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A Local Limit Theorem for Nonlattice Multidimensional Random Walks in Cones 锥上非格多维随机行走的一个局部极限定理
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-06-04 DOI: 10.1007/s40306-026-00600-3
D. C. Pham, M. Peigné, D. T. Son
{"title":"A Local Limit Theorem for Nonlattice Multidimensional Random Walks in Cones","authors":"D. C. Pham,&nbsp;M. Peigné,&nbsp;D. T. Son","doi":"10.1007/s40306-026-00600-3","DOIUrl":"10.1007/s40306-026-00600-3","url":null,"abstract":"<div><p>We study the asymptotic behavior of a nonlattice random walk in a general cone of <span>(mathbb {R}^d)</span>. Following the approach initiated by D. Denisov and V. Wachtel in [8], we use a strong approximation of random walks by the Brownian motion and prove local limit theorems, combining integral theorems for random walks in cones with classical theorems for unrestricted random walks.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 1","pages":"1 - 21"},"PeriodicalIF":0.6,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613460","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
On the Global Attractor for the 3D Viscous Camassa-Holm Equations with Damping Term in the Whole Space 全空间带阻尼项的三维粘性Camassa-Holm方程的全局吸引子
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-06-03 DOI: 10.1007/s40306-025-00593-5
Nguyen Hai Ha Giang, Trinh Dang Duong, Vu Manh Toi
{"title":"On the Global Attractor for the 3D Viscous Camassa-Holm Equations with Damping Term in the Whole Space","authors":"Nguyen Hai Ha Giang,&nbsp;Trinh Dang Duong,&nbsp;Vu Manh Toi","doi":"10.1007/s40306-025-00593-5","DOIUrl":"10.1007/s40306-025-00593-5","url":null,"abstract":"<div><p>We consider the 3D viscous Camassa-Holm equations with damping term in the whole space. Firstly, we prove the existence, uniqueness and regularity of global weak solutions to the equations. Then we prove the existence of a compact global attractor for the associated continuous semigroup. To overcome the essential difficulty when proving the asymptotic compactness of the semigroup, which arises due to the lack of compactness of the Sobolev embeddings, we exploit the energy equation method. Next, by using the regularity of weak solutions and inductive arguments, we study the Sobolev regularity of the global attractor. Finally, we give an explicit upper bound for the fractal dimension of the global attractor.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 1","pages":"37 - 64"},"PeriodicalIF":0.6,"publicationDate":"2026-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613122","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
Correction to: A Priori Error Analysis of a Space–Time Finite Element Method for Advection–Diffusion Equations 修正：平流扩散方程时空有限元法的先验误差分析
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-04-22 DOI: 10.1007/s40306-026-00598-8
Thi Thanh Mai Ta
{"title":"Correction to: A Priori Error Analysis of a Space–Time Finite Element Method for Advection–Diffusion Equations","authors":"Thi Thanh Mai Ta","doi":"10.1007/s40306-026-00598-8","DOIUrl":"10.1007/s40306-026-00598-8","url":null,"abstract":"","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 1","pages":"159 - 159"},"PeriodicalIF":0.6,"publicationDate":"2026-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613655","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 Depth Formula for Modules Over Quotients of Gorenstein Rings Gorenstein环商上模的深度公式
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-04-15 DOI: 10.1007/s40306-026-00602-1
Tran Nguyen An, Pham Hung Quy
{"title":"The Depth Formula for Modules Over Quotients of Gorenstein Rings","authors":"Tran Nguyen An,&nbsp;Pham Hung Quy","doi":"10.1007/s40306-026-00602-1","DOIUrl":"10.1007/s40306-026-00602-1","url":null,"abstract":"<div><p>A foundational result by C. Huneke and V. Trivedi provides a formula for the depth of an ideal in terms of height, computed over a finite set of prime ideals, for rings that are homomorphic images of regular rings. Building on a result by the first author for local quotients of Cohen-Macaulay rings, this paper first gives a new proof for the depth formula and derives a similar formula for the finiteness dimension. Our main result then establishes the depth formula for non-local rings that are homomorphic images of a finite-dimensional Gorenstein ring.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 1","pages":"65 - 73"},"PeriodicalIF":0.6,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613301","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
Solution Existence and Stability of the Semi-Affine Variational Inequality Problem on Hilbert Spaces Hilbert空间上半仿射变分不等式问题解的存在性与稳定性
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-04-10 DOI: 10.1007/s40306-026-00599-7
Vu Van Dong, Nguyen Nang Tam
{"title":"Solution Existence and Stability of the Semi-Affine Variational Inequality Problem on Hilbert Spaces","authors":"Vu Van Dong,&nbsp;Nguyen Nang Tam","doi":"10.1007/s40306-026-00599-7","DOIUrl":"10.1007/s40306-026-00599-7","url":null,"abstract":"<div><p>This paper investigates the solution existence and stability of the semi-affine variational inequality problem in real separable Hilbert spaces. We demonstrate that, under suitable conditions, the solution set of the semi-affine variational inequality problem is nonempty. Additionally, we consider some related stability analyses of the problem. The obtained results contribute to and complement the existing literature.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 1","pages":"123 - 141"},"PeriodicalIF":0.6,"publicationDate":"2026-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613473","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
An Improvement on Discrete Li–Yau Inequality 离散Li-Yau不等式的一个改进
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-03-30 DOI: 10.1007/s40306-026-00601-2
