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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 加法范畴与高等差分加法范畴之间的同构转移
IF 0.8 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,&nbsp;Zhao Yong Huang","doi":"10.1007/s10114-023-2193-8","DOIUrl":"10.1007/s10114-023-2193-8","url":null,"abstract":"<div><p>Given an additive category <span>({cal C})</span> and an integer <i>n</i> ≥ 2. The higher differential additive category consists of objects <i>X</i> in <span>({cal C})</span> equipped with an endomorphism <i>ϵ</i><sub><i>X</i></sub> satisfying <span>(epsilon_X^n = 0)</span>. Let <i>R</i> be a finite-dimensional basic algebra over an algebraically closed field and <i>T</i> the augmenting functor from the category of finitely generated left <i>R</i>-modules to that of finitely generated left <i>R</i>/(<i>t</i><sup><i>n</i></sup>)-modules. It is proved that a finitely generated left <i>R</i>-module <i>M</i> is <i>τ</i>-rigid (respectively, (support) <i>τ</i>-tilting, almost complete <i>τ</i>-tilting) if and only if so is <i>T</i>(<i>M</i>)as a left <i>R</i>[<i>t</i>]/(<i>t</i><sup><i>n</i></sup>)-module. Moreover, <i>R</i> is <i>τ</i><sub><i>m</i></sub>-selfinjective if and only if so is <i>R</i>[t]/(<i>t</i><sup><i>n</i></sup>).</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"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
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
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和有限可再现性
IF 0.8 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,&nbsp;Ji Cheng Tao,&nbsp;Ya Fei Zhao","doi":"10.1007/s10114-023-2103-0","DOIUrl":"10.1007/s10114-023-2103-0","url":null,"abstract":"<div><p>In this paper, we investigate local properties in the system of completely integral mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity, finite-representability and WEP in the system of completely integral mapping spaces. First we obtain that any finite-dimensional operator space is injective in the system of completely integral mapping spaces. Furthermore we prove that ℂ is the unique nuclear operator space and the unique exact operator space in this system. We also show that ℂ is the unique operator space which is finitely representable in {<i>T</i><sub><i>n</i></sub>}<sub><i>n</i>∈ℕ</sub> in this system. As corollaries, Kirchberg’s conjecture and QWEP conjecture in the system of completely integral mapping spaces are false.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"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
On the Structure of Quantum Toroidal Superalgebra ({{cal E}_{m|n}}) 关于量子环面超代数的结构 ({{cal E}_{m|n}})
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-2426-x
Xiang Hua Wu, Hong Da Lin, Hong Lian Zhang
{"title":"On the Structure of Quantum Toroidal Superalgebra ({{cal E}_{m|n}})","authors":"Xiang Hua Wu,&nbsp;Hong Da Lin,&nbsp;Hong Lian Zhang","doi":"10.1007/s10114-023-2426-x","DOIUrl":"10.1007/s10114-023-2426-x","url":null,"abstract":"<div><p>Recently the quantum toroidal superalgebra <span>({{cal E}_{m|n}})</span> associated with <span>({mathfrak{g}mathfrak{l}_{m|n}})</span> was introduced by L. Bezerra and E. Mukhin, which is not a quantum Kac–Moody algebra. The quantum toroidal superalgebra <span>({{cal E}_{m|n}})</span> exploits infinite sequences of generators and relations of the form, which are called Drinfeld realization. In this paper, we use only finite set of generators and relations to define an associative algebra <span>({cal E}_{m|n}^prime )</span> and show that there exists an epimorphism from <span>({cal E}_{m|n}^prime )</span> to the quantum toroidal superalgebra <span>({{cal E}_{m|n}})</span>. In particular, the structure of <span>({cal E}_{m|n}^prime )</span> enjoys some properties like Drinfeld–Jimbo realization.</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":"134796296","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
Character Sheaves for Classical Graded Lie Algebras 经典级列代数的特征波
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-10-17 DOI: 10.1007/s10114-023-2079-9
Ting Xue
{"title":"Character Sheaves for Classical Graded Lie Algebras","authors":"Ting Xue","doi":"10.1007/s10114-023-2079-9","DOIUrl":"10.1007/s10114-023-2079-9","url":null,"abstract":"<div><p>In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg’s type II classical graded Lie algebras.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135993370","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 Enhanced Period Map and Equivariant Deformation Quantizations of Nilpotent Orbits 增强周期图和零势轨道的等变变形量子化
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-10-17 DOI: 10.1007/s10114-023-2215-6
Shi Lin Yu
{"title":"The Enhanced Period Map and Equivariant Deformation Quantizations of Nilpotent Orbits","authors":"Shi Lin Yu","doi":"10.1007/s10114-023-2215-6","DOIUrl":"10.1007/s10114-023-2215-6","url":null,"abstract":"<div><p>In a previous paper, the author and his collaborator studied the problem of lifting Hamiltonian group actions on symplectic varieties and Lagrangian subvarieties to their graded deformation quantizations and apply the general results to coadjoint orbit method for semisimple Lie groups. Only even quantizations were considered there. In this paper, these results are generalized to the case of general quantizations with arbitrary periods. The key step is to introduce an enhanced version of the (truncated) period map defined by Bezrukavnikov and Kaledin for quantizations of any smooth symplectic variety <i>X</i>, with values in the space of Picard Lie algebroid over <i>X</i>. As an application, we study quantizations of nilpotent orbits of real semisimple groups satisfying certain codimension condition.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944177","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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