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Products of Commutators of Involutions in Skew Linear Groups 斜线性群中卷积的换元积
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-05-09 DOI: 10.1007/s40306-024-00532-w
Nguyen Thi Thai Ha, Phan Hoang Nam, Tran Nam Son
{"title":"Products of Commutators of Involutions in Skew Linear Groups","authors":"Nguyen Thi Thai Ha,&nbsp;Phan Hoang Nam,&nbsp;Tran Nam Son","doi":"10.1007/s40306-024-00532-w","DOIUrl":"10.1007/s40306-024-00532-w","url":null,"abstract":"<div><p>In connection with [Theorem 4.6, Linear Algebra Appl. <b>646</b>, 119–131, (2022)], we show that each matrix in the commutator subgroup of the general linear group over a centrally-finite division ring <i>D</i>, in which each element in the commutator subgroup of <i>D</i> is a product of at most <i>s</i> commutators, can be written as a product of at most <span>(3+3leftlceil frac{s}{lfloor n/2 rfloor } rightrceil )</span> commutators of involutions if <span>(mathrm {char,}Dne 2)</span>, where <span>({displaystyle lceil x rceil })</span>, <span>({displaystyle lfloor x rfloor })</span> denote the ceiling and floor functions of <i>x</i>, respectively. Moreover, we also present the special case when <span>(D= mathbb {H})</span>, the division ring of quaternions, and an application in real group algebras.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 2","pages":"253 - 263"},"PeriodicalIF":0.3,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140994344","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 Schmidt’s Subspace Theorem for Moving Hyperplane Targets Over Function Fields 函数场上移动超平面目标的施密特子空间定理
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-05-07 DOI: 10.1007/s40306-024-00529-5
Le Giang, Tran Van Tan, Nguyen Van Thin
{"title":"A Schmidt’s Subspace Theorem for Moving Hyperplane Targets Over Function Fields","authors":"Le Giang,&nbsp;Tran Van Tan,&nbsp;Nguyen Van Thin","doi":"10.1007/s40306-024-00529-5","DOIUrl":"10.1007/s40306-024-00529-5","url":null,"abstract":"<div><p>The Schmidt subspace theorem has been studied extensively for both cases of fixed and moving targets in projective spaces over number fields and the case of fixed targets in projective spaces over function fields. This paper studies the case of function fields with moving targets; in particular, we extend the result of Min Ru and Paul Vojta in the Inventiones Mathematicae (1997) to the case of moving hyperplane targets in projective spaces over function fields.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 2","pages":"241 - 251"},"PeriodicalIF":0.3,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141002436","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
Sparse-grid Sampling Recovery and Numerical Integration of Functions Having Mixed Smoothness 具有混合平滑性的函数的稀疏网格采样恢复和数值积分
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-04-23 DOI: 10.1007/s40306-024-00527-7
Dinh Dũng
{"title":"Sparse-grid Sampling Recovery and Numerical Integration of Functions Having Mixed Smoothness","authors":"Dinh Dũng","doi":"10.1007/s40306-024-00527-7","DOIUrl":"10.1007/s40306-024-00527-7","url":null,"abstract":"<div><p>We give a short survey of recent results on sparse-grid linear algorithms of approximate recovery and integration of functions possessing a unweighted or weighted Sobolev mixed smoothness based on their sampled values at a certain finite set. Some of them are extended to more general cases.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"377 - 426"},"PeriodicalIF":0.3,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714305","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
Uniform Symbolic Topologies and Hypersurfaces 统一符号拓扑和超曲面
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-03-26 DOI: 10.1007/s40306-024-00526-8
Craig Huneke, Daniel Katz
{"title":"Uniform Symbolic Topologies and Hypersurfaces","authors":"Craig Huneke,&nbsp;Daniel Katz","doi":"10.1007/s40306-024-00526-8","DOIUrl":"10.1007/s40306-024-00526-8","url":null,"abstract":"<div><p>We study the question of which rings, and which families of ideals, have uniform symbolic topologies. In particular, we show that the uniform symbolic topology property holds for all dimension one primes in any normal complete local domain, provided dimension one primes in hypersurfaces have the uniform symbolic topology property. We also discuss bootstrapping techniques and provide a strong bootstrapping statement in positive characteristic. We apply these techniques to give families of primes in hypersurfaces of positive characteristic which have uniform symbolic topologies.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 1","pages":"99 - 113"},"PeriodicalIF":0.3,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-024-00526-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140378297","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
