Acta Mathematica Vietnamica最新文献_第4页

Kantorovich’s Theorem on Mann’s Iteration Method in Riemannian Manifold 黎曼流形中Mann迭代法的Kantorovich定理

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Acta Mathematica Vietnamica Pub Date : 2024-06-29 DOI: 10.1007/s40306-024-00541-9

Babita Mehta, P. K. Parida, Sapan Kumar Nayak

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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

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Acta Mathematica Vietnamica Pub Date : 2024-06-28 DOI: 10.1007/s40306-024-00535-7

Vũ Công Bằng, Dimitri Papadimitriou, Vũ Xuân Nhâm

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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

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Acta Mathematica Vietnamica Pub Date : 2024-06-15 DOI: 10.1007/s40306-024-00537-5

Cuong Manh Tran, Chien Van Ta, Hang Bui Khanh

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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

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Acta Mathematica Vietnamica Pub Date : 2024-06-14 DOI: 10.1007/s40306-024-00534-8

Vu Ngoc Phat, Nguyen Truong Thanh

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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

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Acta Mathematica Vietnamica Pub Date : 2024-06-11 DOI: 10.1007/s40306-024-00530-y

P. Charpentier, Y. Dupain

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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

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Acta Mathematica Vietnamica Pub Date : 2024-06-11 DOI: 10.1007/s40306-024-00536-6

Nguyen Thi Ngoc Oanh

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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

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Acta Mathematica Vietnamica Pub Date : 2024-06-05 DOI: 10.1007/s40306-024-00538-4

Peter Marius Flydal, Gereon Quick, Eirik Eik Svanes

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Meromorphic Solutions of a Certain Type of Nonlinear Differential Equations 某类非线性微分方程的同态解

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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, Jun-Fan Chen","doi":"10.1007/s40306-024-00539-3","DOIUrl":"10.1007/s40306-024-00539-3","url":null,"abstract":"<div>In this paper, using Nevanlinna theory and linear algebra, we characterize transcendental meromorphic solutions of nonlinear differential equation of the form <div><div>$$begin{aligned} f^n+Q_d(z,f)=sum _{i=1}^{l}p_{i}(z)e^{alpha _{i}(z)}, end{aligned}$$</div></div>where (lge 2), (nge l+2) are integers, f(z) is a meromorphic function, (Q_d(z,f)) is a differential polynomial in f(z) of degree (dle n-(l+1)) with rational functions as its coefficients, (p_{1}(z)), (p_{2}(z)), (dots ), (p_{l}(z)) are non-vanishing rational functions and (alpha _{1}(z)), (alpha _{2}(z)), (dots ), (alpha _{l}(z)) are nonconstant polynomials such that (alpha _{1}^prime (z)), (alpha _{2}^prime (z)), (dots ), (alpha _{l}^prime (z)) 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.</div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 2","pages":"173 - 186"},"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}

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Tight Closure, Coherence, and Localization at Single Elements 单元素的紧密闭合、相干和定位

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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>In this note, a condition (open persistence) is presented under which a (pre)closure operation on submodules (resp. ideals) over rings of global sections over a scheme X can be extended to a (pre)closure operation on sheaves of submodules of a coherent (mathcal {O}_X)-module (resp. sheaves of ideals in (mathcal {O}_X)). A second condition (glueability) 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 (semi F-regularity) 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.</div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 2","pages":"201 - 215"},"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}

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On Topological Representation Theory from Quivers 从Quivers论拓扑表示理论

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Acta Mathematica Vietnamica Pub Date : 2024-05-21 DOI: 10.1007/s40306-024-00531-x

Fang Li, Zhihao Wang, Jie Wu, Bin Yu

{"title":"On Topological Representation Theory from Quivers","authors":"Fang Li, Zhihao Wang, Jie Wu, Bin Yu","doi":"10.1007/s40306-024-00531-x","DOIUrl":"10.1007/s40306-024-00531-x","url":null,"abstract":"<div>In this work, we introduce topological representations of a quiver as a system consisting of topological spaces and its relationships determined by the quiver. Such a setting gives a natural connection between topological representations of a quiver and diagrams of topological spaces. Firstly, we investigate the relation between the category of topological representations and that of linear representations of a quiver via (P(varGamma ))-(mathcal {TOP}^o) and (kvarGamma )-Mod, concerning (positively) graded or vertex (positively) graded modules. Secondly, we discuss the homological theory of topological representations of quivers via the (varGamma )-limit functor (lim ^{varGamma }), and use it to define the homology groups of topological representations of quivers via (H _n). It is found that some properties of a quiver can be read from homology groups. Thirdly, we investigate the homotopy theory of topological representations of quivers. We define the homotopy equivalence between two morphisms in ({textbf {Top}}text{- }{} {textbf {Rep}}varGamma ) and show that the parallel Homotopy Axiom also holds for top-representations based on the homotopy equivalence. Last, we obtain the functor (At^{varGamma }) from ({textbf {Top}}text{- }{} {textbf {Rep}}varGamma ) to ({textbf {Top}}) and show that (At^{varGamma }) preserves homotopy equivalence between morphisms. The relationship between the homotopy groups of a top-representation (T, f) and the homotopy groups of (At^{varGamma }(T,f)) is also established.</div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 4","pages":"563 - 594"},"PeriodicalIF":0.3,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142761893","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