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Acta Mathematica Vietnamica最新文献

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Integral Closure of Powers of Edge Ideals of Weighted Oriented Graphs 加权有向图边理想幂的积分闭包
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-10-17 DOI: 10.1007/s40306-024-00558-0
Arindam Banerjee, Kanoy Kumar Das, Sirajul Haque
{"title":"Integral Closure of Powers of Edge Ideals of Weighted Oriented Graphs","authors":"Arindam Banerjee,&nbsp;Kanoy Kumar Das,&nbsp;Sirajul Haque","doi":"10.1007/s40306-024-00558-0","DOIUrl":"10.1007/s40306-024-00558-0","url":null,"abstract":"<div><p>In this article, we study monomial ideals associated with a simple graph, namely edge ideals of weighted oriented graphs. Let <i>D</i> be a weighted oriented graph. Assuming that all the vertices of <i>D</i> have weights greater than 1, we completely characterize weighted oriented graphs <i>D</i> for which <i>I</i>(<i>D</i>) is integrally closed, and show that this is equivalent to <i>I</i>(<i>D</i>) being normal. We also give an equivalent condition for <span>(overline{I(D)}=I(D))</span> when the underlying simple graph of <i>D</i> is a complete graph. Finally, we give a necessary and sufficient condition when the edge ideal of a uniform whiskered graph is integrally closed.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 1","pages":"33 - 49"},"PeriodicalIF":0.3,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
General Form of Second Main Theorem on Generalized p-Parabolic Manifolds for Arbitrary Closed Subschemes 广义p-抛物流形的第二主要定理的一般形式
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-10-12 DOI: 10.1007/s40306-024-00553-5
Duc Quang Si
{"title":"General Form of Second Main Theorem on Generalized p-Parabolic Manifolds for Arbitrary Closed Subschemes","authors":"Duc Quang Si","doi":"10.1007/s40306-024-00553-5","DOIUrl":"10.1007/s40306-024-00553-5","url":null,"abstract":"<div><p>By introducing the notion of distributive constant for a family of closed subschemes, we establish a general form of the second main theorem for algebraic non-degenerate meromorphic mappings from a generalized <i>p</i>-Parabolic manifold into a projective variety with arbitrary families of closed subschemes. As its consequence, we give a second main theorem for such meromorphic mappings intersecting arbitrary hypersurfaces with an explicitly truncation level for the counting functions.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 1","pages":"51 - 66"},"PeriodicalIF":0.3,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized Semi-infinite Polynomial Optimization and Semidefinite Programming Relaxations 广义半无限多项式优化和半无限编程松弛
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-10-10 DOI: 10.1007/s40306-024-00551-7
Liguo Jiao, Jae Hyoung Lee, Tiến-Sơn Phạm
{"title":"Generalized Semi-infinite Polynomial Optimization and Semidefinite Programming Relaxations","authors":"Liguo Jiao,&nbsp;Jae Hyoung Lee,&nbsp;Tiến-Sơn Phạm","doi":"10.1007/s40306-024-00551-7","DOIUrl":"10.1007/s40306-024-00551-7","url":null,"abstract":"<div><p>This paper focuses on the study of a generalized semi-infinite programming, where the objective and the constraint functions are all real polynomials. We present a method for finding its global minimizers and global minimum using a hierarchy of semidefinite programming relaxations and prove the convergence result for the method. Numerical experiments are presented to show the efficiency of the proposed algorithm.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"441 - 457"},"PeriodicalIF":0.3,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Normalization of Singular Contact Forms and Primitive 1-forms 奇异接触形式和原始 1-形式的规范化
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-10-09 DOI: 10.1007/s40306-024-00545-5
Kai Jiang, Hong Minh Truong, Nguyen Tien Zung
