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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
Solving Variational Inequalities Related to the Split Common Fixed Point Problem with Multiple Output Sets Constraints 求解具有多输出集约束的分裂公共不动点问题的变分不等式
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2026-02-04 DOI: 10.1007/s40306-025-00587-3
Tran Viet Anh
{"title":"Solving Variational Inequalities Related to the Split Common Fixed Point Problem with Multiple Output Sets Constraints","authors":"Tran Viet Anh","doi":"10.1007/s40306-025-00587-3","DOIUrl":"10.1007/s40306-025-00587-3","url":null,"abstract":"<div><p>In this paper, we explore the task of addressing strongly monotone variational inequalities over the solution set of the split common fixed point problem with multiple output sets in real Hilbert spaces. We propose a new iterative algorithm designed specifically for this task, which incorporates dynamic step sizes that adapt based on information from previous iterations. This approach ensures strong convergence without the need for prior knowledge of the norm of the bounded linear operator involved. Additionally, our method does not require information about the Lipschitz constants or the strongly monotone constants of the mappings. We also present several corollaries derived from our main result. Finally, we present an application of the split common fixed point problem with multiple output sets to supply chain planning, and provide numerical experiments to evaluate the performance of the proposed algorithm in comparison with existing methods.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 4","pages":"541 - 562"},"PeriodicalIF":0.3,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147734976","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 Dirichlet Problem for Nonsymmetric Augmented Hessian Quotient Type Equations 非对称增广Hessian商型方程的Dirichlet问题
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2026-01-28 DOI: 10.1007/s40306-025-00590-8
Van-Bang Tran, Tien-Ngoan Ha, Huu-Tho Nguyen, Trong-Tien Phan, Hong-Quang Dinh
{"title":"The Dirichlet Problem for Nonsymmetric Augmented Hessian Quotient Type Equations","authors":"Van-Bang Tran,&nbsp;Tien-Ngoan Ha,&nbsp;Huu-Tho Nguyen,&nbsp;Trong-Tien Phan,&nbsp;Hong-Quang Dinh","doi":"10.1007/s40306-025-00590-8","DOIUrl":"10.1007/s40306-025-00590-8","url":null,"abstract":"<div>\u0000 \u0000 <p>We deal with the Dirichlet problem for nonsymmetric augmented Hessian quotient type equations. First, we look for an admissible solution to the problem for corresponding symmetric augmented Hessian quotient type equations. Then we apply the Banach fixed point theorem to prove the existence of a <span>(delta)</span>-admissible solution in <span>(C^{2,alpha })</span> to the problem by assuming that the augmented skew-symmetric matrix is sufficiently small in a certain sense. We also give a necessary condition for the existence and sufficient conditions for uniqueness of this kind of <span>(delta)</span>-admissible solutions.</p>\u0000 </div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 4","pages":"563 - 594"},"PeriodicalIF":0.3,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147734979","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 First Approach to the Burchnall-Chaundy Theory for Quadratic Algebras Having PBW Bases 具有PBW基的二次代数Burchnall-Chaundy理论的初步探讨
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2026-01-22 DOI: 10.1007/s40306-025-00584-6
Arturo Niño, María Camila Ramírez, Armando Reyes
{"title":"A First Approach to the Burchnall-Chaundy Theory for Quadratic Algebras Having PBW Bases","authors":"Arturo Niño,&nbsp;María Camila Ramírez,&nbsp;Armando Reyes","doi":"10.1007/s40306-025-00584-6","DOIUrl":"10.1007/s40306-025-00584-6","url":null,"abstract":"<div><p>In this paper, we present a first approach toward a Burchnall-Chaundy theory for the skew Ore polynomials of higher order generated by quadratic relations defined by Golovashkin and Maksimov (Russian Math. Surv. <b>53</b>(2), 384–386 1998).</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 4","pages":"495 - 519"},"PeriodicalIF":0.3,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147734982","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