Bin Shen, Yuhan Zhu
{"title":"An Improvement on Discrete Li–Yau Inequality","authors":"Bin Shen,&nbsp;Yuhan Zhu","doi":"10.1007/s40306-026-00601-2","DOIUrl":"10.1007/s40306-026-00601-2","url":null,"abstract":"<div><p>In this paper, we study the discrete Li–Yau gradient estimates for the positive solutions <i>u</i> to the heat equation on graphs under <span>(CDE(n,-K))</span> condition and derive a sharper estimate than Bauer et al. (J. Differ. Geom. <b>99</b>(3), 359–405, 2015) and Wang and Zhang (Comm. Anal. Geom. <b>27</b>(4), 969–989, 2019).</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 1","pages":"75 - 84"},"PeriodicalIF":0.6,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614885","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
Products of Reflections and Commutators of Reflections Over Division Algebras 除法代数上反射的积与反射的对易子
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2026-03-24 DOI: 10.1007/s40306-025-00588-2
M. H. Bien, N. T. T. Ha, T. N. N. Hung, D. T. Toan
{"title":"Products of Reflections and Commutators of Reflections Over Division Algebras","authors":"M. H. Bien,&nbsp;N. T. T. Ha,&nbsp;T. N. N. Hung,&nbsp;D. T. Toan","doi":"10.1007/s40306-025-00588-2","DOIUrl":"10.1007/s40306-025-00588-2","url":null,"abstract":"<div><p>Let <i>D</i> be a division algebra and let <span>(n)</span> be a positive integer greater than 1. Assume that the commutator width <span>(omega (D))</span> of <span>(D^{*})</span> is positive and finite. First, we revisit a question posed by F. S. Cater concerning the decomposition of matrices into a product of reflections over a division ring. Among results, we show that every matrix <span>(A)</span> in the special linear group <span>(textrm{SL}_n(D))</span> can be expressed as a product of at most <span>(textrm{rank} (A-mathrm I_n)+4omega (D))</span> reflections. Next, we study the decomposition of matrices in <span>(textrm{SL}_n(D))</span> into products of commutators of reflections in the general linear group <span>(textrm{GL}_n(D))</span>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 4","pages":"521 - 539"},"PeriodicalIF":0.3,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147734981","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
Global Error Bounds for Nonmonotone Affine Variational Inequalities 非单调仿射变分不等式的全局误差界
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-03-03 DOI: 10.1007/s40306-025-00592-6
Hoang Ngoc Tuan
{"title":"Global Error Bounds for Nonmonotone Affine Variational Inequalities","authors":"Hoang Ngoc Tuan","doi":"10.1007/s40306-025-00592-6","DOIUrl":"10.1007/s40306-025-00592-6","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we investigate global error bounds for nonmonotone affine variational inequalities in finite-dimensional spaces. We establish a characterization of global error bounds on the feasible sets of these problems. Furthermore, we derive several sufficient conditions and necessary conditions for the existence of global error bounds on the feasible sets. Our results complement existing findings for some classes of monotone affine variational inequalities. Several illustrative examples are presented to demonstrate the applicability of the obtained results.</p>\u0000 </div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 1","pages":"103 - 122"},"PeriodicalIF":0.6,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613124","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
Erratum to the Article “Maximal Subgroups of Almost Subnormal Subgroups in Division Rings” [Acta Mathematica Vietnamica (2022) 47:197–209] 文章“除环中几乎次正规子群的极大子群”的勘误[越南数学学报（2022）47:197-209]
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-03-02 DOI: 10.1007/s40306-025-00591-7
Bui Xuan Hai
{"title":"Erratum to the Article “Maximal Subgroups of Almost Subnormal Subgroups in Division Rings” [Acta Mathematica Vietnamica (2022) 47:197–209]","authors":"Bui Xuan Hai","doi":"10.1007/s40306-025-00591-7","DOIUrl":"10.1007/s40306-025-00591-7","url":null,"abstract":"<div>\u0000 \u0000 <p>The aim of this short communication is to say about some mistake in the proof of Theorem 2 in my original article “Maximal subgroups of almost subnormal subgroups in division rings” (Bui Xuan Hai, Acta Mathematica Vietnamica <b>47</b>, 197–209, 2022). Further, some weaker version of this theorem will be provided.</p>\u0000 </div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 1","pages":"157 - 158"},"PeriodicalIF":0.6,"publicationDate":"2026-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613268","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
A Priori Error Analysis of a Space-Time Finite Element Method for Advection-Diffusion Equations 平流扩散方程时空有限元法的先验误差分析
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-02-23 DOI: 10.1007/s40306-025-00596-2
Thi Thanh Mai Ta
{"title":"A Priori Error Analysis of a Space-Time Finite Element Method for Advection-Diffusion Equations","authors":"Thi Thanh Mai Ta","doi":"10.1007/s40306-025-00596-2","DOIUrl":"10.1007/s40306-025-00596-2","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate a space-time finite element method for solving a parabolic advection-diffusion problem. We use the Banach-Nečas-Babuška theorem to show the well-posedness of the continuous Petrov-Galerkin variational formulation for this problem. A fully discrete finite-element scheme is analyzed using the standard Galerkin method and unstructured meshes. An optimal error estimate is established in a discrete energy norm under a globally regularity condition. Some numerical results corroborate our theoretical results.</p>\u0000 </div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 1","pages":"85 - 102"},"PeriodicalIF":0.6,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613748","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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