Acta Mathematica Vietnamica最新文献

{"title":"Hamilton Type Gradient Estimates for a Heat Equation under the Ricci-harmonic Flow","authors":"Liang-Chu Chang,&nbsp;Nguyen Thac Dung,&nbsp;Chiung-Jue Anna Sung","doi":"10.1007/s40306-025-00570-y","DOIUrl":"10.1007/s40306-025-00570-y","url":null,"abstract":"<div><p>Our aim in this paper is to study the linear heat equation on a Riemannian manifold evolving by the Ricci-harmonic flow. We first show a Hamilton type gradient estimate for the positive solution of the heat equation, which allows us to derive a Harnack inequality. It is worthy to note that comparing with the Li-Yau type estimate by Bailesteanu [1], our gradient estimate can be obtained without any assumption on the harmonic quantity in the flow.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 2","pages":"273 - 283"},"PeriodicalIF":0.3,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167310","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}

{"title":"The Dirichlet Problem Associated to Operators Defined on the Nuclear Algebra of Entire Functions","authors":"Sonia Chaari,&nbsp;Afef Ben Farah","doi":"10.1007/s40306-025-00565-9","DOIUrl":"10.1007/s40306-025-00565-9","url":null,"abstract":"<div><p>This paper is devoted to the Dirichlet problem associated to operators defined on the nuclear algebra of entire functions. Firstly, we give a probabilistic representation of the solution of the Dirichlet problem associated to the extended <i>K</i>-Gross Laplacian in terms of <i>K</i>-Wiener process. Secondly, we prove that the Dirichlet problem associated to the operator <span>(mathcal {F}_{t(-K),I})</span>-transform has an explicit solution. Finally, an application to the large deviation principle is given.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 2","pages":"159 - 172"},"PeriodicalIF":0.3,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170443","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}

{"title":"Spanning Trees of (K_{1,4})-free Graphs with a Bounded Number of Leaves and Branch Vertices","authors":"Pham Hoang Ha","doi":"10.1007/s40306-025-00568-6","DOIUrl":"10.1007/s40306-025-00568-6","url":null,"abstract":"<div><p>Let <i>T</i> be a tree. A vertex of degree one is a <i>leaf</i> of <i>T</i> and a vertex of degree at least three is a <i>branch vertex</i> of <i>T</i>. A graph is said to be <span>(K_{1,4})</span><i>-free</i> if it does not contain <span>(K_{1,4})</span> as an induced subgraph. In this paper, we study the spanning trees with a bounded number of leaves and branch vertices of <span>(K_ {1,4})</span>-free graphs. Applying the main results, we also give some improvements of previous results on the spanning tree with few branch vertices for the case of <span>(K_{1,4})</span>-free graphs.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 2","pages":"263 - 271"},"PeriodicalIF":0.3,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169187","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}

{"title":"Well-posedness, Regularity of Solutions and the (theta )-Euler-Maruyama Scheme for Stochastic Volterra Integral Equations with General Singular Kernels and Jumps","authors":"Phan Thi Huong,&nbsp;Hoang-Long Ngo,&nbsp;Peter Kloeden","doi":"10.1007/s40306-025-00566-8","DOIUrl":"10.1007/s40306-025-00566-8","url":null,"abstract":"<div><p>In this paper, we consider a class of stochastic Volterra integral equations with general singular kernels, driven by a Brownian motion and a pure jump Lévy process. We first show that these equations have a unique strong solution under certain regular conditions on their coefficients. Furthermore, the solutions of this equation depend continuously on the initial value and on the kernels <i>k</i>, <span>(k_B)</span>, and <span>(k_Z)</span>. We will then show the regularity of solutions for these equations. Finally, we propose a <span>(theta )</span>-Euler-Maruyama approximation scheme for these equations and demonstrate its convergence at a certain rate in the <span>(L^2)</span>-norm. Some numerical simulations is also presented to support for the theoretical results.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 2","pages":"173 - 195"},"PeriodicalIF":0.3,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168393","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}

{"title":"Large Deviation for a 2D Cahn-Hilliard-Oldroyd Model of Order One Under Random Influences","authors":"Salvador Awo Kougang,&nbsp;Calvin Tadmon,&nbsp;Gabriel Deugoué","doi":"10.1007/s40306-025-00567-7","DOIUrl":"10.1007/s40306-025-00567-7","url":null,"abstract":"<div><p>This paper establishes a large deviation principle for a stochastic 2D Cahn-Hilliard-Oldroyd model of order one under random influences. The model used in the analysis consists of the stochastic Oldroyd model of order one, coupled with a Cahn-Hilliard equation for the order parameter. The approach used is the weak convergence method with the main idea laid on a variational representation formula for the Laplace transform of continuous and bounded functionals.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 2","pages":"197 - 231"},"PeriodicalIF":0.3,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163348","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}

{"title":"Measure Pressure for Measure Preserving Maps and an Upper Bound for the Case of (C^2) Endomorphisms","authors":"Sanaz Lamei,&nbsp;Pouya Mehdipour,&nbsp;Maryam Razi","doi":"10.1007/s40306-025-00564-w","DOIUrl":"10.1007/s40306-025-00564-w","url":null,"abstract":"<div><p>A measure-theoretic pressure was defined by [L. He, J. Lv and L. Zhou: Definition of measure-theoretic pressure using spanning sets, <i>Acta Math. Sinica</i> (English Series) <b>20</b>, 709–718 (2004)] based on the Katok entropy formula. For a measure preserving map <i>f</i>, we generalized this definition to define a measure-theoretic pressure by using both <span>((n,epsilon ))</span>-spanning and <span>((n,epsilon ))</span>-separated sets. A variational principle for this pressure is established. Furthermore, we investigate an upper bound for the measure theoretic pressure of a <span>(C^{2})</span> endomorphism preserving a hyperbolic measure.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 1","pages":"143 - 157"},"PeriodicalIF":0.3,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638588","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}

