Ye, Guanghao Feng
{"title":"A Derivative-Hilbert operator acting on Hardy spaces","authors":"Shanli Ye,&nbsp;Guanghao Feng","doi":"10.1007/s10473-023-0605-6","DOIUrl":"10.1007/s10473-023-0605-6","url":null,"abstract":"<div><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,k ge 0}})</span> with entries <i>μ</i><sub><i>n,k</i></sub> = <i>μ</i><sub><i>n+k</i></sub>, where <i>μ</i><sub><i>n</i></sub> = <i>∫</i><sub>[0,1)</sub><i>t</i><sup><i>n</i></sup>d<i>μ</i>(<i>t</i>), induces formally the operator as </p><div><div><span>${cal D}{{cal H}_mu}(f)(z) = sumlimits_{n = 0}^infty {left({sumlimits_{k = 0}^infty {{mu _{n,k}}{a_k}}} right)(n + 1){z^n},z in mathbb{D}} $</span></div></div><p> where <span>(f(z) = sumlimits_{n = 0}^infty {{a_n}{z^n}} )</span> is an analytic function in <span>(mathbb{D})</span>. We characterize the positive Borel measures on [0,1) such that <span>({cal D}{{cal H}_mu}(f)(z) = int_{[0,1)} {{{f(t)} over {{{(1 - tz)}^2}}}{rm{d}}mu (t)} )</span> for all <i>f</i> in the Hardy spaces <i>H</i><sup><i>p</i></sup>(0 &lt; <i>p</i> &lt; ∞), and among these we describe those for which <span>({cal D}{{cal H}_mu})</span> is a bounded (resp., compact) operator from <i>H</i><sup><i>p</i></sup> (0 &lt; <i>p</i> &lt; ∞) into <i>H</i><sup><i>q</i></sup> (<i>q</i> &gt; <i>p</i> and <i>q</i> ≥ 1). We also study the analogous problem in the Hardy spaces <i>H</i><sup><i>p</i></sup>(1 ≤ <i>p</i> ≤ 2).</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2398 - 2412"},"PeriodicalIF":1.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71908889","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
Theoretical results on the existence, regularity and asymptotic stability of enhanced pullback attractors: applications to 3D primitive equations 关于增强回拉吸引子存在性、正则性和渐近稳定性的理论结果：在三维原始方程中的应用
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-06 DOI: 10.1007/s10473-023-0611-8
Renhai Wang, Boling Guo, Daiwen Huang
{"title":"Theoretical results on the existence, regularity and asymptotic stability of enhanced pullback attractors: applications to 3D primitive equations","authors":"Renhai Wang,&nbsp;Boling Guo,&nbsp;Daiwen Huang","doi":"10.1007/s10473-023-0611-8","DOIUrl":"10.1007/s10473-023-0611-8","url":null,"abstract":"<div><p>Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forward time-interval under strong and weak topologies. Then we provide some theoretical results for the existence, regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which can be applied to a large class of PDEs. The existence of these enhanced attractors is harder to obtain than the backward case [33], since it is difficult to uniformly control the long-time pullback behavior of the systems over the forward time-interval. As applications of our theoretical results, we consider the famous 3D primitive equations modelling the large-scale ocean and atmosphere dynamics, and prove the existence, regularity and asymptotic stability of the enhanced pullback attractors in <b>V</b> × <i>V</i> and <b>H</b><sup>2</sup> × <i>H</i><sup>2</sup> for the time-dependent forces which satisfy some weak conditions.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2493 - 2518"},"PeriodicalIF":1.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71908936","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
Isometry and phase-isometry of non-Archimedean normed spaces 非阿基米德赋范空间的等距和相位等距
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-06 DOI: 10.1007/s10473-023-0603-8
Ruidong Wang, Wenting Yao
{"title":"Isometry and phase-isometry of non-Archimedean normed spaces","authors":"Ruidong Wang,&nbsp;Wenting Yao","doi":"10.1007/s10473-023-0603-8","DOIUrl":"10.1007/s10473-023-0603-8","url":null,"abstract":"<div><p>In this paper, we study isometries and phase-isometries of non-Archimedean normed spaces. We show that every isometry <i>f</i> : <i>S</i><sub><i>r</i></sub> (<i>X</i>) → <i>S</i><sub><i>r</i></sub> (<i>X</i>), where <i>X</i> is a finite-dimensional non-Archimedean normed space and <i>S</i><sub><i>r</i></sub>(<i>X</i>) is a sphere with radius <i>r</i> ∈ ∥X∥, is surjective if and only if <span>(mathbb{K})</span> is spherically complete and <i>k</i> is finite. Moreover, we prove that if <i>X</i> and <i>Y</i> are non-Archimedean normed spaces over non-trivially non-Archimedean valued fields with |2| = 1, any phase-isometry <i>f</i>: <i>X</i> → <i>Y</i> is phase equivalent to an isometric operator.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2377 - 2386"},"PeriodicalIF":1.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71908938","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 multiple q-exponential differential operational identity 多重q指数微分运算恒等式
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-06 DOI: 10.1007/s10473-023-0608-3
Zhiguo Liu
