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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
On Some Operator Inequalities with Respect to the s-Convexity 论关于 s 凸性的一些算子不等式
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-12-23 DOI: 10.1007/s40306-023-00519-z
Lahcen Tarik, Mustapha Raïssouli, Mohamed Chergui, Bouazza El Wahbi
{"title":"On Some Operator Inequalities with Respect to the s-Convexity","authors":"Lahcen Tarik,&nbsp;Mustapha Raïssouli,&nbsp;Mohamed Chergui,&nbsp;Bouazza El Wahbi","doi":"10.1007/s40306-023-00519-z","DOIUrl":"10.1007/s40306-023-00519-z","url":null,"abstract":"<div><p>In this paper, we extend the concept of <i>s</i>-convexity from the case where the functions are with real variables to the case where the functions are with operator arguments. Afterwards, we investigate some related properties and operator inequalities. As an application, some inequalities of Hermite-Hadamard and Jensen types involving some operator means are established.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 4","pages":"671 - 690"},"PeriodicalIF":0.3,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139162721","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
Some Types of Carathéodory Scheme for Caputo Stochastic Fractional Differential Equations in (L^p) Spaces 针对 $$L^p$$ 空间中卡普托随机分微分方程的几类 Carathéodory 方案
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-12-19 DOI: 10.1007/s40306-023-00518-0
Phan Thi Huong, Pham The Anh
{"title":"Some Types of Carathéodory Scheme for Caputo Stochastic Fractional Differential Equations in (L^p) Spaces","authors":"Phan Thi Huong,&nbsp;Pham The Anh","doi":"10.1007/s40306-023-00518-0","DOIUrl":"10.1007/s40306-023-00518-0","url":null,"abstract":"<div><p>In this paper, we construct Carathéodory type and exponential Carathéodory type schemes for Caputo stochastic fractional differential equations (CSFDEs) of order <span>(alpha in (frac{1}{2},1))</span> in <span>(L^p)</span> spaces with <span>(p ge 2)</span> whose coefficients satisfy a standard Lipschitz and a linear growth bound conditions. The strong convergence and the convergence rate of these schemes are also established.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 4","pages":"651 - 669"},"PeriodicalIF":0.3,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138960670","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 Tor Algebra of Trimmings of Gorenstein Ideals 戈伦斯坦理想的修剪的托尔代数
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-12-13 DOI: 10.1007/s40306-023-00512-6
Luigi Ferraro, Alexis Hardesty
{"title":"The Tor Algebra of Trimmings of Gorenstein Ideals","authors":"Luigi Ferraro,&nbsp;Alexis Hardesty","doi":"10.1007/s40306-023-00512-6","DOIUrl":"10.1007/s40306-023-00512-6","url":null,"abstract":"<div><p>Let <span>((R,mathfrak m,Bbbk ))</span> be a regular local ring of dimension 3. Let <i>I</i> be a Gorenstein ideal of <i>R</i> of grade 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric matrix of odd size such that <i>I</i> is generated by the sub-maximal pfaffians of this matrix. Let <i>J</i> be the ideal obtained by multiplying some of the pfaffian generators of <i>I</i> by <span>(mathfrak m)</span>; we say that <i>J</i> is a trimming of <i>I</i>. Building on a recent paper of Vandebogert, we construct an explicit free resolution of <i>R/J</i> and compute a partial DG algebra structure on this resolution. We provide the full DG algebra structure in the appendix. We use the products on this resolution to study the Tor algebra of such trimmed ideals and we use the information obtained to prove that recent conjectures of Christensen, Veliche and Weyman on ideals of class <span>(textbf{G})</span> hold true in our context. Furthermore, we address the realizability question for ideals of class <span>(textbf{G})</span>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 4","pages":"567 - 604"},"PeriodicalIF":0.3,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411556","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 Set of Chern Numbers in Local Rings 论局部环中的切尔数集
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-12-05 DOI: 10.1007/s40306-023-00517-1
Le Truong Hoang, Ngoc Yen Hoang
{"title":"On the Set of Chern Numbers in Local Rings","authors":"Le Truong Hoang,&nbsp;Ngoc Yen Hoang","doi":"10.1007/s40306-023-00517-1","DOIUrl":"10.1007/s40306-023-00517-1","url":null,"abstract":"<div><p>The purpose of this paper is to characterize Noetherian local rings <span>((R, mathfrak {m}))</span> such that the Chern numbers of certain <span>(mathfrak {m})</span>-primary ideals in <i>R</i> are bounded above or range among only finitely many values. Consequently, we characterize the Gorensteinness, Cohen-Macaulayness, and generalized Cohen-Macaulayness of local rings in terms of the behavior of their Chern numbers.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 1","pages":"139 - 157"},"PeriodicalIF":0.3,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138601167","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 Infinitely Generated Locus of Frobenius Algebras of Rings of Prime Characteristic 论素性环的弗罗贝纽斯代数的无限生成焦点