{"title":"Differences of Products of Volterra Type Operators and Composition Operators Between Fock Spaces","authors":"Pham The Hao,&nbsp;Pham Trong Tien","doi":"10.1007/s40306-025-00563-x","DOIUrl":"10.1007/s40306-025-00563-x","url":null,"abstract":"<div><p>We characterize boundedness and compactness of the differences of products of Volterra integral operators <span>(V_g)</span> (Volterra companion operators <span>(J_g)</span>) and composition operators <span>(C_{varphi })</span> between different Fock spaces <span>(mathcal {F}^p(mathbb {C}))</span> and <span>(mathcal {F}^q(mathbb {C}))</span> for every <span>(p, q in (0, infty ])</span>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 1","pages":"123 - 141"},"PeriodicalIF":0.3,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638511","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}

{"title":"Dual-ADS, ADS(^#) and ADS* Modules","authors":"Abyzov Adel Nailevich,&nbsp;Bui Tien Dat,&nbsp;Truong Cong Quynh","doi":"10.1007/s40306-024-00562-4","DOIUrl":"10.1007/s40306-024-00562-4","url":null,"abstract":"<div><p>A right <i>R</i>-module <i>M</i> is said to be dual-ADS if for every decomposition <span>(M=Aoplus B)</span> then <i>A</i> and <i>B</i> are mutually projective. The class of ADS*-modules contains the class of dual-ADS modules. In this article, we study several properties of these modules. It is shown that a module <i>M</i> is dual-ADS if and only if for any direct summand <i>S</i> and <span>(T^prime le M)</span> with <span>(T^prime +S)</span> a direct summand of <i>M</i>, then <span>(T^prime )</span> contains a direct complement of <i>S</i> in <span>(T^prime +S)</span>. A generalization of dual-ADS modules is considered, namely, ADS<span>(^#)</span>-modules. It is shown that a module <i>M</i> is ADS<span>(^#)</span> if and only if for any direct summand <i>S</i> of <i>M</i>, and any weak supplement <span>(T^prime )</span> of <i>S</i> in <span>(T^prime +S)</span> such that <span>(T^prime +S)</span> is a direct summand of <i>M</i>, then <span>(T^prime )</span> contains a direct complement of <i>S</i> in <span>(T^prime +S)</span>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 1","pages":"101 - 121"},"PeriodicalIF":0.3,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638602","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}

{"title":"Blow-up and Decay of Global Solutions for a Free Boundary Problem with Competing Nonlocal Nonlinearity and Absorption","authors":"Hoang Huy Truong,&nbsp;Dung Tien Nguyen,&nbsp;Hoang-Hung Vo","doi":"10.1007/s40306-024-00561-5","DOIUrl":"10.1007/s40306-024-00561-5","url":null,"abstract":"<div><p>In this paper, we are concerned with the characterization of the blow-up and global solutions for free boundary parabolic equation with competing nonlocal nonlinearity and absorption </p><div><div><span>$$begin{aligned} u_t(t,x) = u_{xx}(t,x) + u^{p}(t,x) int _0^{s(t)}u^{q}(t,x)dx -gamma u^alpha (t,x), t&gt;0, 0&lt;x &lt;s(t), end{aligned}$$</span></div><div>\u0000 (1)\u0000 </div></div><p>where <span>(q, alpha ge 1)</span>, <span>(p=0)</span> or <span>(pge 1)</span> and <span>(gamma &gt; 0)</span> are given constants. This study is motivated from the works [Abdelhedi and Zaag: J. Differential Equations <b>272</b>, 1–45, \u0000(2021); Souplet: SIAM J. Math. Anal. <b>29</b>, 1301–1334, \u0000(1998); Zhou and Lin: J. Funct. Anal. <b>262</b>, 3409–3429, \u0000(2012)] arisen from the investigation of many physical and biological phenomena such as population dynamics, combustion theory, phase separation in binary mixtures, theory of nuclear reactor dynamics... We first prove the local existence, uniqueness and stability of solution thanks to the “extension trick\" introduced in [Du et al.: Math. Ann. <b>386</b>(3-4), 2061–2106, \u0000(2023); Wang and Du: Discrete Contin. Dyn. Syst. Ser. B <b>26</b>(4), 2201–2238, \u0000(2021)]. Second, by improving the comparison principle used in [Souplet: SIAM J. Math. Anal. <b>29</b>, 1301–1334, \u0000(1998); Zhou and Lin: J. Funct. Anal. <b>262</b>, 3409–3429, \u0000(2012)], we find a sharp criterion characterizing the blow-up and global solutions of (1) in term of power coefficients and initial data. We further show that there exists a threshold for the initial data that determines whether blow-up, global fast, or global slow solutions occur and find an upper bound for the existence time of blow-up solutions in two different cases <span>(alpha &gt;1)</span> and <span>(alpha =1)</span>. Our proofs are mainly based on the comparison principle by improving several techniques in previous works, combined new idea to handle differential inequalities and unified local existence theory for nonlocal semilinear parabolic equations.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 1","pages":"1 - 31"},"PeriodicalIF":0.3,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638259","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}

{"title":"Correction to: Generalized Semi-infinite Polynomial Optimization and Semidefinite Programming Relaxations","authors":"Liguo Jiao,&nbsp;Jae Hyoung Lee,&nbsp;Tiến-Sơn Phạm","doi":"10.1007/s40306-024-00560-6","DOIUrl":"10.1007/s40306-024-00560-6","url":null,"abstract":"","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"50 2","pages":"303 - 303"},"PeriodicalIF":0.3,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166103","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}