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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, Manish Kumar, A. J. Parameswaran","doi":"10.1007/s40306-024-00542-8","DOIUrl":"https://doi.org/10.1007/s40306-024-00542-8","url":null,"abstract":"","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"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
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":null,"pages":null},"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":null,"pages":null},"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 0.5
Acta Mathematica Vietnamica Pub Date : 2024-06-14 DOI: 10.1007/s40306-024-00534-8
V. Phat, N. T. Thanh
{"title":"Linear Singular Continuous Time-varying Delay Equations: Stability and Filtering via LMI Approach","authors":"V. Phat, N. T. Thanh","doi":"10.1007/s40306-024-00534-8","DOIUrl":"https://doi.org/10.1007/s40306-024-00534-8","url":null,"abstract":"","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.5,"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":null,"pages":null},"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":null,"pages":null},"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
A Note on Real Line Bundles with Connection and Real Smooth Deligne Cohomology 关于带连接的实线束和实光滑德利涅同调的说明
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-06-05 DOI: 10.1007/s40306-024-00538-4
Peter Marius Flydal, Gereon Quick, Eirik Eik Svanes
{"title":"A Note on Real Line Bundles with Connection and Real Smooth Deligne Cohomology","authors":"Peter Marius Flydal,&nbsp;Gereon Quick,&nbsp;Eirik Eik Svanes","doi":"10.1007/s40306-024-00538-4","DOIUrl":"10.1007/s40306-024-00538-4","url":null,"abstract":"<div><p>We define a Real version of smooth Deligne cohomology for manifolds with involution which interpolates between equivariant sheaf cohomology and smooth imaginary-valued forms. Our main result is a classification of Real line bundles with Real connection on manifolds with involution.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-024-00538-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410022","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
Meromorphic Solutions of a Certain Type of Nonlinear Differential Equations 某类非线性微分方程的同态解
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-05-31 DOI: 10.1007/s40306-024-00539-3
Yan-Yan Feng, Jun-Fan Chen
{"title":"Meromorphic Solutions of a Certain Type of Nonlinear Differential Equations","authors":"Yan-Yan Feng,&nbsp;Jun-Fan Chen","doi":"10.1007/s40306-024-00539-3","DOIUrl":"10.1007/s40306-024-00539-3","url":null,"abstract":"<div><p>In this paper, using Nevanlinna theory and linear algebra, we characterize transcendental meromorphic solutions of nonlinear differential equation of the form </p><div><div><span>$$begin{aligned} f^n+Q_d(z,f)=sum _{i=1}^{l}p_{i}(z)e^{alpha _{i}(z)}, end{aligned}$$</span></div></div><p>where <span>(lge 2)</span>, <span>(nge l+2)</span> are integers, <i>f</i>(<i>z</i>) is a meromorphic function, <span>(Q_d(z,f))</span> is a differential polynomial in <i>f</i>(<i>z</i>) of degree <span>(dle n-(l+1))</span> with rational functions as its coefficients, <span>(p_{1}(z))</span>, <span>(p_{2}(z))</span>, <span>(dots )</span>, <span>(p_{l}(z))</span> are non-vanishing rational functions and <span>(alpha _{1}(z))</span>, <span>(alpha _{2}(z))</span>, <span>(dots )</span>, <span>(alpha _{l}(z))</span> are nonconstant polynomials such that <span>(alpha _{1}^prime (z))</span>, <span>(alpha _{2}^prime (z))</span>, <span>(dots )</span>, <span>(alpha _{l}^prime (z))</span> are distinct. Further, we give the necessary conditions for the existence of meromorphic solutions of the above equation, and supply the example to demonstrate the sharpness of the condition of the obtained theorem.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415235","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
Tight Closure, Coherence, and Localization at Single Elements 单元素的紧密闭合、相干和定位
IF 0.3
Acta Mathematica Vietnamica Pub Date : 2024-05-24 DOI: 10.1007/s40306-024-00533-9
Neil Epstein
{"title":"Tight Closure, Coherence, and Localization at Single Elements","authors":"Neil Epstein","doi":"10.1007/s40306-024-00533-9","DOIUrl":"10.1007/s40306-024-00533-9","url":null,"abstract":"<div><p>In this note, a condition (<i>open persistence</i>) is presented under which a (pre)closure operation on submodules (resp. ideals) over rings of global sections over a scheme <i>X</i> can be extended to a (pre)closure operation on sheaves of submodules of a coherent <span>(mathcal {O}_X)</span>-module (resp. sheaves of ideals in <span>(mathcal {O}_X)</span>). A second condition (<i>glueability</i>) is given for such an operation to behave nicely. It is shown that for an operation that satisfies both conditions, the question of whether the operation commutes with localization at single elements is equivalent to the question of whether the new operation preserves quasi-coherence. It is shown that both conditions hold for tight closure and some of its important variants, thus yielding a geometric reframing of the open question of whether tight closure localizes at single elements. A new singularity type (<i>semi F-regularity</i>) arises, which sits between F-regularity and weak F-regularity. The paper ends with (1) a case where semi F-regularity and weak F-regularity coincide, and (2) a case where they cannot coincide without implying a solution to a major conjecture.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-024-00533-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413482","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
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":null,"pages":null},"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
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