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Stability Estimates for the Heisenberg Uncertainty Principle with Dunkl Weights 具有Dunkl权值的海森堡测不准原理的稳定性估计
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-09-16 DOI: 10.1007/s40306-026-00631-w
Nguyen Tuan Duy, Nguyen Van Phong, Lam Thi Bich Thuy
{"title":"Stability Estimates for the Heisenberg Uncertainty Principle with Dunkl Weights","authors":"Nguyen Tuan Duy,&nbsp;Nguyen Van Phong,&nbsp;Lam Thi Bich Thuy","doi":"10.1007/s40306-026-00631-w","DOIUrl":"10.1007/s40306-026-00631-w","url":null,"abstract":"<div><p>We study the stability of the Heisenberg Uncertainty Principle with Dunkl weights, inspired by recent progress on stability in functional and geometric inequalities. First, using the Bakry-Émery <span>(varGamma _2)</span>-calculus, we establish several versions of the Poincaré inequality for measures involving Dunkl-Gaussian weights. We then prove a Heisenberg-type uncertainty principle adapted to Dunkl weights through suitable identities. By combining these results, we obtain several stability estimates for the Dunkl-weighted Heisenberg uncertainty principle. Our work extends existing methods developed for monomial weights to the more complex Dunkl setting.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 3","pages":"449 - 462"},"PeriodicalIF":0.6,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125619","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
Existence of Optimal Solutions for Learning-based PDEs Governed by Time-Dependent p-Laplace and 1-Laplace Operators 时变p-拉普拉斯算子和1-拉普拉斯算子控制下基于学习的偏微分方程最优解的存在性
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-09-14 DOI: 10.1007/s40306-026-00633-8
Van Thanh Nguyen, Thuan Quang Thai, Minh Hien Huynh
{"title":"Existence of Optimal Solutions for Learning-based PDEs Governed by Time-Dependent p-Laplace and 1-Laplace Operators","authors":"Van Thanh Nguyen,&nbsp;Thuan Quang Thai,&nbsp;Minh Hien Huynh","doi":"10.1007/s40306-026-00633-8","DOIUrl":"10.1007/s40306-026-00633-8","url":null,"abstract":"<div><p>Learning-based partial differential equations, with applications in image processing and computer vision, are often formulated as optimal control problems constrained by PDEs. In this paper, we consider PDE constraints governed by the combination of the time-dependent <i>p</i>-Laplace and singular 1-Laplace type operators. Models of this type–and more general formulations–have been proposed and investigated numerically in Liu et al. [15, 16]. Theoretical results on the existence of optimal solutions have so far been established only for constant-coefficient operators in recent work [17]. The extension to time-dependent coefficients is more delicate, due to the lack of suitable stability results for nonlinear semigroups generated by the sum of two time-dependent monotone operators, together with the degeneracy of the multi-valued 1-Laplace operator. The main contribution of this paper is to address these issues and to establish the existence of optimal solutions for a class of singular PDE-constrained optimal control problems governed by the sum of time-dependent <i>p</i>-Laplace and multi-valued 1-Laplace operators.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 3","pages":"377 - 399"},"PeriodicalIF":0.6,"publicationDate":"2026-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125618","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
Gradient Estimates for the Heat Kernel of Schrödinger Operators on Stratified Lie Groups and Their Applications 分层李群上Schrödinger算子热核的梯度估计及其应用
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-09-14 DOI: 10.1007/s40306-026-00623-w
Tran Phuoc An, Nguyen Ngoc Trong, Huynh Cao Truong
{"title":"Gradient Estimates for the Heat Kernel of Schrödinger Operators on Stratified Lie Groups and Their Applications","authors":"Tran Phuoc An,&nbsp;Nguyen Ngoc Trong,&nbsp;Huynh Cao Truong","doi":"10.1007/s40306-026-00623-w","DOIUrl":"10.1007/s40306-026-00623-w","url":null,"abstract":"<div><p>In this paper, we investigate the pointwise <span>(L^infty )</span> estimates and Hölder continuity of the difference between the gradients of the heat kernels of <span>(-Delta )</span> and the Schrödinger operators <span>(-Delta + mathbb {V})</span> on a Lie group, where <span>(mathbb {V})</span> is a non-negative polynomial potential. These results have significant implications for gradient estimates of solutions to the parabolic Schrödinger equation. Consequently, we prove the boundedness of the Riesz transform on the <span>(textrm{BMO})</span>-type space associated with <span>(mathbb {L})</span> and provide an application to the regularity of solutions of the Schrödinger equation. Some of these findings are novel even in the Euclidean setting <span>(mathbb {R}^n)</span>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 3","pages":"415 - 447"},"PeriodicalIF":0.6,"publicationDate":"2026-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125620","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