Stability in a Two-dimensional Keller-Segel-Navier-Stokes System 二维Keller-Segel-Navier-Stokes系统的稳定性
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2026-01-22 DOI: 10.1007/s40306-025-00589-1
Qiong Chen, Qian Zhang
{"title":"Stability in a Two-dimensional Keller-Segel-Navier-Stokes System","authors":"Qiong Chen,&nbsp;Qian Zhang","doi":"10.1007/s40306-025-00589-1","DOIUrl":"10.1007/s40306-025-00589-1","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the initial-boundary value problem for a Keller-Segel-Navier-Stokes model that includes a logistic source term. The system is considered in a two-dimensional bounded domain with a smooth boundary as follows </p><div><div><span>$$begin{aligned},, left{ begin{aligned}&amp;n_{t}+ucdot nabla n=Delta n-nabla cdot (nnabla c)+mu n-kappa n^{2},&amp;c_{t}+ucdot nabla c=Delta c -nc,&amp;v_{t}+ucdot nabla v=Delta v -gamma v+n,&amp;u_{t}+(ucdot nabla ) u+nabla pi =Delta u-nf,&amp;nabla cdot u=0. end{aligned} right. end{aligned}$$</span></div></div><p>This system characterizes the interaction of chemotactic microorganisms with an incompressible fluid. Under the conditions of positive <span>(mu)</span> and non-negative <span>(kappa)</span>, sufficiently regular initial data <span>((n_{0}, c_{0}, v_{0}, u_{0}))</span> with <span>(n_{0} not equiv 0)</span> yield a uniformly bounded global classical solution. Moreover, when <span>(mu =0)</span>, the solution obeys </p><div><div><span>$$begin{aligned} n(cdot ,t)rightarrow 0,quad c(cdot ,t)rightarrow 0,quad v(cdot ,t)rightarrow 0quad textrm{and} quad u(cdot ,t)rightarrow 0qquad textrm{in} L^{infty }(Omega ) end{aligned}$$</span></div></div><p>as <span>(trightarrow infty)</span>.</p>\u0000 </div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 4","pages":"595 - 622"},"PeriodicalIF":0.3,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147734950","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
Relative Cohen-Macaulay Modules under Ring Homomorphisms 环同态下的相对Cohen-Macaulay模
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2026-01-22 DOI: 10.1007/s40306-025-00582-8
Parisa Pourghobadian, Kamran Divaani-Aazar, Ahad Rahimi
{"title":"Relative Cohen-Macaulay Modules under Ring Homomorphisms","authors":"Parisa Pourghobadian,&nbsp;Kamran Divaani-Aazar,&nbsp;Ahad Rahimi","doi":"10.1007/s40306-025-00582-8","DOIUrl":"10.1007/s40306-025-00582-8","url":null,"abstract":"<div>\u0000 \u0000 <p>Let <span>(R)</span> be a commutative Noetherian ring with identity (not necessarily local), and let <span>(mathfrak {a})</span> be a proper ideal of <span>(R)</span>. We investigate the invariance of certain classes of <span>(mathfrak {a})</span>-relative Cohen-Macaulay modules under pure ring homomorphisms and ring homomorphisms of finite flat dimension. Our results generalize several existing results in the literature on homological modules.</p>\u0000 </div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 4","pages":"449 - 466"},"PeriodicalIF":0.3,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147734977","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-uniform Bounds for Non-normal Approximation via Stein’s Method with Applications to the Curie–Weiss Model and the Imitative Monomer-dimer Model Stein法非正态近似的非均匀界及其在Curie-Weiss模型和模拟单体-二聚体模型中的应用
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2026-01-22 DOI: 10.1007/s40306-025-00583-7
Lê Vǎn Thành, Nguyen Ngoc Tu
