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Acta Mathematica Vietnamica最新文献

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A Proof of the Lieb–Thirring Inequality via the Besicovitch Covering Lemma 用Besicovitch覆盖引理证明Lieb–Thirring不等式
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2023-01-04 DOI: 10.1007/s40306-022-00490-1
Phan Thành Nam
{"title":"A Proof of the Lieb–Thirring Inequality via the Besicovitch Covering Lemma","authors":"Phan Thành Nam","doi":"10.1007/s40306-022-00490-1","DOIUrl":"10.1007/s40306-022-00490-1","url":null,"abstract":"<div><p>We give a proof of the Lieb–Thirring inequality on the kinetic energy of orthonormal functions by using a microlocal technique, in which the uncertainty and exclusion principles are combined through the use of the Besicovitch covering lemma.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 1","pages":"75 - 81"},"PeriodicalIF":0.5,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-022-00490-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46840929","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: 1
Necessary Optimality Conditions for Second-Order Local Strict Efficiency for Constrained Nonsmooth Vector Equilibrium Problems 约束非光滑矢量平衡问题二阶局部严格效率的必要最优性条件
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-12-17 DOI: 10.1007/s40306-022-00491-0
Tran Van Su, Dinh Dieu Hang
{"title":"Necessary Optimality Conditions for Second-Order Local Strict Efficiency for Constrained Nonsmooth Vector Equilibrium Problems","authors":"Tran Van Su,&nbsp;Dinh Dieu Hang","doi":"10.1007/s40306-022-00491-0","DOIUrl":"10.1007/s40306-022-00491-0","url":null,"abstract":"<div><p>This paper is concerned with primal and dual second-order optimality conditions for the second-order strict efficiency of nonsmooth vector equilibrium problem with set, cone and equality conditions. First, we propose some second-order constraint qualifications via the second-order tangent sets. Second, we establish necessary optimality conditions of order two in terms of second-order contingent derivatives and second-order Shi sets for a second-order strict local Pareto minima to such problem under suitable assumptions on the second-order constraint qualifications. An application of the result for the twice Fréchet differentiable functions for the second-order local strict efficiency of that problem is also presented. Some illustrative examples are also provided for our findings.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 2","pages":"321 - 341"},"PeriodicalIF":0.5,"publicationDate":"2022-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45386460","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 Spherical Maximal Function on Choquet Spaces Choquet空间上的球面极大函数
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-12-11 DOI: 10.1007/s40306-022-00488-9
Nguyen Cong Phuc
{"title":"The Spherical Maximal Function on Choquet Spaces","authors":"Nguyen Cong Phuc","doi":"10.1007/s40306-022-00488-9","DOIUrl":"10.1007/s40306-022-00488-9","url":null,"abstract":"<div><p>Endpoint weak-type bounds and non-endpoint strong type bounds are obtained for the spherical maximal function in the setting of Choquet spaces with respect to certain Hausdorff contents or Sobolev capacities.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 1","pages":"63 - 74"},"PeriodicalIF":0.5,"publicationDate":"2022-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-022-00488-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48030782","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
Iterative Methods with Nonconforming Time Grids for Nonlinear Flow Problems in Porous Media 多孔介质非线性流动问题的非协调时间网格迭代方法
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-12-07 DOI: 10.1007/s40306-022-00486-x
Thi-Thao-Phuong Hoang, Iuliu Sorin Pop