Problems on the Conductor of Finite Group Characters 有限群特征导体的若干问题
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-09-14 DOI: 10.1007/s40306-026-00635-6
Nguyen N. Hung
{"title":"Problems on the Conductor of Finite Group Characters","authors":"Nguyen N. Hung","doi":"10.1007/s40306-026-00635-6","DOIUrl":"10.1007/s40306-026-00635-6","url":null,"abstract":"<div><p>This paper reviews recent results and open problems on the conductor of finite group characters, highlighting their connections to one another and to broader topics in the representation theory of finite groups.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 3","pages":"337 - 351"},"PeriodicalIF":0.6,"publicationDate":"2026-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125567","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
Study on Special Features of New h-functions of Some Simply Connected Planar Regions 平面单连通区域新h函数的特殊性质研究
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-08-18 DOI: 10.1007/s40306-026-00622-x
Arunmaran Mahenthiram, Piriyalucksan Paramesvarampillai
{"title":"Study on Special Features of New h-functions of Some Simply Connected Planar Regions","authors":"Arunmaran Mahenthiram,&nbsp;Piriyalucksan Paramesvarampillai","doi":"10.1007/s40306-026-00622-x","DOIUrl":"10.1007/s40306-026-00622-x","url":null,"abstract":"<div><p>The <i>h</i>-function <i>h</i>(<i>r</i>), or the harmonic-measure distribution function, is defined as the probability that a Brownian particle released from a basepoint <span>(z_{0})</span> in a region <span>({varOmega })</span> first leaves the region <span>(varOmega )</span> within distance <i>r</i> of <span>(z_0)</span>. In this paper, we compute the <i>h</i>-function formulas explicitly in terms of <i>r</i> for some new simply connected planar regions by using the method of conformal maps. Especially, we investigate the behaviour of these <i>h</i>-functions at certain values of <i>r</i> that correspond to specific points on the boundary of the respective regions <span>(varOmega )</span>. In some cases, we explain the asymptotic behaviour as <i>r</i> decreases to the minimum distance between the basepoint <span>(z_{0})</span> and the boundary.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 3","pages":"477 - 497"},"PeriodicalIF":0.6,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125661","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 Cartier Duals of Certain Finite Group Schemes of Prime Power Order 一类素数幂阶有限群格式的Cartier对偶的注记
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-08-18 DOI: 10.1007/s40306-026-00624-9
Michio Amano
{"title":"A Note on Cartier Duals of Certain Finite Group Schemes of Prime Power Order","authors":"Michio Amano","doi":"10.1007/s40306-026-00624-9","DOIUrl":"10.1007/s40306-026-00624-9","url":null,"abstract":"<div><p>Let <span>(mathcal {G}^{(lambda )})</span> be a group scheme that specializes to <span>({mathbb {G}}_a)</span> when <span>(lambda =0)</span> and to <span>({mathbb {G}}_m)</span> when <span>(lambda in A^times )</span>, and let <span>(psi ^{(l)}:mathcal {G}^{(lambda )}rightarrow mathcal {G}^{(lambda ^{p^l})})</span> denote the <i>l</i>-th Kummer-Artin-Schreier type homomorphism determined by <span>(lambda )</span>. We construct the Cartier dual of <span>(textrm{Ker}(psi ^{(l)}))</span> over a <span>(mathbb {Z}/p^nmathbb {Z})</span>-algebra.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 3","pages":"363 - 376"},"PeriodicalIF":0.6,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125662","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
Limit Theorems for the Number of Up-crossings of the Conjunction Set of Stationary Gaussian Processes 平稳高斯过程的连接集上交叉数的极限定理
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-08-18 DOI: 10.1007/s40306-026-00629-4
Viet-Hung Pham
{"title":"Limit Theorems for the Number of Up-crossings of the Conjunction Set of Stationary Gaussian Processes","authors":"Viet-Hung Pham","doi":"10.1007/s40306-026-00629-4","DOIUrl":"10.1007/s40306-026-00629-4","url":null,"abstract":"<div><p>In this paper, we investigate the limit theorem for the number of up-crossings of the conjunction set of stationary Gaussian processes. We prove that as the level tends to infinity then the normalized point process of the number of up-crossings converges weakly to a standard Poisson process. Our proof is based on a discretization argument and a Normal comparison lemma for the order statistics.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 3","pages":"401 - 413"},"PeriodicalIF":0.6,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125587","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
