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Lower Bounds for Moments of Quadratic Twisted Self-dual GL(3) Central L-values 二次扭曲自对偶GL(3)中心l值的矩下界
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-2009-x
Sheng Hao Hua, Bing Rong Huang
{"title":"Lower Bounds for Moments of Quadratic Twisted Self-dual GL(3) Central L-values","authors":"Sheng Hao Hua,&nbsp;Bing Rong Huang","doi":"10.1007/s10114-023-2009-x","DOIUrl":"10.1007/s10114-023-2009-x","url":null,"abstract":"<div><p>In this paper, we prove the conjectured order lower bound for the <i>k</i>-th moment of central values of quadratic twisted self-dual GL(3) <i>L</i>-functions for all <i>k</i> ≥ 1, based on our recent work on the twisted first moment of central values in this family of <i>L</i>-functions.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796297","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
Improved Hardy–Littlewood–Sobolev Inequality on ({mathbb{S}^n}) under Constraints 约束下({mathbb{S}^n})上改进的Hardy-Littlewood-Sobolev不等式
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-2630-8
Yun Yun Hu, Jing Bo Dou
{"title":"Improved Hardy–Littlewood–Sobolev Inequality on ({mathbb{S}^n}) under Constraints","authors":"Yun Yun Hu,&nbsp;Jing Bo Dou","doi":"10.1007/s10114-023-2630-8","DOIUrl":"10.1007/s10114-023-2630-8","url":null,"abstract":"<div><p>In this paper, we establish an improved Hardy–Littlewood–Sobolev inequality on <span>({mathbb{S}^n})</span> under higher-order moments constraint. Moreover, by constructing precise test functions, using improved Hardy–Littlewood–Sobolev inequality on <span>({mathbb{S}^n})</span>, we show such inequality is almost optimal in critical case. As an application, we give a simpler proof of the existence of the maximizer for conformal Hardy–Littlewood–Sobolev inequality.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10114-023-2630-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796298","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
The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains 无界区域上分数阶p-拉普拉斯算子的Brezis-Nirenberg问题
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-2108-8
Yan Sheng Shen
{"title":"The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains","authors":"Yan Sheng Shen","doi":"10.1007/s10114-023-2108-8","DOIUrl":"10.1007/s10114-023-2108-8","url":null,"abstract":"<div><p>In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional <i>p</i>-Laplace operator in unbounded cylinder type domains. By means of the fractional Poincaré inequality in unbounded cylindrical domains, we first study the asymptotic property of the first eigenvalue <span>({lambda _{p,s}}(widehat {{omega _delta }}))</span> with respect to the domain <span>((widehat {{omega _delta }}))</span>. Then, by applying the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove the existence results. The present work complements the results of Mosconi–Perera–Squassina–Yang [The Brezis–Nirenberg problem for the fractional <i>p</i>-Laplacian. <i>C</i>alc. Var. Partial Differential Equations, 55(4), 25 pp. 2016] to unbounded domains and extends the classical Brezis–Nirenberg type results of Ramos–Wang–Willem [Positive solutions for elliptic equations with critical growth in unbounded domains. In: Chapman Hall/CRC Press, Boca Raton, 2000, 192–199] to the fractional <i>p</i>-Laplacian setting.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796300","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
Partial Regularity of Suitable Weak Solutions of the Model Arising in Amorphous Molecular Beam Epitaxy 非晶分子束外延模型弱解的部分正则性
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-2458-2
Yan Qing Wang, Yi Ke Huang, Gang Wu, Dao Guo Zhou