{"title":"Non-uniform Bounds for Non-normal Approximation via Stein’s Method with Applications to the Curie–Weiss Model and the Imitative Monomer-dimer Model","authors":"Lê Vǎn Thành,&nbsp;Nguyen Ngoc Tu","doi":"10.1007/s40306-025-00583-7","DOIUrl":"10.1007/s40306-025-00583-7","url":null,"abstract":"<div><p>This paper establishes a non-uniform Berry–Esseen bound for non-normal approximation using Stein’s method. The main theorem generalizes the result of the authors in [Comptes Rendus Mathématique, 2024] to the context of non-normal approximation. As applications of the main result, we derive non-uniform Berry–Esseen bounds in non-central limit theorems for the magnetization in the Curie–Weiss model and the imitative monomer-dimer model. These extend some existing results in the literature, including Theorem 2.1 of Chatterjee and Shao [Ann. Appl. Probab., 2011] and Theorem 1 of Chen [J. Math. Physics, 2016].</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 4","pages":"467 - 486"},"PeriodicalIF":0.3,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147734980","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 articles with equations and figures incorrectly displayed 对公式和数字显示不正确的文章进行更正
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2025-11-26 DOI: 10.1007/s40306-025-00586-4
{"title":"Correction to articles with equations and figures incorrectly displayed","authors":"","doi":"10.1007/s40306-025-00586-4","DOIUrl":"10.1007/s40306-025-00586-4","url":null,"abstract":"","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 3","pages":"447 - 447"},"PeriodicalIF":0.3,"publicationDate":"2025-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754439","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
S-forms of a Finitely Generated Field Extension 有限生成域扩展的s -形式
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2025-11-03 DOI: 10.1007/s40306-025-00580-w
EL Hassane Fliouet
{"title":"S-forms of a Finitely Generated Field Extension","authors":"EL Hassane Fliouet","doi":"10.1007/s40306-025-00580-w","DOIUrl":"10.1007/s40306-025-00580-w","url":null,"abstract":"<div><p>Let <i>K</i> be a finitely generated extension of a field <i>k</i> of characteristic <span>(pnot =0)</span>. By means of exponents of <i>K</i>/<i>k</i>, we introduce the notion of <i>s</i>-forms (<i>s</i> being a positive integer less than or equal to <i>insep</i>(<i>K</i>/<i>k</i>) of <i>K</i>/<i>k</i> as a natural generalization of forms of <i>K</i>/<i>k</i>. In light of results obtained by James K. Deveney and John N. Mordeson in their investigation on the forms of a finitely generated field extension [Deveney and Mordeson: Can. J. Math. <b>31</b>(3), 655–662 (1979)], necessary and sufficient conditions characterizing <i>s</i>-forms of <i>K</i>/<i>k</i> are given allowing in particular the existence of a unique minimal <i>s</i>-form (irreducible <i>s</i>-form) of <i>K</i>/<i>k</i> and, accordingly, the development of properties of irreducible <i>s</i>-forms of <i>K</i>/<i>k</i>. We also seek to identify possible relationships between the structure and invariants of <i>K</i>/<i>k</i> and those of its irreducible <i>s</i>-form.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 3","pages":"419 - 428"},"PeriodicalIF":0.3,"publicationDate":"2025-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754302","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
Asymptotic Regularity Results for Halpern-type Inexact Iterations for Coincidence Problems 符合问题的halpern型不精确迭代的渐近正则性结果
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2025-10-27 DOI: 10.1007/s40306-025-00579-3
Alexander J. Zaslavski
{"title":"Asymptotic Regularity Results for Halpern-type Inexact Iterations for Coincidence Problems","authors":"Alexander J. Zaslavski","doi":"10.1007/s40306-025-00579-3","DOIUrl":"10.1007/s40306-025-00579-3","url":null,"abstract":"<div><p>In our recent work we computed linear rates of asymptotic regularity for a viscosity version of Halpern-type iterations for coincidence problem in a metric space with a hyperbolic structure. In the present paper we extend this result for inexact iterations under the presence of computational errors.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 3","pages":"429 - 443"},"PeriodicalIF":0.3,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-025-00579-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754436","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
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