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Acta Mathematica Vietnamica最新文献

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On the Diagonal Subgroup of the Special Linear Group Over a Division Ring 论划分环上特殊线性群的对角线子群
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-08-02 DOI: 10.1007/s40306-024-00544-6
Bui Xuan Hai
{"title":"On the Diagonal Subgroup of the Special Linear Group Over a Division Ring","authors":"Bui Xuan Hai","doi":"10.1007/s40306-024-00544-6","DOIUrl":"10.1007/s40306-024-00544-6","url":null,"abstract":"<div><p>Let <i>K</i> be a division ring with center <i>Z</i>(<i>K</i>), and <i>n</i> a positive integer. Let <span>(textrm{SL}(n,K))</span> be the special linear group of degree <i>n</i> over <i>K</i> and <span>(textrm{SD}(n,K))</span> its subgroup consisting of all diagonal matrices whose Dieudonne’s determinant is <span>(overline{1})</span>. We prove that <span>(textrm{SD}(n,K))</span> is weakly pronormal, but not pronormal in <span>(textrm{SL}(n,K))</span> provided either <i>Z</i>(<i>K</i>) is an infinite field in case <span>(nge 3)</span> or <i>Z</i>(<i>K</i>) is a finite field containing at least seven elements in case <span>(nge 5)</span>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"427 - 440"},"PeriodicalIF":0.3,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714385","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 Index of Depth Stability of Symbolic Powers of Cover Ideals of Graphs 论图的盖顶点的符号幂的深度稳定性指数
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-07-31 DOI: 10.1007/s40306-024-00550-8
S. A. Seyed Fakhari, S. Yassemi
{"title":"On the Index of Depth Stability of Symbolic Powers of Cover Ideals of Graphs","authors":"S. A. Seyed Fakhari,&nbsp;S. Yassemi","doi":"10.1007/s40306-024-00550-8","DOIUrl":"10.1007/s40306-024-00550-8","url":null,"abstract":"<div><p>Let <i>G</i> be a graph with <i>n</i> vertices and let <span>(S=mathbb {K}[x_1,dots ,x_n])</span> be the polynomial ring in <i>n</i> variables over a field <span>(mathbb {K})</span>. Assume that <i>I</i>(<i>G</i>) and <i>J</i>(<i>G</i>) denote the edge ideal and the cover ideal of <i>G</i>, respectively. We provide a combinatorial upper bound for the index of depth stability of symbolic powers of <i>J</i>(<i>G</i>). As a consequence, we compute the depth of symbolic powers of cover ideals of fully clique-whiskered graphs. Meanwhile, we determine a class of graphs <i>G</i> with the property that the Castelnuovo–Mumford regularity of <i>S</i>/<i>I</i>(<i>G</i>) is equal to the induced matching number of <i>G</i>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"367 - 376"},"PeriodicalIF":0.3,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714652","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
Bertini Type Results and Their Applications 贝尔蒂尼式结果及其应用
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-07-17 DOI: 10.1007/s40306-024-00542-8
Indranil Biswas, Manish Kumar, A. J. Parameswaran
{"title":"Bertini Type Results and Their Applications","authors":"Indranil Biswas,&nbsp;Manish Kumar,&nbsp;A. J. Parameswaran","doi":"10.1007/s40306-024-00542-8","DOIUrl":"10.1007/s40306-024-00542-8","url":null,"abstract":"<div><p>We prove Bertini type theorems and give some applications of them. The applications are in the context of Lefschetz theorem for Nori fundamental group for normal varieties as well as for geometric formal orbifolds. In another application, it is shown that a certain class of a smooth quasi-projective variety contains a smooth curve such that irreducible lisse <span>(ell )</span>–adic sheaves on the variety with “ramification bounded by a branch data” remains irreducible when restricted to the curve.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 4","pages":"649 - 665"},"PeriodicalIF":0.3,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141830113","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 v-Number of Binomial Edge Ideals 二项边理想的v数
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-07-04 DOI: 10.1007/s40306-024-00540-w
Siddhi Balu Ambhore, Kamalesh Saha, Indranath Sengupta