{"title":"Partial Regularity of Suitable Weak Solutions of the Model Arising in Amorphous Molecular Beam Epitaxy","authors":"Yan Qing Wang,&nbsp;Yi Ke Huang,&nbsp;Gang Wu,&nbsp;Dao Guo Zhou","doi":"10.1007/s10114-023-2458-2","DOIUrl":"10.1007/s10114-023-2458-2","url":null,"abstract":"<div><p>In this paper, we are concerned with the precise relationship between the Hausdorff dimension of possible singular point set <span>({cal S})</span> of suitable weak solutions and the parameter <i>α</i> in the nonlinear term in the following parabolic equation </p><div><div><span>$${h_t} + {h_{xxxx}} + {partial _{xx}}|{h_x}{|^alpha } = f.$$</span></div></div><p> It is shown that when <span>(5/3 le alpha &lt; 7/3)</span>, the <span>({{3alpha - 5} over {alpha - 1}})</span> dimensional parabolic Hausdorff measure of <span>({cal S})</span> is zero, which generalizes the recent corresponding work of Ozánski and Robinson in [<i>SIAM J. Math. Anal.</i>, <b>51</b>, 228–255 (2019)] for <i>α</i> = 2 and <i>f</i> = 0. The same result is valid for a 3D modified Navier–Stokes system.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10114-023-2458-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796302","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
Classification of Proper Holomorphic Mappings between Hartogs Domains over Homogeneous Siegel Domains 齐次Siegel域上Hartogs域间真全纯映射的分类
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-2278-4
Lei Wang
{"title":"Classification of Proper Holomorphic Mappings between Hartogs Domains over Homogeneous Siegel Domains","authors":"Lei Wang","doi":"10.1007/s10114-023-2278-4","DOIUrl":"10.1007/s10114-023-2278-4","url":null,"abstract":"<div><p>The Hartogs domain over homogeneous Siegel domain <i>D</i><sub><i>N,s</i></sub> (<i>s</i> &gt; 0) is defined by the inequality ∥ζ∥<sup>2</sup> &lt; <i>K</i><sub><i>D</i></sub>(<i>z, z</i>)<sup>−<i>s</i></sup>, where <i>D</i> is a homogeneous Siegel domain of type II, (<i>z, ζ</i>) ∈ <i>D</i> × ℂ<sup><i>N</i></sup> and <i>K</i><sub><i>D</i></sub>(<i>z, z</i>) is the Bergman kernel of <i>D</i>. Recently, Seo obtained the rigidity result that proper holomorphic mappings between two equidimensional domains <i>D</i><sub><i>N,s</i></sub> and <i>D′</i><sub><i>N′,s′</i></sub> are biholomorphisms for <i>N</i> ≥ 2. In this article, we find a counter-example to show that the rigidity result is not true for <i>D</i><sub>1,<i>s</i></sub> and obtain a classification of proper holomorphic mappings between <i>D</i><sub>1,<i>s</i></sub> and <i>D′</i><sub>1,<i>s′</i></sub>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796308","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
Homological Transfer between Additive Categories and Higher Differential Additive Categories 加性范畴与高微分加性范畴间的同调转移
3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-2193-8
Xi Tang, Zhao Yong Huang
{"title":"Homological Transfer between Additive Categories and Higher Differential Additive Categories","authors":"Xi Tang, Zhao Yong Huang","doi":"10.1007/s10114-023-2193-8","DOIUrl":"https://doi.org/10.1007/s10114-023-2193-8","url":null,"abstract":"","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136229408","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
Resonant-Superlinear Nonhomogeneous Dirichlet Problems 共振-超线性非齐次狄利克雷问题
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-2343-z
Zhen Hai Liu, Nikolaos S. Papageorgiou
{"title":"Resonant-Superlinear Nonhomogeneous Dirichlet Problems","authors":"Zhen Hai Liu,&nbsp;Nikolaos S. Papageorgiou","doi":"10.1007/s10114-023-2343-z","DOIUrl":"10.1007/s10114-023-2343-z","url":null,"abstract":"<div><p>We consider a Dirichlet nonlinear equation driven by the (<i>p</i>, 2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant perturbation. We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions all with sign information.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796295","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
Nuclearity and Finite-Representability in the System of Completely Integral Mapping Spaces 完全积分映射空间系统中的核性与有限可表示性
3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-2103-0