{"title":"Normalization of Singular Contact Forms and Primitive 1-forms","authors":"Kai Jiang,&nbsp;Hong Minh Truong,&nbsp;Nguyen Tien Zung","doi":"10.1007/s40306-024-00545-5","DOIUrl":"10.1007/s40306-024-00545-5","url":null,"abstract":"<div><p>A differential 1-form <span>(alpha )</span> on a manifold of odd dimension <span>(2n+1)</span>, which satisfies the contact condition <span>(alpha wedge (dalpha )^n ne 0)</span> almost everywhere, but which vanishes at a point <i>O</i>, i.e., <span>(alpha (O) = 0)</span>, is called a <i>singular contact form</i> at <i>O</i>. The aim of this paper is to study local normal forms (formal, analytic and smooth) of such singular contact forms. Our study leads naturally to the study of normal forms of singular primitive 1-forms of a symplectic form <span>(omega )</span> in dimension 2<i>n</i>, i.e., differential 1-forms <span>(gamma )</span> which vanish at a point and such that <span>(dgamma = omega )</span>, and their corresponding conformal vector fields. Our results are an extension and improvement of previous results obtained by other authors, in particular Lychagin (1975), Webster (Amer. J. Math. <b>109</b>, 807–832 (1987)) and Zhitomirskii (1986, 1992). Besides the classical normalization techniques, such as the step-by step normalization methods based on the cohomological equations and the Moser path method, we also use the toric approach to the normalization problem for dynamical systems (Jiang et al. 2019; Zung, Ann. Math. <b>161</b>, 141–156 2005; Zung 2016; Zung, Arch. Rational Mech. Anal. <b>229</b>, 789–833 (2018)).</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"327 - 345"},"PeriodicalIF":0.3,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-024-00545-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Degenerate Forward-backward Problem Involving the Spectral Dirichlet Laplacian 涉及谱Dirichlet拉普拉斯算子的退化正向后问题
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-10-02 DOI: 10.1007/s40306-024-00555-3
Nguyen Ngoc Trong, Bui Le Trong Thanh, Tan Duc Do
{"title":"A Degenerate Forward-backward Problem Involving the Spectral Dirichlet Laplacian","authors":"Nguyen Ngoc Trong,&nbsp;Bui Le Trong Thanh,&nbsp;Tan Duc Do","doi":"10.1007/s40306-024-00555-3","DOIUrl":"10.1007/s40306-024-00555-3","url":null,"abstract":"<div><p>Let <span>(varOmega )</span> be an open bounded subset of <span>({mathbb {R}})</span>, <span>(s in (frac{1}{2},1))</span> and <span>(epsilon &gt; 0)</span>. We investigate the problem </p><div><div><span>$$begin{aligned} (P_epsilon ) quad left{ begin{array}{ll} {partial }_t u = -(-Delta )^s big ( varphi (u) + epsilon , {partial }_t(psi (u)) big ) &amp; text { in } varOmega times (0,T], varphi (u) + epsilon , {partial }_t(psi (u)) = 0 &amp; text { on } {partial }varOmega times (0,T], u = u_0 &amp; text { in } varOmega times {0}, end{array}right. end{aligned}$$</span></div></div><p>where <span>(varphi , psi in C^infty ({mathbb {R}}))</span> and <span>(u_0 in {mathcal {M}}^+(varOmega ))</span> satisfy certain assumptions. Here <span>((-Delta )^s)</span> denotes the spectral Dirichlet Laplacian and <span>({mathcal {M}}^+(varOmega ))</span> is the set of positive Radon measures on <span>(varOmega )</span>. We show that <span>((P_epsilon ))</span> has a unique weak solution.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 4","pages":"691 - 718"},"PeriodicalIF":0.3,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142762002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotically Almost Periodic and Almost Automorphic Solutions to the Non-autonomous Oseen-Navier-Stokes Equations 非自治奥森-纳维尔-斯托克斯方程的近似近周期和近自形解
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-09-28 DOI: 10.1007/s40306-024-00557-1
Ngoc Huy Nguyen, Thieu Huy Nguyen, Thi Ngoc Ha Vu
{"title":"Asymptotically Almost Periodic and Almost Automorphic Solutions to the Non-autonomous Oseen-Navier-Stokes Equations","authors":"Ngoc Huy Nguyen,&nbsp;Thieu Huy Nguyen,&nbsp;Thi Ngoc Ha Vu","doi":"10.1007/s40306-024-00557-1","DOIUrl":"10.1007/s40306-024-00557-1","url":null,"abstract":"<div><p>In this paper, we investigate the existence, uniqueness and stability of asymptotically almost periodic and almost automorphic solutions to the non-autonomous Oseen-Navier-Stokes Equations (ONSE) in an unbounded domain <span>(varOmega subset mathbb {R}^{3})</span> exterior to a rigid body <i>D</i>, i.e., <span>(varOmega =mathbb {R}^{3}backslash D)</span>, with the data belonging to <i>L</i><span>(^{p})</span>-spaces and with the asymptotically almost periodic or almost automorphic external forces, respectively. Our method is based on the <i>L</i><span>(^{p}-L^{q})</span> smoothness of the evolution family corresponding to linearized equations in combination with interpolation functors and fixed-point arguments.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 1","pages":"79 - 99"},"PeriodicalIF":0.3,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Upper Bound for the Conjunction Probability of Smooth Stationary Two-dimensional Gaussian Fields 光滑平稳二维高斯场连接概率的上界