{"title":"The v-Number of Binomial Edge Ideals","authors":"Siddhi Balu Ambhore,&nbsp;Kamalesh Saha,&nbsp;Indranath Sengupta","doi":"10.1007/s40306-024-00540-w","DOIUrl":"10.1007/s40306-024-00540-w","url":null,"abstract":"<div><p>The invariant <span>(textrm{v})</span>-number was introduced very recently in the study of Reed-Muller-type codes. Jaramillo and Villarreal (J. Combin. Theory Ser. A 177:105310, 2021) initiated the study of the <span>(textrm{v})</span>-number of edge ideals. Inspired by their work, we take the initiation to study the <span>(textrm{v})</span>-number of binomial edge ideals in this paper. We discuss some properties and bounds of the <span>(textrm{v})</span>-number of binomial edge ideals. We explicitly find the <span>(textrm{v})</span>-number of binomial edge ideals locally at the associated prime corresponding to the cutset <span>(emptyset )</span>. We show that the <span>(textrm{v})</span>-number of Knutson binomial edge ideals is less than or equal to the <span>(textrm{v})</span>-number of their initial ideals. Also, we classify all binomial edge ideals whose <span>(textrm{v})</span>-number is 1. Moreover, we try to relate the <span>(textrm{v})</span>-number with the Castelnuvo-Mumford regularity of binomial edge ideals and give a conjecture in this direction.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 4","pages":"611 - 628"},"PeriodicalIF":0.3,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761993","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
Kantorovich’s Theorem on Mann’s Iteration Method in Riemannian Manifold 黎曼流形中Mann迭代法的Kantorovich定理
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-06-29 DOI: 10.1007/s40306-024-00541-9
Babita Mehta, P. K. Parida, Sapan Kumar Nayak
{"title":"Kantorovich’s Theorem on Mann’s Iteration Method in Riemannian Manifold","authors":"Babita Mehta,&nbsp;P. K. Parida,&nbsp;Sapan Kumar Nayak","doi":"10.1007/s40306-024-00541-9","DOIUrl":"10.1007/s40306-024-00541-9","url":null,"abstract":"<div><p>Convergence analysis of Mann’s iteration method using Kantorovich’s theorem in the context of connected and complete Riemannian manifolds has been examined in this paper. We also provide an algorithm for Mann’s method to find a singularity in a two dimensional sphere <span>(S^2)</span>. Finally, we provide an example that shows the better convergence result of Mann’s method in comparison to that of Newton’s method.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 4","pages":"629 - 648"},"PeriodicalIF":0.3,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142762043","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 Primal-dual Backward Reflected Forward Splitting Algorithm for Structured Monotone Inclusions 结构单调夹杂的原点-双向后向反射前向分裂算法
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-06-28 DOI: 10.1007/s40306-024-00535-7
Vũ Công Bằng, Dimitri Papadimitriou, Vũ Xuân Nhâm
{"title":"A Primal-dual Backward Reflected Forward Splitting Algorithm for Structured Monotone Inclusions","authors":"Vũ Công Bằng,&nbsp;Dimitri Papadimitriou,&nbsp;Vũ Xuân Nhâm","doi":"10.1007/s40306-024-00535-7","DOIUrl":"10.1007/s40306-024-00535-7","url":null,"abstract":"<div><p>We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusions in real Hilbert spaces. The algorithm allows to use the inexact computations of Lipschitzian and cocoercive operators. The strong convergence of the generated iterative sequence is proved under the strong monotonicity condition, whilst the weak convergence is formally proved under several conditions used in the literature. An application to a structured minimization problem is provided.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 2","pages":"159 - 172"},"PeriodicalIF":0.3,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414659","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 Convergence for Randomly Weighted Sums of Hilbert-valued Coordinatewise Pairwise NQD Random Variables 论希尔伯特值坐标性成对 NQD 随机变量的随机加权和的收敛性
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-06-15 DOI: 10.1007/s40306-024-00537-5
Cuong Manh Tran, Chien Van Ta, Hang Bui Khanh
{"title":"On the Convergence for Randomly Weighted Sums of Hilbert-valued Coordinatewise Pairwise NQD Random Variables","authors":"Cuong Manh Tran,&nbsp;Chien Van Ta,&nbsp;Hang Bui Khanh","doi":"10.1007/s40306-024-00537-5","DOIUrl":"10.1007/s40306-024-00537-5","url":null,"abstract":"<div><p>In this paper, we present the complete convergence for weighted sums of coordinatewise pairwise negative quadrant dependent random variables taking values in Hilbert spaces. As an application of the results, the complete convergence of degenerate von Mises statistics is investigated.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 2","pages":"265 - 281"},"PeriodicalIF":0.3,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141337202","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