Modular Invariant Rings and the Weyl Groups of Special Unitary Groups 模不变环与特殊酉群的Weyl群
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-08-17 DOI: 10.1007/s40306-026-00621-y
Kenshi Ishiguro, Naito Nishihara
{"title":"Modular Invariant Rings and the Weyl Groups of Special Unitary Groups","authors":"Kenshi Ishiguro,&nbsp;Naito Nishihara","doi":"10.1007/s40306-026-00621-y","DOIUrl":"10.1007/s40306-026-00621-y","url":null,"abstract":"<div><p>For a compact connected Lie group <i>G</i>, the rational cohomology ring of its classifying space <i>BG</i> can be expressed as an invariant ring. Namely, for a maximal torus <span>(T^{n})</span> of <i>G</i>, it is well–known that <span>(H^{*}(BG; mathbb {Q} ) cong H^{*}(BT^{n}; mathbb {Q} )^{W(G)})</span> which is a polynomial ring. If <i>d</i> divides <i>n</i>, the quotient <span>(SU(n)/mathbb {Z}_d)</span> is also a Lie group. Their rational cohomology rings are isomorphic, however, the integral representations of the Weyl groups <span>(W(SU(n)/mathbb {Z}_d))</span> are not equivalent. So we ask if the modular invariant rings under the actions are polynomial. Our main theorem is a generalization of some results in [4] and [12].</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 2","pages":"191 - 200"},"PeriodicalIF":0.6,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148859846","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
Global and Nonglobal Solutions for a Mixed Local-nonlocal Heat Equation 一类混合局部-非局部热方程的全局解和非全局解
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-08-13 DOI: 10.1007/s40306-026-00627-6
Brandon Carhuas-Torre, Ricardo Castillo, Ricardo Freire, Alex Lira, Miguel Loayza
{"title":"Global and Nonglobal Solutions for a Mixed Local-nonlocal Heat Equation","authors":"Brandon Carhuas-Torre,&nbsp;Ricardo Castillo,&nbsp;Ricardo Freire,&nbsp;Alex Lira,&nbsp;Miguel Loayza","doi":"10.1007/s40306-026-00627-6","DOIUrl":"10.1007/s40306-026-00627-6","url":null,"abstract":"<div><p>In this work, we establish optimal criteria characterizing the global and nonglobal existence of solutions to a semilinear parabolic equation with a general source term <i>f</i>. The equation is governed by the mixed operator </p><div><div><span>$$ mathcal {L} = -Delta + (-Delta )^s, quad text {with } 0&lt; s &lt; 1. $$</span></div></div><p>In our analysis, we study supersolutions and obtain estimates on the semigroup generated by <span>(mathcal {L})</span>. In particular, we recover Fujita’s critical exponent <span>(1 + tfrac{2s}{N})</span>, previously established by Biagi, Punzo, and Vecchi [2], and by Del Pezzo and Ferreira [18].</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 3","pages":"463 - 476"},"PeriodicalIF":0.6,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149125660","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 Cumulative Distribution Function of a Mixture Model with Normal Error 具有正态误差的混合模型的累积分布函数
IF 0.6
Acta Mathematica Vietnamica Pub Date : 2026-08-13 DOI: 10.1007/s40306-026-00630-x
Dang Duc Trong, Nguyen Hoang Thanh, Nguyen Tien Dat, Thai Phuc Hung
{"title":"The Cumulative Distribution Function of a Mixture Model with Normal Error","authors":"Dang Duc Trong,&nbsp;Nguyen Hoang Thanh,&nbsp;Nguyen Tien Dat,&nbsp;Thai Phuc Hung","doi":"10.1007/s40306-026-00630-x","DOIUrl":"10.1007/s40306-026-00630-x","url":null,"abstract":"<div><p>This paper studies statistical deconvolution, focusing on estimating the cumulative distribution function <span>(F_X)</span> of a random variable <i>X</i> from observations <span>(Y_j = X_j + sigma xi _j)</span>, where <span>(X_j)</span> and <span>(xi _j)</span> are independent copies of <i>X</i> and <span>(xi )</span>, respectively. We assume that the noise <span>(sigma xi _j)</span> is normally distributed with zero mean and unknown variance <span>(sigma ^2)</span>. Under this framework, we propose a new semi-parametric estimator for <span>(F_X)</span>. Our results show that, over a subclass of Sobolev-type distributions, the estimator achieves a convergence rate comparable to previous studies, demonstrating that the accurate semi-parametric inference for <span>(F_X)</span> is feasible even when the noise variance is unknown.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"51 2","pages":"307 - 336"},"PeriodicalIF":0.6,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148859850","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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