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-09-27 DOI: 10.1007/s40306-024-00556-2
Viet-Hung Pham
{"title":"Upper Bound for the Conjunction Probability of Smooth Stationary Two-dimensional Gaussian Fields","authors":"Viet-Hung Pham","doi":"10.1007/s40306-024-00556-2","DOIUrl":"10.1007/s40306-024-00556-2","url":null,"abstract":"<div><p>In this paper, we provide an upper bound for the conjunction probability of smooth stationary two-dimensional Gaussian fields. The key ingredient is the record method, which is generalized from the problem of estimating the distribution of the maximum. The given upper bound is also a good asymptotic formula.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 1","pages":"67 - 77"},"PeriodicalIF":0.3,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Note on the Linear Independence of Alternating Multiple Zeta Values in Positive Characteristic 关于正特征交替多重泽塔值线性无关性的说明
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-09-10 DOI: 10.1007/s40306-024-00554-4
Bo-Hae Im, Hojin Kim, Khac Nhuan Le, Tuan Ngo Dac, Lan Huong Pham
{"title":"Note on the Linear Independence of Alternating Multiple Zeta Values in Positive Characteristic","authors":"Bo-Hae Im,&nbsp;Hojin Kim,&nbsp;Khac Nhuan Le,&nbsp;Tuan Ngo Dac,&nbsp;Lan Huong Pham","doi":"10.1007/s40306-024-00554-4","DOIUrl":"10.1007/s40306-024-00554-4","url":null,"abstract":"<div><p>We discuss certain results related to the linear independence of alternating multiple zeta values introduced by Harada in 2021.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"485 - 521"},"PeriodicalIF":0.3,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Weak Lefschetz Property of Artinian Algebras Associated to Paths and Cycles 与路径和循环相关的阿尔丁代数的弱勒夫谢茨性质
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-08-14 DOI: 10.1007/s40306-024-00549-1
Hop D. Nguyen, Quang Hoa Tran
{"title":"The Weak Lefschetz Property of Artinian Algebras Associated to Paths and Cycles","authors":"Hop D. Nguyen,&nbsp;Quang Hoa Tran","doi":"10.1007/s40306-024-00549-1","DOIUrl":"10.1007/s40306-024-00549-1","url":null,"abstract":"<div><p>Given a base field <span>(Bbbk )</span> of characteristic zero, for each graph <i>G</i>, we associate the artinian algebra <i>A</i>(<i>G</i>) defined by the edge ideal of <i>G</i> and the squares of the variables. We study the weak Lefschetz property of <i>A</i>(<i>G</i>). We classify some classes of graphs with relatively few edges, including paths and cycles, such that its associated artinian ring has the weak Lefschetz property.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"523 - 544"},"PeriodicalIF":0.3,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New Algorithms for Solving the Split Equality Problems in Hilbert Spaces 求解Hilbert空间中分裂等式问题的新算法
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-08-13 DOI: 10.1007/s40306-024-00552-6
Nguyen Song Ha, Truong Minh Tuyen
{"title":"New Algorithms for Solving the Split Equality Problems in Hilbert Spaces","authors":"Nguyen Song Ha,&nbsp;Truong Minh Tuyen","doi":"10.1007/s40306-024-00552-6","DOIUrl":"10.1007/s40306-024-00552-6","url":null,"abstract":"<div><p>We introduce a new approach by using unconstrained optimization to find a solution to the system of the split equality problems in real Hilbert spaces. Our new algorithms do not depend on the norm of the transfer mappings. We also give the relaxed iterative algorithms corresponding to the proposed algorithms. Finally, we present some numerical experiments to demonstrate the performance of the main results.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 4","pages":"667 - 689"},"PeriodicalIF":0.3,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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