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-12-05 DOI: 10.1007/s40306-023-00515-3
Alberto F. Boix, Danny A. J. Gómez–Ramírez, Santiago Zarzuela
{"title":"On the Infinitely Generated Locus of Frobenius Algebras of Rings of Prime Characteristic","authors":"Alberto F. Boix,&nbsp;Danny A. J. Gómez–Ramírez,&nbsp;Santiago Zarzuela","doi":"10.1007/s40306-023-00515-3","DOIUrl":"10.1007/s40306-023-00515-3","url":null,"abstract":"<div><p>Let <i>R</i> be a commutative Noetherian ring of prime characteristic <i>p</i>. The main goal of this paper is to study in some detail when </p><div><div><span>$$ {mathfrak {p}in {text {Spec}} (R),:, mathcal {F}^{E_{mathfrak {p}}}text { is finitely generated as a ring over its degree zero piece}} $$</span></div></div><p>is an open set in the Zariski topology, where <span>(mathcal {F}^{E_{mathfrak {p}}})</span> denotes the Frobenius algebra attached to the injective hull of the residue field of <span>(R_{mathfrak {p}}.)</span> We show that this is true when <i>R</i> is a Stanley–Reisner ring; moreover, in this case, we explicitly compute its closed complement, providing an algorithmic method for doing so.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 1","pages":"3 - 18"},"PeriodicalIF":0.3,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409994","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
Noetherian Rings of the Form ({mathcal {A}}[X,Y;lambda ]) Noetherian Rings of the Form （{mathcal {A}}[X,Y;lambda ])
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-11-11 DOI: 10.1007/s40306-023-00516-2
Abdelamir Dabbabi, Ali Benhissi
{"title":"Noetherian Rings of the Form ({mathcal {A}}[X,Y;lambda ])","authors":"Abdelamir Dabbabi,&nbsp;Ali Benhissi","doi":"10.1007/s40306-023-00516-2","DOIUrl":"10.1007/s40306-023-00516-2","url":null,"abstract":"<div><p>In this paper, we use composite ring extensions to construct a new class of Noetherian rings. Composite ring extensions are examples of pullback constructions, and they are useful in constructing of (counter)-examples.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 4","pages":"523 - 531"},"PeriodicalIF":0.3,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135043146","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 Numerical Solution to an Inverse Medium Scattering Problem 关于反介质散射问题的数值解法
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-11-06 DOI: 10.1007/s40306-023-00513-5
Dinh-Liem Nguyen, Trung Truong
{"title":"On the Numerical Solution to an Inverse Medium Scattering Problem","authors":"Dinh-Liem Nguyen,&nbsp;Trung Truong","doi":"10.1007/s40306-023-00513-5","DOIUrl":"10.1007/s40306-023-00513-5","url":null,"abstract":"<div><p>This paper is concerned with the inverse medium scattering problem of determining the location and shape of penetrable scattering objects from measurements of the scattered field. We study a sampling indicator function for recovering the scattering object in a fast and robust way. A flexibility of this indicator function is that it is applicable to data measured in near-field regime or far-field regime. The implementation of the function is simple and does not involve solving any ill-posed problems. The resolution analysis and stability estimate of the indicator function are investigated using the factorization analysis of the far-field operator along with the Funk-Hecke formula. The performance of the method is verified on both simulated and experimental data.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 4","pages":"551 - 566"},"PeriodicalIF":0.3,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135636959","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
Taylor Polynomials of Rational Functions 有理函数的泰勒多项式
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2023-11-03 DOI: 10.1007/s40306-023-00514-4
Aldo Conca, Simone Naldi, Giorgio Ottaviani, Bernd Sturmfels
{"title":"Taylor Polynomials of Rational Functions","authors":"Aldo Conca,&nbsp;Simone Naldi,&nbsp;Giorgio Ottaviani,&nbsp;Bernd Sturmfels","doi":"10.1007/s40306-023-00514-4","DOIUrl":"10.1007/s40306-023-00514-4","url":null,"abstract":"<div><p>A Taylor variety consists of all fixed order Taylor polynomials of rational functions, where the number of variables and degrees of numerators and denominators are fixed. In one variable, Taylor varieties are given by rank constraints on Hankel matrices. Inversion of the natural parametrization is known as Padé approximation. We study the dimension and defining ideals of Taylor varieties. Taylor hypersurfaces are interesting for projective geometry, since their Hessians tend to vanish. In three and more variables, there exist defective Taylor varieties whose dimension is smaller than the number of parameters. We explain this with Fröberg’s Conjecture in commutative algebra.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 1","pages":"19 - 37"},"PeriodicalIF":0.3,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135819889","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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