Linear Singular Continuous Time-varying Delay Equations: Stability and Filtering via LMI Approach 线性奇异连续时变延迟方程：通过 LMI 方法实现稳定性和滤波
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-06-14 DOI: 10.1007/s40306-024-00534-8
Vu Ngoc Phat, Nguyen Truong Thanh
{"title":"Linear Singular Continuous Time-varying Delay Equations: Stability and Filtering via LMI Approach","authors":"Vu Ngoc Phat,&nbsp;Nguyen Truong Thanh","doi":"10.1007/s40306-024-00534-8","DOIUrl":"10.1007/s40306-024-00534-8","url":null,"abstract":"<div><p>In this paper, we propose an LMI-based approach to study stability and <span>(H_infty )</span> filtering for linear singular continuous equations with time-varying delay. Particularly, the delay pattern is quite general and includes non-differentiable time-varying delay. First, new delay-dependent sufficient conditions for the admissibility of the equation are extended to the time-varying delay case. Then, we propose a design of <span>(H_infty )</span> filters via feasibility problem involving linear matrix inequalities, which can be solved by the standard numerical algorithm. The proposed result is demonstrated through an example and simulations.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 4","pages":"595 - 609"},"PeriodicalIF":0.3,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141342653","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 Weighted (L^{p})-Sobolev Estimates for Solutions of the (overline{partial })-equation on Linearly Convex Domains of Finite Type and Application 关于有限线性凸域上(overline{partial })方程解的加权(L^{p})-Sobolev估计及其应用
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-06-11 DOI: 10.1007/s40306-024-00530-y
P. Charpentier, Y. Dupain
{"title":"On Weighted (L^{p})-Sobolev Estimates for Solutions of the (overline{partial })-equation on Linearly Convex Domains of Finite Type and Application","authors":"P. Charpentier,&nbsp;Y. Dupain","doi":"10.1007/s40306-024-00530-y","DOIUrl":"10.1007/s40306-024-00530-y","url":null,"abstract":"<div><p>We obtain some weighted <span>(L^{p})</span>-Sobolev estimates with gain on <i>p</i> and the weight for solutions of the <span>(overline{partial })</span>-equation in linearly convex domains of finite type in <span>(mathbb {C}^{n})</span> and apply them to obtain weighted <span>(L^{p})</span>-Sobolev estimates for weighted Bergman projections of convex domains of finite type for quite general weights equivalent to a power of the distance to the boundary.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 2","pages":"217 - 240"},"PeriodicalIF":0.3,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411272","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
Source Identification for Parabolic Equations from Integral Observations by the Finite Difference Splitting Method 用有限差分法从积分观测中识别抛物线方程的来源
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-06-11 DOI: 10.1007/s40306-024-00536-6
Nguyen Thi Ngoc Oanh
{"title":"Source Identification for Parabolic Equations from Integral Observations by the Finite Difference Splitting Method","authors":"Nguyen Thi Ngoc Oanh","doi":"10.1007/s40306-024-00536-6","DOIUrl":"10.1007/s40306-024-00536-6","url":null,"abstract":"<div><p>We study the problem of reconstructing an unknown source term in parabolic equations from integral observations. It is reformulated into a variational problem in combination with Tikhonov regularization and then a formula for the gradient of the objective functional to be minimized is computed via a solution of an adjoint problem. The variational problem is discretized by the splitting method based on finite difference schemes and solved by the conjugate gradient method. A numerical scheme for numerically estimating singular values of the solution operator in the inverse problem is suggested. Some numerical examples are presented to show the efficiency of the method.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 2","pages":"283 - 308"},"PeriodicalIF":0.3,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141360103","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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