Zhe Dong, Ji Cheng Tao, Ya Fei Zhao
{"title":"Nuclearity and Finite-Representability in the System of Completely Integral Mapping Spaces","authors":"Zhe Dong, Ji Cheng Tao, Ya Fei Zhao","doi":"10.1007/s10114-023-2103-0","DOIUrl":"https://doi.org/10.1007/s10114-023-2103-0","url":null,"abstract":"","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136229241","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
Spectrum and Spectral Singularities of a Quadratic Pencil of a Schrödinger Operator with Boundary Conditions Dependent on the Eigenparameter 边界条件依赖于特征参数的Schrödinger算子二次束的谱和谱奇异性
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-1413-6
Xiang Zhu, Zhao Wen Zheng, Kun Li
{"title":"Spectrum and Spectral Singularities of a Quadratic Pencil of a Schrödinger Operator with Boundary Conditions Dependent on the Eigenparameter","authors":"Xiang Zhu,&nbsp;Zhao Wen Zheng,&nbsp;Kun Li","doi":"10.1007/s10114-023-1413-6","DOIUrl":"10.1007/s10114-023-1413-6","url":null,"abstract":"<div><p>In this paper, we consider the following quadratic pencil of Schrödinger operators <i>L</i>(λ) generated in <span>({L^2}({mathbb{R}^ + }))</span> by the equation </p><div><div><span>$$ - {y^{prime prime }} + [p(x) + 2lambda q(x)]y = {lambda ^2}y,,,,,,x in {mathbb{R}^ + } = [0, + infty )$$</span></div></div><p> with the boundary condition </p><div><div><span>$${{{y^prime }(0)} over {y(0)}} = {{{beta _1}lambda + {beta _0}} over {{alpha _1}lambda + {alpha _0}}},$$</span></div></div><p> where <i>p</i>(<i>x</i>)and <i>q</i>(<i>x</i>) are complex valued functions and <i>α</i><sub>0</sub>, <i>α</i><sub>1</sub>, <i>β</i><sub>0</sub>, <i>β</i><sub>1</sub> are complex numbers with <span>({alpha _0}{beta _1} - {alpha _1}{beta _0} ne 0)</span>. It is proved that <i>L</i>(λ) has a finite number of eigenvalues and spectral singularities, and each of them is of a finite multiplicity, if the conditions </p><div><div><span>$$p(x),{q^prime }(x) in AC({mathbb{R}^ + }),,,,,,,,mathop {lim }limits_{x to infty } [|p(x)| + |q(x)| + |{q^prime }(x)|] = 0$$</span></div></div><p> and </p><div><div><span>$$mathop {sup }limits_{0 le x &lt; + infty } { {{rm{e}}^{varepsilon sqrt x }}[|{p^prime }(x)| + |{q^{prime prime }}(x)|]} &lt; + infty $$</span></div></div><p> hold, where <i>ε</i>&gt; 0.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796299","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: 1
The Isomorphism Problem of Normalized Unit Groups of Group Algebras of a Class of Finite 2-groups 一类有限2群群代数的归一化单位群的同构问题
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-2261-0
Yu Lei Wang, He Guo Liu
{"title":"The Isomorphism Problem of Normalized Unit Groups of Group Algebras of a Class of Finite 2-groups","authors":"Yu Lei Wang,&nbsp;He Guo Liu","doi":"10.1007/s10114-023-2261-0","DOIUrl":"10.1007/s10114-023-2261-0","url":null,"abstract":"<div><p>Let <i>p</i> be a prime and <span>({mathbb{F}_p})</span> be a finite field of <i>p</i> elements. Let <span>({mathbb{F}_p}G)</span> denote the group algebra of the finite <i>p</i>-group <i>G</i> over the field <span>({mathbb{F}_p})</span> and <span>(V({mathbb{F}_p}G))</span> denote the group of normalized units in <span>({mathbb{F}_p}G)</span>. Suppose that <i>G</i> and <i>H</i> are finite <i>p</i>-groups given by a central extension of the form </p><div><div><span>$$1 to {mathbb{Z}_{{p^m}}} to G to {mathbb{Z}_p} times cdots times {mathbb{Z}_p} to 1$$</span></div></div><p> and <span>({G^prime } cong {mathbb{Z}_p},,,m ge 1)</span>. Then <span>(V({mathbb{F}_p}G) cong V({mathbb{F}_p}H))</span> if and only if <i>G</i> ≅ <i>H</i>. Balogh and Bovdi only solved the isomorphism problem when <i>p</i> is odd. In this paper, the case <i>p</i> = 2 is determined.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10114-023-2261-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796309","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
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