On Nilpotent-invariant One-sided Ideals 论无穷不变的单边理想
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-03-16 DOI: 10.1007/s40306-024-00524-w
Truong Cong Quynh, Truong Thi Thuy Van
{"title":"On Nilpotent-invariant One-sided Ideals","authors":"Truong Cong Quynh,&nbsp;Truong Thi Thuy Van","doi":"10.1007/s40306-024-00524-w","DOIUrl":"10.1007/s40306-024-00524-w","url":null,"abstract":"<div><p>The notion of a nilpotent-invariant module was introduced and thoroughly investigated in Koşan and Quynh (Comm. Algebra <b>45</b>, 2775–2782 2017) as a proper extension of an automorphism-invariant module. In this paper a ring is called a right <span>(mathfrak {n})</span>-ring if every right ideal is nilpotent-invariant. We show that a right <span>(mathfrak {n})</span>-ring is the direct sum of a square full semisimple artinian ring and a right square-free ring. Moreover, right <span>(mathfrak {n})</span>-rings are shown to be stably finite, and if the ring is also an exchange ring then it satisfies the substitution property, has stable range 1. These results are non-trivial extensions of similar ones on rings every right ideal is automorphism-invariant.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 1","pages":"115 - 128"},"PeriodicalIF":0.3,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140236097","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
Bounds for the Hilbert-Kunz Multiplicity of Singular Rings 奇异环的希尔伯特-昆兹乘数界限
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-03-04 DOI: 10.1007/s40306-024-00525-9
Nicholas O. Cox-Steib, Ian M. Aberbach
{"title":"Bounds for the Hilbert-Kunz Multiplicity of Singular Rings","authors":"Nicholas O. Cox-Steib,&nbsp;Ian M. Aberbach","doi":"10.1007/s40306-024-00525-9","DOIUrl":"10.1007/s40306-024-00525-9","url":null,"abstract":"<div><p>In this paper, we prove that the Watanabe-Yoshida conjecture holds up to dimension 7. Our primary new tool is a function, <span>(varphi _J(R;z^t),)</span> that interpolates between the Hilbert-Kunz multiplicities of a base ring, <i>R</i>, and various radical extensions, <span>(R_n)</span>. We prove that this function is concave and show that its rate of growth is related to the size of <span>(e_{textrm{HK}}(R))</span>. We combine techniques from Celikbas et al. (Nagoya Math. J. <b>205</b>, 149–165, 2012) and Aberbach and Enescu (Nagoya Math. J. <b>212</b>, 59–85, 2013) to get effective lower bounds for <span>(varphi ,)</span> which translate to improved bounds on the size of Hilbert-Kunz multiplicities of singular rings. The improved inequalities are powerful enough to show that the conjecture of Watanabe and Yoshida holds in dimension 7.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 1","pages":"39 - 60"},"PeriodicalIF":0.3,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140460246","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 Asymptotic Samuel Function of a Filtration 滤波的渐近萨缪尔函数
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-02-26 DOI: 10.1007/s40306-024-00523-x
Steven Dale Cutkosky, Smita Praharaj
{"title":"The Asymptotic Samuel Function of a Filtration","authors":"Steven Dale Cutkosky,&nbsp;Smita Praharaj","doi":"10.1007/s40306-024-00523-x","DOIUrl":"10.1007/s40306-024-00523-x","url":null,"abstract":"<div><p>We extend the asymptotic Samuel function of an ideal to a filtration and show that many of the good properties of this function for an ideal are true for filtrations. There are, however, interesting differences, which we explore. We study the notion of projective equivalence of filtrations and the relation between the asymptotic Samuel function and the multiplicity of a filtration. We further consider the case of discrete valued filtrations and show that they have particularly nice properties.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 1","pages":"61 - 81"},"PeriodicalIF":0.3,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140428666","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
Non-normal Edge Rings Satisfying ((S_{2}))-condition 满足（(S_{2}）条件的非正态边缘环
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-01-12 DOI: 10.1007/s40306-023-00520-6