{"title":"Iterative Methods with Nonconforming Time Grids for Nonlinear Flow Problems in Porous Media","authors":"Thi-Thao-Phuong Hoang,&nbsp;Iuliu Sorin Pop","doi":"10.1007/s40306-022-00486-x","DOIUrl":"10.1007/s40306-022-00486-x","url":null,"abstract":"<div><p>Partially saturated flow in a porous medium is typically modeled by the Richards equation, which is nonlinear, parabolic and possibly degenerated. This paper presents domain decomposition-based numerical schemes for the Richards equation, in which different time steps can be used in different subdomains. Two global-in-time domain decomposition methods are derived in mixed formulations: the first method is based on the physical transmission conditions and the second method is based on equivalent Robin transmission conditions. For each method, we use substructuring techniques to rewrite the original problem as a nonlinear problem defined on the space-time interfaces between the subdomains. Such a space-time interface problem is linearized using Newton’s method and then solved iteratively by GMRES; each GMRES iteration involves parallel solution of time-dependent problems in the subdomains. Numerical experiments in two dimensions are carried out to verify and compare the convergence and accuracy of the proposed methods with local time stepping.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 1","pages":"29 - 49"},"PeriodicalIF":0.5,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41453129","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: 2
Hilbert Genus Fields of Some Number Fields with High Degrees 一些高阶数域的Hilbert亏格域
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-12-02 DOI: 10.1007/s40306-022-00489-8
Mohamed Mahmoud Chems-Eddin, Moulay Ahmed Hajjami, Mohammed Taous
{"title":"Hilbert Genus Fields of Some Number Fields with High Degrees","authors":"Mohamed Mahmoud Chems-Eddin,&nbsp;Moulay Ahmed Hajjami,&nbsp;Mohammed Taous","doi":"10.1007/s40306-022-00489-8","DOIUrl":"10.1007/s40306-022-00489-8","url":null,"abstract":"<div><p>The aim of this paper is to give some properties of Hilbert genus fields and construct the Hilbert genus fields of the fields <span>(L_{m,d}:=mathbb {Q}(zeta _{2^{m}},sqrt {d}))</span>, where <i>m</i> ≥ 3 is a positive integer and <i>d</i> is a square-free integer whose prime divisors are congruent to ± 3 (mod 8) or 9 (mod 16).</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 2","pages":"359 - 369"},"PeriodicalIF":0.5,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-022-00489-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42367731","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
Finite Decomposition of Herz-Type Hardy Spaces for the Dunkl Operator Dunkl算子的herz型Hardy空间的有限分解
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-11-05 DOI: 10.1007/s40306-022-00483-0
Mehdi Lachiheb
{"title":"Finite Decomposition of Herz-Type Hardy Spaces for the Dunkl Operator","authors":"Mehdi Lachiheb","doi":"10.1007/s40306-022-00483-0","DOIUrl":"10.1007/s40306-022-00483-0","url":null,"abstract":"<div><p>The corresponding Herz-type Hardy spaces to new weighted Herz spaces <span>(HK^{beta ,p}_{alpha ,q})</span> associated with the Dunkl operator on <span>(mathbb {R})</span> have been characterized by atomic decompositions. Later a new characterization of <span>(HK^{beta ,p}_{alpha ,q})</span> on the real line is introduced. This helped us in the work to characterize that the norms of the Herz-type Hardy spaces for the Dunkl Operator can be achieved by finite central atomic decomposition in some dense subspaces of them. Secondly, as an application we prove that a sublinear operator satisfying many conditions can be uniquely extended to a bounded operator in the Herz-type Hardy spaces for the Dunkl Operator.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 2","pages":"295 - 306"},"PeriodicalIF":0.5,"publicationDate":"2022-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41366653","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 Existence of Balanced Neighborly Polynomials 平衡邻域多项式的存在性
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-11-03 DOI: 10.1007/s40306-022-00482-1
Nguyen Thi Thanh Tam
{"title":"The Existence of Balanced Neighborly Polynomials","authors":"Nguyen Thi Thanh Tam","doi":"10.1007/s40306-022-00482-1","DOIUrl":"10.1007/s40306-022-00482-1","url":null,"abstract":"<div><p>Inspired by the definition of balanced neighborly spheres, we define balanced neighborly polynomials and study the existence of these polynomials. The goal of this article is to construct balanced neighborly polynomials of type (<i>k</i>,<i>k</i>,<i>k</i>,<i>k</i>) over any field <i>K</i> for all <i>k</i>≠ 2, and show that a balanced neighborly polynomial of type (2,2,2,2) exists if and only if char(<i>K</i>)≠ 2. Besides, we also discuss a relation between balanced neighborly polynomials and balanced neighborly simplicial spheres.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 2","pages":"307 - 319"},"PeriodicalIF":0.5,"publicationDate":"2022-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42811361","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