{"title":"A multiple q-exponential differential operational identity","authors":"Zhiguo Liu","doi":"10.1007/s10473-023-0608-3","DOIUrl":"10.1007/s10473-023-0608-3","url":null,"abstract":"<div><p>Using Hartogs’ fundamental theorem for analytic functions in several complex variables and <i>q</i>-partial differential equations, we establish a multiple <i>q</i>-exponential differential formula for analytic functions in several variables. With this identity, we give new proofs of a variety of important classical formulas including Bailey’s <sub>6</sub><i>ψ</i><sub>6</sub> series summation formula and the Atakishiyev integral. A new transformation formula for a double <i>q</i>-series with several interesting special cases is given. A new transformation formula for a <sub>3</sub><i>ψ</i><sub>3</sub> series is proved.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2449 - 2470"},"PeriodicalIF":1.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71908926","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
Conformally flat affine hypersurfaces with semi-parallel cubic form 具有半平行三次形式的共形平坦仿射超曲面
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-06 DOI: 10.1007/s10473-023-0606-5
Huiyang Xu, Cece Li
{"title":"Conformally flat affine hypersurfaces with semi-parallel cubic form","authors":"Huiyang Xu,&nbsp;Cece Li","doi":"10.1007/s10473-023-0606-5","DOIUrl":"10.1007/s10473-023-0606-5","url":null,"abstract":"<div><p>In this paper, we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine metric. As a main result, we classify these hypersurfaces as not being of a flat affine metric. In particular, 2 and 3-dimensional locally strongly convex affine hypersurfaces with semi-parallel cubic forms are completely determined.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2413 - 2429"},"PeriodicalIF":1.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909003","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: 2
On a super polyharmonic property of a higher-order fractional Laplacian 关于一个高阶分数拉普拉斯算子的超多谐性质
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-06 DOI: 10.1007/s10473-023-0616-3
Meiqing Xu
{"title":"On a super polyharmonic property of a higher-order fractional Laplacian","authors":"Meiqing Xu","doi":"10.1007/s10473-023-0616-3","DOIUrl":"10.1007/s10473-023-0616-3","url":null,"abstract":"<div><p>Let 0 &lt; <i>α</i> &lt; 2, <i>p</i> ≥ 1, m ∞ ℕ<sub>+</sub>. Consider the positive solution <i>u</i> of the PDE </p><div><div><span>$${(- Delta)^{{alpha over 2} + m}}u(x) = {u^p}(x),,,{rm{in}},,{mathbb{R}^n}.$$</span></div><div>\u0000 ((0.1))\u0000 </div></div><p> In [1] (Transactions of the American Mathematical Society, 2021), Cao, Dai and Qin showed that, under the condition <span>(u in {{cal L}_alpha})</span>, (0.1) possesses a super polyharmonic property <span>({(- Delta)^{k + {alpha over 2}}}u ge 0)</span> for <i>k</i> = 0,1, ⋯, <i>m</i> − 1. In this paper, we show another kind of super polyharmonic property (−Δ)<sup><i>k</i></sup><i>u</i> &gt; 0 for <i>k</i> = 1, ⋯, <i>m</i> − 1, under the conditions <span>({(- Delta)^m}u in {{cal L}_alpha})</span> and (−Δ)<sup><i>m</i></sup><i>u</i> ≥ 0. Both kinds of super polyharmonic properties can lead to an equivalence between (0.1) and the integral equation <span>(u(x) = int_{{mathbb{R}^n}} {{{{u^p}(y)} over {|x - y{|^{n - 2m - alpha}}}}{rm{d}}y} )</span>. One can classify solutions to (0.1) following the work of [2] and [3] by Chen, Li, Ou.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2589 - 2596"},"PeriodicalIF":1.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71908931","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
Relative entropy dimension for countable amenable group actions 可数服从群作用的相对熵维数
IF 1 4区 数学
Acta Mathematica Scientia Pub Date : 2023-11-06 DOI: 10.1007/s10473-023-0607-4
Zubiao Xiao, Zhengyu Yin
{"title":"Relative entropy dimension for countable amenable group actions","authors":"Zubiao Xiao,&nbsp;Zhengyu Yin","doi":"10.1007/s10473-023-0607-4","DOIUrl":"10.1007/s10473-023-0607-4","url":null,"abstract":"<div><p>We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups. First, for a given Følner sequence <span>({{F_n}}_{n = 0}^{+ infty})</span>, we define the relative entropy dimensions and the dimensions of the relative entropy generating sets to characterize the sub-exponential growth of the relative topological complexity. we also investigate the relations among these. Second, we introduce the notion of a relative dimension set. Moreover, using the method, we discuss the disjointness between the relative entropy zero extensions via the relative dimension sets of two extensions, which says that if the relative dimension sets of two extensions are different, then the extensions are disjoint.</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2430 - 2448"},"PeriodicalIF":1.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909002","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
首页 上一页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信