Nayana Shibu Deepthi
{"title":"Non-normal Edge Rings Satisfying ((S_{2}))-condition","authors":"Nayana Shibu Deepthi","doi":"10.1007/s40306-023-00520-6","DOIUrl":"10.1007/s40306-023-00520-6","url":null,"abstract":"<div><p>Let <i>G</i> be a finite simple connected graph on the vertex set <span>(V(G)=[d]={1,dots ,d})</span> with edge set <span>(E(G)={e_{1},dots , e_{n}})</span>. Let <span>(mathbb {K}[textbf{t}]=mathbb {K}[t_{1},dots ,t_{d}])</span> be the polynomial ring in <i>d</i> variables over a field <span>(mathbb {K})</span>. The edge ring of <i>G</i> is the affine semigroup ring <span>(mathbb {K}[G])</span> generated by monomials <span>(textbf{t}^{e}:=t_{i}t_{j})</span>, for <span>(e={i,j} in E(G))</span>. In this paper, we will prove that, given integers <i>d</i> and <i>n</i>, where <span>(dge 7)</span> and <span>(d+1le nle frac{d^{2}-7d+24}{2})</span>, there exists a finite simple connected graph <i>G</i> with <span>(|V(G)|=d)</span> and <span>(|E(G)|=n)</span>, such that <span>(mathbb {K}[G])</span> is non-normal and satisfies <span>((S_{2}))</span>-condition.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 4","pages":"605 - 619"},"PeriodicalIF":0.3,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411450","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 Inertial Iterative Algorithm for Approximating Common Solutions to Split Equalities of Some Nonlinear Optimization Problems 用于逼近某些非线性优化问题分割等式常见解的惯性迭代算法
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-01-10 DOI: 10.1007/s40306-023-00521-5
O. T. Mewomo, G. N. Ogwo, T. O. Alakoya
{"title":"An Inertial Iterative Algorithm for Approximating Common Solutions to Split Equalities of Some Nonlinear Optimization Problems","authors":"O. T. Mewomo,&nbsp;G. N. Ogwo,&nbsp;T. O. Alakoya","doi":"10.1007/s40306-023-00521-5","DOIUrl":"10.1007/s40306-023-00521-5","url":null,"abstract":"<div><p>In this paper, we introduce a new inertial Tseng’s extragradient method with self-adaptive step sizes for approximating a common solution of split equalities of equilibrium problem (EP), non-Lipschitz pseudomonotone variational inequality problem (VIP) and fixed point problem (FPP) of nonexpansive semigroups in real Hilbert spaces. We prove that the sequence generated by our proposed method converges strongly to a common solution of the EP, pseudomonotone VIP and FPP of nonexpansive semigroups without any linesearch procedure nor the sequential weak continuity condition often assumed by authors when solving non-Lipschitz VIPs. Finally, we provide some numerical experiments for the proposed method in comparison with related methods in the literature. Our result improves, extends and generalizes several of the existing results in this direction.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 4","pages":"621 - 650"},"PeriodicalIF":0.3,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-023-00521-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139441309","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
Differential Stability in a Multi-Objective Optimal Control Problems with a Possibly Empty Solution Set 具有可能空解集的多目标最优控制问题中的微分稳定性
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-01-03 DOI: 10.1007/s40306-023-00522-4
N. T. Toan, L. Q. Thuy
{"title":"Differential Stability in a Multi-Objective Optimal Control Problems with a Possibly Empty Solution Set","authors":"N. T. Toan,&nbsp;L. Q. Thuy","doi":"10.1007/s40306-023-00522-4","DOIUrl":"10.1007/s40306-023-00522-4","url":null,"abstract":"<div><p>This paper studies the first-order behavior of the weak optimal value mapping in a parametric multi-objective discrete optimal control problem under linear state equations, where the solution set may be empty. By establishing an abstract result on the <span>(varepsilon )</span>-weak subdifferential of the weak optimal value mapping in a parametric multi-objective mathematical programming problem with an inclusion constraint, we derive a formula for computing the <span>(varepsilon )</span>-weak subdifferential of the weak optimal value mapping in a parametric multi-objective discrete optimal control problem. The obtained results are proved directly without using scalarization techniques.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 4","pages":"691 - 707"},"PeriodicalIF":0.3,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139388920","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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