Coercivity of the Dirichlet-to-Neumann Operator and Applications to the Muskat Problem Dirichlet对Neumann算子的强制性及其在Muscat问题中的应用
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-11-03 DOI: 10.1007/s40306-022-00484-z
Huy Q. Nguyen
{"title":"Coercivity of the Dirichlet-to-Neumann Operator and Applications to the Muskat Problem","authors":"Huy Q. Nguyen","doi":"10.1007/s40306-022-00484-z","DOIUrl":"10.1007/s40306-022-00484-z","url":null,"abstract":"<div><p>We consider the Dirichlet-to-Neumann operator in strip-like and half-space domains with Lipschitz boundary. It is shown that the quadratic form generated by the Dirichlet-to-Neumann operator controls some sharp homogeneous fractional Sobolev norms. As an application, we prove that the global Lipschitz solutions constructed in Dong et al. (2021) for the one-phase Muskat problem decays exponentially in time in any Hölder norm <i>C</i><sup><i>α</i></sup>, <i>α</i> ∈ (0,1).</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 1","pages":"51 - 62"},"PeriodicalIF":0.5,"publicationDate":"2022-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40306-022-00484-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46349907","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: 1
Existence and Multiplicity Results for Nonlocal Lane-Emden Systems 非局部Lane-Emden系统的存在性和多重性结果
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-10-25 DOI: 10.1007/s40306-022-00485-y
Rakesh Arora, Phuoc-Tai Nguyen
{"title":"Existence and Multiplicity Results for Nonlocal Lane-Emden Systems","authors":"Rakesh Arora,&nbsp;Phuoc-Tai Nguyen","doi":"10.1007/s40306-022-00485-y","DOIUrl":"10.1007/s40306-022-00485-y","url":null,"abstract":"<div><p>In this work, we show the existence and multiplicity for the nonlocal Lane-Emden system of the form\u0000</p><div><div><span>$$ begin{array}{@{}rcl@{}} left{ begin{aligned} mathbb L u &amp;= v^{p} + rho nu quad &amp;&amp;text{in } {varOmega}, mathbb L v &amp;= u^{q} + sigma tau quad &amp;&amp;text{in } {varOmega}, u&amp;=v = 0 quad &amp;&amp;text{on } partial {varOmega} text{ or in } {varOmega}^{c} text{ if applicable}, end{aligned} right. end{array} $$</span></div></div><p> where <span>({varOmega } subset mathbb {R}^{N})</span> is a <i>C</i><sup>2</sup> bounded domain, <span>(mathbb L)</span> is a nonlocal operator, <i>ν</i>,<i>τ</i> are Radon measures on <i>Ω</i>, <i>p</i>,<i>q</i> are positive exponents, and <i>ρ</i>,<i>σ</i> &gt; 0 are positive parameters. Based on a fine analysis of the interaction between the Green kernel associated with <span>(mathbb L)</span>, the source terms <i>u</i><sup><i>q</i></sup>,<i>v</i><sup><i>p</i></sup> and the measure data, we prove the existence of a positive minimal solution. Furthermore, by analyzing the geometry of Palais-Smale sequences in finite dimensional spaces given by the Galerkin type approximations and their appropriate uniform estimates, we establish the existence of a second positive solution, under a smallness condition on the positive parameters <i>ρ</i>,<i>σ</i> and superlinear growth conditions on source terms. The contribution of the paper lies on our unifying technique that is applicable to various types of local and nonlocal operators.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 1","pages":"3 - 28"},"PeriodicalIF":0.5,"publicationDate":"2022-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50514409","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: 1
Existence and Multiplicity Results for Nonlocal Lane-Emden Systems 非局部Lane-Emden系统的存在性和多重性结果
IF 0.5
Acta Mathematica Vietnamica Pub Date : 2022-10-25 DOI: 10.1007/s40306-022-00485-y
R. Arora, P. Nguyen
{"title":"Existence and Multiplicity Results for Nonlocal Lane-Emden Systems","authors":"R. Arora, P. Nguyen","doi":"10.1007/s40306-022-00485-y","DOIUrl":"https://doi.org/10.1007/s40306-022-00485-y","url":null,"abstract":"","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"48 1","pages":"3-28"},"PeriodicalIF":0.5,"publicationDate":"2022-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52714348","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: 1
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